JP7436291B2 - Time series optimization program and time series optimization system - Google Patents

Description

The present invention relates to a time series optimization program and a time series optimization system.

An example of a time-series optimization target is a dam. Dams are installed for purposes such as flood control and power generation. In order to best realize these objectives, dam storage levels and discharge volumes should be optimized. This applies not only to a single dam, but also to water systems in which multiple dams are connected in series or parallel (connected water systems).

On the other hand, the operation of linking dam groups in a connected water system (dam group cooperative operation) requires complex considerations, such as considering the effect of the discharge amount of an upstream dam on the water storage amount of a downstream dam. Therefore, it is difficult to realize dam group cooperative operation based on human intuition and experience. Computer systems that support human decision-making regarding the operation of multiple water supply systems, such as this cooperative operation of dam groups, have been proposed.

Patent Document 1 discloses a "water supply operation control device". This invention develops operation schedules for pumps that make up the water supply system, such as intake pumps that take water from water intake points such as rivers and lakes and send it to water treatment plants, and water transmission pumps that send water from the water treatment plants to distribution reservoirs. This relates to a water supply operation control device. In water supply facilities, water supply operation plans are drawn up for the water pumps that make up the water supply system, depending on the daily water demand. In order to formulate a water supply operation plan that can reduce pump power costs, a water supply operation control device is used that uses mathematical methods to formulate a water supply operation plan and presents the water supply operation plan to the operator. There is.

The invention disclosed in Patent Document 1 implements a linear programming method with the water demand predicted by a water demand forecasting means as a condition, and tentatively determines the operation schedule of pumps that constitute a water supply system for waterworks. A provisional operation schedule means and a preset possible range of the amount of water delivered by the pump, including a predetermined amount of water delivered by the pump when the pump is operated according to the operation schedule provisionally set by the provisional operation schedule means. A possible range limiting means for limiting the amount of water to be delivered is provided, and an operation schedule for the pump is formulated by implementing a dynamic programming method that is conditioned on the possible range of water delivery amount limited by the possible range limiting means. This is what I did.

Japanese Patent Application Publication No. 2007-070829

The above conventional method executes dynamic programming by setting a limited search range using a possible range limiting means, so it is possible to determine optimal control variables in a short time without deteriorating solution accuracy. . in particular,
The optimal operation schedule search range = linear programming solution ± a predetermined amount, and dynamic programming is used to search for a solution limited to this range.

In the case of dynamic programming, the size of the search range is determined by how many stages the range is divided into. That is, the size of the search range is the value obtained by dividing the search range by the resolution (value per step). When trying to obtain a solution with fine resolution, it is necessary to increase the number of stages, which increases the search range. In this case, a long calculation time is required and a practical device cannot be manufactured. In order to complete the calculation in a short time, it is necessary to reduce the search range, and therefore it is necessary to reduce the number of stages (roughen the resolution). However, solutions with coarse resolution may not be practical.

The present invention has been made in view of this problem mentioned above. The problem to be solved by the present invention is to provide a system for solving optimization problems with fine resolution.

In order to solve the above problems, the present invention provides a time series optimization program that causes a computer to execute an optimization process that optimizes a time series of target states that change with time. A first process of accepting as an input time series a time series of the state that gives the best evaluation value for evaluating the state transition between each time when the state at each time is represented by a discrete value discretized in units of 1. and, when the state at each time is expressed by a discrete value obtained by discretizing the continuous value in a second unit smaller than the first unit, the evaluation value is the best within a predetermined neighborhood of the input time series. and a second process of calculating a time series of the states.

According to the present invention, optimization problems can be solved with fine resolution.

FIG. 3 is a diagram for explaining the formulation of dam group cooperative operation. FIG. 2 is a diagram for explaining an overview of dynamic programming (DP). FIG. 2 is a diagram for explaining an overview of discrete differential dynamic programming (DDDP). FIG. 2 is a diagram for explaining an overview of progressive dynamic programming (PDP). It is a flowchart for explaining the outline of progressive dynamic programming (PDP). FIG. 1 is a schematic block diagram showing the configuration of a computer system for implementing an embodiment. FIG. 2 is a software configuration diagram of a dam group cooperative operation program. This is the GUI displayed by the GUI module. FIG. 2 is a sequence diagram illustrating processing executed by a computer system for implementing the embodiment. 10 is a sequence diagram showing details of step S907 in FIG. 9. FIG. 3 is a flowchart showing details of optimization processing by DP/DDDP. 3 is a flowchart showing details of optimization processing by DP/DDDP. This is an example of a time series graph of dam water storage rate and dam discharge amount based on basic operation. This is an example of a time series graph of dam water storage rate and dam discharge amount based on the optimized dam group cooperative operation output by the dam group cooperative operation program. This is an example of polynomial approximation of the discharge amount that does not cause sudden changes in water level downstream. FIG. 3 is a diagram showing a data structure of project data regarding a dam model. FIG. 3 is a diagram showing a data structure of project data regarding a river model.

Embodiments of the present invention will be described below with reference to the drawings. The embodiments are examples for explaining the present invention, and are omitted and simplified as appropriate for clarity of explanation. The present invention can also be implemented in various other forms. Unless specifically limited, each component may be singular or plural.

