JP2009048353A - Combinatorial optimization system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a combinatorial optimization system that can solve a combinatorial optimization problem fast with a reduced probability of ending with a local solution. <P>SOLUTION: The combinatorial optimization system comprises: a second neighborhood search means 33 for defining a set of adjacent states whose discrete variable values are changed to a great extent from a current state as a second neighborhood, and executing the processing of a second neighborhood generation means 22, an optimum solution/best solution updating means 24, a taboo list updating means 25 and a second neighborhood search end determination means 26 to perform optimization by regarding the second neighborhood as the adjacent state; and a first neighborhood search means 34 for defining a set of adjacent states whose discrete variables are changed to a lesser extent from the current state as a first neighborhood, and executing the processing of a first neighborhood generation means 28, the optimum solution/best solution updating means 24, the taboo list updating means 25 and a first neighborhood search end determination means 29 to perform optimization by regarding the first neighborhood as the adjacent state. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a combination optimization system for solving a combination optimization problem using discrete values as variables, which can be applied to an operation plan of a plurality of power supplies (generators).

  In general, it is known that many combinatorial optimization problems are extremely difficult to obtain a strict optimal solution. In recent years, research on metaheuristics such as local search, tabu search, and simulated annealing has been actively conducted as a system for obtaining a sufficiently accurate solution in practical calculation time. Conventionally, a technique for efficiently obtaining an optimal solution has been proposed irrespective of the metaheuristic framework.

  A technology that reduces the scale of combinatorial optimization problems to be solved and achieves speedup by treating some or all of the discrete variables as continuous variables in order to achieve speedup as a conventional combinatorial optimization system Has been proposed (see, for example, Patent Document 1).

In addition, as another conventional system, in order to reduce the probability of falling into a local optimum solution, a technique of allowing a transition to a state that does not satisfy the constraint condition has been proposed (for example, see Patent Document 2).
Furthermore, as another conventional system, in order to increase the speed and reduce the probability of falling into a local optimal solution, the target is limited to the generator operation plan and the operation state at a certain characteristic time is fixed. A technique for solving the problem has also been proposed (see, for example, Patent Document 3).

Here, a general framework for solving the combinatorial optimization problem by metaheuristics will be described with reference to the explanatory diagram of FIG. 6 showing an image.
In general, metaheuristics is a solution based on neighborhood search, and a plurality of “adjacent states” (in the upper left part of FIG. 6 are taken as an example) in which some values of discrete variables are changed with respect to the current state. And white circles and black circles within a one-dot chain line frame, and compare the evaluation function value of the current state with the evaluation function values of these adjacent states, and the point with the best evaluation function value (adjacent state) Or the current state) is updated as the next current state. Hereinafter, the optimum solution is obtained by repeatedly executing this process.

However, in the combinatorial optimization system for solving the combinatorial optimization problem as described above, as shown by the lower characteristic curve in FIG. 6, it generally takes time to converge the evaluation function value, and the search does not easily proceed. That is, the problem on a practical scale has a problem that it takes enormous processing time to obtain an optimal solution.
Note that if the search area is set small, the calculation time can be shortened. However, in this case, there is a problem that a local solution that depends on the initial value falls.

  For example, in Patent Document 1, in order to improve the first problem, that is, the problem that it takes an enormous amount of processing time to obtain an optimal solution, it should be solved by treating some or all of the discrete variables as continuous variables. A system that reduces the scale of the combinatorial optimization problem and realizes high speed has been proposed. However, in this system, depending on the problem to be addressed, it is not always possible to convert a discrete variable into a continuous variable due to the non-linearity of the constraint condition. However, the first problem cannot still be solved.

  Patent Document 2 proposes a system that searches a wider area by allowing a transition to a state that does not satisfy the constraints in order to improve the second problem, that is, the problem that the probability of falling into a local solution is high. Has been. However, in this system, depending on the target problem, it is difficult to make a transition to a region that does not satisfy the constraints, and the system does not function effectively. Therefore, when such a problem is targeted, the second problem is still solved. It is not possible.

For example, as a specific example, in order to minimize the operation cost, there is a start / stop planning problem of a plurality of generators. Usually, since a generator is costly to start up, there is a restriction condition that the start and stop is not repeated many times a day, and the start and stop is once a day at the maximum.
Now, it is assumed that the solution at a certain point in the middle of the combination optimization is an operation time of a certain generator from 10:00 to 17:00.

  The adjacent state that does not satisfy the constraint condition is, for example, a state in which the generator is operated by being divided into two times of 10:00 to 12:00 and 13: 0 to 17:00. Even if the transition to the state divided into two times is admitted, the original state, that is, the state of driving once at 10: 00 to 17:00 is obviously better when considering the cost of starting. The evaluation function value is small, and the transition to the state divided into two times does not occur.

  On the other hand, in Patent Document 3, in order to improve both the first and second problems, the target is limited to the start / stop plan of the generator, the start / stop state at a characteristic time is fixed, and this condition is satisfied. A system that searches below is proposed. However, in this system, since the operation state at a characteristic time (for example, the time when the maximum value or minimum value of demand occurs) is fixed, the search area is limited, so a global optimum solution is obtained. Is difficult.

The system described in Patent Document 3 also proposes a technique for changing the operating state at a characteristic time. However, if the operating state at a characteristic time is changed, the search for the original entire area is eventually performed. Although it can only reduce the probability of falling into a local solution, the processing time increases, so it is difficult to solve the two problems simultaneously.
Furthermore, the number of generators targeted in the example described in Patent Document 3 is about 10 at most, and the scale of the problem to be optimized is not large, and only applicable to start-up / stop plans for generators. Not practical.

JP 2003-204624 A JP-A-5-143572 JP 2001-258157 A

  According to the methods described in Patent Documents 1 to 3, the conventional combination optimization system is effective depending on the target problem, but still requires a large amount of processing time due to a problem on a practical scale, and is set to an initial value. There was a problem that there was a strong tendency to fall into a dependent local optimal solution.

  The present invention has been made to solve the above-described problems, and is a combinatorial optimization system capable of obtaining an optimal solution at high speed while reducing the probability that a combinatorial optimization problem will fall into a local solution. The purpose is to obtain.

  The combinatorial optimization system according to the present invention is a combinatorial optimization system for solving a combinatorial optimization problem, and is a discrete variable list defined by optimization conditions, a list of all discrete variables, and a minimum fluctuation range and upper and lower limit values. And a storage means for storing a list of discrete variables for adjusting the variation range in the optimization process and a variation range adjustment variable list defined by each initial variation range of the list of discrete variables, and at the initial stage of the search The second neighborhood search means for performing optimization while changing the fluctuation range of the fluctuation range adjustment variable list with the initial fluctuation range, and after the second neighborhood search by the second neighborhood search means, the fluctuation range of all the discrete variables is minimized. A first neighborhood search unit that performs optimization while varying the width, and a control program that executes a second neighborhood search and a first neighborhood search by the first neighborhood search unit are provided.

  According to the present invention, first, in order to quickly identify a concentrated search region in which the existence of an optimal solution is promising, the variation range of a part or all of the discrete variables is adjusted (largely set), and the second neighborhood search (global Search), and then, by setting the fluctuation range of the discrete variable to be small, the first neighborhood search (the intensive search of promising intensive search regions) is performed, and the second neighborhood search and the first neighborhood search are combined. By executing it, it is possible to reduce the probability of falling into a local solution and to reach a more global solution at high speed.

Embodiment 1 FIG.
Hereinafter, as a specific optimization target, Embodiment 1 of the present invention will be described by taking as an example a case where it is applied to an operation plan for a plurality of power supplies as necessary.
FIG. 1 is a block diagram showing an overall configuration of a combinational optimization system according to Embodiment 1 of the present invention.

  In FIG. 1, the combination optimization system includes a computer system, and includes a central processing unit 40, a main memory 41, a hard disk 44, an input device 45, an output device 46, and a bus 47. The main memory 41, hard disk 44, input device 45 and output device 46 are connected to the central processing unit 40 via a bus 47.

  The main memory 41 includes a control program 42 that executes various processes, a default value 43 of optimization conditions, an optimization condition storage unit 2, a fluctuation range adjustment variable list storage unit 7, a discrete variable list storage unit 12, The optimum solution storage means 18, the best solution storage means 19, the tabu list storage means 21, and the adjacent state storage means 23 are provided.

  The control program 42 includes an optimization condition record data acquisition means 4, an optimization condition default value acquisition means 5, a fluctuation range adjustment variable list record data acquisition means 9, a fluctuation range adjustment variable list default value acquisition means 10, a discrete Variable list recording data acquisition means 14, discrete variable list default value acquisition means 15, initial solution generation means 16, evaluation function value calculation means 17, taboo list initialization means 20, second neighborhood generation means 22, Best solution / optimum solution update unit 24, tabu list update unit 25, second neighborhood search end determination unit 26, first neighborhood search initial solution generation unit 27, first neighborhood generation unit 28, and first neighborhood search An end determination unit 29, an optimization result recording / output processing unit 30, a second neighborhood searching unit 33, and a first neighborhood searching unit 34 are provided.

