JP6476565B2 - Pitch array determination method, pitch array determination device, pitch array determination program - Google Patents

Description

  The present invention relates to a method for determining a pitch arrangement of a tire tread pattern, a determination apparatus, and a program for determining a pitch arrangement using a computer.

The tread pattern of a tire has a pitch arrangement in which a plurality of types of pitches having different pitch lengths are appropriately combined and arranged in the tire circumferential direction. For example, in a tire adopting a pitch arrangement in which pitch length types are randomly arranged in the tire circumferential direction, the frequency of pattern noise generated by each pitch is dispersed, and a quiet tire that does not concentrate on a specific frequency can be obtained.
In a pitch arrangement in which the types of pitch lengths are arranged at random, there are innumerable combinations and arrangements of pitches that determine the pitch arrangement. In such a situation where an infinite number of pitch arrangements can be created, there are methods using a random search method or a full search method as a method for obtaining a tire having excellent tire noise characteristics. However, in the method using the random search method, the pitch arrangement (optimum solution) with the best noise index is not always obtained. Also, in the method using the full search method, the time required for searching for a solution becomes enormous, and the number of combinations may occur so that it is impossible to actually perform all the searches.

  On the other hand, it is also known to efficiently search for a good quality approximate solution by a method using a genetic algorithm imitating the evolution of a living organism (see Patent Document 1). In the method using the genetic algorithm, by performing crossover, a new individual that inherits an excellent sequence contained in a certain individual (pitch sequence) can be generated, and by performing mutation, a new one is generated. Diversity of individuals can be given.

Japanese Patent No. 3432573

However, in the method described in Patent Document 1, there is a case where a pitch arrangement which is not adopted by an actual tire and which is not desired by the tire designer may occur in the process of crossover or mutation. When such a pitch arrangement is newly generated, a new individual is created based on these pitch arrangements, so that an efficient solution search cannot be performed.
The present invention relates to a tire tread pattern pitch arrangement determination method, a determination apparatus, and a computer, which can efficiently obtain a pitch arrangement exhibiting high tire characteristics using a genetic algorithm. Provide a program to make decisions.

One embodiment of the present invention is a method for determining a pitch arrangement of a tread pattern of a tire, comprising:
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint compatible trial sequence conditions, possess and determining a pitch arrangement of a tread pattern of a tire, and
In the step (e), a crossover method of selecting a plurality of pairs from the plurality of trial arrays based on the fitness and crossing a part of the pitch array in each of the plurality of pairs. And the crossover method is
An operation of arranging the first trial arrangement and the second trial arrangement forming each pair of the plurality of pairs in parallel with the arrangement direction of the pitch arrangement to determine a crossing position;
An operation of changing the crossover position when a new trial arrangement generated by crossing at the crossover position does not satisfy the pitch arrangement condition;
When a new trial array generated by crossing at the crossover position satisfies the pitch array condition, the first trial pitch array on one side of the crossover position is maintained among the first trial arrays. The pitch arrangement on the second side that is the other side of the crossover position in the first trial arrangement is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement. Operation, and
The crossover method further includes:
(E1) In the first trial arrangement, the pitch length of the first pitch end, which is the pitch located at the end on the second side in the pitch arrangement on the first side from the crossing position, and the second A first comparison operation for comparing a pitch length of a second pitch end that is a pitch located at an end of the first side in the pitch array on the second side from the crossing position in the trial arrangement of:
(E2) The pitch length of the first pitch portion, which is another pitch type arranged adjacent to the second side with respect to the pitch type including the first pitch end, and the second pitch end A second comparison operation for comparing a pitch length of a second pitch portion which is another pitch type arranged adjacent to the second side with respect to the pitch type including:
(E3) a third comparison operation for comparing pitch lengths of the first pitch portion and the second pitch end;
(E4) The pitch length of the third pitch portion, which is another pitch type arranged adjacent to the second side with respect to the first pitch portion, is compared with the pitch length of the second pitch portion. And a fourth comparison operation to
After the operation for determining the crossing position, so that a new trial arrangement generated by crossing at the crossing position satisfies the pitch arrangement condition,
The first comparison operation (e1) and the second comparison operation (e2),
The first comparison operation (e1) and the third comparison operation (e3), and
One of three combinations of the first comparison operation (e1), the third comparison operation (e3), and the fourth comparison operation (e4) is performed .

The crossover method further includes:
(E1) In the first trial arrangement, the pitch length of the first pitch end, which is the pitch located at the end on the second side in the pitch arrangement on the first side from the crossing position, and the second A first comparison operation for comparing a pitch length of a second pitch end that is a pitch located at an end of the first side in the pitch array on the second side from the crossing position in the trial arrangement of:
(E2) The pitch length of the first pitch portion, which is another pitch type arranged adjacent to the second side with respect to the pitch type including the first pitch end, and the second pitch end A second comparison operation for comparing a pitch length of a second pitch portion which is another pitch type arranged adjacent to the second side with respect to the pitch type including:
(E3) a third comparison operation for comparing pitch lengths of the first pitch portion and the second pitch end;
(E4) The pitch length of the third pitch portion, which is another pitch type arranged adjacent to the second side with respect to the first pitch portion, is compared with the pitch length of the second pitch portion. And a fourth comparison operation to
After the operation for determining the crossing position, so that a new trial arrangement generated by crossing at the crossing position satisfies the pitch arrangement condition,
The first comparison operation (e1) and the second comparison operation (e2),
The first comparison operation (e1) and the third comparison operation (e3), and
Any one of three combinations including the first comparison operation (e1), the third comparison operation (e3), and the fourth comparison operation (e4) may be performed.

Of the three combinations, when performing the first comparison operation (e1) and the second comparison operation (e2),
In the first comparison operation (e1), when the two pitch lengths to be compared are the same, the second comparison operation (e2) is performed,
In the second comparison operation (e2), when the two pitch lengths to be compared are different, an operation for changing the crossing position is performed, and when the two pitch lengths are the same, the replacement operation is performed. Also good.

When performing the first comparison operation (e1) and the third comparison operation (e3) among the three combinations,
In the first comparison operation (e1), when the two pitch lengths to be compared are different, the third comparison operation (e3) is performed,
In the third comparison operation (e3), when the two pitch lengths to be compared are different, an operation for changing the crossing position may be performed.

Among the three combinations, when performing the first comparison operation (e1), the third comparison operation (e3) and the fourth comparison operation (e4),
In the first comparison operation (e1), when the two pitch lengths to be compared are different, the third comparison operation (e3) is performed,
In the third comparison operation (e3), when the two pitch lengths to be compared are the same, the fourth comparison operation (e4) is performed,
In the fourth comparison operation (e4), when the two pitch lengths to be compared are different, an operation to change the crossing position is performed, and when the two pitch lengths are the same, the replacement operation is performed. Also good.

Another aspect of the present invention is a method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
In the step (e), the change is performed using a mutation method that forcibly changes the partial pitch arrangement, and the mutation method includes:
An operation of selecting one pitch A from the trial arrangement with a predetermined probability;
The pitch A includes a pitch B having a pitch length different from that of the pitch A, and is a pitch portion positioned closest to the pitch A in the arrangement direction of the pitch arrangement, and a pitch C having a pitch length different from the pitch B is an arrangement of the pitch arrangement. pitch portions adjacent in the direction, the pitch length of the at least one pitch included in the operation and, replacing the same pitch length and the pitch a and said containing Mukoto.

Another aspect of the present invention is a method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
In the step (e), the change is performed using a mutation method that forcibly changes the partial pitch arrangement, and the mutation method includes:
From the trial arrangement, a pitch part which has one kind of pitch with a predetermined probability and is adjacent to another kind of pitch in the arrangement direction of the pitch arrangement is selected as the first pitch part. Furthermore, an operation of selecting another pitch part different from the first pitch part and having the same pitch length as the first pitch part as the second pitch part;
The total number of pitches of the first pitch part and the second pitch part is redistributed to each of the first pitch part and the second pitch part while maintaining a constant number of pitches. There operations and assigning a pitch length of said one type to the pitch of first pitch portion and a second pitch portion which is redistributed, the characterized by containing Mukoto.

  In the assigning operation, the redistribution may be performed by switching the number of pitches of the first pitch portion and the second pitch portion.

  In the selecting operation, after selecting the first pitch portion, the first pitch portion is first found when viewed in order from the other pitch portions arranged adjacent to the first pitch portion in the arrangement direction of the pitch array. Another pitch part having the same pitch length as the first pitch part may be selected as the second pitch part.

Another aspect of the present invention is a method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
The specific pitch arrangement includes a pitch arrangement that satisfies the condition (C) and the condition (D) as a second pitch arrangement, and the condition (C) and the condition (D) are:
(C) A third region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is long, and a fourth region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is short are the arrangement direction. Are arranged alternately,
(D) When two different pitch types that are not arranged adjacent to each other when the pitch types are arranged in the order of the pitch length are referred to as non-adjacent pitch types, the non-adjacent pitch types are viewed in order in the arrangement direction of the pitch arrangement. the kind of two pitches corresponding to the adjacent pitch species present state, and are,
In the step (e), a crossover method of selecting a plurality of pairs from the plurality of trial arrays based on the fitness and crossing a part of the pitch array in each of the plurality of pairs. And the crossover method is
An operation of arranging the first trial arrangement and the second trial arrangement forming each pair of the plurality of pairs in parallel with the arrangement direction of the pitch arrangement to determine a crossing position;
An operation of changing the crossover position when a new trial arrangement generated by crossing at the crossover position does not satisfy the pitch arrangement condition;
When a new trial array generated by crossing at the crossover position satisfies the pitch array condition, the first trial pitch array on one side of the crossover position is maintained among the first trial arrays. The pitch arrangement on the second side that is the other side of the crossover position in the first trial arrangement is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement. Operation, and
In the replacement operation, in the first trial arrangement, a first pitch end that is a pitch located at an end on the second side in the pitch arrangement on the first side from the crossing position; In the trial arrangement, the new trial arrangement is generated by connecting a second pitch end that is a pitch located at an end of the first side of the pitch arrangement on the second side from the crossing position,
The crossover method further includes:
(E5) a fifth comparison operation for comparing the pitch lengths of the first pitch end and the second pitch end;
(E6) Among the pitch lengths of the second pitch end and all types of pitches, the maximum pitch type that is the longest pitch type or the minimum pitch type that is the shortest pitch length And a sixth comparison operation for comparing the pitch length of the seeds.

Wherein in the step of (e), when the two different pitch variations of that not arranged adjacent when arranged all kinds of the pitches in the order of the pitch length of the non-adjacent pitch species, corresponding to the prior SL nonadjacent pitch species The second pitch array may be generated so that the number of pitch types having a pitch length of a size between the two pitch types is 1 (one ).

Another aspect of the present invention is a method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
The specific pitch arrangement includes a pitch arrangement that satisfies the conditions (E) and (F) as a third pitch arrangement, and the conditions (E) and (F) are:
(E) A fifth region arranged in the arrangement direction so that a plurality of pitch types have a longer pitch length, and a sixth area arranged in the arrangement direction so that a plurality of pitch types have a shorter pitch length. Are arranged alternately,
(F) Among all types of pitches, when the pitch type with the longest pitch length is the maximum pitch type and the pitch type with the shortest pitch length is the minimum pitch type, the pitch types are viewed in order in the arrangement direction of the pitch array. The maximum pitch species does not exist in the connection portion from the fifth region to the sixth region, or the minimum pitch species does not exist in the region from the sixth region to the fifth region, der is,
In the step (e), a crossover method of selecting a plurality of pairs from the plurality of trial arrays based on the fitness and crossing a part of the pitch array in each of the plurality of pairs. And the crossover method is
An operation of arranging the first trial arrangement and the second trial arrangement forming each pair of the plurality of pairs in parallel with the arrangement direction of the pitch arrangement to determine a crossing position;
An operation of changing the crossover position when a new trial arrangement generated by crossing at the crossover position does not satisfy the pitch arrangement condition;
When a new trial array generated by crossing at the crossover position satisfies the pitch array condition, the first trial pitch array on one side of the crossover position is maintained among the first trial arrays. The pitch arrangement on the second side that is the other side of the crossover position in the first trial arrangement is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement. Operation, and
In the replacement operation, in the first trial arrangement, a first pitch end that is a pitch located at an end on the second side in the pitch arrangement on the first side from the crossing position; In the trial arrangement, the new trial arrangement is generated by connecting a second pitch end that is a pitch located at an end of the first side of the pitch arrangement on the second side from the crossing position,
The crossover method further includes:
(E7) The pitch length of the first pitch portion that is another pitch type arranged adjacent to the second side with respect to the pitch type including the first pitch end, and the maximum pitch type or the minimum A seventh comparison operation for comparing the pitch length of the pitch type is included.

