Solution search device and solution search method

Abstract

The solution search device (1) includes a setting unit (12) that sets a first aspiration level, which is a target value for multiple objective functions in a multi-objective optimization problem, a first optimal solution calculation unit (13) that calculates a first optimal solution using the first aspiration level set by the setting unit and a frontier, which is a solution set for optimizing the multiple objective functions, and a first optimal solution adjustment unit (15) that, when an instruction to not adopt the first optimal solution calculated by the first optimal solution calculation unit is received from a user, receives an input of an adjustment amount for adjusting the first optimal solution from the user, and adjusts the first optimal solution within the range of the frontier based on the received adjustment amount.

Description

[Technical field]

[0001] The present disclosure relates to a solution searching device and a solution searching method. [Background technology]

[0002] In a multi-objective optimization problem in which multiple objective functions are optimized, it is difficult to express all the objective functions by aggregating them into an evaluation function such as a linear weighted sum. Therefore, various methods have been proposed for obtaining an optimal solution to a multi-objective optimization problem. For example, Patent Document 1 discloses a predictive control method using a satisficing trade-off method for a multi-objective optimization problem. The satisficing trade-off method is one of the interactive multi-objective programming methods using aspiration levels, and is one of the methods for formulating a multi-objective optimization problem.

[0003] The predictive control method described in Patent Document 1 (hereinafter also referred to as the "conventional method") accepts an input of an aspiration level, which is a target value for multiple objective functions (controlled quantities), to set the aspiration level, calculates an optimal solution close to the aspiration level, displays the optimal solution, and if the optimal solution does not satisfy a specified criterion, accepts an input to change the aspiration level and changes the setting of the aspiration level, and repeats these steps to determine an optimal solution that satisfies the specified criterion.

[0004] Specifically, in the conventional method, the intersection point between a straight line connecting the ideal point, which is the minimum value of the objective function, and a first aspiration level set by a decision maker (operator), and a line showing the Pareto frontier, which is a trade-off set of optimal solutions, is calculated as a first optimal solution. If the decision maker is not satisfied with this first optimal solution, the aspiration level setting is changed from the first aspiration level to a second aspiration level through a trade-off analysis using a sensitivity analysis, and the intersection point between the straight line connecting this second aspiration level and the ideal point and the line showing the Pareto frontier is calculated as a second optimal solution. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2010-152767 A Summary of the Invention [Problem to be solved by the invention]

[0006] However, as described above, in conventional methods, if the decision maker is not satisfied with the calculated optimal solution, the aspiration level setting is changed and a different optimal solution is calculated based on the changed aspiration level, and this process is repeated until the decision maker is satisfied with the calculated optimal solution, which has the problem that it takes a long time to obtain an optimal solution that satisfies the decision maker.

[0007] The present disclosure has been made to solve the above-mentioned problems, and has an object to provide a solution search device that can reduce the time required to find an optimal solution that satisfies a decision maker compared to conventional methods. [Means for solving the problem]

[0008] The solution search device according to the present disclosure includes a setting unit that sets a first aspiration level, which is a target value for multiple objective functions in a multi-objective optimization problem; a first optimal solution calculation unit that calculates a first optimal solution using the first aspiration level set by the setting unit and a frontier, which is a solution set for optimizing the multiple objective functions; and a first optimal solution adjustment unit that, when receiving an instruction from a user not to adopt the first optimal solution calculated by the first optimal solution calculation unit, receives an input of an adjustment amount for adjusting the first optimal solution from the user and adjusts the first optimal solution within the range of the frontier based on the received adjustment amount. Effect of the Invention

[0009] According to the present disclosure, it is possible to reduce the time required to obtain an optimal solution that satisfies a decision maker, compared to the conventional method. [Brief description of the drawings]

[0010] [Figure 1]FIG. 1 is a diagram illustrating an example of the configuration of a solution searching device according to a first embodiment. [Diagram 2] 4 is a flowchart showing an example of the operation of the solution search device according to the first embodiment. [Diagram 3] FIG. 2 is a diagram showing an example of extraction of a Pareto frontier by a solution extraction unit in the first embodiment. [Figure 4] FIG. 4 is a diagram showing an example of calculation of a first optimum solution in the first embodiment. [Diagram 5] FIG. 11 is a diagram showing an example of calculation of a second optimal solution and a second aspiration level in the first embodiment. [Figure 6] FIG. 11 is a diagram showing details of a calculation example of a second optimal solution and a second aspiration level in the first embodiment. [Figure 7] 4 is a diagram showing details of a calculation example of a first optimum solution and a second optimum solution in a case where the solution space is a three-dimensional space in the first embodiment. FIG. [Figure 8] 13 is a diagram showing details of an example of calculating a second aspiration level when the solution space is a three-dimensional space in the first embodiment. FIG. [Figure 9] 9A and 9B are diagrams illustrating an example of a hardware configuration of the solution searching device according to the first embodiment. [Figure 10] FIG. 11 is a diagram showing an example of a support screen in the second embodiment. [Figure 11] FIG. 13 is a diagram for explaining an example of extraction of an efficient frontier in the third embodiment. [Figure 12] FIG. 11 is a diagram for explaining a CCR model in the third embodiment. [Figure 13] FIG. 13 is a diagram for explaining an ultra-CCR model in the third embodiment. [Figure 14] FIG. 13 is a diagram illustrating an example of the configuration of a solution searching device according to a fourth embodiment. [Figure 15] FIG. 13 is a diagram showing an example of calculation of an aspiration level frontier in the fourth embodiment. [Figure 16] FIG. 13 is a diagram showing an example of calculation of a second optimal solution and a second aspiration level in the fourth embodiment. [Figure 17]FIG. 13 is a diagram for explaining a reference region and an extension region in the fifth embodiment. [Figure 18] FIG. 13 is a diagram for explaining a search region in the fifth embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Embodiment 1