The hard disk 44 includes optimization condition recording means 3, fluctuation range adjustment variable list recording means 8, discrete variable list recording means 13, and optimization result recording means 32. In this case, the optimization result recording means 32 is constituted by the hard disk 44.
The input device 45 includes a keyboard (not shown) and the like, and includes an optimization condition input unit 1, a fluctuation range adjustment variable list input unit 6, and a discrete variable list input unit 11. The output device 46 includes an optimization result output unit 31. The optimization result output unit 31 includes a display or a printer (not shown).

The optimization condition input means 1 inputs an optimization condition including an optimization purpose, constraint conditions, and facility data.
The optimization condition recording means 3 records at least a part of the optimization conditions input from the optimization condition input means 1 as a file database.
The optimization condition recording data acquisition unit 4 reads out the optimization condition from the optimization condition recording unit 3 and stores it in the optimization condition storage unit 2.
The optimization condition default value acquisition unit 5 acquires the optimization condition default value 43 set by the control program 42 and stores it in the optimization condition storage unit 2.

The fluctuation range adjustment variable list input means 6 inputs, as a fluctuation range adjustment variable list, a list of discrete variables for adjusting the fluctuation range in the optimization process and an initial fluctuation range of each discrete variable.
The fluctuation range adjustment variable list recording unit 8 records at least a part of the fluctuation range adjustment variable list as a file database.
The fluctuation range adjustment variable list record data acquisition unit 9 reads the fluctuation range adjustment variable list from the fluctuation range adjustment variable list recording unit 8 and stores it in the fluctuation range adjustment variable list storage unit 7.
The fluctuation range adjustment variable list default value acquisition unit 10 acquires the default value 43 of the fluctuation range adjustment variable list set by the control program 42 and stores it in the fluctuation range adjustment variable list storage unit 7.

The discrete variable list input means 11 inputs a list relating to all discrete variables, the upper and lower limit values, and the minimum fluctuation range as a discrete variable list.
The discrete variable list recording unit 13 records at least a part of the discrete variable list as a file database.
The discrete variable list record data acquisition means 14 reads the discrete variable list from the discrete variable list record means 13 and stores it in the discrete variable list storage means 12.
The discrete variable list default value acquisition unit 10 acquires the default value 43 of the discrete variable list set by the control program 42 and stores it in the discrete variable list storage unit 12.

The evaluation function value calculation means 17 calculates the evaluation function value for the given discrete variable value according to the optimization condition in the optimization condition storage means 2.
The optimal solution storage means 18 stores the discrete variable value and the evaluation function value of the optimal solution that is the solution having the best evaluation function value in the past in the optimization process.
The best solution storage means 19 stores discrete variable values and evaluation function values of the best solution, which are temporary solutions in the optimization process.

  The initial solution generation means 16 reads the list of all discrete variables from the discrete variable list storage means 12, generates initial values of all discrete variables so as to satisfy the optimization conditions read from the optimization condition storage means 2, and evaluates them. The evaluation function value calculated by the function value calculation means 17 is stored in the optimum solution storage means 18 and the best solution storage means 19.

The taboo list storage means 21 stores a taboo list including a list of past best solutions.
The tabu list initialization unit 20 clears the tabu list and causes the tabu list storage unit 21 to store the tabu list to which the optimum solution read from the optimum solution storage unit 18 is added.
The adjacent state storage unit 23 stores discrete variable values and evaluation function values of all adjacent states (described later).

  The second neighborhood generation unit 33 includes an optimization condition read from the optimization condition storage unit 2, a list and variation range of discrete variables for adjusting the variation range read from the variation range adjustment variable list storage unit 7, and discrete variables A list of discrete variables whose fluctuation width is not adjusted, the minimum fluctuation width and the upper and lower limit values of all the discrete variables read from the list storage means 12, and the discrete variable values constituting the current best solution read from the best solution storage means 19, and Based on the evaluation function value, a plurality of adjacent states that are the next best solution candidates are generated, the evaluation function value calculating means 17 calculates the evaluation function values of all adjacent states, and the discrete variable values and evaluation functions of all adjacent states. The value is stored in the adjacent state storage unit 23 in which an area is secured in advance on the main memory 41.

  The optimal solution / best solution update unit 24 reads all adjacent states from the adjacent state storage unit 23, reads the current optimal solution from the optimal solution storage unit 18, and reads the current best solution from the best solution storage unit 19. The next best solution is selected from the adjacent state and the current best solution, the discrete variable value and the evaluation function value constituting the next best solution are stored in the best solution storage means 19, and the evaluation function value of the next best solution is determined. If it is superior to the evaluation function value of the current optimum solution, the optimum solution storage means 18 stores the discrete variable value and the evaluation function value constituting the next best solution.

  The tabu list update unit 25 reads the best solution from the best solution storage unit 19, reads the tabu list from the tabu list storage unit 21, and the number of the best solutions stored in the tabu list reaches the length of the tabu list. In this case, the oldest best solution in the taboo list is discarded, and a new taboo list in which the current best solution is added is stored in the taboo list storage means 21.

  Based on the optimization condition read from the optimization condition storage unit 2, the second neighborhood search end determination unit 26 determines whether or not the second neighborhood search end condition is satisfied, and sets the second neighborhood search end condition. When it is determined that the condition is satisfied, the process proceeds to the first vicinity search, and when the end condition for the second vicinity search is not satisfied, the process returns to the process of the second vicinity generation unit 22.

The second neighborhood searching unit 33 executes a series of processes by the second neighborhood generating unit 22, the optimum solution / best solution updating unit 24, the taboo list updating unit 25, and the second neighborhood search end determining unit 26.
The first neighborhood search initial solution generation means 27 reads the optimum solution from the optimum solution storage means 18 and stores it in the best solution storage means 19.

  The first neighborhood generation unit 28 includes an optimization condition read from the optimization condition storage unit 2, a list of all discrete variables read from the discrete variable list storage unit 12, a minimum fluctuation range and upper and lower limit values, and a best solution storage unit Based on the discrete variable value and the evaluation function value constituting the current best solution read from 19, a plurality of adjacent states that are the next best solution candidates are generated, and the evaluation function of all adjacent states is evaluated by the evaluation function value calculation means 17 The value is calculated, and the discrete variable values and the evaluation function values of all adjacent states are stored in the adjacent state storage means 23.

The first neighborhood search end determination means 29 determines whether or not the first neighborhood search end condition is satisfied based on the optimization condition read from the optimization condition storage means 2, and sets the first neighborhood search end condition. If it is determined that the first neighborhood search is satisfied, the first neighborhood search is terminated. If the first neighborhood search termination condition is not satisfied, the first neighborhood generation means 28 is returned to the processing.
The first neighborhood search unit 34 executes a series of processes by the first neighborhood generation unit 28, the optimum solution / best solution update unit 24, the tabu list update unit 25, and the first neighborhood search end determination unit 29.

The optimization result output means 31 includes an output device 46 including a display or a printer, and outputs discrete variable values and evaluation function values that constitute an optimal solution.
The optimization result recording means 32 is constituted by a hard disk or the like, and records discrete variable values and evaluation function values constituting the optimal solution as a file database.
The optimization result recording / output processing means 30 records the optimization result in the optimization result recording means 32 and causes the optimization result output means 31 to output the optimization result after the end of the first neighborhood search.

Next, a processing procedure executed by the combinational optimization system of FIG. 1 will be described with reference to the flowchart of FIG.
In FIG. 2, first, optimization conditions are input or read and stored (step S1).

Specifically, when the operator operates the optimization condition input means 1 (keyboard or the like) in the input device 45, the optimization purpose (such as minimizing CO2 emissions) and the constraint conditions (power demand at each time) = Power output + power purchase + storage battery charge / discharge, etc.) and facility data (power supply capacity, etc.) are input as optimization conditions.
Thereafter, the central processing unit 40 receives the instruction of the control program 42 in the main memory 41 and stores the input optimization conditions in the optimization condition storage means 2 in which an area is secured in the main memory 41 in advance. Let

  However, if at least a part of the optimization conditions is recorded in advance in the optimization condition recording means 3 in the hard disk 44 as a file database or the like, and it is not necessary to change the contents, the optimization conditions in the control program 42 The recording data acquisition means 4 reads out the optimization conditions from the optimization condition recording means 3 and stores them in the optimization condition storage means 2.