The specific pitch arrangement further includes a pitch arrangement satisfying the condition (C) and the condition (D) as a second pitch arrangement, and the condition (C) and the condition (D) are:
(C) A third region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is long, and a fourth region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is short are the arrangement direction. Are arranged alternately,
(D) When two different pitch types that are not arranged adjacent to each other when the pitch types are arranged in the order of the pitch length are referred to as non-adjacent pitch types, the non-adjacent pitch types are viewed in order in the arrangement direction of the pitch arrangement. There may be two pitch types corresponding to adjacent pitch types.

The specific pitch arrangement further includes a pitch arrangement that satisfies the conditions (A) and (B) as the first pitch arrangement, and the conditions (A) and (B) are:
(A) A first in which the pitch length continuously changes from the maximum pitch type, which is the pitch type having the shortest pitch length, to the minimum pitch type, which is the longest pitch type, among all types of pitch types. And a second region in which the pitch length continuously changes from the minimum pitch type to the maximum pitch type,
(B) The first region and the second region may be alternately arranged in the arrangement direction while sharing the maximum pitch type and the minimum pitch type.

  In the step (e), when the ratio of the pitch lengths of the first pitch end and the second pitch end is referred to as a first adjacent pitch ratio, the longer pitch length with respect to the shorter pitch end. The second pitch array may be generated when the first adjacent pitch ratio expressed by the ratio of the pitch lengths at the pitch ends is greater than 1 and less than or equal to 2.

  In the step (e), there are three types of pitches including the first pitch end and the second pitch end, and the first pitch end and the second pitch end are connected by the replacement operation. If the ratio of the two types of pitch lengths located at both ends of the pitch arrangement direction among the three types of pitches arranged adjacent to each other is referred to as a second adjacent pitch ratio, the shorter pitch length The second pitch array may be generated when the second adjacent pitch ratio is 1 to 2 when expressed by the ratio of the pitch length of the longer pitch type to the pitch type. .

The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
In the step (d), the fitness is preferably calculated in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ).
Another aspect of the present invention is a method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
In the step (d), the fitness is calculated in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). To do.

  In the step (b), it is preferable to set the trial arrangement composed of the first pitch arrangement.

Another aspect of the present invention is an apparatus for determining a pitch arrangement of a tread pattern of a tire,
Constraints imposed on the pitch arrangement of the tread pattern, including pitch arrangement conditions for creating a specific pitch arrangement in which a plurality of types of pitches having different pitch lengths are arranged, and tire characteristics based on the pitch arrangement A condition setting unit that defines an objective function that outputs a physical quantity of tire characteristics when a simulation for output is performed, and a target that the output tire characteristics should achieve;
Under the constraint conditions, a trial arrangement setting unit that sets a plurality of pitch arrangements of tire tread patterns as trial arrangements,
An output unit that outputs the tire characteristics using the objective function by performing the simulation using each pitch length of the pitches included in the trial arrangement;
An fitness calculation unit for calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity to the constraint condition;
Based on the fitness, a part of the trial arrangement is selected from the plurality of trial arrangements, and a part of the pitch arrangement in the selected trial arrangement is changed so as to satisfy the pitch arrangement condition. A trial array modification unit for generating a plurality of trial arrays;
A control unit that controls operations of the condition setting unit, the trial sequence setting unit, the output unit, the fitness calculation unit, and the trial sequence change unit,
The control unit repeats the operations of the output unit, the fitness calculation unit, and the trial sequence changing unit using the generated trial sequence a plurality of times, and then the tire characteristics when the simulation is performed A trial arrangement that satisfies the target and meets the constraints is determined as a pitch arrangement of a tire tread pattern ,
The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
The fitness calculation unit calculates the fitness in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). To do.

Yet another embodiment of the present invention is a computer-executable program for causing a pitch arrangement of a tire tread pattern to be determined using a computer,
(A) Based on the constraints imposed on the pitch arrangement of the tread pattern, including the pitch arrangement conditions for creating a specific pitch arrangement in which a plurality of types of pitches having different pitch lengths are arranged. An objective function for outputting a physical quantity of tire characteristics when a simulation for outputting tire characteristics is performed, a target to be achieved by the output tire characteristics, and a procedure for causing a computer to determine,
(B) Under the above constraints, a procedure for causing a computer to set a plurality of pitch arrangements of tire tread patterns as trial arrangements;
(C) a procedure for causing the computer to output the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement;
(D) using the output tire characteristics and a value indicating the degree of conformity to the constraint condition, and causing the computer to calculate the fitness for the target and the constraint condition for each of the trial arrangements;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition , Having a computer generate a number of new trial sequences,
(F) After repeating the steps (c) to (e) a plurality of times using the modified trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint compatible trial sequence conditions, possess a procedure for determining the computer as a pitch arrangement of a tread pattern of a tire, and
The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
In the step (d), the fitness is calculated in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). To do.

  According to the present invention, a pitch arrangement exhibiting high tire characteristics can be efficiently obtained using a genetic algorithm.

It is a flowchart which shows the determination method of the pitch arrangement | sequence of one Embodiment of this invention. It is a flowchart explaining the crossover process routine of a 1st form. It is a figure explaining the change of the pitch arrangement | sequence by the crossover method of a 1st form. It is a figure explaining the change of the pitch arrangement | sequence by the conventional crossover process routine. It is a flowchart explaining the mutation process routine of a 1st form. It is a figure explaining the change of the pitch arrangement | sequence by the mutation process routine of a 1st form. It is a figure explaining the change of the pitch arrangement | sequence by the conventional mutation process routine. It is a figure explaining another example of the change shown in FIG. It is a figure explaining the change of the pitch arrangement | sequence by the mutation process routine of the modification of a 1st form. (A) is a figure which illustrates a part pitch arrangement of the individual which has the 2nd pitch arrangement, and (b) is a figure which illustrates a part pitch arrangement of the individual which has the 3rd pitch arrangement. is there. It is a flowchart explaining the crossover process routine of a 2nd form. It is a figure explaining the change of the pitch arrangement | sequence by the crossover method of a 2nd form. It is a flowchart explaining the crossover process routine of a 3rd form. It is a figure explaining the change of the pitch arrangement | sequence by the crossover method of a 3rd form. It is a block diagram which shows the determination apparatus of the pitch arrangement | sequence of one Embodiment of this invention. It is a figure which shows the example of the initial stage arrangement | sequence used for an Example and a comparative example. It is a figure which shows the result of the Example which concerns on a 1st form, and a comparative example. It is a figure which shows the result of the Example which concerns on a 2nd and 3rd form, and a comparative example. It is a figure which shows the pitch arrangement | sequence of some individuals shown in FIG.

  The pitch arrangement determining method, pitch arrangement determining apparatus, and pitch arrangement determining program of the present invention will be described in detail below.

(Pitch arrangement determination method)
The method of this embodiment is a method for determining the pitch arrangement of a tire tread pattern using a genetic algorithm, and includes the following steps (a) to (f).
(A) A step of setting a constraint condition including a pitch arrangement condition (hereinafter also referred to as a first constraint condition) and another constraint condition (hereinafter also referred to as a second constraint condition), an objective function, and a target.
(B) A step of creating a predetermined number of initial arrays as trial arrays (also referred to as individuals) and creating an initial population (also referred to as individual groups) in consideration of constraints.
(C) A step of outputting tire noise characteristics of each trial arrangement included in the initial group using an objective function.
(D) Using the fitness function determined by the noise index calculated using the objective function (the tire characteristics output by the objective function) and the value indicating the degree of conformance with the constraint, the target and the constraint Calculating fitness for.
(E) selecting individuals from the individual population in consideration of fitness, changing a part of pitch arrangement included in the selected individuals to satisfy the pitch arrangement condition, and adding a new individual (trial arrangement) Step to create.
(F) After repeating the generational change to create a new individual using a new individual, a step in which an individual whose noise index satisfies the target and meets the constraint condition is used as a pitch arrangement of the tread pattern.
According to this method, when a new individual is created in the step (e), the new individual to be generated is changed so as to satisfy the pitch arrangement condition. Can be done. In this specification, the optimal solution includes an approximate solution.

1st form Hereinafter, the determination method of the pitch arrangement | sequence which concerns on the 1st form of this invention is demonstrated.
FIG. 1 is a flowchart for explaining a pitch arrangement determining method according to the first embodiment.
Specifically, the method according to the first mode includes setting of constraint conditions and objective functions (step 100), creation of an initial array (step 102), output of tire noise characteristics (step 104), and calculation of fitness (step 106). ), Selection of individuals (step 108), crossover or mutation (step 110), determination of whether an end condition has been reached (step 112), determination of suitability (step 114), storage of pitch arrangement (step 116) Comprising steps. Note that the method of the first embodiment can be performed using, for example, a computer that functions as a pitch arrangement determining device described later.

In step 100, a constraint condition, an objective function, and a target are determined.
The constraint condition is a condition imposed on the pitch arrangement of the tread pattern of the tire, and includes a pitch arrangement condition that is a first constraint condition and another constraint condition that is a second constraint condition. The second constraint condition further includes (i) a condition not desired by the tire designer and (ii) a condition related to the pitch arrangement.

The pitch arrangement condition is a condition for creating a specific pitch arrangement by arranging a plurality of types of pitches having different pitch lengths. “To create a specific pitch arrangement by arranging a plurality of types of pitches having different pitch lengths” includes one pitch included in the trial arrangement,
(A) a plurality of pitches that are continuous (adjacently arranged) in the tire circumferential direction (also referred to as arrangement direction) having the same pitch length as the certain pitch, or
(B) one certain pitch when a pitch having the same pitch length as the certain pitch does not exist adjacent to the arrangement direction;
Is regarded as one lump (hereinafter also referred to as pitch type or pitch portion), a plurality of pitch lumps are appropriately combined and arranged in the arrangement direction to form a specific pitch arrangement.
“Specific pitch arrangement” means an arrangement of pitches that a tire designer thinks should have as a pitch arrangement used in an actual tire in terms of tire wear resistance, tire appearance, etc. A pitch arrangement. In the first form, the specific pitch arrangement includes the first pitch arrangement. The first pitch arrangement is a pitch arrangement that satisfies the following conditions (A) and (B).
(A) A first pitch length that continuously changes from a pitch type having the shortest pitch length (hereinafter also referred to as a minimum pitch type) to a pitch type having the longest pitch length (hereinafter also referred to as a maximum pitch type). And a second region where the pitch length continuously changes from the maximum pitch type to the minimum pitch type.
(B) The first region and the second region are alternately arranged in the arrangement direction while sharing the maximum pitch type and the minimum pitch type.
Note that “the pitch length changes continuously” means that the pitch length increases or decreases (changes) in order when the arrangement of pitch types is viewed in order in the arrangement direction. This means that the pitch length becomes longer or shorter each time one pitch in the pitch array moves from one pitch in the arrangement direction to the next adjacent pitch in the arrangement direction. In some cases, the pitch length may be longer or shorter when the pitch type is viewed in units while the pitches having the same pitch length are continuously arranged in the arrangement direction.
Hereinafter, the first pitch arrangement is also referred to as a complete periodic arrangement. The specific pitch arrangement of the present invention is not limited to a complete periodic arrangement, and may be another pitch arrangement. Other pitch arrangements will be described in second and third embodiments to be described later. The specific pitch arrangement of the present invention may include only one type of pitch arrangement, or may include two or more types of pitch arrangement.

Next, among the second constraints, the condition (i) that the tire designer does not want refers to a condition related to the pitch arrangement that the tire designer wants to exclude from the pitch arrangement employed in the actual tire, For example, there are the following three.
(Ia) A predetermined number or more of pitches having the same pitch length are continuously arranged in the arrangement direction in the pitch arrangement.
(Ib) The tire circumferential direction length of pitch portions (lumps) composed of pitches of the same pitch length arranged continuously in the arrangement direction occupies a predetermined ratio or more with respect to the tire circumferential length.
(Ic) A ratio of pitch lengths (hereinafter also referred to as adjacent pitch ratios) between two pitches adjacent in the arrangement direction (hereinafter also referred to as adjacent 2 pitches) is not less than a predetermined value.