[0012] Fig. 1 is a diagram showing an example of the configuration of a solution search device 1 according to embodiment 1. For example, as shown in Fig. 1, the solution search device 1 includes a population generation unit 10, a solution extraction unit 11, an aspiration level / ideal point setting unit 12, a first optimal solution calculation unit 13, a first optimization calculation unit 14, a first optimal solution adjustment unit 15, a second aspiration level calculation unit 16, a second optimization calculation unit 17, a judgment unit 18, an interface unit 20 (an input unit 21 and a display unit 22), a display control unit 23, and a screen generation unit 24.

[0013] The population generation unit 10 generates a set (population) of solutions for a multi-objective optimization problem in which multiple objective functions are optimized. For example, the population generation unit 10 generates a set (population) of solutions in a space (hereinafter also referred to as a "solution space") defined by multiple objective functions using a known optimization algorithm such as NSGA-II (Non-Dominated Sorting Genetic Algorithm-II).

[0014] The solution extraction unit 11 extracts a frontier, which is a set of solutions for optimizing multiple objective functions, from the set of solutions generated by the population generation unit 10. For example, the solution extraction unit 11 extracts a Pareto frontier from the set of solutions generated by the population generation unit 10 using a known optimization algorithm such as the above-mentioned NSGA-II.

[0015] The Pareto frontier is a set of Pareto solutions. A Pareto solution is a solution in which optimizing one of multiple objective functions results in the deterioration of the other objective functions. When there are two objective functions, that is, when the solution space is two-dimensional, the Pareto frontier is expressed as a line connecting the Pareto solutions in the solution space. When there are three objective functions, that is, when the solution space is three-dimensional, the Pareto frontier is expressed as a surface including the Pareto solutions in the solution space.

[0016] A decision maker, who is a user of the solution search device 1, inputs an ideal point and a first aspiration level to the solution search device 1 via the interface unit 20. The aspiration level / ideal point setting unit 12 accepts the ideal point and the first aspiration level input by the decision maker via the interface unit 20, and sets the accepted ideal point and first aspiration level in the solution space.

[0017] The ideal point is a point that represents the optimal solution (e.g., the minimum value) for all of the multiple objective functions. The aspiration level is a point that represents the minimum standard that should be satisfied for each of the multiple objective functions, and the first aspiration level is the aspiration level that the decision maker first inputs (specifies).

[0018] The first optimal solution calculation unit 13 calculates a first optimal solution by using the ideal point and the first aspiration level set by the aspiration level / ideal point setting unit 12 and the frontier (e.g., Pareto frontier) extracted by the solution extraction unit 11.

[0019] For example, the first optimal solution calculation unit 13 identifies an intersection point between a straight line connecting the ideal point set by the aspiration level / ideal point setting unit 12 and the first aspiration level, and a line indicating the frontier extracted by the solution extraction unit 11, in the solution space, and calculates the identified intersection point as a first optimal solution. The first optimal solution calculated here is presented to a decision maker via the interface unit 20.

[0020] The decision maker checks the presented first optimal solution and determines the following points. Then, the decision maker inputs the determination result to the solution search device 1 via the interface unit 20. (1) Whether to adopt the first optimal solution presented (2) If the first optimal solution presented is not adopted, whether or not to optimize the first optimal solution based on the first aspiration level (3) If the first optimal solution presented is not adopted and the first optimal solution is not optimized based on the first aspiration level, whether or not to adjust the first optimal solution within the range of the frontier If the above judgment result indicates that the first optimal solution presented in (1) above should be adopted, the solution search device 1 ends the process at that stage.

[0021] When the judgment result indicates that the first optimal solution presented in (2) is not adopted and the first optimal solution is optimized based on the first aspiration level, the first optimization calculation unit 14 searches for a solution that is in the vicinity of the first optimal solution in the solution space and different from the first optimal solution based on the judgment result. The first optimization calculation unit 14 presents the searched solution to the decision maker via the interface unit 20, and the decision maker judges whether to adopt the presented solution. Hereinafter, the first optimization calculation unit 14 repeats the search for the solution until the presented solution is adopted by the decision maker. Details of the solution search by the first optimization calculation unit 14 will be described in the fifth and sixth embodiments.