The position, size, shape, range, etc. of each component shown in the drawings may not represent the actual position, size, shape, range, etc. in order to facilitate understanding of the invention. Therefore, the present invention is not necessarily limited to the position, size, shape, range, etc. disclosed in the drawings.

Examples of various types of information will be described using expressions such as "table," "list," and "queue," but various information may also be expressed using data structures other than these. For example, various information such as "XX table", "XX list", "XX queue", etc. may be referred to as "XX information". When describing identification information, expressions such as "identification information", "identifier", "name", "ID", and "number" are used, but these expressions can be replaced with each other.

When there are multiple components having the same or similar functions, the same reference numerals may be given different suffixes for explanation. Furthermore, if there is no need to distinguish between these multiple components, the subscripts may be omitted from the description.

In the embodiments, processing performed by executing a program may be described. Here, a computer executes a program (module) using a processor (eg, CPU, GPU), and performs processing determined by the program using storage resources (eg, memory), interface devices (eg, communication port), and the like. Therefore, the main body of processing performed by executing a program may be a processor. Similarly, the subject of processing performed by executing a program may be a controller, device, system, computer, or node having a processor. The main body of processing performed by executing the program may be an arithmetic unit, and may include a dedicated circuit that performs specific processing. Here, the dedicated circuit is, for example, an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), or a CPLD (Complex Programmable Logic Device).

A program may be installed on a computer from a program source. The program source may be, for example, a program distribution server or a computer-readable storage medium. When the program source is a program distribution server, the program distribution server includes a processor and a storage resource for storing the program to be distributed, and the processor of the program distribution server may distribute the program to be distributed to other computers. Furthermore, in the embodiments, two or more programs may be implemented as one program, or one program may be implemented as two or more programs.

First, an overview of this embodiment will be explained with reference to FIGS. 1 to 5.

<Formulation of dam group cooperative operation>
FIG. 1 is a diagram for explaining the formulation of dam group cooperative operation. In order to realize dam group operation optimization using a computer, the dam group operation is formulated as follows.

Figure 1 shows an example of a dam group. In this specification, the dam group shown in FIG. 1 will be described as an example of a cooperative operation target. As shown in FIG. 1, there are a dam D0 (101), a dam D1 (102), and a dam D2 (103). Upstream of water level gauge G0 (111) are dam D0 (101) and dam D1 (102). Dam D2 (103) is upstream of water level gauge G1 (112). Upstream of water level gauge G2 (113) are water level gauge G0 (111) and water level gauge G1 (112).

River R0 (121) leaves dam D0 (101) and passes through water level gauge G0 (111) and water level gauge G2 (113). River R1 (122) leaves dam D1 (102) and joins river R0 upstream of water level gauge G0 (111). River R2 (123) leaves dam D2 (103), passes through water level gauge G1 (112), and joins river R0 upstream of water level gauge G2 (113).

It is assumed that the dam group is expressed by the state variable STATE[t] at discretized time t=0,1,...,T-1. However, the state variable STATE[t] is an N-dimensional vector.
STATE[t]=(state[t,0],state[t,1],...,state[t,N-1])
Here, state[t,i] is an index of the amount of water stored in dam i, and indicates which stage of the effective water storage capacity divided into K stages the water is stored. Therefore, state[i,t] takes any value from 0, 1,...,K-1.

The state of the dam satisfies the continuity equation expressed by (Equation 1).
STATE[t]=VTOS(STOV(STATE[t-1])+(INFLOW[t]-OUTFLOW[t])*ΔT)
...(Formula 1)
However, INFLOW[t] and OUTFLOW[t] are the average amount of inflow into the dam and the average amount of discharge from the dam at time ΔT from time t-1 to t. STOV(STATE) is a function that converts STATE to dam water storage amount VOLUME, and VTOS(VOLUME) is a function that converts dam water storage amount VOLUME to STATE, an index of water storage amount.

Further, the flow rate RIVERFLOW[t] at the water level gauge j=0,1,...,J-1 is expressed as in (Equation 2) using the function SIM that simulates flood flow.
RIVERFLOW[t]=(riverflow[0,t],riverflow[1,t],riverflow[J-1,t])
=SIM(RIVERFLOW[t-1],OUTFLOW[t],LATERALFLOW[t])...(Formula 2)
The function SIM may be implemented as a first-order unsteady flow, or as a model in which the flow rate at the upstream end reaches the downstream end after a certain time (delay time model). Here, LATERALFLOW[t] is the amount flowing into the river from sources other than the dam at the water level gauge j=0,1,...,J-1 (main river lateral inflow amount and tributary flow amount).

Dam group operation optimization is a state transition (STATE[0],STATE[1],...,STATE [T-1]).
Objective function:OBJECTIVE(STATE[0],STATE[1],...,STATE[T-1])

A problem formulated in this way is called a multistep decision process. Dynamic programming (DP) is known as a method for efficiently solving multi-step decision processes.