  For the optimization conditions for which the default value 43 is set in advance by the control program 42 and the contents of the default value 43 do not need to be changed, the optimization condition default value acquisition means 5 in the control program 42 stores the optimization value on the main memory 41. Is obtained and stored in the optimization condition storage means 2.

Next, a list of discrete variables for adjusting the fluctuation range is input or read and stored (step S2).
Specifically, the operator operates the fluctuation range adjustment variable list input means 6 (keyboard or the like) in the input device 45, so that a list of discrete variables for adjusting the fluctuation range in the optimization process and each discrete variable The initial fluctuation range is input.
Thereafter, the central processing unit 40 receives the command of the control program 42 in the main memory 41 and stores the input discrete variable information in the fluctuation range adjustment variable list storage means 7 in which an area is secured in advance on the main memory 41. Remember me.

  However, a list of discrete variables for adjusting the fluctuation range and at least a part of the fluctuation ranges are recorded in advance in the fluctuation range adjustment variable list recording unit 8 in the hard disk 44 as a file database or the like, and the discrete contents that do not require changing contents Regarding the variable information, the variable range adjustment variable list record data acquisition unit 9 in the control program 42 reads the discrete variable information from the range adjustment variable list record unit 8 and stores it in the range adjustment variable list storage unit 7.

  Also, the default value 43 on the main memory 41 is obtained by the variable range adjustment variable list default value acquisition means 10 in the control program 42 for the discrete variable information for which the default value 43 is set by the control program 42 and the content change is unnecessary. And stored in the fluctuation range adjustment variable list storage means 7.

  As a specific example of the discrete variable for adjusting the fluctuation range, for example, when the combinational optimization system of FIG. 1 is applied to an operation plan for a plurality of power sources, the time for changing the ON / OFF state of each power source can be given. . In this case, if the optimization problem is a problem of planning an operation plan for 24 hours the next day, and the time increment of the plan is “30 minute intervals”, the minimum time for changing the ON / OFF state of each power supply While the fluctuation range is “30 minutes”, the initial fluctuation range is set to “60 minutes” or “90 minutes”.

Next, in order to input or read out all the discrete variables, a list of discrete variables whose fluctuation width is not adjusted is input or read and stored (step S3).
Specifically, when the operator operates the discrete variable list input means 11 (keyboard or the like) in the input device 45, a list of all discrete variables including the discrete variables whose fluctuation width is not adjusted, and the top of all the discrete variables. The lower limit value and the minimum fluctuation range of all discrete variables are input.
Thereafter, the central processing unit 40 receives the command of the control program 42 in the main memory 41 and stores the input discrete variable information in the discrete variable list storage unit 12 in which an area is secured in advance on the main memory 41. Let

  However, if at least a part of all the discrete variable information is recorded in advance in the discrete variable list recording means 13 in the hard disk 44 as a file database or the like, and it is not necessary to change the contents, the discrete variable in the control program 42 is used. Discrete variable information is read out by the list record data acquisition means 14 and stored in the discrete variable list storage means 12.

  Further, for the discrete variable for which the default value 43 is set by the control program 42 and the contents need not be changed, the default value 43 on the main memory 41 is acquired by the discrete variable default value acquisition means 15 in the control program 42. And stored in the discrete variable list storage means 12.

Next, an initial solution is generated and stored as an optimal solution (a solution with the highest evaluation function value in the past search) and a best solution (a temporary solution during the search) (step S4).
Specifically, the central processing unit 40 receives an instruction from the control program 42 in the main memory 41 and reads out the optimization condition from the optimization condition storage unit 2 by the initial solution generation unit 16 in the control program 42. Then, a list of all discrete variables is read from the discrete variable list storage means 12.

  Further, the central processing unit 40 generates initial values of all discrete variables so as to satisfy the constraint conditions that are part of the optimization conditions, and sets the evaluation function values for the discrete variable values given by the evaluation function value calculation means 17. The calculation is performed according to the optimization condition in the optimization condition storage means 2 and the discrete variable value and the evaluation function value are stored in the optimal solution storage means 18 in which a region is secured in advance in the main memory 41, and the discrete variable value and The evaluation function value is stored in the best solution storage means 19 in which an area is secured in advance on the main memory 41.

Here, for the sake of convenience, the one with the highest evaluation function value in the past search is referred to as “optimal solution”, and the temporary solution during the search is referred to as “best solution”.
In addition, how to give the initial value of all the discrete variables is arbitrary, For example, you may set randomly and may set with the appropriate method known empirically in the problem made into object.
The specific calculation contents of the evaluation function value calculation means 17 are described in advance in the control program 42 for each problem.

  For example, when “CO2 emission minimization” is selected as the optimization condition in the operation plan of the cogeneration power source, the evaluation function value E is calculated as follows: the fuel consumption amount Fc of the cogeneration power source and the CO2 emission coefficient Kc of the fuel for the cogeneration power source. The following equation (1) is obtained using the power purchase amount Qb from the commercial system, the CO2 emission coefficient Kq of the system power, the fuel consumption Fp for supplying the insufficient heat quantity, and the CO2 emission coefficient Kp of the fuel for supplying insufficient heat ( It is calculated as in 1).

  E = Fc × Kc + Qb × Kq + Fp × Kp (1)

  However, in equation (1), the fuel consumption amount Fc of the cogeneration power source, the power purchase amount Qb from the commercial system, and the fuel consumption amount Fp for supplying the insufficient heat amount are uniquely determined from the discrete variable value itself or the discrete variable value. This is a possible value, and each CO2 emission coefficient Kc, Kq, Kp is an item of optimization conditions.

Next, the following processing is performed by the second neighborhood search means 33 in the control program 42 as the second neighborhood search that is the first stage of optimization.
That is, when the basic algorithm of the combinatorial optimization system is based on tabu search, first, the tabu list is initialized (cleared) by the tabu list initialization unit 20 in the control program 42, and the optimum solution storage unit 18. The optimum solution is read out from the table and added to the tabu list, and the updated taboo list is stored in the tabu list storage means 21 in which an area is secured in advance on the main memory 41 (step S5).

  Next, the central processing unit 40 generates a set of adjacent states (second neighborhood) in a region slightly away from the current best solution and calculates an evaluation function value in the control program 42 in the main memory 41. In response to the command, the second neighborhood generation unit 22 reads the optimization condition from the optimization condition storage unit 2, reads the list of variation variables for adjusting the variation range and the variation range from the variation range adjustment variable list storage unit 7, A list of discrete variables that do not adjust the fluctuation range and the minimum fluctuation width and the upper and lower limit values of all the discrete variables are read from the discrete variable list storage means 12, and the discrete variable values and evaluations constituting the current best solution are read from the best solution storage means 19. Read the function value.

  Thereafter, the central processing unit 40 generates a plurality of adjacent states which are the next best solution candidates based on each read information, and calculates the evaluation function value of all adjacent states by the evaluation function value calculating unit 17, The state discrete variable value and the evaluation function value are stored in the adjacent state storage means 23 in which an area is secured in advance on the main memory 41 (step S6).

  Specifically, the adjacent state is generated by increasing or decreasing the value of any one of all the discrete variables by a different width for each of the following discrete variables. By performing this process on all discrete variables, a neighborhood of the current optimal solution, that is, a set of adjacent states is generated.

  Among all the discrete variables, the value of the discrete variable for adjusting the fluctuation range is changed by the fluctuation range acquired together with the adjustment variable list. For other discrete variables, only the minimum fluctuation range is changed. However, when the changed discrete variable value is larger than the upper limit value, the upper limit value is set. When the changed discrete variable value is smaller than the lower limit value, the lower limit value is set to limit the discrete variable value within a predetermined range.

  Next, the central processing unit 40 receives a command from the control program 42 in the main memory 41 in order to compare the optimum solution and the best solution with each state in the second neighborhood and update the optimum solution and the best solution. Then, the optimum solution / best solution update unit 24 reads all adjacent states from the adjacent state storage unit 23, reads the current optimum solution from the optimum solution storage unit 18, and reads the current best solution from the best solution storage unit 19.

  Hereinafter, the central processing unit 40 selects the next best solution from all adjacent states and the current best solution, and stores the discrete variable value and the evaluation function value constituting the next best solution in the best solution storage means 18, If the evaluation function value of the next best solution is superior to the evaluation function value of the current optimum solution, the discrete variable value and the evaluation function value constituting the next best solution are updated in the optimum solution storage means 18. (Step S7).

  Specifically, the next best solution selection method follows the basic algorithm of the applied combinatorial optimization system. For example, when the combinatorial optimization system is based on local search, the next best solution is the one with the best evaluation function value among all the adjacent states. When the combinatorial optimization system is based on tabu search, the next best solution is the one that does not include the tabu list and has the best evaluation function value among all adjacent states.