[0022] If the judgment result in (3) indicates that the presented first optimal solution is not adopted, the first optimal solution is not optimized based on the first aspiration level, and the first optimal solution is adjusted within the range of the frontier, the first optimal solution adjustment unit 15 adjusts the first optimal solution within the range of the frontier based on the judgment result. As a result, the first optimal solution adjustment unit 15 calculates a second optimal solution different from the first optimal solution.

[0023] For example, when the solution space is a two-dimensional space, the first optimal solution adjustment unit 15 moves the first optimal solution calculated by the first optimal solution calculation unit 13 on the line indicating the frontier. At this time, the first optimal solution adjustment unit 15 receives an adjustment amount (movement amount) of the first optimal solution from the decision maker, and adjusts (moves) the first optimal solution on the line indicating the frontier based on the received adjustment amount.

[0024] Furthermore, for example, when the solution space is a three-dimensional space, the first optimal solution adjustment unit 15 moves the first optimal solution calculated by the first optimal solution calculation unit 13 on a plane representing the frontier. At this time, the first optimal solution adjustment unit 15 receives an adjustment amount (movement amount) of the first optimal solution from the decision maker, and adjusts (moves) the first optimal solution on the plane representing the frontier based on the received adjustment amount.

[0025] The first optimal solution (ie, the second optimal solution) adjusted as described above is presented to a decision maker via the interface unit 20.

[0026] The second aspiration level calculation unit 16 calculates a second aspiration level different from the first aspiration level, based on the first optimal solution (i.e., the second optimal solution) adjusted by the first optimal solution adjustment unit 15 and the ideal point indicating the optimal solutions in all of the objective functions among the multiple objective functions. The second aspiration level calculated here is presented to the decision maker via the interface unit 20.

[0027] The decision maker checks the presented second optimal solution and second aspiration level, and judges the following points. Then, the decision maker inputs the judgment result to the solution search device 1 via the interface unit 20. (4) Whether or not to adopt the second optimal solution presented (5) If the second optimal solution is not adopted, whether to optimize the second optimal solution based on the second aspiration level. (6) If the second optimal solution is not adopted and the second optimal solution is not optimized based on the second aspiration level, should the user start over from setting the first aspiration level? If the above judgment result indicates that the presented second optimal solution should be adopted in (4) above, the solution search device 1 ends the process at that stage.

[0028] When the judgment result indicates that the second optimal solution presented in (5) is not adopted and the second optimal solution is optimized based on the second aspiration level, the second optimization calculation unit 17 searches for a solution that is in the vicinity of the second optimal solution in the solution space and different from the second optimal solution based on the judgment result. The second optimization calculation unit 17 presents the searched solution to the decision maker via the interface unit 20, and the decision maker judges whether to adopt the presented solution. Thereafter, the second optimization calculation unit 17 repeats the search for the solution until the presented solution is adopted by the decision maker. Details of the search for a solution by the second optimization calculation unit 17 will be described in the fifth and sixth embodiments.

[0029] If the judgment result indicates in (6) that the presented second optimal solution is not adopted, the second optimal solution is not optimized based on the second aspiration level, and the first aspiration level is not reset, the first optimal solution adjustment unit 15 adjusts (readjusts) the second optimal solution within the range of the frontier based on the judgment result. As a result, the first optimal solution adjustment unit 15 calculates a new second optimal solution different from the previously calculated second optimal solution. At this time, the first optimal solution adjustment unit 15 again receives an adjustment amount (movement amount) from the decision maker, and adjusts (moves) the second optimal solution within the range of the frontier based on the received adjustment amount.

[0030] Furthermore, if the judgment result indicates in (6) above that the presented second optimal solution is not to be adopted, the second optimal solution is not to be optimized based on the second aspiration level, and the setting of the first aspiration level is to be started over again, the decision maker inputs an aspiration level different from the first aspiration level previously input to the solution search device 1 via the interface unit 20 as a new first aspiration level. The aspiration level / ideal point setting unit 12 accepts the new first aspiration level input by the decision maker via the interface unit 20, and sets the accepted new first aspiration level in the solution space. Thereafter, in the same manner as above, the first optimal solution based on the new first aspiration level is recalculated by the first optimal solution calculation unit 13.

[0031] The judgment unit 18 judges the content of each of the judgment results input by the decision maker.

[0032] The interface unit 20 realizes an interface function for a decision maker who is a user. The interface unit 20 includes an input unit 21 constituted by, for example, a keyboard and a mouse, and a display unit 22 constituted by a display or the like.

[0033] The display control unit 23 causes the display unit 22 to display a screen indicated by the data generated by the screen generation unit 24 .

[0034] The screen generation unit 24 generates data showing a specified screen for the decision maker to input the ideal point, the first aspiration level, the adjustment amount, etc., and to confirm the first optimal solution and the second optimal solution, etc.