  In addition, (ii) the conditions relating to the pitch array include, for example, that the number of pitches included in one trial array is a predetermined number, and the number of types of pitch lengths included in the trial array is a predetermined number. Etc.

  The objective function outputs a physical quantity of the tire characteristic when a simulation for outputting the tire characteristic is performed based on the pitch arrangement. In the present embodiment, tire noise characteristics are used as tire characteristics. The simulation uses the waveform of the sound that can be generated by the pitch assigned to each pitch according to the pitch length, and converts the pitch arrangement of the trial arrangement into discrete Fourier transform (DFT), fast Fourier transform (FFT), Fourier series. This is performed by calculating a noise index, which is a physical quantity of tire noise characteristics, by developing and the like. The noise index at this time is represented by the maximum value of the peak (spectrum) of the sound amplitude, the maximum value of the third-order sum, the variance or average, the value of the frequency, and the like. The cubic sum is the sum of the size of a certain peak and the sizes of two peaks appearing on both sides of the peak. The variance is the square of the deviation of a peak size from the average of all peak sizes. The tire characteristics are not limited to the tire noise characteristics, and for example, tire rigidity, rolling resistance, friction energy between the tire tread portion and the road surface, or the like may be used. There may be a plurality of objective functions, not just one.

  The target is a range of values that the tire designer considers that the tire characteristics output by the objective function should be achieved, and is represented by a range of preferable noise index values, for example.

  In step 100, in addition to the above-described constraint conditions, objective function, and target, setting conditions are also determined. The setting condition is specifically a condition related to the objective function, for example, the number of objective functions that can be set, and the weighting between the objective functions when a plurality of objective functions are set. . The setting condition is not a condition imposed on the pitch arrangement, but is referred to, for example, when determining the fitness function described later.

In the next step 102, an initial array is created as a 0th generation trial array. A plurality of initial arrays are created, for example, 100 are created. The created initial arrays constitute an initial population. The initial array is created in consideration of constraints. As a result, a new pitch is not used based on the initial arrangement including a pitch arrangement that does not satisfy the pitch arrangement condition and a pitch arrangement that does not satisfy the conditions (i) and (ii), which is a pitch arrangement that is not employed in an actual tire. Creating an individual is avoided. In the present specification, the initial sequence and the trial sequence are also referred to as individuals.
When the initial arrangement is created in consideration of the pitch arrangement conditions, it is preferable to create an arrangement that satisfies the complete periodic arrangement because it is easy to obtain an individual of the next generation that satisfies the complete periodic arrangement. At this time, the initial population may be configured only by the initial array satisfying the complete periodic array.

  Of the constraint conditions, the pitch constraint condition, which is the first constraint condition, is used by selecting an individual to be changed based on the fitness in step 108, which will be described later, and using an individual that does not satisfy this condition. However, with respect to other constraints that are the second constraint, the initial array that does not satisfy this is surely excluded from the initial population in this step 102.

  In the next step 104, tire noise characteristics are output using an objective function for each trial array included in the trial array group (also referred to as an individual group or simply a group). The output of the tire noise characteristic is performed by calculating an objective function. Specifically, the tire noise characteristic is output by performing simulation using the pitch lengths of the pitches included in the trial arrangement and outputting the tire characteristic. The simulation is performed in the same manner as described in step 100.

In the next step 106, fitness is calculated for each trial array included in the group. The fitness is an index indicating the adaptability of the individual with respect to the target and the constraint condition, and is used for easily determining the preference of the individual. The fitness is calculated using a fitness function. In the present embodiment, the fitness function is defined as the following formula (1).
Fitness F = O + γmaX (G, 0) (1)
In Expression (1), O is a tire characteristic output by the calculation of the objective function, and represents a noise index. G of the maX function is a value given when the pitch arrangement condition is satisfied. For example, G = 0 is set when the pitch arrangement condition is satisfied. In other cases, G = 1. γ is a weighting factor, and is determined in consideration of the magnitude of the influence on the fitness F when the condition of the pitch arrangement is compared with the achievement of the target by the tire characteristics O. For example, since an individual that does not satisfy the pitch arrangement condition is not preferable, in the equation (1), the value of γ is such that γmaX (1, 0) is clearly a large value with respect to the value of the tire characteristic O. An appropriate large number is determined. According to this, the fitness F of the individual satisfying the pitch arrangement condition becomes γmaX (0,0) = 0 regardless of the magnitude of γ, and the value becomes smaller (becomes better) while satisfying the pitch arrangement condition. The fitness F of a non-individual increases (becomes worse) depending on γ for which a large value is set. Therefore, when the fitness function of Equation (1) is used, the fitness F value does not necessarily decrease when the individual noise index is low (good), and greatly depends on whether or not the pitch arrangement condition is satisfied. Thus, the magnitude of the fitness value F is determined.

  When multiple objective functions are set, for example, when evaluating a Pareto solution representing the preference of a noise index using a Pareto ranking method, the fitness function is ranked by repeating generation changes. It is determined that the number of individuals with high will increase. The Pareto solution here refers to a solution that is superior in one or more tire characteristics and not inferior in other tire characteristics in a plurality of output tire characteristics.

  In the next step 108, based on the fitness, an individual to be changed when the change is performed using the crossover method or the mutation method in the next step 110 is selected. The fitness is the fitness calculated in step 106. Here, the fitness value of the next generation individual is improved by preferentially selecting the one with a small fitness value (good), and the individual with the large fitness value (bad) is selected as little as possible. In this way, the quality of the next generation individuals is prevented from deteriorating. Here, individuals with small fitness values may be selected in duplicate, and in that case, individuals with smaller fitness values may be selected with higher frequency. Alternatively, a preferable fitness value may be determined in advance as a threshold value, and randomly selected from individuals having a fitness value smaller than the threshold value. By making a selection based on the fitness in this way, an individual with a higher fitness value is more easily deceived. In the case where a change is made using the crossover method in the next step 110, two individuals are selected as one pair in order to create one individual. In addition, when a change is made using a mutation method, one individual is selected in order to create one individual.

  In addition, when an individual is changed using the crossover method or the mutation method in the next step 110, there is a possibility that an individual that does not satisfy the other constraint condition that is the second constraint condition is generated. By using the fitness function that also considers whether other constraint conditions are satisfied or not, individuals that do not satisfy other constraint conditions can be excluded from the change target when individuals are selected. it can. Thereby, the fall of calculation efficiency by changing using the individual which does not satisfy other constraints is suppressed.

  In the next step 110, the pitch arrangement of a part of the trial arrangement selected in step 108 is changed using the crossover method or the mutation method to generate a new trial arrangement. The change here is performed so that a new individual to be generated satisfies the pitch arrangement condition. Thereby, it is possible to suppress generation of a trial array having a pitch array that is not desired by the designer, for example, a pitch array in which the above-described complete periodic array is destroyed. Here, a change processing routine using each of the crossover method and the mutation method will be described.

(A) Processing routine by crossover method The crossover method used in step 110 specifically includes an operation for determining a crossover position, an operation for changing the crossover position, a replacement operation, and first to fourth comparison operations (e1). To (e4).
In the operation of determining the crossing position, the crossing position is determined by arranging the first trial array and the second trial array forming the respective pairs of the trial arrays in parallel with the arrangement direction of the pitch array. In the operation of changing the crossing position, the crossing position is changed when the complete periodic array is destroyed when crossing is performed at the crossing position determined by the operation of determining the crossing position.
In the replacement operation, two trial arrays (first trial array and second trial array) forming each pair of a plurality of pairs are placed on one side (first side) of the first trial array from the crossover position. The pitch arrangement on the other side (second side) from the crossover position is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement.
In the first to fourth comparison operations (e1) to (e4), the processing of step 204, step 208, step 206, and step 210 shown in FIG. 2 is performed.

Here, a processing routine based on the crossover method will be described with reference to FIG.
In step 200, it is determined whether or not crossover is to be performed for a plurality of pairs of trial arrays selected in step. The probability of whether or not to cross is determined by, for example, a designer.
In the next step 202, an operation for determining the crossover position is performed. The crossover position is determined with a predetermined probability.

In the next step 204, the first comparison operation (e1) is performed. In the first comparison operation, when crossover is performed, the pitch lengths of two pitches (the first pitch end and the second pitch end) connected to each other so as to sandwich the crossover position are compared, and the two pitch lengths are compared. Judge the difference. One pitch (first pitch end) of the two pitches is a pitch in contact with the first side with respect to the crossing position in the first trial arrangement, and the other pitch (second pitch end) is The pitch is in contact with the second side of the cross position in the second trial arrangement. The first side refers to one side in the arrangement direction, and the second side refers to the other side in the arrangement direction.
In the following description of the processing routine using the crossover method, for the sake of simplicity, the first trial array is also referred to as “self” and the second trial array is also referred to as “partner”. “Self” is a trial sequence that is left as an individual of the next generation. The “partner” is a trial sequence to be multiplied with “self” and is not adopted as an individual of the next generation. Further, the first pitch end is also referred to as “own end”, and the second pitch end is also referred to as “partner end”. In step 204, the own end included in the own pitch arrangement is compared with the other end included in the other pitch arrangement. When crossover is performed, the self end and the other end are connected to each other so as to sandwich the crossover position.

  As a result of the determination in step 204, if it is determined that the pitch length of the own end is different from the pitch length of the opponent end, in the next step 206, a third comparison operation (e3) is performed. In the third comparison operation, the pitch portion including the own end (type of pitch) is different from the pitch length of the own end adjacent to the second side (first pitch portion. The pitch length of the “adjacent” is compared with the pitch length of the other end, and the difference between the two pitch lengths is determined.

On the other hand, if it is determined in step 204 that the pitch lengths are the same, in the next step 208, the second comparison operation (e2) is performed. In the second comparison operation, the pitch length of the pitch portion (neighboring) adjacent to the second side with respect to the pitch portion including the own end and the pitch length different from the own end pitch length and the other end is included. The pitch lengths of the pitch portions adjacent to the second side and having a pitch length different from the pitch length of the counterpart end (second pitch portion; hereinafter also referred to as “partner neighbor”) are compared with each other. Judge the difference. In short, here, the pitch lengths of two pitch portions (the neighbor and the opponent) adjacent to the second side of the pitch portion including the own end and the pitch portion including the opponent end are compared.
If it is determined in step 206 that the pitch lengths are the same, in the next step 210, a fourth comparison operation (e4) is performed. In the fourth comparison operation, the pitch length of the pitch portion adjacent to the second side next to itself and having a pitch length different from the pitch length next to the self (third pitch portion, hereinafter also referred to as “neighbor next to me”). And the pitch length of the pitch portion (adjacent to the other end) that is adjacent to the second side with respect to the pitch portion including the opposite end and is different from the pitch length of the opposite end, and determines the difference between the two pitch lengths To do. In short, here, the pitch lengths of the two pitch parts (the neighbor next to the opponent and the neighbor next) adjacent to the second side of each of the neighbor and the pitch part including the opponent end are compared.

If it is determined in step 208 and step 210 that the pitch lengths are the same, in the next step 212, the replacement operation is performed to generate the new trial array. In the present embodiment, only the new trial arrangement in which the first pitch arrangement on the first side and the pitch arrangement on the second side of the partner are connected is adopted as the individual of the next generation. This is because there is a possibility that the complete periodic arrangement may be broken by crossover in the other pitch arrangement. Since at least the self-periodic arrangement is maintained even after crossover, it is possible to create a high-quality individual population at high speed by limiting the new trial arrangement adopted as an individual of the next generation to itself.
On the other hand, if it is determined that the pitch lengths are different as a result of the determination in step 206, step 208, and step 210, the process returns to step 202 to perform an operation for changing the crossover position. That is, the crossover position is determined again. After re-determining the crossover position, the first to fourth comparison operations are performed again to determine whether or not crossover is performed at the re-determined crossover position.

  Here, an example of the change by the change processing routine will be described with reference to FIG. Each of FIGS. 3A to 3C shows a pitch arrangement in the vicinity of the crossover position, which is included in the pitch arrangement of two trial arrangements (self and the other party) forming a pair of trial arrangements. 3A to 3C, the pitch arrangement is indicated by a band-like region extending in the left-right direction. Numbers 1 to 3 representing the pitch lengths of the pitches included in the pitch array are shown in the band-like region. Here, 1 has the shortest pitch length and 3 has the longest pitch length.