DP achieves efficiency by using the "principle of optimality." That is, it is assumed that "the optimal policy consists of only optimal sub-policies", and the problem is to find STATE[t] that minimizes the value of the recurrence formula expressed by (Equation 3).
OBJECTIVE(STATE[0],STATE[1],...,STATE[t])
=COST(STATE[t-1],STATE[t])+OBJECTIVE(STATE[0],STATE[1],
...,STATE[t-1]))...(Formula 3)
Here, COST is a function (cost function) that evaluates the quality of state transition (STATE[t-1], STATE[t]). COST always returns a value greater than or equal to 0, and the better the evaluation, the smaller the value.

<Overview of dynamic programming (DP)>
FIG. 2 is a diagram for explaining an overview of dynamic programming (DP). DP can efficiently find global solutions for multi-step decision processes with discontinuous, non-differentiable, and non-convex objective functions. On the other hand, DP has a disadvantage called the ``curse of dimensionality,'' in which the amount of calculation increases exponentially with the dimensionality of the state variable.

For optimal control of dam groups, if the number of dams is divided into N, the amount of water storage is divided into K stages, and the target period is divided into T stages, it is necessary to find pow(TK,2N) state transitions. However, pow(x,y) is a function that returns x to the y power. For example, if the number of dams is 3 and the amount of water stored is divided into 50 stages, and the optimal amount of water stored every hour for 24 hours is to be determined, 375 billion state transitions need to be calculated. Handling this with a computer is impractical in terms of processing speed.

DP first finds the optimal solution while moving forward in the time direction, and stores the optimal state transition. The processing at each time is as follows. Each node (○ mark, for example 211) shown in FIG. 2 indicates a possible state of the system. If the number of dams is N and the amount of water storage is divided into K stages, there are pow(K,N) nodes at each time. All state transitions leading to node 212 (STATE[t]=k1) at time t are indicated by links (for example, 213). The cost of these links is determined by the cost function COST. From the obtained values, find the state transition (minimum cost link) with the smallest value of the next objective function.
Objective function: OBJECTIVE(STATE[0],STATE[1],...,STATE[t]=k1)

If the minimum cost link is link 215, this link 215 (link 215 from node 214 (STATE[t-1]=k0) to node 212) is stored. Similar processing is executed for all nodes at time t. These processes are executed from time t=1 to t=T-1. The implementation of this process will be explained with reference to FIG.

Next, find the node with the smallest objective function value among all the nodes at time t=T-1. The state transition leading to this node has already been memorized from the calculation process up to now, so by tracing backward in time to the node at time t=0, the state transition that minimizes the objective function value ( STATE[0],STATE[1],...,STATE[T-1]) can be found. The implementation of this process will be explained with reference to FIG.

<Overview of Discrete Differential Dynamic Programming (DDDP)>
FIG. 3 is a diagram for explaining an overview of discrete differential dynamic programming (DDDP). Approximate solutions have been proposed to overcome the so-called "curse of dimensionality" of dynamic programming. One of these methods, Discrete Differential Dynamic Programming (DDDP), is a process to obtain a quasi-optimal solution by constraining the number of stages K of the state variable (water storage amount in this embodiment) to a small value dK. is repeated.

In DDDP, an appropriate water storage amount time series is given as the initial trajectory 301, and the optimal solution is found only within a range in which the water storage amount is increased or decreased by several steps (for example, 3 steps of -1, 0, +1, in this case dK = 3). The value is searched and used as the initial value for the next optimal solution search process. Nodes within this search range (nodes connected by broken lines in FIG. 3, for example, node 303) are called a corridor 302. In this way, the optimal sequence is finally determined by repeating the process of searching for the optimal solution within the corridor. If the optimal solution is reached in 10 search iterations, the same result as the 375 billion state transition calculations described above can be obtained with approximately 1/2 millionth (approximately 170,000 ways) the amount of calculation.

DDDP requires that the objective function be convex from the initial trajectory to the optimal solution. For example, this can be done by setting the objective function to the square of the river flow rate at the water level gauge. For example, the objective function is expressed as (Equation 4).
COST(STATE[t-1],STATE[t])=
SIGMA(j=0,J-1,pow(riverflow[j,t]/designFlow[j], 2))...(Formula 4)
And it is sufficient. However, SIGMA(i=0,I-1,Expression) is a function that sums up the value of expression Expression while increasing variable i by 1 from 0 to I-1, and designFlow[j] is the planned high water level at water level gauge j. It is the flow rate.

However, flood control requires simultaneous realization of multiple objectives, such as taking into account sudden fluctuations in flow rate. In the case of multiple objectives, the objective function is multimodal, so it is not a convex function. For example, dam operating rules require that the discharge amount not exceed the amount that does not cause sudden changes in the water level downstream (observing the so-called "discharge principle"). An example of polynomial approximation of the discharge amount that does not cause sudden changes in water level downstream will be explained with reference to FIG.

An objective function that reduces the river flow rate at the water level gauge and adheres to the "principle of discharge" can be expressed, for example, by (Equation 5).
COST(STATE[t-1],STATE[t])=
SIGMA(j=0,J-1,pow(riverflow[j,t]/designFlow[j],2))
+SIGMA(i=0,I-1,pow((outflow[i,t]-outflow[i,t-1])/outflowLimit[i],2))
...(Formula 5)
However, outflowLimit[i] is the discharge amount that does not cause sudden changes in the water level downstream at dam i, and its value is determined by outflow[i,t].