[0035] Next, an example of the operation of the solution search device 1 according to the first embodiment will be described with reference to the flowchart shown in FIG.

[0036] In the following description, for simplicity, an example will be described in which an optimal solution is calculated by the solution search device 1 for a multi-objective optimization problem having two objective functions. Also, in the following description, an example will be described in which the solution extraction unit 11 extracts a Pareto frontier as a frontier by using a known optimization algorithm such as the above-mentioned NSGA-II.

[0037] First, the population generation unit 10 uses the above-mentioned optimization algorithm to generate a set (population) of solutions to a multi-objective optimization problem for optimizing two objective functions (step ST1).

[0038] Next, the solution extractor 11 uses the above-mentioned optimization algorithm to extract a Pareto frontier from the set of solutions generated by the population generator 10 (step ST2).

[0039] An example of the Pareto frontier extracted by the solution extractor 11 is shown in Fig. 3. In Fig. 3, the horizontal axis indicates the first objective function (g1) and the vertical axis indicates the second objective function (g2). In this case, the solution space K is a two-dimensional space.

[0040] 3, points A to J indicate a set of solutions (population) generated by the population generation unit 10, and among these, points A to F indicate Pareto solutions. In FIG. 3, a line PF connecting points A to F indicates the Pareto frontier (set of Pareto solutions). Note that points G to J indicate those among the set of solutions (population) generated by the population generation unit 10 that are not Pareto solutions. Note that in the following explanation, for convenience of explanation, each of points A to F that are Pareto solutions will also be referred to as a "solution on the Pareto frontier."

[0041] Next, the decision maker inputs the ideal point and the first aspiration level to the solution search device 1 via the interface unit 20. The aspiration level / ideal point setting unit 12 accepts the ideal point and the first aspiration level input by the decision maker via the interface unit 20, and sets the accepted ideal point and first aspiration level in the solution space K (step ST3).

[0042] Next, the first optimal solution calculation unit 13 calculates a first optimal solution by using the ideal point and the first aspiration level set by the aspiration level / ideal point setting unit 12 and the Pareto frontier extracted by the solution extraction unit 11 (step ST4).

[0043] An example of the first optimum solution calculated by the first optimum solution calculation unit 13 is shown in Fig. 4. In Fig. 4, point P1 indicates the ideal point, point Q1 indicates the first aspiration level, and point R indicates the first optimum solution.

[0044] For example, the first optimal solution calculation unit 13 identifies an intersection between a straight line connecting the ideal point P1 set by the aspiration level / ideal point setting unit 12 and the first aspiration level Q1 and a line PF indicating the Pareto frontier extracted by the solution extraction unit 11, and calculates the identified intersection as a first optimal solution R. The first optimal solution R is a solution on the Pareto frontier. The first optimal solution R calculated here is presented to a decision maker via the interface unit 20.

[0045] Next, the decision maker checks the presented first optimal solution R, judges the above points (1) to (3), and inputs the judgment results to the solution search device 1 via the interface unit 20.

[0046] Next, the judgment unit 18 judges whether or not the judgment result indicates that the first optimal solution R presented in the above (1) is to be adopted (step ST5). As a result, if it is judged that the judgment result indicates that the first optimal solution R presented in the above (1) is to be adopted (step ST5; YES), the process ends. On the other hand, if it is judged that the judgment result does not indicate that the first optimal solution R presented in the above (1) is to be adopted (step ST5; NO), the process proceeds to step ST6.

[0047] In step ST6, the judgment unit 18 judges whether or not the judgment result indicates that the first optimal solution R is optimized based on the first aspiration level Q1 in the above (2) (step ST6). As a result, if it is judged that the judgment result indicates that the first optimal solution R is optimized based on the first aspiration level Q1 in the above (2) (step ST6; YES), the process proceeds to step ST7. On the other hand, if it is judged that the judgment result does not indicate that the first optimal solution R is optimized based on the first aspiration level Q1 in the above (2) (step ST6; NO), the process proceeds to step ST8.

[0048] In step ST7, the first optimization calculation unit 14 searches for a solution that is in the vicinity of the first optimal solution R in the solution space K and is different from the first optimal solution R. The first optimization calculation unit 14 presents the searched solution to the decision maker via the interface unit 20, and the decision maker determines whether or not to adopt the presented solution. Thereafter, the first optimization calculation unit 14 repeats the search for the above solution until the presented solution is adopted by the decision maker. Note that, at the point in time when the presented solution is adopted by the decision maker, the solution search device 1 ends the processing.

[0049] In step ST8, the judgment unit 18 judges whether or not the judgment result indicates that the first optimal solution R is to be adjusted within the range of the Pareto frontier in the above (3) (step ST8).