In the example shown in FIG. 3A, the pitch length 1 of the own end is different from the pitch length 2 of the other end, so that the pitch length 2 adjacent to itself and the pitch length 2 of the other end are compared. As a result, since both of them are the same, the pitch length 3 adjacent to itself and the pitch length 1 adjacent to the opponent are further compared. As a result, since they are different, the crossover position is determined again without performing crossover at the crossover position shown in the figure.
In the example shown in FIG. 3B, the pitch length 2 of the own end and the pitch length 2 of the opponent end are the same, so the pitch length 3 adjacent to the opponent and the pitch length 1 adjacent to the opponent are compared. As a result, since they are different, the crossover position is determined again without performing crossover at the crossover position shown in the figure.
In the example shown in FIG. 3 (c), the pitch length 2 at the own end and the pitch length 2 at the other end are the same, so the pitch length 3 next to the other end is compared with the pitch length 3 next to the other end. As a result, since both are the same, crossover is performed at the crossover position shown in the figure.

Next, with reference to FIG. 4, the change using the conventional crossover method will be described. Of the four pitch arrays a, b, c, and d shown in FIG. 4, the pitch arrays a and b are pitch arrays included in the pair before the change, and the pitch arrays c and d are the pairs after the crossover. It is an included pitch arrangement. Further, on the right side of each pitch arrangement a to d, an image diagram showing the change in pitch length in the arrangement direction of the pitch arrangement shown on the left side in an easy-to-understand manner is shown. In these image diagrams, the vertical axis indicates three types of positions corresponding to the three types of pitch lengths, and the horizontal axis indicates the arrangement direction. According to these image diagrams, in the pitch arrays a and b before crossover, the pitch length changes from the pitch length 1 to the pitch length 3 in a stepwise manner in the arrangement direction, and then the pitch length 3 to the pitch length 1 pitch. It can be seen that a complete periodic array that changes stepwise until a peak-shaped portion and a valley-shaped portion alternately appear in the array direction.
Here, when crossover is performed at the crossover position shown in the figure, which is randomly determined by the conventional crossover method, in the pitch arrangements c and d after the crossover, as shown by the region surrounded by the square in the image diagram, A part having a large gap between two adjacent pitches is generated, and the complete periodic arrangement is broken. As described above, in the change using the conventional crossover method, crossover is performed at the crossover position determined without considering that the complete periodic array is maintained in the new individual, so that the complete periodic array is destroyed. Or individuals that do not satisfy the constraint condition of the adjacent pitch ratio may be generated.

  On the other hand, according to the crossover method of the first embodiment, crossover is performed at a crossover position determined so that the complete periodic array is not broken in a new individual. Not generated. Therefore, the next generation of individuals is not created using such individuals, and a solution search can be performed efficiently.

(B) Processing routine by mutation method The mutation method is a method of forcibly changing a part of pitch arrangement selected with a predetermined probability with respect to the trial arrangement selected in step 108.
FIG. 5 shows an example of a processing routine based on the mutation method.
In step 300, it is determined whether or not the trial sequence selected in step 108 is changed by mutation.
In the next step 302, for example, a random number is generated from the pitch arrangement of the selected trial arrangement to select one pitch portion (first pitch portion). The pitch portion refers to each of a plurality of types of pitches arranged in the arrangement direction constituting the pitch arrangement. In other words, the pitch portion is composed of one pitch or a plurality of pitches having the same pitch length arranged continuously in the arrangement direction, and one or a plurality of pitches having different pitch lengths adjacent to each other in the arrangement direction. A part consisting of individual pitches.

  In the next step 304, another pitch part (second pitch part) different from the pitch part (first pitch part) selected in step 302 and having the same pitch length as the pitch part is selected. The second pitch part may be selected with a predetermined probability. For example, the second pitch part is located closest to the first pitch part in the arrangement direction and has the same pitch length as the first pitch part. Another pitch part may be sufficient.

In the next step 306, the total sum of the number of pitches of the first pitch portion and the second pitch portion is redistributed to each of the first pitch portion and the second pitch portion while keeping constant. One pitch length is assigned to the pitches of the first pitch portion and the second pitch portion to which the number of pitches has been redistributed.
Here, an example of the change by the change processing routine will be described with reference to FIG. In FIG. 6, the pitch arrangement shown on the left side is a part of the pitch arrangement included in the trial arrangement, and the pitch arrangement shown on the right side is a pitch arrangement after change obtained by mutating the left pitch arrangement. In this example, let us consider a case where the pitch portion 310 is selected as the first pitch portion and the pitch portion 312 is selected as the second pitch portion in the pre-mutation pitch arrangement shown on the left side of FIG. In this case, the sum 4 of the pitch number 1 of the pitch part 310 and the pitch number 3 of the pitch part 312 is redistributed in step 306, for example, the pitch numbers of the pitch part 310 and the pitch part 312 are each two. Be changed. Through this change, the sum 4 of the pitch numbers of the pitch part 310 and the pitch part 312 is maintained. Then, the pitch length 1 is newly assigned to the pitches included in the pitch part 310 and the pitch 312 after the redistribution. The redistribution is performed so that the number of pitches after the redistribution becomes 1 or more in any selected pitch portion. Thereby, a complete periodic arrangement is maintained in the pitch arrangement after redistribution.

  Next, with reference to FIG. 7, the change by the conventional mutation method is demonstrated. Of the two pitch arrays e and f shown in FIG. 7, the pitch array e indicates a pitch array before mutation, and the pitch array f indicates a pitch array after mutation. On the right side of each of the pitch arrays e and f, there is shown an image diagram showing a change in pitch length in the arrangement direction of the pitch array shown on the left side, similar to that shown in FIG. Here, it is assumed that the pitch of pitch length 3 marked above is selected in the pitch array e by the conventional mutation method, and the pitch length of this pitch is changed to 1. In this case, in the pitch array f after the mutation, as shown in the region surrounded by the square in the image diagram, a part having a large gap between two adjacent pitches is generated, and the complete periodic array is broken. Thus, in the change using the conventional mutation method, the pitch to be mutated is selected without considering that the complete periodic sequence is maintained in the new individual, and the pitch type is randomly selected. Since it is changed, there is a possibility that an individual in which the complete periodic array is destroyed is generated.

  On the other hand, according to the mutation method of the first embodiment, even if the pitch part is selected at random, the number of pitches only changes in the selected pitch part, and the pitch length does not change. Therefore, the complete periodic arrangement is maintained in the changed pitch arrangement, and the tire circumference does not change. Further, according to the mutation method of the first embodiment, even if the first pitch portion is selected at random, the complete periodic arrangement is maintained even after the change, so there is no need to re-determine the change location, The degree of freedom increases.

  Note that the redistribution may be performed, for example, by exchanging the number of pitches of the two selected pitch portions as shown in FIG. In FIG. 8, the pitch arrangement before the change is shown on the left side, and the pitch arrangement after the change is shown on the right side. As shown in FIG. 8, when two pitch portions 320 and 322 are selected, the number of pitches before the change is 2 in the pitch portion 320 and 1 in the pitch portion 322, but the number of pitches after the change is the pitch portion. 320 is 1 and pitch part 322 is 2, and the pitch numbers of the two pitch parts 320 and 322 are interchanged. Even when such redistribution is performed, since only the number of pitches is changed without changing the pitch lengths of the two selected pitch portions, the complete periodic arrangement is maintained in the changed pitch arrangement.

(Modification)
Next, with reference to FIG. 9, the modification of the change using a mutation method is demonstrated.
In FIG. 9, the left side shows a part of pitch arrangement included in the trial arrangement, and the right side shows the pitch arrangement after changing the left side pitch arrangement.
In this modification, unlike the mutation method described above, one pitch to be changed is selected and the type of the pitch is changed.

  In the present modification, as shown in FIG. 9, a pitch A having a pitch length of 2 (pitch marked above) is selected from the pitch arrangement of the selected trial arrangement with a predetermined probability. A pitch portion P that is located closest to the pitch A in the arrangement direction and includes a pitch B having a pitch length 1 different from the pitch A is found. A pitch C having a pitch length 2 different from the pitch length 1 of the pitch B is adjacent to the pitch portion P in the arrangement direction. Then, by replacing the pitch length 1 of the pitch B included in the pitch portion P with the same pitch length 2 as the pitch A, the right pitch arrangement shown in FIG. 9 is generated. Even when the modification according to the modification is performed, the complete periodic arrangement is maintained in the individual after the modification.

In addition, when the change by this modification is performed, the tire circumferential length is changing because the pitch length of the pitch B is changed. Therefore, after the change is made, the tire circumference changed by the change of the pitch length is adjusted. In this adjustment, for example, the pitch length of all pitches included in the trial arrangement is changed to be a certain percentage shorter or longer than the pitch length before adjustment, and the total pitch length after the change matches the tire circumference. To be done.
In the modification, the pitch to be changed is not limited to one, and may be a plurality of pitches equal to or less than the number of pitches included in the pitch portion P, for example.

In step 110, a more preferable individual can be generated by crossing and mutating the individual selected based on the fitness. Especially when creating a new individual by crossover, individuals of the next generation who inherited the superior pitch arrangement of the current generation individual by multiplying individuals with the preferred pitch arrangement selected based on fitness Can be created. In addition, when a new individual is created by mutation, the bias of the individual (solution) can be corrected.
In the change processing routine using the crossover method and the mutation method described above, the case where there are three types of pitch length has been described, but the number of types of pitch length may be four, five, and the like.

  In step 110, all the individuals of the next generation may be created using only one of the crossover method and the mutation method, and some individuals are created using the crossover method, The remaining individuals may be created using mutation methods. The individual population of the next generation may include individuals created by a method other than the crossover method or the mutation method. For example, in parallel with step 110, the one with the highest fitness may be copied from the population of the current generation and included in the next generation of individuals. Also, some individuals may be created using a method other than a genetic algorithm such as a local search method, a tabu method, or an annealing method.

In the next step 112, it is determined whether or not an end condition for ending individual creation has been reached. In the present embodiment, the end condition is whether or not the Nth generation individual population, which is the final generation, has been created. N is a natural number, for example, 100. If it is determined that the Nth generation individual group has not been created, the process returns to Step 104 and the procedure from Step 104 to Step 110 is repeated until the Nth generation individual group is created. When the Nth generation individual population is created, the individual creation is terminated, and the current generation individual population is replaced with the next generation individual population.
In step 112, instead of determining the end when the Nth generation individual population is created, the optimal solution is reached before the Nth generation individual population is created, or the fitness of the individual is It may be determined that the process has ended when the value does not become better (the value does not become smaller).

  In the next step 114, the suitability of each individual included in the final generation individual population is determined. The suitability is determined based on whether or not the output individual tire characteristics satisfy the target and satisfy the constraint conditions. The constraints are all constraints including the pitch arrangement condition and other constraints. In step 114, an individual whose tire characteristics output satisfy the target and satisfy the constraint condition is determined to be compatible, and in the next step 116, the pitch arrangement of the individual is, for example, described later. Save to computer memory. On the other hand, if the individual tire characteristics do not satisfy the target and / or the constraint condition is not satisfied, it is determined that there is no suitability and is excluded from the final generation individual population.

In the first embodiment, the pitch arrangement condition (first restriction condition) has been described as a restriction condition considered in the fitness function. However, in addition to the pitch arrangement condition, another restriction condition (second condition) Constraints) may be taken into account. For example, a predetermined value may be further input to G in the formula (1). For example, as described above, when G = 0 is satisfied when the pitch arrangement is satisfied, and G = 1 is satisfied otherwise, 0 or a negative number is added to G to satisfy other constraint conditions, When other constraints are not satisfied, a positive number smaller than 1 may be added to G. Or you may use the fitness function of following formula (2), for example as a fitness function which considers another constraint condition.
Fitness F = O + γ ₁ maX (G ₁ , 0) + γ ₂ maX (G ₂ , 0) (2)
In the equation, γ ₁ maX (G ₁ , 0) is a term relating to whether or not the pitch arrangement is satisfied, and γ ₂ maX (G ₂ , 0) is a term relating to whether or not other constraint conditions are satisfied.
There may be a plurality of objective functions considered in the fitness function. As the fitness function in that case, for example, the fitness function of the following equation (3) may be used.
Fitness F = O ₁ + αO ₂ + γmaX (G, 0) (3)
In the equation, O ₁ is a noise index represented by the maximum value of the third-order sum, and O ₂ is a noise index represented by the maximum peak of the sound amplitude. α is a weighting coefficient determined as a setting condition.
Further, when evaluating a plurality of objective functions using a Pareto ranking method, the following equation (4) may be used as the fitness function.
Fitness F = O + γmaX (G ₁ , 0) (4)
In the equation, O is an index obtained by indexing a plurality of objective functions using a Pareto ranking method.