Also, in DDDP, if the number of stages K of the state variable is a large value, it is necessary to widen the width of the corridor, and the search will be repeated many times before reaching the optimal solution. In order to find a solution in a realistic amount of time, the number of stages K of state variables needs to be approximately 10 to 100. However, in order to operate the dam, it is necessary to determine the time series of the dam discharge amount on the order of 1 m3/s. For example, if the effective water storage capacity of the dam is 10 MCM and the operation is performed in units of 1 hour, the number of stages K needs to be 5120 in order to optimize in units of 1 m3/s or less. It is not realistic to solve state variables with this many stages using DDDP.

In other words, it can be said that DDDP has two issues when applied to real problems. The first challenge is to make it applicable to multimodal objective functions. The second challenge is to make it applicable even when the number of stages K of the state variable is large.

<Overview of progressive dynamic programming (PDP)>
FIG. 4 is a diagram for explaining an overview of progressive dynamic programming (PDP). FIG. 5 is a flowchart for explaining an overview of progressive dynamic programming (PDP). This embodiment proposes progressive dynamic programming in order to be applied when the objective function is multimodal and the number of stages K of the state variables is a large value as described above. The main processing entity in FIG. 5 is a dam group cooperative operation program 621, which will be described later.

The result of step S501 explained with reference to FIG. 5 or the result of the previous processing of step S502 which is repeatedly processed is assumed to be a trajectory 401 as shown in FIG. A corridor 402 (nodes connected by broken lines in FIG. 4) is installed near this trajectory 401. However, the number of stages of the state variable is twice the number of stages at which the trajectory 401 was obtained. As a result, a new node 403 and the like are prepared. In this corridor 402, an optimal solution is obtained by DDDP.

In progressive dynamic programming (PDP), which is an optimization method disclosed in this embodiment, initial values are first obtained using DP (step S501). Let the number of stages of the state variable at this time be KInit. Next, DDDP is performed by doubling the stage number K of the state variable near the initial value to obtain a new initial value (step S502). This step S502 is repeated M times (step S503). That is, the number of stages K of the state variable is K=pow(2,M)*KInit.

The step number K of the previous time r=i in repeating step S502 M times is a "first unit" when representing the state at each time with a discrete value obtained by discretizing a continuous value in a first unit. In addition, the number of stages K for r=i+1 this time is the "second unit" when expressing the state at each time with a discrete value that is a continuous value discretized in a second unit smaller than the first unit. be. M gives the number of stages K at which the dam's flow rate resolution, which will be described later, based on the second unit becomes the resolution desired by the user.

PDP attempts to solve the first problem mentioned above, which is to make it applicable to multimodal objective functions, by finding the initial trajectory using dynamic programming. In addition, by making the DDDP corridor wide enough for the new number of stages, it is possible to support multimodal objective functions. For example, the width can be set to 5 for twice the number of stages.

The second problem, which is to make it applicable even if the number of stages K of the state variable is large, is solved by PDP by gradually increasing the number of stages. Since the global optimal solution is determined by the dynamic programming method in step S501, the subsequent DDDP reaches a local solution in the vicinity of the global optimal solution with a smaller amount of calculation compared to the dynamic programming method. This reduces the overall amount of calculation. For example, if the effective storage capacity of the dam is 10 MCM and the operation is performed in hourly increments, the number of stages KInit is set to 10 and step S502 is repeated 9 times to achieve the number of stages 5,120 (flow resolution 0.54 m3/s). . In this way, the optimization problem of a non-convex objective function can be solved with fine resolution and the time series can be optimized.

The details of the embodiment will be described below.

<Configuration of a computer system for realizing the embodiment>
FIG. 6 is a schematic block diagram showing the configuration of a computer system for implementing the embodiment. The computer system of this embodiment includes a computer 610 such as a PC (Personal Computer) connected to a network 660, and a rainfall prediction server 680.

The computer 610 includes a memory 620, a processor 630 such as a CPU (Central Processing Unit), a storage 640 that is a secondary storage device such as an HDD (Hard Disk Drive), and an input/output unit 650. A dam group cooperative operation program 621, which is an example of a time series optimization program, is developed in the memory 620. This dam group cooperative operation program 621 is configured by instructions to the processor 630. The processor 630 performs calculations, accesses the storage 640, responds to requests from the client terminal 670, etc. according to instructions from the dam group cooperative operation program 621.

The processing executed by the dam group cooperative operation program 621 in the following description is actually executed by the processor 630 according to instructions written in the dam group cooperative operation program 621. The processing results of the dam group cooperative operation program 621 are stored in the storage 640 as dam group cooperative operation data 642.

Rainfall prediction data 641 is transmitted from the rainfall prediction server 680. The dam group cooperative operation program 621 receives this data and stores it in the storage 640. Rainfall prediction data 641 is time series data related to prediction of rainfall intensity distribution. This data is stored as time series mesh data. In other words, space-time is defined by four axes: initial time, predicted time, latitude, and longitude. A start point, end point, and resolution are defined for each axis. Based on that, space-time is divided into cells, and values are assigned to the cells. is stored. The dam group cooperative operation program 621 can obtain values corresponding to initial time, predicted time, latitude, and longitude by specifying them. To store this data, use NetCDF format or the like.