[0050] As a result, when it is determined in the above (3) that the above judgment result does not indicate that the first optimal solution R is to be adjusted within the range of the Pareto frontier (step ST8; NO), the aspiration level / ideal point setting unit 12 prompts the decision maker to re-input the first aspiration level Q1 via the interface unit 20. In response to this, the decision maker re-inputs the first aspiration level Q1 to the solution search device 1 via the interface unit 20. Thereafter, the processing returns to step ST3, and the aspiration level / ideal point setting unit 12 accepts the first aspiration level Q1 re-input by the decision maker via the interface unit 20, and sets the accepted first aspiration level Q1 on the solution space K. Thereafter, the solution search device 1 performs the processing from step ST3 onwards.

[0051] On the other hand, if it is determined in the above (3) that the above judgment result indicates that the first optimal solution R is to be adjusted within the range of the Pareto frontier (step ST8; YES), the process proceeds to step ST9.

[0052] In step ST9, the first optimal solution adjustment unit 15 adjusts the first optimal solution R within the range of the Pareto frontier (step ST9). For example, the first optimal solution adjustment unit 15 moves the first optimal solution R on the line PF indicating the frontier in the solution space K. At this time, the first optimal solution adjustment unit 15 accepts an adjustment amount (amount of movement) of the first optimal solution R from the decision maker, and moves it on the line PF indicating the frontier based on the accepted adjustment amount. As a result, the first optimal solution adjustment unit 15 calculates a second optimal solution different from the first optimal solution R. The first optimal solution (i.e., the second optimal solution) adjusted as described above is presented to the decision maker via the interface unit 20.

[0053] Next, the second aspiration level calculation unit 16 calculates a second aspiration level different from the first aspiration level Q1 based on the first optimal solution (i.e., the second optimal solution) adjusted by the first optimal solution adjustment unit 15 and the ideal point P1 (step ST10). The second aspiration level calculated here is presented to the decision maker via the interface unit 20.

[0054] Here, a calculation example of the second optimal solution and the second aspiration level is shown in Fig. 5. In Fig. 5, point P1 indicates the ideal point, point Q1 indicates the first aspiration level, and point R indicates the first optimal solution. Also in Fig. 5, point Q2 indicates the second aspiration level, and point R' indicates the second optimal solution.

[0055] 5, the first optimal solution adjustment unit 15 adjusts the first optimal solution R by moving the first optimal solution R on the line PF indicating the Pareto frontier based on the adjustment amount received from the decision maker. In this way, the first optimal solution adjustment unit 15 calculates a second optimal solution R' that is different from the first optimal solution R.

[0056] Further, the second aspiration level calculation unit 16 calculates a second aspiration level Q2, which is an aspiration level different from the first aspiration level Q1, based on the second optimal solution R' calculated by the first optimal solution adjustment unit 15 and the ideal point P1. A detailed calculation example of the second optimal solution R' and the second aspiration level Q2 will be described later.

[0057] Next, the decision maker checks the presented second optimal solution R′, judges the above points (4) to (6), and inputs the judgment results to the solution search device 1 via the interface unit 20.

[0058] Next, the judgment unit 18 judges whether or not the judgment result indicates that the presented second optimal solution R' is to be adopted in the above (4) (step ST11). As a result, if it is judged that the judgment result indicates that the presented second optimal solution R' is to be adopted in the above (4) (step ST11; YES), the process ends. On the other hand, if it is judged that the judgment result does not indicate that the presented second optimal solution R' is to be adopted in the above (4) (step ST11; NO), the process proceeds to step ST12.

[0059] In step ST12, the judgment unit 18 judges whether or not the judgment result indicates that the second optimal solution R' is optimized based on the second aspiration level Q2 in the above (5) (step ST6). As a result, if it is judged that the judgment result indicates that the second optimal solution R' is optimized based on the second aspiration level Q2 in the above (5) (step ST12; YES), the process proceeds to step ST13. On the other hand, if it is judged that the judgment result does not indicate that the second optimal solution R' is optimized based on the second aspiration level Q2 in the above (5) (step ST11; NO), the process proceeds to step ST14.

[0060] In step ST13, the second optimization calculation unit 17 searches for a solution that is in the vicinity of the second optimal solution R' in the solution space K and is different from the second optimal solution R'. The second optimization calculation unit 17 presents the searched solution to the decision maker via the interface unit 20, and the decision maker determines whether or not to adopt the presented solution. Thereafter, the second optimization calculation unit 17 repeats the search for the above solution until the presented solution is adopted by the decision maker. Note that, at the point in time when the presented solution is adopted by the decision maker, the solution search device 1 ends the processing.

[0061] In step ST14, the judgment unit 18 judges whether or not the judgment result indicates that the setting of the first aspiration level Q1 should be restarted in the above (6) (step ST14).

[0062] As a result, when it is determined that the above judgment result does not indicate that the setting of the first aspiration level Q1 should be started over in the above (6) (step ST14; NO), the first optimal solution adjustment unit 15 prompts the decision maker to re-input the adjustment amount via the interface unit 20. In response to this, the decision maker re-inputs the adjustment amount to the solution search device 1 via the interface unit 20. Thereafter, the process returns to step ST9, and the first optimal solution adjustment unit 15 accepts the adjustment amount re-input from the decision maker, and moves the first optimal solution R on the line PF indicating the Pareto frontier based on the accepted adjustment amount. Thereafter, the solution search device 1 performs the processes from step ST9 onwards.