Second Embodiment Next, a pitch arrangement determining method according to the second embodiment of the present invention will be described.
Here, a description will be given focusing on differences from the first embodiment. In the second mode, operations similar to those in steps 102 to 116 are performed except for points specific to the second mode described below. For convenience, the same reference numerals as those in the first mode are used. This will be described using reference numerals.

In the second embodiment, the specific pitch arrangement includes a second pitch arrangement described below. The second pitch arrangement is a pitch arrangement that satisfies the following condition (C) and condition (D). FIG. 10A shows an example of a part of pitch arrangement included in the trial arrangement having the second pitch arrangement. FIG. 10A shows the pitch arrangement direction in the left-right direction, and the pitch length in the up-down direction. The example shown in FIG. 10A is composed of five types of pitches A to E, and the pitch length decreases in order from the pitch A having the maximum pitch length to the pitch E having the minimum pitch length. This also applies to FIG. 10B referred later.
(C) a third region a in which a plurality of pitch types are arranged in the arrangement direction so that the pitch length is long, and a fourth region b in which a plurality of pitch types are arranged in the arrangement direction so that the pitch length is short are: Alternatingly arranged in the array direction.
(D) When two different pitch types that are not arranged adjacent to each other when the pitch types are arranged in the order of the pitch length are called non-adjacent pitch types, the non-adjacent pitches are viewed in order in the arrangement direction of the pitch arrangement. There are two pitch types that correspond to the seed.
In short, the second pitch arrangement is based on an arrangement in which the types of the plurality of pitches constituting the second pitch arrangement are repeatedly increased and decreased in the arrangement direction (condition (C)), and at least one location. Thus, there are two adjacent pitch types (non-adjacent pitch types) that are not arranged in the order of the pitch length, and there is a place where the order of the pitch types is interrupted in the basic arrangement (condition (D)). ). Such a second pitch arrangement has a relaxed condition for the completeness of the periodic arrangement compared to the first pitch arrangement, and is also referred to as a relaxed periodic arrangement in the following description.

  In the example shown in FIG. 10A, two pitches C and E surrounded by a broken-line square correspond to the non-adjacent pitch types. In the example shown in FIG. 10A, the third area a includes the pitch A having the maximum pitch length, and the fourth area b includes the pitch E having the minimum pitch length. Contrary to the example, the pitch E may be included in the third region a, and the pitch A may be included in the fourth region b. Alternatively, both the pitch A and the pitch E may be included in any of the third region a and the fourth region b. In addition, the second pitch arrangement does not have to be configured only by the third region a and the fourth region b, and there is a region that does not correspond to either the third region a or the fourth region b. You may do it.

  In the second mode, in step 110, an individual is specifically generated using a crossover method. The crossover method used here includes an operation for determining a crossover position, an operation for changing the crossover position, and a replacement operation similar to the crossover method used in the first embodiment. Among these, in the replacement operation, a new individual is generated by connecting the first pitch end (own end) and the second pitch end (partner end) in the same manner as in the first embodiment.

(C) Processing Routine of Second Embodiment A processing routine of the second embodiment will be described with reference to FIGS. 11 and 12.
FIG. 11 is a flowchart for explaining a crossover processing routine according to the second embodiment. FIG. 12 is a diagram for explaining a change in pitch arrangement by the crossover method of the second embodiment.
Here, a case where the specific pitch arrangement includes the first pitch arrangement in addition to the second pitch arrangement will be described as an example. In another example of the second mode, the specific pitch array may include at least the second pitch array, and may not include the first pitch array. A third pitch arrangement may be included.
Also, for convenience, of the two trial sequences to be crossed, the trial sequence of itself is referred to as “X”, and the trial sequence of the other party is referred to as “Y”.

Step 400 is the same as step 200 described in the first embodiment, and determines whether or not to perform crossover.
The next step 402 is the same as step 202, and performs an operation for determining the crossover position.
In the next step 404, paying attention to the first pitch end (hereinafter also referred to as X end), the type of pitch (X in the direction from left to right in FIG. 12) adjacent to the X end is considered. It is determined whether or not the pitch length (also called right adjacent) is longer than the pitch length at the X end.
In FIGS. 11 and 12, the case where the pitch lengths of two adjacent types of pitches are long in the arrangement direction is indicated by an arrow pointing to the upper right, and in the following description, there is an “up” relationship. Say. A case where the pitch length is short is represented by an arrow pointing downward to the right, and is also referred to as “downward” in the following description.
In other words, the determination made in step 404 is whether or not the pitch length on the X end and the right side of the X has an “up” relationship. Note that the expressions “up” and “down” are related to the vertical direction indicating the change in pitch length in the arrangement direction of the types of pitches arranged in the pitch arrangement, as shown in FIG. The third area may be referred to as an upstream area, and the fourth area may be referred to as a downstream area.

In the next step 406, if it is determined in step 404 that it is “up”, the fifth comparison operation (e5) is performed to determine whether or not the following condition 1 is satisfied.
In the fifth comparison operation (e5), the pitch lengths of the X end and the second pitch end (hereinafter also referred to as Y end) are compared.
Condition 1 is a condition 1 for determining whether or not two trial arrays may be crossed at the crossover positions determined in step 402 in order to generate the second pitch array and the first pitch array. One. Specifically, the condition 1 is that when the distance between two pitch lengths to be compared is expressed by the number of types when all pitch types are arranged in order of the pitch length, the distance is 0 or more. And it is below the number below the number of kinds of pitch at least. Regarding the “distance” here, for example, in the example shown in FIG. 10, the distance between the pitch A and the pitch B is 1, and the distance between the pitch A and the pitch D is 3. Further, the distance between the same pitch types is zero. By satisfying such condition 1, even when a non-adjacent pitch type is generated in the pitch arrangement by crossover, it is avoided that the gap between the two pitch types forming the non-adjacent pitch type becomes too large, which is not desirable. Generation of pitch arrangement can be prevented. The specific number of “distance” is not particularly limited, but is, for example, 0, 1, or 2 when the number of pitch types is five. When the distance is 0 or 1, the first pitch array is generated, and the pitch array having no non-adjacent pitch seed is generated. If the separation is 2, a second pitch array having non-adjacent pitch seeds is generated. The ratio of the number of gaps to the number of pitch types is set as the second constraint condition described above, and is taken into account when performing crossover in step (e).

  In step 410, if the determination in step 406 is affirmative, a sixth comparison operation (e6) is performed to determine whether the pitch length of the Y end matches the pitch length of the maximum pitch type. Note that “maximum” shown in step 410 of FIG. 11 means the pitch length of the maximum pitch type. When the pitch length of the Y end matches the pitch length of the maximum pitch type, the complete periodic array or an array close to the complete periodic array is maintained in the individual obtained by crossing.

  In step 414, if the determination in step 410 is negative, paying attention to the Y end, the pitch length of the type of pitch adjacent to the Y end in the arrangement direction (hereinafter also referred to as the right adjacent to Y) is set to the Y end. On the other hand, it is determined whether or not it is up. If it is determined that the pitch length on the right side of Y is ascending with respect to the Y end, the first side from the X end and the second side from the Y end coincide in the ascending direction. In the obtained individual, it is avoided that the direction of the up region changes to the down direction without passing through the maximum pitch species.

Steps 408, 412, and 416 are determinations that are performed when it is determined that the determination in step 404 is not “up”.
In step 408, the determination is substantially the same as step 406. If the determination in step 404 is negative, a fifth comparison operation (e5) is performed to determine whether or not the above condition 1 is satisfied. To do.
In step 412, if the determination in step 408 is affirmative, a sixth comparison operation (e6) is performed to determine whether the pitch length of the Y end matches the pitch length of the minimum pitch type. “Minimum” shown in step 412 of FIG. 11 means the pitch length of the minimum pitch type. Step 410 differs from step 410 in that the minimum pitch type is used instead of the maximum pitch type as a comparison target of the pitch length at the Y end.
If the result of step 412 is negative in step 412, it is determined whether or not the pitch length on the right side of Y is downward relative to the Y end. If it is determined that the pitch length on the right side of Y is down with respect to the Y end, the first side from the X end and the second side from the Y end match in the down direction, so In the obtained individual, it is avoided that the direction of the downstream region changes to the upstream without passing through the minimum pitch type.

In step 418, if the determination in step 410, step 412, step 414, or step 416 is affirmative, crossover is performed at the crossover position, and only the trial array (trial array X) of the newly generated trial arrays is included. Adopt and add to the population.
If the determination in step 414 or step 416 is negative, the process returns to step 402 and the crossover position is changed.

Here, with reference to FIG. 12, the change of the pitch arrangement according to the second embodiment will be specifically described.
FIG. 12 shows a pair of trial arrays X and trial arrays Y that are crossover targets. Here, a case will be described in which the crossing positions are determined at four locations (1), (2), (3), and (4) illustrated in the trial arrays X and Y.

  When the crossing position is (1), the X end is the pitch C and the Y end is the pitch B. In this case, in step 404, it is determined that the X end and the right side of X are in an upstream relationship. Next, at step 406, it is determined that the distance between the X end and the Y end is 1, and it is determined that the condition 1 is satisfied. At subsequent step 410, it is determined that the pitch length of the Y end is different from the pitch length of the maximum pitch type. The Next, in step 414, since it is determined that the Y end and the right side of Y are in an upward relationship, crossover is performed at the position (1). In this case, a first pitch array is generated.

  When the crossover position is (2), the X end is the pitch A and the Y end is the pitch C. In this case, in step 404, it is determined that the X end and the X right neighbor are in a downward relationship. Next, in step 408, it is determined that the distance between the X end and the Y end is 2, and it is determined that the condition 1 is satisfied. In subsequent step 412, it is determined that the pitch length of the Y end is different from the pitch length of the minimum pitch type. The In step 416, since it is determined that the Y end and the right side of Y are in a downward relationship, crossover is performed at the position (2). In this case, a second pitch arrangement is generated.

  When the crossover position is (3), the X end is the pitch D and the Y end is the pitch A. In this case, in step 404, it is determined that the X end and the right side of X are in an upstream relationship. Next, in step 406, the above-mentioned distance between the X end and the Y end is 3, and it is determined that the condition 1 is not satisfied. Therefore, no crossover is performed at the position (3), and the crossover position is changed in step 402. The

  When the crossover position is (4), the X end is the pitch A and the Y end is the pitch D. In this case, in step 404, it is determined that the X end and the X right neighbor are in a downward relationship. However, in step 406, the distance between the X end and the Y end is 3, and it is determined that the condition 1 is not satisfied. Therefore, the crossover is not performed at the position (4), and the crossover position is changed in step 402. The

  According to the above-described method, the pitch arrangement condition is relaxed compared to the first embodiment, and an individual having a relaxed periodic array is generated as a new individual in addition to an individual having a complete periodic array. Thereby, an individual group including more types of individuals is obtained, and various optimal solutions can be obtained as compared with the first form. For this reason, the freedom degree of the tire designer's choice with respect to a solution increases.

In the second mode, in Step 110, it is preferable to generate the second pitch arrangement when the adjacent pitch ratio is more than 1 and 2 or less. This avoids creating a second pitch array having non-adjacent pitch types when the gap between the pitch lengths of the two pitch types is large. The adjacent pitch ratio here is the ratio of the pitch lengths of the first pitch end and the second pitch end (first adjacent pitch ratio), and the pitch length with respect to the pitch end having the shorter pitch length is The ratio when expressed by the ratio of the pitch lengths of the longer pitch ends. A specific numerical range of the adjacent pitch ratio is determined in advance in step 100 as the second constraint condition.
In step 110, instead of the above-described first adjacent pitch ratio, a second pitch arrangement may be generated when a second adjacent pitch ratio described below is 1 to 2. Again, the creation of the second pitch array is avoided when the gap between the pitch lengths of the two pitch types included in the pitch array is large. The adjacent pitch ratio here is three kinds of pitches including the first pitch end and the second pitch end, and it is assumed that the first pitch end and the second pitch end are connected by the above replacement operation. In this case, among the three types of pitches arranged adjacent to each other, the ratio of the two types of pitch lengths (second adjacent pitch ratios) positioned at both ends in the arrangement direction of the pitch arrangement is the shorter pitch length. When the pitch length with respect to the pitch type is represented by the ratio of the pitch length of the longer pitch type to 1 to 2, the second pitch arrangement is generated. A specific numerical range of the adjacent pitch ratio is determined in advance in step 100 as the second constraint condition.