The storage 640 also stores dam group cooperative operation data 642. This data consists of time series of the amount of water stored in the dam, the amount of inflow into the dam, the amount of discharge from the dam, the amount of lateral inflow into the main river, the amount of tributary river flow, and the amount of flow at the river water level gauge. A proprietary binary format may be used to store these time series data.

Storage 640 also stores map data 643. The map data 643 is, for example, a map image. These map images may be stored in compliance with Web Map Tile Service (WMTS).

Storage 640 also stores project data 644. The project data 644 is data necessary for simulating the target dam group. These data may be stored in accordance with, for example, XML. The details of the data structure will be explained in detail in FIGS. 16 and 17.

The input/output unit 650 includes an input unit including a keyboard 651 and a mouse 652, and an output unit including a display 653. The user can input commands from the keyboard 651 and mouse 652 of the input section, and visually check the results from the display 653 of the output section.

<Software configuration diagram of dam group cooperative operation program 621>
FIG. 7 is a software configuration diagram of the dam group cooperative operation program 621. The dam group cooperative operation program 621 is composed of four modules: a simulator module 710, an optimization module 720, a basic operation module 730, and a GUI module 740.

In the simulator module 710, a model controller 711 controls a base model 712 and its derived classes. Dam model 713, river model 714, and outflow model 715 are derived classes of basic model 712.

The dam model 713 performs state transition according to (Equation 1) explained in conjunction with FIG. The river model 714 performs state transition according to (Equation 2) explained in conjunction with FIG. The runoff model 715 may be implemented as a distributed runoff model, a storage function method, or the like. The runoff model 715 is a model that uses the rainfall prediction data 641 as input data and represents the rainfall flowing from the mountains to the dam based on the time series of the dam inflow amount obtained by converting the time series of predicted rainfall.

All of the dam model 713, river model 714, and runoff model 715 have a function to transition from the state STATE[t] at discretized time t to the state STATE[t+1] at the next time t+1. has. Additionally, either model can save state to memory 620 and read saved state from memory 620. The state (initial state) STATE[0] at initial time t=0 is given by the user.

The model controller 711 receives instructions from the optimization module 720 to read the initial state STATE[0], save and read the state STATE[t] at time t, state transition from state STATE[t] to STATE[t+1], The cost function value for the state transition is calculated. The model controller 711 then receives a command to save the dam group cooperative operation data 642 obtained through the state transition in the storage 640.

Optimization module 720 instructs simulator module 710 to simulate an optimization process for dam group operations. The optimization module 720 is composed of two modules: a PDP controller 721 and a DP/DDDP controller 722. PDP controller 721 issues instructions to DP/DDDP controller 722. Optimization module 720 accepts instructions from GUI module 740.

The basic operations module 730 instructs the simulator module 710 to simulate dam group operations based on the basic operations. The main operation module 730 receives commands from the GUI module 740. The model controller 711 of the simulator module 710 accepts a command to save in the storage 640 dam group cooperative operation data 642 obtained by state transition by dam group operation based on the basic operation.

The GUI module 740 provides a GUI (Graphical User Interface) for the dam group cooperative operation program 621. This GUI will be explained with reference to FIG.

<GUI displayed by GUI module 740>
FIG. 8 is a GUI displayed by the GUI module 740. This GUI is displayed on the display 653 and accepts instructions from the user through the keyboard 651 and mouse 652. This GUI consists of windows 800.

A message is displayed in the message section 801. For example, if the user is on flood alert at the current time, "Flood alert" is displayed in the message section 801.

The river flow time series graph section 810 displays a time series graph of river flow. The horizontal axis of the displayed graph is time, and the vertical axis is river flow rate. The three time series graphs of the river flow rate time series graph section 810 correspond to the water level gauges 111, 112, and 113 (FIG. 1), respectively.

The dam state time series graph section 820 displays a time series graph of the dam state. The dam status is, for example, the dam inflow amount (dotted line), the dam discharge amount (solid line), and the dam water storage rate (dotted line). The horizontal axis of the displayed graph is time, the first vertical axis is flow rate, and the second vertical axis is water storage rate. The three time series graphs in the dam state time series graph section 820 correspond to the dams 101, 102, and 103 (FIG. 1), respectively.

A map section 830 displays a map showing dam groups and water level gauges to be operated in conjunction. A dam icon 831, a river water level gauge icon 832, and a river 833 are shown on the map. The connection relationship between this dam, river water level gauge, and river is the same as the connection relationship between the dam group shown in FIG. 1.

Three graphs in the dam status time series graph section 820 are displayed in correspondence with each of the three dam icons 831 in the map section 830. Similarly, three graphs in the river flow rate time series graph section 810 are displayed in correspondence with each of the three river water level gauge icons 832 in the map section 830. When the user selects either icon, the corresponding graph is highlighted. In FIG. 8, one dam icon 831 is selected and the graph corresponding to that icon is highlighted.

Status bar 840 displays the current status of the GUI.