[0063] On the other hand, if it is determined in the above (6) that the above judgment result indicates that setting of the first aspiration level Q1 should be started over (step ST14; YES), the aspiration level / ideal point setting unit 12 prompts the decision maker to re-input the first aspiration level Q1 via the interface unit 20. In response to this, the decision maker re-inputs the first aspiration level Q1 to the solution search device 1 via the interface unit 20. Thereafter, the processing returns to step ST3, and the aspiration level / ideal point setting unit 12 accepts the first aspiration level Q1 re-input by the decision maker via the interface unit 20, and sets the accepted first aspiration level Q1 in the solution space K. Thereafter, the solution search device 1 performs the processing from step ST3 onwards.

[0064] Next, a detailed calculation example of the second optimal solution R' and the second aspiration level Q2 will be described with reference to FIG.

[0065] In Fig. 6, the horizontal axis indicates the first objective function (g1), and the vertical axis indicates the second objective function (g2). Also in Fig. 6, point P1 indicates the ideal point, point Q1 indicates the first aspiration level, and point R indicates the first optimal solution. Also in Fig. 6, point Q2 indicates the second aspiration level, and point R' indicates the second optimal solution.

[0066] In addition, in Fig. 6, points C and D indicate solutions on the Pareto frontier. Here, points C and D are referred to as current solutions. In the example of Fig. 6, the first optimal solution R exists on the line segment connecting the current solution C and the current solution D.

[0067] In FIG. 6, the coordinates of each point in the solution space K are defined as follows: First optimal solution R:(x, y) Second optimal solution R´:(x´, y´) Ideal point P1: (x1, y1) First aspiration level Q1:(x0, y0) The second aspiration level Q2: (x´0, y´0) Current solution C: (x2, y2) Current solution D:(x3, y3)

[0068] Here, the first optimal solution adjustment unit 15 adjusts the first optimal solution R by moving the first optimal solution R on the line segment connecting the current solution C and the current solution D, and calculates a second optimal solution R' different from the first optimal solution R. At this time, the decision maker inputs the adjustment amount of the first optimal solution R as a coefficient t.

[0069] The coefficient t corresponds to the ratio between the length of the line segment connecting the current solution C and the current solution D in the solution space and the length of the line segment connecting the current solution C (or the current solution D) and the second optimal solution R', as shown in Fig. 6 for example. The decision maker inputs this coefficient t in the range of 0≦t≦1 via the interface unit 20. Then, the first optimal solution adjustment unit 15 uses the input coefficient t to calculate the second optimal solution R' according to the following formula (1). TIFF0007621575000001.tif15166

[0070] For example, when the coefficient t is 0, the second optimal solution R' is equal to the current solution C, but as the coefficient t increases from 0, the second optimal solution R' approaches the current solution D on the line segment connecting the current solution C and the current solution D. Then, when the coefficient t becomes 1, the second optimal solution R' becomes equal to the current solution D. Furthermore, when the coefficient t is set to 0.5, the second optimal solution R' is located at the midpoint between the current solution C and the current solution D on the line segment connecting the current solution C and the current solution D.

[0071] After the second optimal solution R' is calculated as described above, the second aspiration level calculation unit 16 calculates a second aspiration level Q2, which is an aspiration level different from the first aspiration level Q1, based on the calculated second optimal solution R' and the ideal point P1. For example, the second aspiration level calculation unit 16 calculates the second aspiration level Q2 by the following formula (2). TIFF0007621575000002.tif17166

[0072] In addition, in formula (2), 1-s is the ratio of the length of the line segment connecting the ideal point P1 and the current solution D to the length of the line segment connecting the ideal point P1 and point U. Note that point U can be uniquely determined as the intersection point of a line connecting the ideal point P1 and the current solution D and a line passing through the first aspiration level Q1 and parallel to the line segment connecting the current solution C and the current solution D. In other words, the second aspiration level calculation unit 16 calculates the second aspiration level Q2 by applying the relationship of the ratio of the line segments that holds between the ideal point P1, the current solution D, and point U to the relationship between the ideal point P1, the second optimal solution R', and the second aspiration level Q2.

[0073] In this way, the first optimal solution adjustment unit 15 calculates the second optimal solution R' by adjusting the first optimal solution R within the range of the Pareto frontier based on the coefficient t, which is the adjustment amount specified by the decision maker. The second aspiration level calculation unit 16 calculates the second aspiration level Q2 based on the second optimal solution R' calculated by the first optimal solution adjustment unit 15 and the ideal point P1. At this time, the first optimal solution adjustment unit 15 calculates the second optimal solution R' by adjusting the first optimal solution R within the range of the Pareto frontier, rather than changing the aspiration level setting from the first aspiration level to the second aspiration level and obtaining the second optimal solution based on the changed second aspiration level as in the conventional method, so that the efficiency of searching for the second optimal solution R' is improved compared to the conventional method. Therefore, the solution search device 1 can shorten the time required to obtain an optimal solution that satisfies the decision maker compared to the conventional method.