  In step 110, the second pitch arrangement has a ratio of the number of pitch types having a pitch length of a size between two pitch types corresponding to the non-adjacent pitch types described below as 1. It is preferable that it is made to satisfy ~ 2. In short, when all the pitch types are arranged in the order of the pitch length, the ratio of the pitch types that may exist between the two pitch types forming the non-adjacent pitch types is within a predetermined value. Preferably, a trial array having a pitch array of 2 is created. Thereby, it is suppressed that the individual | organism | solid with a big gap of the kind of two pitch which makes non-adjacent pitch seed | species is produced.

  Also in the second embodiment, it is preferable to set an initial arrangement consisting of the first pitch arrangement in step (b). By using an individual having a complete periodic arrangement that the tire designer considers preferable from the beginning, a solution search can be efficiently performed.

Third Embodiment Next, a pitch arrangement determining method according to the third embodiment of the present invention will be described.
Here, a description will be given by paying attention to the difference between the first embodiment and the second embodiment. Also in the third mode, operations similar to those in steps 102 to 116 are performed except for points specific to the third mode described below. For convenience, the same reference numerals as those in the first mode are used. This will be described using reference numerals.

In the third embodiment, the specific pitch arrangement includes a third pitch arrangement described below. The third pitch arrangement is a pitch arrangement that satisfies the following condition (E) and condition (F). FIG. 10B shows an example of a trial arrangement having the second pitch arrangement.
(E) A fifth region arranged in the arrangement direction so that a plurality of pitch types have a longer pitch length, and a sixth area arranged in the arrangement direction so that a plurality of pitch types have a shorter pitch length. It is arranged alternately.
(F) When viewed in order in the arrangement direction of the pitch arrangement, there is no maximum pitch species in the connection portion extending from the fifth area to the sixth area, or the minimum pitch in the area extending from the sixth area to the fifth area. There are no seeds.
In short, the third pitch arrangement is based on an arrangement in which a plurality of types of pitches constituting the third pitch arrangement repeatedly increase and decrease in the arrangement direction (condition (E)), The maximum pitch type or the minimum pitch type does not exist (condition (F)) in at least one of the connection portions of the region and the sixth region. Such a third pitch arrangement has relaxed conditions for the completeness of the periodic arrangement compared to the first pitch arrangement, and is also referred to as a relaxed periodic arrangement in the following description.
The condition (E) is substantially the same as the condition (C) of the second embodiment, the fifth region corresponds to the third region of the condition (C), and the sixth region is This is the same as the fourth region of the condition (C). In addition, the “connection portion” in the above condition (F) is a portion where the fifth region and the sixth region are connected, and the pitch or pitch forming the end of the fifth region on the sixth region side. It may be comprised by the kind of pitch which makes the edge by the side of the 5th area | region of a 6th area | region, or a pitch.

In the example shown in FIG. 10B, as indicated by the broken-line square, the pitch E of the minimum pitch type does not exist at the connection portion between the fifth region a and the sixth region b, and does not pass through the pitch E. In addition, the direction of the pitch length changes from ascending to descending.
Also in the third embodiment, in step 110, an individual is generated using a crossover method.

(D) Third Embodiment Processing Routine A third embodiment processing routine will be described with reference to FIGS. 13 and 14.
FIG. 13 is a flowchart for explaining a crossover processing routine according to the third embodiment. FIG. 14 is a diagram for explaining a change in pitch arrangement by the crossover method of the third embodiment. Here, the case where the specific pitch arrangement includes the first pitch arrangement and the second pitch arrangement in addition to the third pitch arrangement will be described as an example. In another example of the third embodiment, the specific pitch array only needs to include at least the third pitch array, and does not include the first pitch array and the second pitch array. Also good.

  Steps 500 to 516, step 520, and step 522 are substantially the same as steps 400 to 416, step 420, and step 422 of the second embodiment, respectively. The third embodiment is different from the second embodiment in that the determinations in step 518 and step 520 are performed.

In step 518, if it is determined that “upward” is determined in step 504, and the determinations in steps 506, 510, and 514 are affirmative, the seventh comparison operation (e 7) is performed to satisfy the condition 2 Judge whether or not.
In the seventh comparison operation (e7), the pitch length on the right side of X is compared with the pitch length of the minimum pitch type.
Condition 2 is a condition for determining whether or not the two trial arrays may be crossed at the crossover positions determined in step 502 in order to generate the third pitch array.

  Step 520 is determined to be “down” in step 504, and when the determination in step 508, step 512, or step 516 is affirmative, the pitch length to be compared with the pitch length on the right side of X is the maximum pitch. It differs from step 518 in that it is the pitch length of the seed.

In step 522, when the determination in step 514 or step 516 is affirmative, crossover is performed at the crossover position determined in step 502, and only the trial array corresponding to “self” among the newly generated trial arrays is adopted. Add to the population.
If the determination in step 518 or step 520 is negative, the process returns to step 502 and an operation for changing the crossover position is performed.

Here, a specific example of changing the pitch arrangement according to the third embodiment will be described with reference to FIG.
FIG. 13 shows a pair of trial arrays X and trial arrays Y that are crossover targets. Here, a case will be described in which the crossing positions are determined at four locations (1), (2), (3), and (4) illustrated in the trial arrays X and Y.

  When the crossover position is (1), the X end is the pitch D and the Y end is the pitch D. In this case, in step 504, it is determined that the X end and the right adjacent to the X are in an upward relationship. Next, in step 506, it is determined that the distance between the X end and the Y end is 0 and satisfies the condition 1, and in the subsequent step 510, it is determined that the pitch length of the Y end is different from the pitch length of the maximum pitch type. The Next, in step 514, it is determined that the Y end and the right adjacent to the right side are in an upstream relationship. In step 518, the pitch length adjacent to the right side of the X is determined to be different from the pitch length of the minimum pitch type E. Crossing is performed at the position). In this case, a third pitch arrangement is generated.

  When the crossover position is (2), the X end is the pitch D and the Y end is the pitch A. In this case, in step 504, it is determined that the X end and the X right neighbor are in a downward relationship. Next, at step 508, it is determined that the distance between the X end and the Y end is 1, and it is determined that the condition 1 is satisfied. In the following step 512, it is determined that the pitch length of the Y end is different from the pitch length of the minimum pitch type. The Next, in step 516, since it is determined that the Y end and the right side of Y are in a downward relationship, crossover is performed at the position (2). In this case, a third pitch arrangement is generated.

  When the crossover position is (3), the X end is the pitch D and the Y end is the pitch B. In this case, in step 504, it is determined that the X end and the right adjacent to the X are in an upward relationship. Next, at step 506, it is determined that the above-mentioned distance between the X end and the Y end is 2, and it is determined that the condition 1 is satisfied. Is done. Next, in step 514, it is determined that the Y end and the right adjacent to the right side are in an upstream relationship. In step 518, the pitch length adjacent to the right side of the X is determined to be different from the pitch length of the minimum pitch type E. Crossing is performed at the position). In this case, a third pitch arrangement is generated.

  When the crossover position is (4), the pitch type at the X end is B, and the pitch type at the Y end is also B. In this case, in step 504, it is determined that the X end and the X right neighbor are in a downward relationship. Next, in step 508, it is determined that the above-described separation between the X end and the Y end is 0 and the condition 1 is satisfied. However, in the subsequent step 512, the pitch length of the Y end is different from the pitch length of the maximum pitch length A. Therefore, the crossover is not performed at the position (4), and the crossover position is changed in step 502.

If it is determined in steps 514 and 516 that the direction is the same as the upward or downward direction determined in step 504 (if affirmed), a second pitch arrangement is generated.
According to the above-described method, even if it is determined in step 514 or step 516 that the direction is different from the upward or downward direction determined in step 504 (if denied), the next step If it is determined in 518 and 520 that the condition 2 is satisfied, crossover is performed and a third pitch arrangement is generated. Therefore, more types of individuals can be obtained than in the example according to the second embodiment described above.

In the second form and the third form, in step 100, the constraint condition further includes the following condition (α), condition (β), condition (γ), and in step 106, the pitch arrangement condition, condition ( It is preferable to calculate the fitness in consideration of at least one of the four conditions (α), condition (β), and condition (γ). Thereby, in the following step 108, it is possible to suppress selection of individuals that do not satisfy these conditions, and to prevent useless changes using individuals that are not desired by the tire designer.
(Α) In the pitch arrangement, when the ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) Limiting the number of pitches included in each type of pitch in the pitch arrangement.
(Γ) In the pitch arrangement, limit the number of pitches having the same pitch length that are continuously arranged in the arrangement direction.
Of these, the condition (α) is related to the condition (ic) described above. The condition (β) is related to the condition (ib) described above. The condition (γ) is related to the above condition (ia).
In this case, even if the pitch arrangement condition is determined in step 100, the fitness may be calculated in step 106 without considering the pitch arrangement condition.

(Pitch arrangement determination device)
Next, the pitch arrangement determining apparatus of this embodiment will be described.
FIG. 15 shows a pitch arrangement determining apparatus 10 according to this embodiment.
The apparatus 10 is configured using a computer. That is, by calling and starting a program stored in the computer, a software module is generated, and the computer functions as the device 10.
Specifically, the apparatus 10 includes a CPU 12, a memory 14 such as a ROM and a RAM, and an input / output unit 16. The input / output unit 16 is connected to an input operation device 32 and an output device (display or printer) 34. The apparatus 10 configures a processing module 18 for executing the measurement method of the above-described embodiment by activating a program stored in the memory 14.

The apparatus 10 calls the program stored in the memory 14 and starts it, thereby causing the condition setting unit 20, the trial array setting unit 22, the output unit 24, the fitness calculation unit 26, and the trial array changing unit 28 to be processed by the processing module 18. Configure as. At this time, the CPU 12 functions as a control unit 30 that controls the operation of each unit of the processing module 18.
The memory 14 stores a pitch array determination program for executing the pitch array determination method of the above embodiment, and stores a large number of trial array data.

The condition setting unit 20 is a part for determining constraint conditions and an objective function, and the first constraint described above based on the contents that the operator operates and inputs the input operation device 32 while viewing the input screen displayed on the display. The condition and the second constraint condition are set, and the objective function is formulated. The condition setting unit 20 further performs formulation of the fitness function, setting of constraint conditions used for the fitness function, setting of weighting factors, setting of tire characteristic targets, setting of end conditions for searching for optimal solutions, and the like. .
The trial array setting unit 22 sets a plurality of initial arrays as the 0th generation trial array under the constraint condition. The creation of the initial array is performed, for example, by executing a program for creating the initial array in consideration of the constraint conditions set by the condition setting unit 20. The set initial array is stored in the memory 14 as individuals constituting the initial group.

The output unit 24 outputs the tire noise characteristics of each individual using an objective function by performing a simulation using the pitch length. The output tire characteristics (noise index) are stored in the memory 14.
The fitness calculation unit 26 calculates the fitness of each individual using the fitness function. The calculated fitness is stored in the memory 14.
The trial arrangement changing unit 28 selects a part of the trial arrangement from the trial arrangement group based on the fitness, and changes a part of the pitch arrangement in the selected trial arrangement so as to satisfy the pitch arrangement condition. To do. As a result, a new trial sequence group for the next generation is generated and stored in the memory 14. Changes are made using the crossover or mutation methods described above.

  The control unit 30 repeats the operations of the output unit 24, the fitness calculation unit 26, and the trial array changing unit 28 using the newly generated trial array until the end condition is satisfied, and the end condition is satisfied. If so, the suitability is determined for each individual included in the final generation population. A trial arrangement that satisfies the target of the tire characteristics at the time of simulation and that meets the constraints is determined to be compatible, is determined as the pitch arrangement of the tire tread pattern, and is stored in the memory 14. Trial sequences whose tire characteristics do not satisfy the target and trial sequences that do not meet the constraints are determined to be incompatible and are excluded from the group. Individuals that have cleared the suitability are stored in the memory 14.