  Next, when the basic algorithm of the combinatorial optimization system is based on tabu search, the tabu list update unit 25 reads the best solution from the best solution storage unit 19 and the tabu list storage unit 21 reads the tabu list. If the number of best solutions stored in the taboo list has reached the length of the taboo list, a new taboo list in which the oldest best solution in the taboo list is discarded and the current best solution is added is displayed. The list storage means 21 is updated and stored (step S8).

  Next, the central processing unit 40 receives an instruction from the control program 42 in the main memory 41, reads out the optimization condition from the optimization condition storage unit 2 by the second neighborhood search end determination unit 26, and performs the second neighborhood search. Whether or not to end (conditions for ending the second neighborhood search) are determined (step S9).

In step S9, when it is determined that the end condition of the second neighborhood search is satisfied (that is, YES), the process proceeds to the next first neighborhood search (steps S10 to S15), and the end condition is not satisfied (that is, If NO is determined, the process returns to the process of the second neighborhood generation means 22 (step S6).
The processing (steps S6 to S9) of the second neighborhood generation unit 22 to the second neighborhood search end determination unit 26 can be regarded as one loop of the second neighborhood search.

  Whether or not to end the second neighborhood search is determined by, for example, “the maximum number of loops of the second neighborhood search”, “the number of convergence judgments of the second neighborhood search” or “ This is performed using the “maximum search time of 2-neighbor search”. That is, when the number of loops of the second neighborhood search exceeds the “maximum number of loops of the second neighborhood search”, the “number of convergence determinations of the second neighborhood search” is not continuously improved, or When the “maximum search time for the second neighborhood search” has elapsed after the search for the second neighborhood search has started, it is determined that the end condition for the second neighborhood search has been satisfied.

Next, the following processing is performed by the first neighborhood search means 34 in the control program 42 as the first neighborhood search that is the second stage of optimization.
First, in order to update the best solution, the central processing unit 40 receives an instruction from the control program 42 in the main memory 41, and the first neighborhood search initial solution generation unit 27 calculates the optimum solution from the optimum solution storage unit 18. It is read and stored in the best solution storage means 19 (step S10).

  Subsequently, when the basic algorithm of the combinatorial optimization system is based on tabu search, the tabu list initialization means 20 initializes (clears) the taboo list and reads the optimum solution from the optimum solution storage means 18. The updated taboo list is stored in the taboo list storage means 21 (step S11).

  Next, the central processing unit 40 generates a set of adjacent states (first neighborhood) in the immediate region of the current best solution and calculates an evaluation function value by issuing a command from the control program 42 in the main memory 41. Then, the first neighborhood generation means 28 reads out the optimization conditions from the optimization condition storage means 2, reads out the list, minimum fluctuation range, and upper and lower limit values for all the discrete variables from the discrete variable list storage means 12, and stores the best solution. The discrete variable value and the evaluation function value constituting the current best solution are read from the means 19.

  Thereafter, the central processing unit 40 generates a plurality of adjacent states that are the next best solution candidates based on the read information, calculates the evaluation function values of all adjacent states by the evaluation function value calculating unit 17, The state discrete variable value and the evaluation function value are stored in the adjacent state storage means 23 (step S12).

  Specifically, the adjacent state is generated by increasing or decreasing the value of any one of the discrete variables by a minimum fluctuation range. By performing this process on all discrete variables, a neighborhood of the current optimal solution, that is, a set of adjacent states is generated. However, when the changed discrete variable value is larger than the upper limit value, the upper limit value is set. When the changed discrete variable value is smaller than the lower limit value, the lower limit value is set, thereby limiting the discrete variable within a predetermined range.

  Next, the central processing unit 40 receives a command from the control program 42 in the main memory 41 in order to compare the optimum solution and the best solution with each state in the first neighborhood and update the optimum solution and the best solution. Then, the optimum solution / best solution update unit 24 reads all adjacent states from the adjacent state storage unit 23, reads the current optimum solution from the optimum solution storage unit 18, and reads the current best solution from the best solution storage unit 19.

Hereinafter, the central processing unit 40 selects the next best solution from all adjacent states and the current best solution, and stores the discrete variable value and the evaluation function value constituting the next best solution in the best solution storage means 18, If the evaluation function value of the next best solution is superior to the evaluation function value of the current optimum solution, the discrete variable value and the evaluation function value constituting the next best solution are updated in the optimum solution storage means 19. Store (step S13).
The specific method for selecting the next best solution is the same as in the case of the second neighborhood search described above.
Next, when the basic algorithm of the combinatorial optimization system is based on tabu search, the tabu list update unit 25 reads the best solution from the best solution storage unit 19 and the tabu list storage unit 21 reads the tabu list. If the number of best solutions stored in the taboo list has reached the length of the taboo list, a new taboo list in which the oldest best solution in the taboo list is discarded and the current best solution is added is displayed. The list storage means 21 is updated and stored (step S14).

  Next, the central processing unit 40 receives an instruction from the control program 42 in the main memory 41, reads out the optimization condition from the optimization condition storage unit 2 by the first neighborhood search end determination unit 29, and performs the first neighborhood search. Whether or not to end (condition for ending the first neighborhood search) is determined (step S15).

In step S15, when it is determined that the end condition of the first neighborhood search is satisfied (that is, YES), the first vicinity search is ended, and when it is determined that the end condition is not satisfied (that is, NO). The process returns to the processing of the first neighborhood generation means 28 (step S12).
The processing (steps S12 to S15) of the first neighborhood generation unit 27 to the first neighborhood search end determination unit 29 can be regarded as one loop of the first neighborhood search.

  Whether or not to end the first neighborhood search is determined by, for example, “the maximum number of loops of the first neighborhood search”, “the number of convergence judgments of the first neighborhood search” or “ This is performed using the “maximum search time of one neighbor search”. That is, when the number of loops of the first neighborhood search exceeds the “maximum number of loops of the first neighborhood search”, the “number of convergence judgments of the first neighborhood search” is not continuously improved, or When the “maximum search time for the first neighborhood search” has elapsed after the search for the first neighborhood search has started, it is determined that the end condition for the first neighborhood search has been satisfied.

  Finally, the central processing unit 40 receives an instruction from the control program 42 in the main memory 41 as processing after the end of the first neighborhood search, and the optimization result recording / output processing means 30 performs optimization in the hard disk 44. The optimization result (discrete variable value and evaluation function value constituting the optimal solution) is recorded in the optimization result recording means 32 as a file database or the like, and the optimization result output means 31 (display, printer, etc.) in the output device 46 Thus, the optimization result is output (step S16), and the processing routine of FIG. 1 is terminated.

FIG. 3 is an explanatory diagram showing an image of the combinational optimization system according to the first embodiment of the present invention.
In FIG. 3, first, the variation range of some discrete variables or all discrete variables is set to be large, and a set of adjacent states in which the value of the discrete variable is greatly varied from the current state is set to the second neighborhood (in FIG. 3). A global second neighborhood search is performed to optimize the second neighborhood as an adjacent state.
As a result, it is possible to specify at high speed an area in which a central search is promising that an optimal solution exists.

When the evaluation function value of the adjacent state is converged by the second neighborhood search, subsequently, the fluctuation range of the discrete variable is set to be small, and a set of adjacent states in which the discrete variable is changed from the current state to the first neighborhood (see FIG. The first neighborhood search is performed by optimizing the first neighborhood as an adjacent state.
Thereby, as shown in the characteristic diagram on the lower right in FIG. 3, a promising region can be intensively searched in a short time.

As described above, the combination optimization system for solving the combination optimization problem according to the first embodiment of the present invention is as follows.
A control program 42 on the main memory 41;
An optimization condition input means 1 for inputting an optimization condition including an optimization purpose, constraint conditions, and equipment data;
An optimization condition storage means 2 for storing optimization conditions;
Optimization condition recording means 3 for recording at least a part of the optimization conditions as a file database;
An optimization condition recording data acquisition means 4 for reading out the optimization conditions from the optimization condition recording means 3 and storing them in the optimization condition storage means 2;
And an optimization condition default value acquisition means 5 that acquires the optimization condition default value 43 set by the control program 42 and stores it in the optimization condition storage means 2.