[0074] Next, a detailed example of calculation of the first optimal solution R, the second optimal solution R', and the second aspiration level Q2 will be described with reference to FIGS. 7 and 8, taking an example in which the solution space K is a three-dimensional space.

[0075] 7 and 8, the solution space K is a three-dimensional space. That is, there are three objective functions. As an example, the three objective functions are "age of building," "area," and "rent," and a multi-objective optimization problem intended to find a rental property that optimizes these three objective functions will be described below.

[0076] 7, point P1 indicates the ideal point, point Q1 indicates the first aspiration level, and point R indicates the first optimal solution. Also, in FIG. 7, symbol PF is a surface indicating the Pareto frontier, and points C to E indicate solutions (current solutions) on the Pareto frontier.

[0077] In FIG. 7, v1 indicates a vector from the ideal point P1 to the current solution C, v2 indicates a vector from the ideal point P1 to the current solution D, and v3 indicates a vector from the ideal point P1 to the current solution E. solindicates a vector from the ideal point P1 to the first optimal solution R. In this case, V sol is also called the first vector, and v1 to v3 are also called the second vector.

[0078] Even when the solution space K is a three-dimensional space, the solution search device 1 basically operates in the same way as when the solution space K is a two-dimensional space. For example, the first optimal solution calculation unit 13 calculates, in the solution space K, the intersection of a line connecting the ideal point P1 accepted by the aspiration level / ideal point setting unit 12 and the first aspiration level Q1 with a surface PF indicating the Pareto frontier as the first optimal solution R.

[0079] At this time, the vector V from the ideal point P1 to the first optimal solution R is sol can be expressed by the following equations (3) and (4) through the addition of v1, v2, and v3, where v1, v2, and v3 are assumed to be linearly independent. TIFF0007621575000003.tif10166 TIFF0007621575000004.tif10166

[0080] In this case, equations (5) to (7) can be obtained from equations (3) and (4). TIFF0007621575000005.tif21166 TIFF0007621575000006.tif23166 TIFF0007621575000007.tif43166

[0081] Here, (α, β, γ) expressed in formula (7) corresponds to the adjustment amount (coefficient t) when the above-mentioned solution space K is a two-dimensional space. In other words, when the solution space K is a three-dimensional space, the decision maker inputs the adjustment amount of the first optimal solution R as the value of (α, β, γ). Then, the first optimal solution adjustment unit 15 adjusts the first optimal solution R on the surface PF based on the input (α, β, γ) using formula (3) to generate a new V sol , i.e., the second optimal solution R' is calculated.

[0082] Similarly to the case where the solution space K is a two-dimensional space, the second aspiration level calculation unit 16 calculates a second aspiration level Q2, which is an aspiration level different from the first aspiration level Q1, based on the second optimal solution R' calculated by the first optimal solution adjustment unit 15 and the ideal point P1. For example, the second aspiration level calculation unit 16 calculates the second aspiration level Q2 by the following formula (8). TIFF0007621575000008.tif45166

[0083] In other words, in the solution space K, the ratio between the distance from the ideal point P1 to the first aspiration level Q1 and the distance from the ideal point P1 to the first optimal solution R is determined, and the second aspiration level calculation unit 16 calculates the second aspiration level Q2 using the determined ratio and the distance from the ideal point P1 to the second optimal solution R'.

[0084] In this way, when the solution space K is a three-dimensional space, the first optimal solution adjustment unit 15 calculates the second optimal solution R' by adjusting the first optimal solution R within the range of the Pareto frontier based on the above (α, β, γ) which are the adjustment amounts specified by the decision maker. Also, the second aspiration level calculation unit 16 calculates the second aspiration level Q2 based on the second optimal solution R' calculated by the first optimal solution adjustment unit 15 and the ideal point P1. Even in this case, the first optimal solution adjustment unit 15 does not change the aspiration level setting from the first aspiration level to the second aspiration level and obtain the second optimal solution based on the changed second aspiration level as in the conventional method, but calculates the second optimal solution R' by adjusting the first optimal solution R within the range of the Pareto frontier, so that the search efficiency of the second optimal solution R' is improved compared to the conventional method. Therefore, it is possible to shorten the time required to obtain an optimal solution that satisfies the decision maker compared to the conventional method.

[0085] Next, a hardware configuration example of the solution search device 1 according to the first embodiment will be described with reference to Fig. 9. The functions of the population generation unit 10, the solution extraction unit 11, the aspiration level / ideal point setting unit 12, the first optimal solution calculation unit 13, the first optimization calculation unit 14, the first optimal solution adjustment unit 15, the second aspiration level calculation unit 16, the second optimization calculation unit 17, the judgment unit 18, the display control unit 23, and the screen generation unit 24 in the solution search device 1 are realized by processing circuits. The processing circuit may be dedicated hardware as shown in Fig. 9A, or may be a CPU (also called a Central Processing Unit, a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a processor, or a DSP (DiP1tal Signal Processor)) 52 that executes a program stored in a memory 53 as shown in Fig. 9B.