(Pitch arrangement determination program)
A program for performing the pitch arrangement determination method of the above embodiment and causing a computer constituting the pitch arrangement determination apparatus 10 to execute has the following procedure. That is, the program
(A) a constraint imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for creating a specific pitch arrangement in which the pitch arrangement of the tread pattern is arranged using a plurality of pitch types having different pitch lengths; An objective function for outputting a physical quantity of tire characteristics when a simulation for outputting tire characteristics based on the pitch arrangement is performed, and a procedure for causing a computer to determine a target to be achieved by the output tire characteristics;
(B) Under the above constraints, a procedure for causing a computer to set a plurality of pitch arrangements of tire tread patterns as trial arrangements;
(C) a procedure for causing the computer to output the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement;
(D) using the output tire characteristics and a value indicating the degree of conformity to the constraint condition, and causing the computer to calculate the fitness for the target and the constraint condition for each of the trial arrangements;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition , Having a computer generate a number of new trial sequences,
(F) After repeating the steps (c) to (e) a plurality of times using the modified trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint conditions And having the computer determine a trial arrangement that conforms to the pitch arrangement of the tire tread pattern.

According to the present embodiment, when a new individual is created using a genetic algorithm, a new individual is created so that the pitch arrangement condition is maintained. It is possible to obtain a high-quality individual population that is excluded. Thereby, it is possible to efficiently search for a solution.
Specifically, by using the fact that the complete periodic arrangement is maintained as the pitch arrangement condition, it is possible to create an individual that the tire designer thinks is more preferable from the viewpoints of tire wear resistance, tire appearance, and the like. In addition, when the initial array is created, a solution that satisfies the complete periodic array is created, so that it is possible to improve the solution using a high-quality initial group.

When creating an individual using the crossover method, the crossover position is determined so that the pitch arrangement condition is maintained in the new individual, so that it is ensured that an individual that does not satisfy the pitch arrangement condition is generated by performing the crossover. Can be suppressed.
In addition, when creating an individual using the mutation method, since the pitch arrangement condition is maintained in the new individual while selecting the pitch part or pitch to be changed with a predetermined probability, While ensuring the diversity of the individual population, it is possible to reliably suppress the generation of individuals that do not satisfy the pitch arrangement.

  In addition, when a relaxed periodic array is included as a specific pitch array, individuals having a pitch array other than a complete periodic array can also be used, and a solution search can be performed using more types of individuals. .

(Example)
Example of Experiment According to First Embodiment As constraints, for example, the number of pitches 72, the type of pitch length 5, and the ratio of the maximum pitch to the minimum pitch 1.4 are defined and include the initial arrays 1 and 2 illustrated in FIG. 100 initial arrays were created. The initial arrays were prepared so as to satisfy the complete periodic array. In FIG. 11, the initial arrays 1 and 2 are represented by columns A to E representing the pitch length of each pitch. Here, A has the longest pitch length and E has the shortest pitch length. The arrangement direction of the initial arrangements 1 and 2 is shown in the left-right direction in FIG. 11, and the vertical length in FIG. 11 shows that the length of the pitch length changes stepwise in the arrangement direction.

  Using the created initial population, according to the pitch arrangement determination method of the above embodiment, the generation change is repeated 100 times, and the final generation individual population is created with individuals determined to be compatible among the final generation individuals. (Example).

On the other hand, an individual population of the final generation was created in the same manner as in the example except that the conventional genetic algorithm was used without considering whether or not to maintain the complete periodic arrangement (Comparative Example). In the comparative example, the individual population of each generation was determined to be incompatible with including the individual in which the complete periodic sequence was destroyed in the final generation, including without excluding the individual in which the complete periodic sequence was destroyed. Individuals were excluded.
The maximum value of the third order sum and the maximum value of the peak were plotted for each individual of the example and the comparative example. The results are shown in the graph of FIG. Since the noise index is more preferable as the maximum value of the third order sum and the maximum value of the peak are smaller, it is more preferable that the noise index is plotted at the lower left of the graph of FIG. 17 and indicates that the solution rank is higher.

  As can be understood from FIG. 17, the final generation individual population (example) obtained using the determination method of the above embodiment is compared with the individual population (comparative example) using the conventional genetic algorithm. There are many individuals that are evaluated to be rank 1 (Pareto solution) or close to rank 1 when evaluated by this method, and more individuals with good noise indexes are obtained.

Experimental examples according to second and third embodiments As constraints, the number of pitches 27, the type of pitch length 5, the ratio 1.4 of the maximum pitch and the minimum pitch is determined, and the specific pitch arrangement of the pitch arrangement conditions is In addition to including a complete periodic array (first pitch array) and a relaxed periodic array (second pitch array and third pitch array), 100 initial arrays that satisfy the complete periodic array were created. Using the created initial population, the generation alternation was repeated 100 times according to the flow of FIG. 13, and the final generation individual population was created with individuals determined to be compatible among the final generation individuals.
For each individual of the final generation, the maximum value of the third order sum and the maximum value of the peak were plotted. The results are shown in the graph of FIG. In FIG. 18, individuals satisfying the complete periodic arrangement are indicated by ◆, individuals satisfying the second pitch arrangement are indicated by □, and individuals satisfying the third pitch arrangement are indicated by Δ. In FIG. 18, as indicated by the arrow c, the case where □ and Δ overlap each other indicates an individual that satisfies both the second pitch arrangement and the third pitch arrangement.
In addition, FIG. 19 shows a pitch arrangement of some of the obtained individuals (three individuals indicated by arrows a, b, and c). The array a indicates the individual pitch array indicated by the arrow a in FIG. 18 and is an individual satisfying the second pitch array. The array b indicates the individual pitch array indicated by the arrow b in FIG. 18 and is an individual satisfying the third pitch array. The array c indicates an individual pitch array indicated by an arrow c in FIG. 18 and is an individual satisfying the second pitch array and the third pitch array.

  As can be understood from FIG. 18, it can be seen that the individual population of the final generation includes more individuals that satisfy the relaxation periodic array than the individuals that satisfy the complete periodic array, and is distributed over a wide area. Thus, it can be said that various solutions were obtained by relaxing the pitch arrangement condition. In addition, since the number of individuals satisfying the relaxed periodic array is larger than the number of individuals of the complete periodic array, the number of individuals that are evaluated to be close to rank 1 (Pareto solution) or rank 1 is greater than the individuals of the complete periodic array. It can be seen that more individuals with a good noise index are obtained.

  As described above, the pitch arrangement determining method, the pitch arrangement determining apparatus, and the pitch arrangement determining program of the present invention have been described in detail, but the present invention is not limited to the above-described embodiment, and in a range not departing from the gist of the present invention, Of course, various improvements and changes may be made.

DESCRIPTION OF SYMBOLS 10 Pitch arrangement | sequence determination apparatus 20 Condition setting unit 22 Trial arrangement setting unit 24 Output unit 26 Fitness calculation unit 28 Trial arrangement change unit 30 Control unit

Claims (21)