Also, a variation adjustment variable list input means 6 for inputting a list of discrete variables for adjusting the variation in the optimization process and initial variation of each of the discrete variables as a variation adjustment variable list,
A fluctuation range adjustment variable list storage means 7 for storing a fluctuation range adjustment variable list;
Fluctuation range adjustment variable list recording means 8 for recording at least a part of the fluctuation range adjustment variable list as a file database;
A fluctuation range adjustment variable list recording data acquisition unit 9 that reads out the fluctuation range adjustment variable list from the fluctuation range adjustment variable list recording unit 8 and stores it in the fluctuation range adjustment variable list storage unit 7;
A fluctuation range adjustment variable list default value acquisition unit 10 that acquires a default value 43 of the fluctuation range adjustment variable list set by the control program 42 and stores the default value 43 in the fluctuation range adjustment variable list storage unit 7;

Also, a discrete variable list input means 11 for inputting a list of all discrete variables, an upper and lower limit value, and a minimum fluctuation range,
Discrete variable list storage means 12 for storing a discrete variable list;
Discrete variable list recording means 13 for recording at least a part of the discrete variable list as a file database;
A discrete variable list recording data acquisition means 14 for reading the discrete variable list from the discrete variable list recording means 13 and storing it in the discrete variable list storage unit 12;
A discrete variable list default value acquisition unit 15 that acquires a default value 43 of the discrete variable list set by the control program 42 and stores it in the discrete variable list storage unit 13.

Also, an evaluation function value calculation means 17 for calculating an evaluation function value for a given discrete variable value according to the optimization condition in the optimization condition storage means 2;
Optimal solution storage means 18 for storing discrete variable values and evaluation function values of the optimal solution, which is the solution with the highest evaluation function value in the past in the optimization process;
A best solution storage means 19 for storing discrete variable values and evaluation function values of the best solution which is a temporary solution in the course of optimization;
The optimization conditions are read from the optimization condition storage means 2, the list of all discrete variables is read from the discrete variable list storage means 12, initial values of all the discrete variables are generated so as to satisfy the optimization conditions, and the evaluation function value calculation means 17 And an initial solution generating means 16 for storing the obtained discrete variable values and evaluation function values in the optimal solution storage means 18 and the best solution storage means 19.

In addition, tabu list storage means 21 for storing a tabu list which is a list of past best solutions;
A tabu list initialization unit 20 that clears the tabu list, reads out the optimum solution from the optimum solution storage unit 18, adds it to the tabu list, and stores the tabu list in the tabu list storage unit 21;
Adjacent state storage means 23 for storing discrete variable values and evaluation function values of all adjacent states;
The optimization condition is read from the optimization condition storage unit 2, the list of discrete variables for adjusting the fluctuation range and the fluctuation range are read from the fluctuation range adjustment variable list storage unit 7, and the discrete range without adjusting the fluctuation range from the discrete variable list storage unit 12. A list of variables, a minimum fluctuation range, and upper and lower limits of all discrete variables are read out, a discrete variable value and an evaluation function value constituting the current best solution are read out from the best solution storage means 19, and an adjacent state which is the next best solution candidate Are generated, and the evaluation function value calculating means 17 calculates the evaluation function values of all adjacent states, and the adjacent state storage in which the area is secured in advance in the main memory 41 for the discrete variable values and evaluation function values of all adjacent states. Second neighborhood generation means 22 to be stored in the means 23.

Further, all adjacent states are read from the adjacent state storage means 23, the current optimum solution is read from the optimum solution storage means 18, the current best solution is read from the best solution storage means 19, and the entire adjacent state and the current best solution are obtained. The next best solution is selected, the discrete variable value and the evaluation function value constituting the next best solution are stored in the best solution storage means 19, and the evaluation function value of the next best solution is greater than the evaluation function value of the current optimal solution. If it is also excellent, the optimum solution / best solution updating means 24 for storing the discrete variable values and the evaluation function values constituting the next best solution in the optimum solution storage means 18;
When the best solution is read from the best solution storage means 19 and the taboo list is read from the taboo list storage means 21, the number of the best solutions stored in the taboo list reaches the length of the taboo list. A taboo list update means 25 for causing the taboo list storage means 21 to store a new taboo list in which the oldest best solution is discarded and the current best solution is added;
The optimization condition is read from the optimization condition storage means 2 to determine whether or not to end the second neighborhood search. If it is determined to end, the process proceeds to the first neighborhood search; Second neighborhood search end determining means 26 for returning to the processing of the 2 neighborhood generating means 22;
And second neighborhood search means 33 for executing a series of processes of second neighborhood generation means 22, optimum solution / best solution update means 24, tabu list update means 25, and second neighborhood search end determination means 26.

A first neighborhood search initial solution generation unit 27 that reads the optimal solution from the optimal solution storage unit 18 and stores it in the best solution storage unit 19;
The optimization conditions are read from the optimization condition storage means 18, the list of all discrete variables, the minimum fluctuation range, and the upper and lower limit values are read from the discrete variable list storage means 12, and the discrete that constitutes the current best solution from the best solution storage means 19. A variable value and an evaluation function value are read, a plurality of adjacent states that are the next best solution candidates are generated, evaluation function values of all adjacent states are calculated by the evaluation function value calculating means 17, and discrete variable values and evaluations of all adjacent states are calculated. First neighborhood generation means 28 for storing the function value in the adjacent state storage means 23;
The optimization condition is read from the optimization condition storage means 2 to determine whether or not to end the first neighborhood search. If it is determined to end, the first neighborhood search is ended. First neighborhood search end determining means 29 for returning to the processing of the 1 neighborhood generating means 28;
A first neighborhood search means for executing a series of processes of a first neighborhood generation means, an optimum solution / best solution update means, a taboo list update means 25, and a first neighborhood search end determination means.

Further, an optimization result output means 31 comprising an output device 46 such as a display or a printer that outputs discrete variable values and evaluation function values constituting an optimal solution;
An optimization result recording means 32 comprising a hard disk 44 for recording discrete variable values and evaluation function values constituting an optimal solution as a file database, etc .;
An optimization result recording / output processing unit 30 for recording the optimization result in the optimization result recording unit 32 after the first neighborhood search and outputting the optimization result by the optimization result output unit 31; Yes.

  Thus, by combining the second neighborhood search (first stage optimization) and the first neighborhood search (second stage optimization), the probability of falling into a local solution is reduced, and a more global solution is obtained. Can be reached fast.

Embodiment 2. FIG.
In the first embodiment, two stages of optimization processing are executed. However, in order to obtain a better solution, three or more stages of optimization processing may be executed.
FIG. 4 is a block diagram showing the overall configuration of a combinational optimization system according to Embodiment 2 of the present invention that enables optimization at an arbitrary stage.

In FIG. 4, the same components as those described above (see FIG. 1) are denoted by the same reference numerals as those described above, or “A” is appended to the reference numerals and detailed description thereof is omitted.
In this case, the main memory 41A includes a counter storage unit 52 that stores a counter variable n indicating whether to search for the n-th neighborhood in addition to the above-described configuration.

The control program 42A includes a counter initialization unit 51 and an N-nth neighborhood generation unit 53 instead of the second neighborhood generation unit 22 described above.
Further, the control program 42A replaces the second neighborhood search end determination means 26 to the first neighborhood search end determination means 29 described above with an N-n neighborhood search end determination means 54, a full search end determination means 55, N-n neighborhood search condition update means 56 is provided.
Furthermore, the control program 42 </ b> A includes an Nn-th neighborhood search unit 57 instead of the second neighborhood search unit 33 and the first neighborhood search unit 34 described above.

The counter initialization unit 51 sets the counter variable n read from the counter storage unit 52 to “0” and stores it in the counter storage unit 52.
The N-nth neighborhood generation means 53 includes the optimization condition read from the optimization condition storage means 2, the list of discrete variables for adjusting the fluctuation width and the fluctuation width W_n read from the fluctuation width adjustment variable list storage means 7. The discrete variable list read out from the discrete variable list storage means 12, the list of discrete variables whose fluctuation width is not adjusted, the minimum fluctuation width and the upper and lower limit values of all the discrete variables, and the discrete that constitutes the current best solution read out from the best solution storage means 19 Based on the variable value and the evaluation function value, a plurality of adjacent states which are the next best solution candidates are generated, the evaluation function value calculating means 17 calculates the evaluation function values of all adjacent states, and the discrete variable values of all adjacent states The evaluation function value is stored in the adjacent state storage means 23 in which an area is secured in advance on the main memory 41A.

The N-n-th neighbor search end determination unit 54 determines whether or not the N-n-th neighbor search end condition is satisfied based on the optimization condition read from the optimization condition storage unit 2. When it is determined that the end condition of the neighborhood search is satisfied, the N−n neighborhood search is ended. When the end condition of the N−n neighborhood search is not satisfied, the process of the N−n neighborhood generation unit 53 is performed. Return to.
The N-n neighborhood searching unit 57 executes a series of processes by the N-n neighborhood generating unit 53, the optimum solution / best solution updating unit 24, the tabu list updating unit 25, and the N-n neighborhood searching end determining unit 54. To do.