When the user selects the optimal operation menu 802 from the menu, graphs are displayed in the river flow rate time series graph section 810 and dam status time series graph section 820 of the window 800 based on the dam group cooperative operation data 642 output by the optimization module 720. Is displayed. The contents of this graph are sequentially updated according to the progress of the optimization process (step S907) described in FIG. Since the number of stages increases as the optimization process progresses, the user can intuitively understand how the flow rate resolution gradually increases through the screen.

Furthermore, by displaying a message 841 and a progress bar 842 on the status bar 840, the user can check the progress of the current optimization process on the screen. The progress of the optimization process may be expressed as the ratio of the number of executions up to now to the total number of repetitions of the iterative process of calculating the time series of the minimum cost state in the corridor for the trajectory while increasing the number of stages. If the user looks at the intermediate results and determines that the results the user expects are not obtained, the user can interrupt the process by pressing the cancel button 843.

The user can use the settings button 805 to display a settings screen, set or change the objective function, and perform optimization processing.

When the user selects the main operation menu 803 from the menu, based on the dam group cooperative operation data 642 output by the simulator module 710 in response to the command from the main operation module 730, the river flow rate time series graph section 810 of the window 800 and the dam status A graph is displayed in the series graph section 820.

When the user selects the rainfall prediction menu 804 from the menu, a rainfall intensity distribution is displayed in the map section 830 of the window 800 based on the rainfall prediction data 641.

<Main processing to realize the embodiment>
FIG. 9 is a sequence diagram illustrating processing executed by a computer system for implementing the embodiment. The dam group cooperative operation program 621 executes a loop process that repeats the following series of steps S901 to S906 and steps S907 to S910 M times.

In step S901, window 800 is displayed on display 653 of input/output unit 650. In step S902, rainfall prediction data 641 is read. In step S903, the basic operation module 730 issues a command to the simulator module 710 to simulate the dam group operation. In step S904, the result of step S903 is stored in storage 640 as dam group cooperative operation data 642. In step S905, the dam group cooperative operation data 642 saved in step S904 is read from the storage 640. In step S906, graphs are displayed in the river flow rate time series graph section 810 and the dam state time series graph section 820. However, the processing in steps S903 to S906 is executed only when the user selects the main operation menu 803 from the menu.

Subsequently, steps S907 to S910 are repeatedly executed for variables r=0,1,...,M-1.

In step S907, optimization module 720 performs optimization. Details of the processing will be explained with reference to FIG. In step S908, the result of step S907 is stored in storage 640 as dam group cooperative operation data 642. In step S909, the dam group cooperative operation data 642 saved in step S908 is read from the storage 640. In step S910, graphs are displayed in the river flow rate time series graph section 810 and the dam state time series graph section 820 read in S909. However, this loop processing of steps S907 to S910 is executed only when the user selects the optimal operation menu 802 from the menu.

<Details of step S907 in Figure 9>
FIG. 10 is a sequence diagram showing details of step S907 in FIG. The dam group cooperation operation program 621 instructs the optimization module 720 from the GUI module 740 to perform optimization processing. The optimization module 720 that has received the instruction instructs the PDP controller 721 to execute step S1001 if the variable r is 0, and to execute step S1004 if not. However, the variable r is the variable described in FIG.

In step S1001, the PDP controller 721 instructs the DP/DDDP controller 722 to execute DP with the number of stages K=Kinit. In step S1002, the DP/DDDP controller 722 issues a command to the simulator module 710 to execute optimization processing to obtain an optimal solution in the DP. In step S1002, simulator module 710 executes optimization processing. Details of the optimization process will be explained with reference to FIGS. 11 and 12. In step S1003, the PDP controller 721 sets the obtained solution as the initial trajectory.

In step S1004, the PDP controller 721 executes DDDP within the given trajectory corridor. The given trajectory is the initial trajectory obtained as a result of the execution of step S1003, or the trajectory obtained as a result of the previous execution of step S1006. However, the number of stages K is set to twice the previous number of stages. The width of the corridor is 5. The multiple of the number of stages may be an integer greater than or equal to 2, and the width of the corridor may be sufficiently appropriate for the new number of stages.

In step S1005, the DP/DDDP controller 722 issues a command to the simulator module 710 to obtain an optimal solution using DDDP. In step S1005, simulator module 710 executes optimization processing similar to step S1002. Details of the processing will be explained with reference to FIGS. 11 and 12. In step S1006, the PDP controller 721 uses the obtained solution as the trajectory for the next step S1004.

<Details of optimization processing using DP/DDDP>
11 and 12 are flowcharts showing details of optimization processing using DP/DDDP. 11 and 12 show details of the processing executed by the simulator module 710 in steps S1002 and S1005 in FIG. 10.

In step S1101, initialization is performed. By initialization, the time of the simulator module 710 becomes initial time t=0, and the state becomes the initial state STATE[0] given by the user. In step S1102, time t is set to 1. In step S1103, if time t is less than T, the process advances to step S1104; otherwise, the process advances to step S1201 in FIG. 12.

In step S1104, time t and the first node in the corridor are assigned to the variable curState. Note that when executing DP, it is assumed that all nodes are in the corridor. When running DDDP, the width of the corridor is given.