A method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
In the step (e), a crossover method of selecting a plurality of pairs from the plurality of trial arrays based on the fitness and crossing a part of the pitch array in each of the plurality of pairs. And the crossover method is
An operation of arranging the first trial arrangement and the second trial arrangement forming each pair of the plurality of pairs in parallel with the arrangement direction of the pitch arrangement to determine a crossing position;
An operation of changing the crossover position when a new trial arrangement generated by crossing at the crossover position does not satisfy the pitch arrangement condition;
When a new trial array generated by crossing at the crossover position satisfies the pitch array condition, the first trial pitch array on one side of the crossover position is maintained among the first trial arrays. The pitch arrangement on the second side that is the other side of the crossover position in the first trial arrangement is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement. Operation, and
The crossover method further includes:
(E1) In the first trial arrangement, the pitch length of the first pitch end, which is the pitch located at the end on the second side in the pitch arrangement on the first side from the crossing position, and the second A first comparison operation for comparing a pitch length of a second pitch end that is a pitch located at an end of the first side in the pitch array on the second side from the crossing position in the trial arrangement of:
(E2) The pitch length of the first pitch portion, which is another pitch type arranged adjacent to the second side with respect to the pitch type including the first pitch end, and the second pitch end A second comparison operation for comparing a pitch length of a second pitch portion which is another pitch type arranged adjacent to the second side with respect to the pitch type including:
(E3) a third comparison operation for comparing pitch lengths of the first pitch portion and the second pitch end;
(E4) The pitch length of the third pitch portion, which is another pitch type arranged adjacent to the second side with respect to the first pitch portion, is compared with the pitch length of the second pitch portion. And a fourth comparison operation to
After the operation for determining the crossing position, so that a new trial arrangement generated by crossing at the crossing position satisfies the pitch arrangement condition,
The first comparison operation (e1) and the second comparison operation (e2),
The first comparison operation (e1) and the third comparison operation (e3), and
A pitch characterized by performing any one of three combinations of the first comparison operation (e1), the third comparison operation (e3), and the fourth comparison operation (e4). How to determine the sequence. Of the three combinations, when performing the first comparison operation (e1) and the second comparison operation (e2),
In the first comparison operation (e1), when the two pitch lengths to be compared are the same, the second comparison operation (e2) is performed,
In the second comparison operation (e2), when two pitch lengths to be compared are different, an operation to change the crossing position is performed, and when the two pitch lengths are the same, the replacement operation is performed. The pitch array determination method according to claim 1. When performing the first comparison operation (e1) and the third comparison operation (e3) among the three combinations,
In the first comparison operation (e1), when the two pitch lengths to be compared are different, the third comparison operation (e3) is performed,
The pitch arrangement determination method according to claim 1, wherein, in the third comparison operation (e3), when two pitch lengths to be compared are different, an operation of changing the crossing position is performed. Among the three combinations, when performing the first comparison operation (e1), the third comparison operation (e3) and the fourth comparison operation (e4),
In the first comparison operation (e1), when the two pitch lengths to be compared are different, the third comparison operation (e3) is performed,
In the third comparison operation (e3), when the two pitch lengths to be compared are the same, the fourth comparison operation (e4) is performed,
In the fourth comparison operation (e4), when two pitch lengths to be compared are different, an operation of changing the crossing position is performed, and when the two pitch lengths are the same, the replacement operation is performed. The pitch array determination method according to claim 1. A method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
In the step (e), the change is performed using a mutation method that forcibly changes the partial pitch arrangement, and the mutation method includes:
An operation of selecting one pitch A from the trial arrangement with a predetermined probability;
The pitch A includes a pitch B having a pitch length different from that of the pitch A, and is a pitch portion positioned closest to the pitch A in the arrangement direction of the pitch arrangement, and a pitch C having a pitch length different from the pitch B is an arrangement of the pitch arrangement. A pitch arrangement determining method comprising: replacing a pitch length of at least one pitch included in a pitch portion adjacent to the direction with the same pitch length as the pitch A. A method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
In the step (e), the change is performed using a mutation method that forcibly changes the partial pitch arrangement, and the mutation method includes:
From the trial arrangement, a pitch part which has one kind of pitch with a predetermined probability and is adjacent to another kind of pitch in the arrangement direction of the pitch arrangement is selected as the first pitch part. Furthermore, an operation of selecting another pitch part different from the first pitch part and having the same pitch length as the first pitch part as the second pitch part;
The total number of pitches of the first pitch part and the second pitch part is redistributed to each of the first pitch part and the second pitch part while maintaining a constant number of pitches. Allocating the one type of pitch length to the pitches of the first pitch portion and the second pitch portion to which redistribution has been redistributed.   The pitch arrangement determination method according to claim 6, wherein in the assigning operation, the redistribution is performed by exchanging the number of pitches of the first pitch portion and the second pitch portion.   In the selecting operation, after selecting the first pitch portion, the first pitch portion is first found when viewed in order from the other pitch portions arranged adjacent to the first pitch portion in the arrangement direction of the pitch array. The pitch arrangement determining method according to claim 6 or 7, wherein another pitch part having the same pitch length as that of the first pitch part is selected as the second pitch part. The specific pitch arrangement includes a pitch arrangement that satisfies the condition (A) and the condition (B) as a first pitch arrangement, and the condition (A) and the condition (B) are:
(A) A first in which the pitch length continuously changes from the maximum pitch type, which is the pitch type having the shortest pitch length, to the minimum pitch type, which is the longest pitch type, among all types of pitch types. And a second region in which the pitch length continuously changes from the minimum pitch type to the maximum pitch type,
(B) The first region and the second region are alternately arranged in the arrangement direction sharing the maximum pitch type and the minimum pitch type. 2. A method for determining a pitch arrangement according to item 1. A method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
The specific pitch arrangement includes a pitch arrangement that satisfies the condition (C) and the condition (D) as a second pitch arrangement, and the condition (C) and the condition (D) are:
(C) A third region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is long, and a fourth region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is short are the arrangement direction. Are arranged alternately,
(D) When two different pitch types that are not arranged adjacent to each other when the pitch types are arranged in the order of pitch length are referred to as non-adjacent pitch types, There are two types of pitches that fall into adjacent pitch types,
In the step (e), a crossover method of selecting a plurality of pairs from the plurality of trial arrays based on the fitness and crossing a part of the pitch array in each of the plurality of pairs. And the crossover method is
An operation of arranging the first trial arrangement and the second trial arrangement forming each pair of the plurality of pairs in parallel with the arrangement direction of the pitch arrangement to determine a crossing position;
An operation of changing the crossover position when a new trial arrangement generated by crossing at the crossover position does not satisfy the pitch arrangement condition;
When a new trial array generated by crossing at the crossover position satisfies the pitch array condition, the first trial pitch array on one side of the crossover position is maintained among the first trial arrays. The pitch arrangement on the second side that is the other side of the crossover position in the first trial arrangement is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement. Operation, and
In the replacement operation, in the first trial arrangement, a first pitch end that is a pitch located at an end on the second side in the pitch arrangement on the first side from the crossing position; In the trial arrangement, the new trial arrangement is generated by connecting a second pitch end that is a pitch located at an end of the first side of the pitch arrangement on the second side from the crossing position,
The crossover method further includes:
(E5) a fifth comparison operation for comparing the pitch lengths of the first pitch end and the second pitch end;
(E6) Among the pitch lengths of the second pitch end and all types of pitches, the maximum pitch type that is the longest pitch type or the minimum pitch type that is the shortest pitch length A pitch arrangement determination method comprising: a sixth comparison operation for comparing the pitch lengths of the seeds.   In the step (e), when all of the pitch types are arranged in order of pitch length, two different pitch types that are not arranged adjacent to each other are referred to as non-adjacent pitch types, which corresponds to the non-adjacent pitch type. 11. The pitch arrangement determination according to claim 10, wherein the second pitch arrangement is generated so that the number of pitch types having a pitch length that is between the pitch lengths of the two pitch types satisfies one. Method. A method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
The specific pitch arrangement includes a pitch arrangement that satisfies the conditions (E) and (F) as a third pitch arrangement, and the conditions (E) and (F) are:
(E) A fifth region arranged in the arrangement direction so that a plurality of pitch types have a longer pitch length, and a sixth area arranged in the arrangement direction so that a plurality of pitch types have a shorter pitch length. Are arranged alternately,
(F) Of all the pitch types, when the pitch type with the longest pitch length is the maximum pitch type and the pitch type with the shortest pitch length is the minimum pitch type, the pitch types are viewed in order in the arrangement direction of the pitch array. Thus, the maximum pitch species does not exist in the connection portion from the fifth region to the sixth region, or the minimum pitch species does not exist in the region from the sixth region to the fifth region. Yes,
In the step (e), a crossover method of selecting a plurality of pairs from the plurality of trial arrays based on the fitness and crossing a part of the pitch array in each of the plurality of pairs. And the crossover method is
An operation of arranging the first trial arrangement and the second trial arrangement forming each pair of the plurality of pairs in parallel with the arrangement direction of the pitch arrangement to determine a crossing position;
An operation of changing the crossover position when a new trial arrangement generated by crossing at the crossover position does not satisfy the pitch arrangement condition;
When a new trial array generated by crossing at the crossover position satisfies the pitch array condition, the first trial pitch array on one side of the crossover position is maintained among the first trial arrays. The pitch arrangement on the second side that is the other side of the crossover position in the first trial arrangement is replaced with the pitch arrangement on the second side from the crossover position in the second trial arrangement. Operation, and
In the replacement operation, in the first trial arrangement, a first pitch end that is a pitch located at an end on the second side in the pitch arrangement on the first side from the crossing position; In the trial arrangement, the new trial arrangement is generated by connecting a second pitch end that is a pitch located at an end of the first side of the pitch arrangement on the second side from the crossing position,
The crossover method further includes:
(E7) The pitch length of the first pitch portion that is another pitch type arranged adjacent to the second side with respect to the pitch type including the first pitch end, and the maximum pitch type or the minimum A pitch arrangement determination method comprising: a seventh comparison operation for comparing a pitch type with a pitch length. The specific pitch arrangement further includes a pitch arrangement satisfying the condition (C) and the condition (D) as a second pitch arrangement, and the condition (C) and the condition (D) are:
(C) A third region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is long, and a fourth region in which the plurality of pitch types are arranged in the arrangement direction so that the pitch length is short are the arrangement direction. Are arranged alternately,
(D) When two different pitch types that are not arranged adjacent to each other when the pitch types are arranged in the order of the pitch length are referred to as non-adjacent pitch types, the non-adjacent pitch types are viewed in order in the arrangement direction of the pitch arrangement. The pitch arrangement determination method according to claim 12, wherein there are two pitch types corresponding to adjacent pitch types. In the step (e), when the ratio of the pitch lengths of the first pitch end and the second pitch end is referred to as a first adjacent pitch ratio, the longer pitch length with respect to the shorter pitch end. The pitch arrangement determination according to claim 13 , wherein the second pitch arrangement is generated when the first adjacent pitch ratio expressed by the ratio of the pitch lengths at the pitch ends exceeds 1 and is 2 or less. Method. In the step (e), there are three types of pitches including the first pitch end and the second pitch end, and the first pitch end and the second pitch end are connected by the replacement operation. If the ratio of the two types of pitch lengths located at both ends of the pitch arrangement direction among the three types of pitches arranged adjacent to each other is referred to as a second adjacent pitch ratio, the shorter pitch length The said 2nd pitch arrangement | sequence is produced | generated when the said 2nd adjacent pitch ratio when it represents with the ratio of the pitch length of the pitch type with a longer pitch length with respect to the kind of pitch is 1-2. 14. A method for determining a pitch arrangement according to 13 . The specific pitch arrangement further includes a pitch arrangement that satisfies the conditions (A) and (B) as the first pitch arrangement, and the conditions (A) and (B) are:
(A) A first in which the pitch length continuously changes from the maximum pitch type, which is the pitch type having the shortest pitch length, to the minimum pitch type, which is the longest pitch type, among all types of pitch types. And a second region in which the pitch length continuously changes from the minimum pitch type to the maximum pitch type,
(B) the first region and the second region, the maximum pitch species and that the is arranged a minimum pitch species alternately shared by the arrangement direction a, one of claims 10 15 2. A method for determining a pitch arrangement according to claim 1. The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
The step (d) calculates the fitness in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). The pitch array determination method according to any one of 16. A method for determining a pitch arrangement of a tread pattern of a tire,
(A) A constraint condition imposed on the pitch arrangement of the tread pattern, including a pitch arrangement condition for arranging a plurality of types of pitches having different pitch lengths to form a specific pitch arrangement, and a tire based on the pitch arrangement A step of determining an objective function for outputting a physical quantity of a tire characteristic when a simulation is performed for outputting the characteristic, and a target to be achieved by the output tire characteristic;
(B) a step of setting a plurality of pitch arrangements of tire tread patterns as trial arrangements under the constraint conditions;
(C) outputting the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement; and
(D) calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity with the constraint condition;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition Generating a new trial sequence; and
(F) After repeating the steps (c) to (e) a plurality of times using the generated trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Determining a trial arrangement that meets the conditions as a pitch arrangement of a tread pattern of the tire, and
The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
In the step (d), the fitness is calculated in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). How to determine the pitch arrangement. The specific pitch arrangement includes a pitch arrangement that satisfies the condition (A) and the condition (B) as a first pitch arrangement, and the condition (A) and the condition (B) are:
(A) A first in which the pitch length continuously changes from the maximum pitch type, which is the pitch type having the shortest pitch length, to the minimum pitch type, which is the longest pitch type, among all types of pitch types. And a second region in which the pitch length continuously changes from the minimum pitch type to the maximum pitch type,
(B) The first region and the second region are alternately arranged in the arrangement direction sharing the maximum pitch type and the minimum pitch type,
The pitch array determination method according to any one of claims 10 to 15, 17, and 18, wherein, in the step (b), the trial array including the first pitch array is set. An apparatus for determining a pitch arrangement of a tread pattern of a tire,
Constraints imposed on the pitch arrangement of the tread pattern, including pitch arrangement conditions for creating a specific pitch arrangement in which a plurality of types of pitches having different pitch lengths are arranged, and tire characteristics based on the pitch arrangement A condition setting unit that defines an objective function that outputs a physical quantity of tire characteristics when a simulation for output is performed, and a target that the output tire characteristics should achieve;
Under the constraint conditions, a trial arrangement setting unit that sets a plurality of pitch arrangements of tire tread patterns as trial arrangements,
An output unit that outputs the tire characteristics using the objective function by performing the simulation using each pitch length of the pitches included in the trial arrangement;
An fitness calculation unit for calculating fitness for the target and the constraint condition for each of the trial arrangements using the output tire characteristics and a value indicating the degree of conformity to the constraint condition;
Based on the fitness, a part of the trial arrangement is selected from the plurality of trial arrangements, and a part of the pitch arrangement in the selected trial arrangement is changed so as to satisfy the pitch arrangement condition. A trial array modification unit for generating a plurality of trial arrays;
A control unit that controls operations of the condition setting unit, the trial sequence setting unit, the output unit, the fitness calculation unit, and the trial sequence change unit,
The control unit repeats the operations of the output unit, the fitness calculation unit, and the trial sequence changing unit using the generated trial sequence a plurality of times, and then the tire characteristics when the simulation is performed A trial arrangement that satisfies the target and meets the constraints is determined as a pitch arrangement of a tire tread pattern,
The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
The fitness calculation unit calculates the fitness in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). A device for determining a pitch arrangement. A computer-executable program for causing a pitch arrangement of a tire tread pattern to be determined using a computer,
(A) Based on the constraints imposed on the pitch arrangement of the tread pattern, including the pitch arrangement conditions for creating a specific pitch arrangement in which a plurality of types of pitches having different pitch lengths are arranged. An objective function for outputting a physical quantity of tire characteristics when a simulation for outputting tire characteristics is performed, a target to be achieved by the output tire characteristics, and a procedure for causing a computer to determine,
(B) Under the above constraints, a procedure for causing a computer to set a plurality of pitch arrangements of tire tread patterns as trial arrangements;
(C) a procedure for causing the computer to output the tire characteristics using the objective function by performing the simulation using the pitch lengths of the pitches included in the trial arrangement;
(D) using the output tire characteristics and a value indicating the degree of conformity to the constraint condition, and causing the computer to calculate the fitness for the target and the constraint condition for each of the trial arrangements;
(E) selecting a part of the trial arrangement from the plurality of trial arrangements based on the fitness, and changing a part of the pitch arrangement in the selected trial arrangement to satisfy the pitch arrangement condition , Having a computer generate a number of new trial sequences,
(F) After repeating the steps (c) to (e) a plurality of times using the modified trial arrangement, the tire characteristics when the simulation is performed satisfy the target, and the constraint Having a computer determine a trial arrangement that meets the conditions as a pitch arrangement of a tire tread pattern,
The constraint conditions further include a condition (α), a condition (β), and a condition (γ). The condition (α), the condition (β), and the condition (γ) are:
(Α) In the pitch arrangement, when a ratio of two types of pitch lengths arranged adjacent to each other in the arrangement direction is referred to as a third adjacent pitch ratio, the third adjacent pitch ratio is limited.
(Β) limiting the number of pitches included in each of the pitch types in the pitch arrangement;
(Γ) In the pitch arrangement, limiting the number of pitches having the same pitch length continuously arranged in the arrangement direction,
In the step (d), the fitness is calculated in consideration of at least one of the pitch arrangement condition, the condition (α), the condition (β), and the condition (γ). Program to do.

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