  The (N−n) th neighbor search condition update unit 56 sets (increments) the counter variable n read from the counter storage unit 52 to “n + 1”, stores the counter variable n in the counter storage unit 52, and the fluctuation range adjustment variable list storage unit 7. The fluctuation range W_n read out from is updated and stored in the fluctuation range adjustment variable list storage unit 7, and the optimal solution read out from the optimal solution storage unit 18 is stored in the best solution storage unit 19.

  The full search end determination means 55 determines whether or not the full search end condition is satisfied based on the optimization condition read from the optimization condition storage means 2, and when it is determined that the full search end condition is satisfied If the full search is not satisfied, the process shifts to the process of the N-nth neighborhood search condition update means.

Next, the processing procedure executed by the combinational optimization system of FIG. 4 will be described with reference to the flowchart of FIG.
In FIG. 5, steps S1 to S4 and S16 are the same as those described above (see FIG. 2), and thus detailed description thereof is omitted here.

In this case, steps S24 to S33 are inserted between step S4 and step S16 in place of steps S5 to S15 described above.
Steps S25 to S29 in FIG. 5 correspond to steps S5 to S9 (S11 to S15) described above (FIG. 2), and step S33 corresponds to step S10 described above.

  First, as described above, the optimization condition is input or read and stored (step S1), the variable for adjusting the fluctuation range is input or read and stored (step S2), and all the discrete variables (variables without adjusting the fluctuation band) are stored. ) Is input or read and stored (step S3), and an initial solution is generated (step S4). In addition, the evaluation function value in the operation plan of the cogeneration power source is calculated as the above-described equation (1).

Next, the counter initialization means 51 sets a counter variable n indicating whether to search for the n-th neighborhood to “0”, and an area is reserved in advance in the main memory 41A for this set value (n = 0). Is stored in the counter storage means 52 (step S24).
However, in the following description, the maximum counter value is “N”.

Next, the N-n neighborhood searching means 57 performs the N-n neighborhood searching process at the n-th stage of optimization as follows.
First, when the basic algorithm of the combinatorial optimization system is based on tabu search, the tabu list initialization unit 20 clears the tabu list, reads the optimum solution from the optimum solution storage unit 18, and adds it to the tabu list. Then, the tabu list is stored in the tabu list storage means 21 in which an area is secured in advance on the main memory 41A (step S25).

  Next, the central processing unit 40 generates a set of adjacent states (near the N−n) in an area separated from the current best solution by the variation width W_n, and calculates an evaluation function value in the main memory 41A. In response to the command of the control program 42A, the N-n-th neighborhood generation means 53 reads the optimization condition from the optimization condition storage means 2, and the discrete variable for adjusting the fluctuation width from the fluctuation width adjustment variable list storage means 7 is read. The list and the fluctuation range at the time of searching for the (N−n) th neighbor are read, the list of discrete variables whose minimum fluctuation width is not adjusted, the minimum fluctuation width, and the upper and lower limit values of all the discrete variables are read from the discrete variable list storage means 12, and the best solution storage means 19, the discrete variable value and the evaluation function value constituting the current best solution are read out.

  Thereafter, the central processing unit 40 generates a plurality of adjacent states, which are the next best solution candidates, based on the read information, calculates the evaluation function values of all adjacent states by the evaluation function value calculating means 17, and determines all adjacent states. These discrete variable values and evaluation function values are stored in the adjacent state storage means 23 in which an area is secured in advance on the main memory 41A (step S26).

  Specifically, the adjacent state is generated by increasing or decreasing the value of any one of all the discrete variables by a different width for each of the following discrete variables. By performing this process on all discrete variables, a neighborhood of the current optimal solution, that is, a set of adjacent states is generated.

Among all the discrete variables, the value of the discrete variable for adjusting the fluctuation range is changed by the fluctuation range W_n acquired together with the adjustment variable list. For other discrete variables, only the minimum fluctuation range is changed.
However, when the changed discrete variable value is larger than the upper limit value, the upper limit value is set. When the changed discrete variable value is smaller than the lower limit value, the lower limit value is set, thereby limiting the discrete variable within a predetermined range.

  Next, the central processing unit 40 compares the optimum solution and the best solution with the respective states in the vicinity of the (Nn) th and updates the optimum solution and the best solution, so that the command of the control program 42A in the main memory 41A is updated. In response, the optimum solution / best solution update unit 24 reads all adjacent states from the adjacent state storage unit 23, reads the current optimum solution from the optimum solution storage unit 18, and obtains the current best solution from the best solution storage unit 19. read out.

  Hereinafter, the central processing unit 40 selects the next best solution from all adjacent states and the current best solution, and stores the discrete variable value and the evaluation function value constituting the next best solution in the best solution storage means 18, If the evaluation function value of the next best solution is superior to the evaluation function value of the current optimum solution, the discrete variable value and the evaluation function value constituting the next best solution are updated in the optimum solution storage means 18. Store (step S27).

  The specific method for selecting the next best solution follows the basic algorithm of the applied combinatorial optimization system, as described above. For example, when the combinatorial optimization system is based on local search, the next best solution is the one with the best evaluation function value among all the adjacent states. When the combinatorial optimization system is based on tabu search, the next best solution is the one that does not include the tabu list and has the highest evaluation function value among all adjacent states.

  Next, when the basic algorithm of the combinatorial optimization system is based on tabu search, the tabu list update unit 25 reads the best solution from the best solution storage unit 19 and the tabu list storage unit 21 reads the tabu list. If the number of best solutions stored in the taboo list has reached the length of the taboo list, the oldest best solution in the taboo list is discarded and a new taboo list with the current best solution added is added. The taboo list storage means 21 is updated and stored (step S28).

  Next, the central processing unit 40 receives an instruction from the control program 42A in the main memory 41A, reads out the optimization condition from the optimization condition storage unit 2 by the N-nth neighborhood search end determination unit 54, -N It is determined whether or not the neighborhood search is to be ended (end condition is satisfied) (step S29).

In step S29, when it is determined that the end condition of the N-nth neighborhood search is satisfied (that is, YES), the process proceeds to the process of all search end determination means 55 (step S30), and the end condition is not satisfied (that is, the end condition is not satisfied). , NO), the process returns to the process (step S26) of the N-n neighborhood generating means 53.
The processing (steps S26 to S29) of the N-n neighborhood generating means 53 to the N-n neighborhood searching end determining means 54 can be regarded as one loop of the N-n neighborhood searching.

Whether or not to end in step S29 is determined by, for example, “the maximum number of loops of the N-n neighborhood search”, “the number of convergence judgments of the N-n neighborhood search” set in the optimization condition or This is performed using the “maximum search time of the (N−n) th neighbor search”.
That is, when the number of loops of the N-n neighborhood search exceeds the “maximum number of loops of the N-n neighborhood search”, the “optimization number of convergence of the N-n neighborhood search” is continuously improved and the optimal solution is improved. If there is not, or if the “maximum search time of the N-n neighborhood search” has elapsed after the search for the N-n neighborhood search has started, it is determined that the end condition for the N-n neighborhood search is satisfied Is done.

Next, the full search end determination means 55 reads out the optimization conditions from the optimization condition storage means 2 and determines whether or not to end the full search (end conditions are satisfied) (step S30).
If it is determined in step S30 that the full search end condition is satisfied (that is, YES), the process proceeds to the final process (step S16) of the optimization result recording / output processing means 30 and the end condition is not satisfied (step S16). That is, if it is determined as NO), the process proceeds to the process of the N-nth neighborhood search condition update unit 56 (step S31).

Next, the N-nth neighborhood search condition update unit 56 reads the counter variable n from the counter storage unit 52, sets (increments) it to “n + 1”, and stores it in the counter storage unit 52 (step S31).
Further, the fluctuation range W_n is read from the fluctuation range adjustment variable list storage unit 7, the updated fluctuation range W_n is stored in the fluctuation range adjustment variable list storage unit 7 (step S 32), and the optimal solution is stored from the optimal solution storage unit 18. The best solution is initialized by reading it out and storing it in the best solution storage means 19 (step S33).

  Thereafter, the process returns to the processing of the tabu list initialization means 20 (step S25), and the N-nth neighborhood search (the counter variable n has been updated in step S31) is repeatedly executed.

As a method of updating the fluctuation range W_n, in order to sequentially set a smaller value, for example, the fluctuation range W_n in the previous search may be halved.
For example, in the power supply operation plan described above, the time width W_n for changing the ON / OFF state of the power supply is sequentially updated in the order of “120 minutes” → “60 minutes” → “30 minutes”. When the value of the fluctuation range W_n reaches the minimum fluctuation range, no further update is performed.

  Further, the end determination of the full search in step S30 is performed using, for example, “maximum search time of full search” set in the optimization condition. That is, when the “maximum search time for all search” has elapsed after the start of the first search, or when the neighborhood search with the minimum fluctuation width of the fluctuation width W_n of all the discrete variables has been completed, It is determined that it has been established.