In step S1105, time t-1 and the first node in the corridor are assigned to the variable prevState. In step S1106, the state transition leading to node prevState is read from memory. The information read here is saved in the memory in step S1112. If there is no information to be read here, skip step S1106.

In step S1107, the state transition cost from prevState to curState is calculated, and the value is assigned to the variable cost. (Equation 5) may be used to calculate the cost. In step S1108, the objective function value obs is determined. As shown in (Equation 3), this is the value obtained by adding the variable cost to the objective function value of prevState. Assign the obtained value to the variable obs.

In step S1109, if there is a next node in the corridor at time t-1, the process advances to step S1110; otherwise, the process advances to step S1111.

In step S1110, time t-1 and the next node in the corridor are assigned to the variable prevState. When step S1110 ends, the process returns to step S1106.

In step S1111, the node with the minimum value of obs at time t-1 is assigned to the variable bestPrevState. In step S1112, the state transition from bestPrevState to curState is stored in memory. In step S1113, if there is a next node in the corridor at time t, the process advances to step S1114; otherwise, the process advances to step S1115.

In step S1114, time t and the next node in the corridor are assigned to the variable curState. When step S1114 ends, the process returns to step S1105.

In step S1115, 1 is added to time t to set the next time, and the process returns to step S1103.

In step S1201 of FIG. 12, the node having the minimum obs value at time T-1 is assigned to the variable bestState. In step S1202, the variable bestState is added to the array bestStates. In step S1203, the node immediately before the variable bestState is assigned to the variable stateFrom.

If a valid node is stored in the variable stateFrom in step S1204, the process proceeds to step S1205; otherwise, the process ends. In step S1205, the variable stateFrom is added to the array bestStates. In step S1206, the node immediately before the variable bestState is assigned to the variable stateFrom. When step S1206 ends, the process returns to step S1204.

When the optimization processing of FIGS. 11 and 12 is completed, the optimal state transition from time t=0 to time t=T-1 is stored in the array bestStates.

<Time series graph of dam water storage rate and dam discharge amount based on basic operations>
FIG. 13 is an example of a time series graph of the dam water storage rate and the dam discharge amount based on the basic operation. Graph 1310 is a dam state time series graph of dam D0. Similarly, graph 1320 is a dam state time series graph of dam D1, and graph 1330 is a dam state time series graph of dam D2. Notes 1311, 1321, and 1331 indicate that emergency releases were made at this time. Emergency water release is a dam operation also called a proviso operation or emergency flood disaster prevention operation, and is an operation in which water is released from the dam in an amount equal to the inflow into the dam in order to prevent the dam from collapsing because the dam is full. As a result, the amount of water released from the dam will increase rapidly in a short period of time.

<Time series graph of dam water storage rate and dam discharge amount based on optimized dam group cooperative operation>
FIG. 14 is an example of a time series graph of the dam water storage rate and the dam discharge amount based on the optimized dam group cooperative operation output by the dam group cooperative operation program 621. The dam inflow amount in FIG. 14 is the same as that shown in FIG. 13, and shows a case where there is an inflow on a scale that would require emergency release if only basic operations were performed. Graph 1410 is a dam state time series graph of dam D0. Similarly, graph 1420 is a dam state time series graph of dam D1, and graph 1430 is a dam state time series graph of dam D2. Notes 1411, 1421, and 1431 indicate that pre-discharges were made during this period. The pre-discharge is performed, for example, based on an increase in water storage in the dam due to predicted rainfall indicated by the rainfall prediction data 641. During the pre-release period, the dam discharge amount exceeds the dam inflow amount. Through optimized dam group cooperative operation, it is possible to release water in advance of predicted sudden rainfall, prevent emergency release, and prevent flooding in downstream rivers. The underlined area downstream of the dam indicates that the rate of increase in the discharge amount complies with the "discharge principle" shown in Figure 15.

<Discharge amount that does not cause sudden changes in water level downstream>
FIG. 15 is an example of polynomial approximation of the discharge amount that does not cause sudden changes in water level downstream. Dam operating rules require that the discharge amount not exceed the amount that does not cause sudden changes in water level downstream (observing the so-called ``discharge principle''). Graph 1500 is an example of approximating the "discharging principle" using a polynomial. The horizontal axis is the amount of water discharged downstream from the dam i immediately before, which corresponds to outflow[i,t] in (Equation 5). In addition, the vertical axis is the amount of discharge at dam i that does not cause sudden changes in the water level downstream, and is the amount equivalent to outflowLimit[i] in (Equation 5). By using the graph 1500, the value outflowLimit[i] on the vertical axis can be determined by the value outflow[i,t] on the horizontal axis.

<Dam model 713 (project data 644)>
FIG. 16 is a diagram showing the data structure of project data 644 (FIG. 6) regarding dam model 713. In this figure, the data structure for the dam group shown in FIG. 1 is shown in table 1600. For each dam, effective water storage capacity, flood control capacity, initial conditions, and downstream model are defined. The contents of table 1600 are saved as project data 644 in XML format.

<River model 714 (project data 644)>
FIG. 17 is a diagram showing the data structure of project data 644 (FIG. 6) regarding river model 714. Similar to FIG. 16, this figure shows the data structure for the dam group shown in FIG. 1 as a table 1700. For each river water level gauge, an upstream model, a delay time from that model, and a downstream model are defined. The contents of table 1700 are saved as project data 644 in XML format.