  Finally, after completion of the all-neighbor search, the central processing unit 40 receives an instruction from the control program 42A in the main memory 41A, and configures an optimum solution by the optimization result recording / output processing means 30 as described above. The discrete variable value and the evaluation function value to be recorded are recorded as a file database or the like in the optimization result recording means 32 composed of the hard disk 44 and optimized to the optimization result output means 31 (display, printer, etc.) composed of the output device 46. Output discrete variable values and evaluation function values that constitute the solution.

  As described above, the combinational optimization system according to the second embodiment of the present invention has the same configuration as described above, the optimization condition input means 1, the optimization condition storage means 2, the optimization condition recording means 3, and the like. Optimization condition record data acquisition means 4, optimization condition default value acquisition means 5, fluctuation width adjustment variable list input means 6, fluctuation width adjustment variable list storage means 7, fluctuation width adjustment variable list recording means 8, , Fluctuation range adjustment variable list record data acquisition means 9, fluctuation range adjustment variable list default value acquisition means 10, discrete variable list input means 11, discrete variable list storage means 12, discrete variable list recording means 13, discrete Variable list record data acquisition means 14, discrete variable list default value acquisition means 15, evaluation function value calculation means 17, optimum solution storage means 18, and best solution storage means 1 An initial solution generating unit 16, a taboo list storage unit 21, a taboo list initialization unit 20, an adjacent state storage unit 23, an optimum solution / best solution update unit 24, a taboo list update unit 25, and an optimization. A result output unit 31, an optimization result recording unit 32, and an optimization result recording / output processing unit 30 are provided.

  Further, as a configuration different from that described above, a counter storage unit 52 that stores a counter variable n that indicates whether to search for the nth neighborhood, and a counter variable n that indicates whether to search for the nth neighborhood from the counter storage unit 52 are set to “0”. Counter initializing means 51, Nn neighborhood generating means 53, Nn neighborhood searching means 57, Nn neighborhood searching condition updating means 56, And an all-search end judging means 55.

  The N-nth neighborhood generation means 53 reads the optimization condition from the optimization condition storage means 2, reads the list of discrete variables for adjusting the fluctuation width and the fluctuation width W_n from the fluctuation width adjustment variable list storage means 7, A list of discrete variables whose fluctuation width is not adjusted, a minimum fluctuation width, and upper and lower limit values of all the discrete variables are read from the variable list storage means 12, and discrete variable values and evaluation functions constituting the current best solution from the best solution storage means 19 A value is read to generate a plurality of adjacent states which are the next best solution candidates, the evaluation function value calculating means 17 calculates the evaluation function values of all adjacent states, and the discrete variable values and evaluation function values of all adjacent states are adjacent It is stored in the state storage means 23.

The N-n neighborhood search end determination means 54 reads the optimization condition from the optimization condition storage means 2 and determines whether or not to end the N-n neighborhood search. The N-n neighborhood search is terminated, and if not, the process returns to the process of the N-n neighborhood generation means 53.
The N-n neighborhood searching unit 57 executes a series of processes of the N-n neighborhood generating unit 53, the optimum solution / best solution updating unit 24, the tabu list updating unit 25, and the N-n neighborhood searching end determining unit 56. To do.

The (N−n) th neighbor search condition update unit 56 reads the counter variable n from the counter storage unit 52, sets (increments) the counter variable n to “n + 1”, stores the counter variable n in the counter storage unit 52, and the fluctuation range adjustment variable list storage unit 7. The fluctuation range W_n is read and the updated fluctuation range W_n is updated and stored in the fluctuation range adjustment variable list storage unit 7, and the optimal solution is read out from the optimal solution storage unit 18 and stored in the best solution storage unit 19.
The full search end determination means 55 reads out the optimization conditions from the optimization condition storage means 2 and determines whether or not to end the full search. When it is determined that the search is complete, the full search is ended. In this case, the process proceeds to the process of the N-nth neighborhood search condition update unit 56.

In this way, a global search is performed by setting the fluctuation range of some or all discrete variables from a large one to a small one in a stepwise manner, and a region for concentrated search where an optimal solution is promising is identified at high speed. Finally, by setting the fluctuation range of the discrete variable to the minimum fluctuation range and combining the neighborhood search that concentrates the promising area, the probability of falling into a local solution is reduced as described above, and more global A realistic solution can be reached at high speed.
In addition, although it takes a longer time than the first embodiment, the reliability of the optimum solution can be further improved.

It is a block diagram which shows the whole structure of the combination optimization system which concerns on Embodiment 1 of this invention. It is a flowchart which shows operation | movement of the combination optimization system which concerns on Embodiment 1 of this invention. It is explanatory drawing which shows the image of the combination optimization system which concerns on Embodiment 1 of this invention. It is a block diagram which shows the whole structure of the combination optimization system which concerns on Embodiment 2 of this invention. It is a flowchart which shows operation | movement of the combination optimization system which concerns on Embodiment 2 of this invention. It is explanatory drawing which shows the image of the conventional combination optimization system.

Explanation of symbols

  1 optimization condition input means, 2 optimization condition storage means, 3 optimization condition recording means, 4 optimization condition record data acquisition means, 5 optimization condition default value acquisition means, 6 fluctuation range adjustment variable list input means, 7 fluctuation Width adjustment variable list storage means, 8 fluctuation width adjustment variable list recording means, 9 fluctuation width adjustment variable list record data acquisition means, 10 fluctuation width adjustment variable list default value acquisition means, 11 discrete variable list input means, 12 discrete variable list storage Means, 13 discrete variable list recording means, 14 discrete variable list recorded data acquisition means, 15 discrete variable list default value acquisition means, 16 initial solution generation means, 17 evaluation function value calculation means, 18 optimal solution storage means, 19 best solution storage Means, 20 tabu list initialization means, 21 tabu list storage means, 22 second neighborhood generation means 23 adjacent state storage means, 24 best solution / optimum solution update means, 25 taboo list update means, 26 second neighborhood search end determination means, 27 first neighborhood search initial solution generation means, 28 first neighborhood generation means, 29 first Neighborhood search end determination means, 30 optimization result recording / output processing means, 31 optimization result output means, 32 optimization result recording means, 33 second neighborhood search means, 34 first neighborhood search means, 40 central processing unit, 41 , 41A main memory, 42, 42A control program, 43 default value, 44 hard disk, 45 input device, 46 output device, 47 bus, 51 counter initialization means, 52 counter storage means, 53 N-n neighborhood generating means, 54 N-n neighborhood search end determination means, 55 full search end determination means, 56 N-n neighborhood search condition update means, 5 The N-n local search means.

Claims (7)

A combinatorial optimization system for solving combinatorial optimization problems,
Each of the optimization conditions, the discrete variable list defined by the list of all discrete variables and the minimum fluctuation range / upper and lower limit values, and the list of discrete variables that adjust the fluctuation range during the optimization process and the list of these discrete variables Storage means for storing a fluctuation range adjustment variable list defined by the initial fluctuation range;
A second neighborhood search means for performing optimization while varying the fluctuation range of the fluctuation range adjustment variable list at the initial fluctuation range at an initial stage of the search;
First neighborhood search means for performing optimization while changing the fluctuation range of all discrete variables by the minimum fluctuation range after the second neighborhood search by the second neighborhood search means;
A combination optimization system, comprising: a control program that executes the second neighborhood search and the first neighborhood search by the first neighborhood search means.   The combination optimization system according to claim 1, wherein the optimization condition includes an optimization purpose, a constraint condition, and facility data. Input means for inputting the optimization condition, the discrete variable list, and the fluctuation range adjustment variable list;
Recording means for recording at least a part of the optimization condition, the discrete variable list, and the variation adjustment variable list as a file database;
Recording data acquisition means for reading out the optimization condition, the discrete variable list and the fluctuation range adjustment variable list from the recording means and storing them in the storage means;
Default value acquisition means for acquiring default values of the optimization condition, the discrete variable list and the fluctuation range adjustment variable list and storing the default values in the storage means;
An evaluation function value calculating means for calculating an evaluation function value for a given discrete variable value according to the optimization condition;
Optimal solution storage means for storing discrete variable values and evaluation function values constituting an optimal solution that is the solution with the best evaluation function value in the past in the optimization process;
Best solution storage means for storing discrete variable values and evaluation function values constituting the best solution which is a temporary solution in the optimization process;
Reading out a list of all discrete variables from the storage means, generating initial values of the all discrete variables so as to satisfy the optimization condition read from the storage means, and an evaluation function value calculated by the evaluation function value calculation means Initial solution generation means for storing the optimum solution storage means and the best solution storage means;
A taboo list storage means for storing a taboo list including a list of past best solutions;
Tabu list initialization means for clearing the tabu list and storing the tabu list added with the optimum solution read from the optimum solution storage means in the tabu list storage means;
Optimization conditions read from the storage means, a list and fluctuation range of discrete variables that adjust the fluctuation range, a list of discrete variables that do not adjust the fluctuation range, the minimum fluctuation range and the upper and lower limit values of all the discrete variables, and the best solution storage Based on the discrete variable value and the evaluation function value constituting the current best solution read from the means, a plurality of adjacent states that are the next best solution candidates are generated, and the evaluation function of all adjacent states is calculated by the evaluation function value calculation means A second neighborhood generating means for calculating a value and storing the discrete variable values and the evaluation function values of the all adjacent states in the storage means;
Reads out all adjacent states from the storage means, reads out the current optimum solution and the best solution from the optimum solution storage means and the best solution storage means, and selects the next best solution from the all adjacent states and the current best solution The discrete variable values and evaluation function values constituting the next best solution are stored in the best solution storage means, and the evaluation function value of the next best solution is superior to the evaluation function value of the current optimal solution In this case, the optimum solution / best solution update means for storing the discrete variable value and the evaluation function value constituting the next best solution in the optimum solution storage means;
The best solution is read from the best solution storage means, the taboo list is read from the taboo list storage means, and the number of the best solutions stored in the taboo list reaches the length of the taboo list, A taboo list update means for discarding the oldest best solution in the taboo list and storing a new taboo list in which the current best solution is added to the taboo list storage means;
Based on the optimization condition read from the storage means, it is determined whether or not an end condition for the second neighborhood search is satisfied. If it is determined that the end condition for the second neighborhood search is satisfied, the first condition is determined. Transition to neighborhood search, and if the second neighborhood search end condition is not satisfied, the second neighborhood search end determination means for returning to the processing of the second neighborhood generation means,
The second neighborhood search means executes a series of processes by the second neighborhood generation means, the optimum solution / best solution update means, the taboo list update means, and the second neighborhood search end determination means. The combinational optimization system according to claim 1 or 2. First neighborhood search initial solution generation means for reading the optimum solution from the optimum solution storage means and storing the optimum solution in the best solution storage means;
Based on the optimization conditions read from the storage means, the list of all discrete variables, the minimum fluctuation range and the upper and lower limit values, and the discrete variable values and evaluation function values constituting the current best solution read from the best solution storage means A plurality of adjacent states that are the next best solution candidates, the evaluation function value calculating means calculates the evaluation function value of all adjacent states, and the discrete variable value and evaluation function value of all adjacent states are calculated as the adjacent state. First neighborhood generation means to be stored in the storage means;
Based on the optimization condition read from the storage means, it is determined whether or not an end condition for the first neighborhood search is satisfied. If it is determined that the end condition for the first neighborhood search is satisfied, the first condition is determined. A first neighborhood search termination determination unit that terminates the neighborhood search and returns to the process of the first neighborhood generation unit when the termination condition of the first neighborhood search is not satisfied;
Optimization result output means for outputting discrete variable values and evaluation function values constituting the optimal solution;
Optimization result recording means for recording discrete variable values and evaluation function values constituting the optimal solution as a file database;
An optimization result recording / output processing means for recording the optimization result in the optimization result recording means after the first neighborhood search and outputting the optimization result by the optimization result output means;
The first neighborhood searching means executes a series of processing by the first neighborhood generating means, the optimum solution / best solution updating means, the taboo list updating means, and the first neighborhood search end judging means. The combination optimization system according to claim 3. A combinatorial optimization system for solving combinatorial optimization problems,
Optimization conditions, a list of all discrete variables, a list of discrete variables defined by the minimum fluctuation range and upper and lower limits, a list of discrete variables that adjust the fluctuation range during the optimization process, and each initial fluctuation of the list of these discrete variables Storage means for storing a variable range adjustment variable list defined by the width, and a counter variable indicating a neighborhood search stage;
N-th neighbor search means for performing optimization while varying the variation width of the variation adjustment variable list with a variation width W_n different for each value n of the counter variable when the counter variable is a value n;
Counter variable updating means for updating the value n of the counter variable;
A fluctuation range updating unit for updating a fluctuation range W_n at the time of execution of the Nn-th neighborhood search by the N-n neighborhood search unit;
And a control program for sequentially executing the N-n-th neighborhood search while increasing the value n of the counter variable.   The combination optimization system according to claim 5, wherein the optimization condition includes an optimization purpose, a constraint condition, and facility data. Input means for inputting the optimization condition, the discrete variable list, and the fluctuation range adjustment variable list;
Recording means for recording at least a part of the optimization condition, the discrete variable list, and the variation adjustment variable list as a file database;
Recording data acquisition means for reading out the optimization condition, the discrete variable list and the fluctuation range adjustment variable list from the recording means and storing them in the storage means;
Default value acquisition means for acquiring default values of the optimization condition, the discrete variable list and the fluctuation range adjustment variable list and storing the default values in the storage means;
An evaluation function value calculating means for calculating an evaluation function value for a given discrete variable value according to the optimization condition;
Optimal solution storage means for storing discrete variable values and evaluation function values constituting an optimal solution that is the solution with the best evaluation function value in the past in the optimization process;
Best solution storage means for storing discrete variable values and evaluation function values constituting the best solution which is a temporary solution in the optimization process;
Reading out a list of all discrete variables from the storage means, generating initial values of the all discrete variables so as to satisfy the optimization condition read from the storage means, and an evaluation function value calculated by the evaluation function value calculation means Initial solution generation means for storing the optimum solution storage means and the best solution storage means;
Counter initialization means for setting the value n of the counter variable read from the storage means to "0" and storing it in the counter storage means;
A taboo list storage means for storing a taboo list including a list of past best solutions;
Tabu list initialization means for clearing the tabu list and storing the tabu list added with the optimum solution read from the optimum solution storage means in the tabu list storage means;
Optimization conditions read from the storage means, discrete variable list and fluctuation range W_n for adjusting the fluctuation range, discrete variable list without fluctuation range adjustment, minimum fluctuation range and upper and lower limit values of all discrete variables, and the best solution Based on the discrete variable value and the evaluation function value constituting the current best solution read from the storage means, a plurality of adjacent states that are the next best solution candidates are generated, and the evaluation function value calculating means evaluates all adjacent states. An N−n-th neighborhood generating unit that calculates a function value and stores the discrete variable value and the evaluation function value in the all adjacent states in the storage unit;
Reads out all adjacent states from the storage means, reads out the current optimum solution and the best solution from the optimum solution storage means and the best solution storage means, and selects the next best solution from the all adjacent states and the current best solution The discrete variable values and evaluation function values constituting the next best solution are stored in the best solution storage means, and the evaluation function value of the next best solution is superior to the evaluation function value of the current optimal solution In this case, the optimum solution / best solution update means for storing the discrete variable value and the evaluation function value constituting the next best solution in the optimum solution storage means;
The best solution is read from the best solution storage means, the taboo list is read from the taboo list storage means, and the number of the best solutions stored in the taboo list reaches the length of the taboo list, A taboo list update means for discarding the oldest best solution in the taboo list and storing a new taboo list in which the current best solution is added to the taboo list storage means;
Based on the optimization condition read from the storage means, it is determined whether or not the end condition of the N-n neighborhood search is satisfied, and when it is determined that the end condition of the N-n neighborhood search is satisfied Terminates the N-n neighborhood search, and if the N-n neighborhood search termination condition is not satisfied, returns to the process of the N-n neighborhood generation means to return to the N-n neighborhood search termination determination. Means,
The counter variable n read from the counter storage means is set to “n + 1” and stored in the counter storage means, and the fluctuation width W_n read from the fluctuation width adjustment variable list storage means is updated to change the fluctuation width adjustment variable list. N-n-th neighborhood search condition update means for storing in the storage means and storing the optimum solution read from the optimum solution storage means in the best solution storage means;
Based on the optimization condition read from the storage means, determine whether or not the end condition of the full search is satisfied, and if it is determined that the end condition of the full search is satisfied, end the full search, A full search end determination unit that shifts to the process of the N-n neighborhood search condition update unit when the full search end condition is not satisfied;
Optimization result output means for outputting discrete variable values and evaluation function values constituting the optimal solution;
Optimization result recording means for recording discrete variable values and evaluation function values constituting the optimal solution as a file database;
An optimization result recording / output processing means for recording the optimization result in the optimization result recording means after completion of the full search and outputting the optimization result by the optimization result output means;
The N-n neighborhood search means executes a series of processes by the N-n neighborhood generation means, the optimum solution / best solution update means, the tabu list update means, and the N-n neighborhood search end determination means. The combinational optimization system according to claim 5 or 6, characterized in that:

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