[Other embodiments]
Note that the applicable field of the present invention is not limited to the optimization of the water storage level time series and discharge amount time series of multipurpose dams. It can be applied to fields that require solving optimization problems with non-convex objective functions with fine resolution. More specifically, the problem is to support the optimal operation of the gate in order to control logistics and people flow in a situation where a certain amount of objects or people enter the space in front of the gate and exit through the gate to the destination. Applicable to

An example is admission management at event venues. In a situation where an event venue has multiple entrance gates and spectators are placed in the space in front of each gate and are seated at their own seats through the aisle in the venue, the average waiting time and waiting time of the spectators can be reduced without overflowing the space in front of the gate. Consider the case where we try to minimize the standard deviation. In conventional methods, it is necessary to reduce the computational load by optimizing for multiple people (for example, 256 people), rather than for each individual audience member. Application of the present invention enables optimization for each audience member.

Note that the "space in front of the gate with a gate" in other embodiments corresponds to the "dam" in the above embodiment, and the "destination from the gate" corresponds to the "river". In addition, the "inflow amount of objects or people into the space in front of the gate" corresponds to the "dam inflow amount", and the "accommodation rate of objects or people in the space in front of the gate" corresponds to the "water storage level (water storage rate)". “The amount of objects or people that pass through the gate from the space in front of the gate” corresponds to the “discharge amount”.

The present invention is not limited to the above-described embodiments, but includes various modifications. For example, the above-described embodiments have been described in detail to explain the present invention in an easy-to-understand manner, and the present invention is not necessarily limited to having all the configurations described. Further, as long as there is no contradiction, it is also possible to replace a part of the configuration of one embodiment with the configuration of another embodiment, and to add the configuration of another embodiment to the configuration of one embodiment. Furthermore, it is possible to add, delete, replace, integrate, or distribute a part of the configuration of each embodiment. Furthermore, the configurations and processes shown in the embodiments can be distributed, integrated, or replaced as appropriate based on processing efficiency or implementation efficiency.

610: Computer, 620: Memory, 621: Dam group cooperative operation program, 630: Processor, 640: Storage, 650: Input/output section

Claims (10)

A time series optimization program that causes a computer to execute an optimization process for optimizing a time series of a target state that changes with time,
to the computer;
When the state at each time is represented by a discrete value obtained by discretizing a continuous value in a first unit, a time series of the state that gives the best evaluation value for evaluating state transition between each time is accepted as an input time series. a first process;
When the state at each time is represented by a discrete value obtained by discretizing the continuous value in a second unit smaller than the first unit, the evaluation value is the best within a predetermined neighborhood of the input time series. A time series optimization program, comprising: a second process for calculating a time series of the states; and a time series optimization program. The time series optimization program according to claim 1,
to the computer;
Repeated processing of the first process and the second process in which the time series of the state calculated in the second process executed last time is the input time series of the first process executed this time is performed under a predetermined condition. A time series optimization program that is characterized by being executed until the condition is satisfied. The time series optimization program according to claim 2,
to the computer;
A time series optimization program, characterized in that the program executes a process of calculating, using dynamic programming, the input time series received in the first process of the first time of the iterative process. The time series optimization program according to claim 1,
to the computer;
A time series optimization program characterized in that, in the second process, a time series of the state in which the evaluation value is the best within a predetermined neighborhood of the input time series is calculated using discrete differential dynamic programming. . The time series optimization program according to claim 1,
The time series optimization program, wherein the first unit is twice as large as the second unit. The time series optimization program according to claim 2,
The time series optimization program, wherein the satisfaction of the predetermined condition is that the flow rate resolution regarding the object based on the second unit becomes a desired resolution. The time series optimization program according to claim 6 ,
to the computer;
For each of the repetitive processes, information indicating the time series of the state calculated in the second process, the flow rate resolution, and the progress of the repetitive process to be executed until the flow rate resolution reaches a desired resolution is displayed on a display unit. A time series optimization program characterized by executing display processing. The time series optimization program according to claim 1,
The target is a dam,
The time-series optimization program, wherein the state is an inflow amount of the dam, a water storage level of the dam, and a discharge amount of the dam based on rainfall prediction data. The time series optimization program according to claim 1,
The target is a space in front of a gate having a gate,
The state is the amount of objects or people flowing into the space in front of the gate, the accommodation rate of objects or people in the space in front of the gate, and the amount of objects or people allowed to pass through the gate from the space in front of the gate. A time series optimization program with special features. A time series optimization system that performs optimization processing to optimize a time series of a target state that changes with time,
The time series optimization system includes a processor that executes processing in cooperation with a memory,
The processor includes:
When the state at each time is represented by a discrete value obtained by discretizing a continuous value in a first unit, a time series of the state that gives the best evaluation value for evaluating state transition between each time is accepted as an input time series. a first process;
When the state at each time is represented by a discrete value obtained by discretizing the continuous value in a second unit smaller than the first unit, the evaluation value is the best within a predetermined neighborhood of the input time series. A time series optimization system, comprising: a second process of calculating a time series of the states;

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