[0086] When the processing circuit is a dedicated hardware, the processing circuit 51 corresponds to, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or a combination of these. The functions of each of the population generation unit 10, the solution extraction unit 11, the aspiration level / ideal point setting unit 12, the first optimal solution calculation unit 13, the first optimization calculation unit 14, the first optimal solution adjustment unit 15, the second aspiration level calculation unit 16, the second optimization calculation unit 17, the judgment unit 18, the display control unit 23, and the screen generation unit 24 may be realized by the processing circuit 51 individually, or the functions of each unit may be realized by the processing circuit 51 collectively.

[0087] When the processing circuit is a CPU 52, the functions of the population generation unit 10, the solution extraction unit 11, the aspiration level / ideal point setting unit 12, the first optimal solution calculation unit 13, the first optimization calculation unit 14, the first optimal solution adjustment unit 15, the second aspiration level calculation unit 16, the second optimization calculation unit 17, the judgment unit 18, the display control unit 23, and the screen generation unit 24 are realized by software, firmware, or a combination of software and firmware. The software and firmware are written as programs and stored in the memory 53. The processing circuit realizes the functions of each unit by reading and executing the programs recorded in the memory 53. That is, the solution search device 1 includes a memory for storing a program that, when executed by the processing circuit, results in the execution of each step shown in FIG. 2, for example. These programs can also be said to cause a computer to execute procedures and methods of the population generation unit 10, solution extraction unit 11, aspiration level / ideal point setting unit 12, first optimal solution calculation unit 13, first optimization calculation unit 14, first optimal solution adjustment unit 15, second aspiration level calculation unit 16, second optimization calculation unit 17, judgment unit 18, display control unit 23, and screen generation unit 24. Here, the memory 53 may be, for example, a non-volatile or volatile semiconductor memory such as a random access memory (RAM), a read only memory (ROM), a flash memory, an erasable programmable ROM (EPROM), or an electrically EPROM (EEPROM), a magnetic disk, a flexible disk, an optical disk, a compact disk, a mini disk, or a digital versatile disk (DVD).

[0088] The functions of the population generation unit 10, the solution extraction unit 11, the aspiration level / ideal point setting unit 12, the first optimal solution calculation unit 13, the first optimization calculation unit 14, the first optimal solution adjustment unit 15, the second aspiration level calculation unit 16, the second optimization calculation unit 17, the judgment unit 18, the display control unit 23, and the screen generation unit 24 may be partially realized by dedicated hardware and partially realized by software or firmware. For example, the population generation unit 10 may be realized by a processing circuit as dedicated hardware, and the functions of the solution extraction unit 11, the aspiration level / ideal point setting unit 12, the first optimal solution calculation unit 13, the first optimization calculation unit 14, the first optimal solution adjustment unit 15, the second aspiration level calculation unit 16, the second optimization calculation unit 17, the judgment unit 18, the display control unit 23, and the screen generation unit 24 may be realized by the processing circuit reading and executing a program stored in the memory 53.

[0089] Thus, the processing circuitry may implement the above-described functions through hardware, software, firmware, or a combination of these.

[0090] In the above description, an example has been described in which the solution search device 1 includes the population generation unit 10 and the solution extraction unit 11, and generates a population (a set of solutions) and extracts a frontier by the population generation unit 10 and the solution extraction unit 11. However, the solution search device 1 is not limited to this, and may acquire information about a frontier extracted in advance by an external device from the device, and perform processing using the acquired information about the frontier. In this case, the population generation unit 10 and the solution extraction unit 11 may be omitted.

[0091] In the above description, an example has been described in which the aspiration level / ideal point setting unit 12 receives an ideal point and a first aspiration level input by a decision maker via the interface unit 20, and sets the received ideal point and first aspiration level in the solution space. However, the aspiration level / ideal point setting unit 12 does not necessarily need to receive an ideal point and a first aspiration level from a decision maker. For example, the aspiration level / ideal point setting unit 12 may read out an ideal point and a first aspiration level that are set in advance in the solution search device 1, and set them in the solution space.

[0092] In addition, in the solution search device 1, each process of optimizing the first optimal solution R based on the first aspiration level Q1 (step ST7 in FIG. 2), calculating the second aspiration level Q2 (step ST10 in FIG. 2), and optimizing the second optimal solution R' based on the second aspiration level Q2 (step ST13 in FIG. 2) does not necessarily have to be performed. In addition, if each of these processes is omitted, in the solution search device 1, the first optimization calculation unit 14, the second aspiration level calculation unit 16, and the second optimization calculation unit 17 are not essential components and may be omitted.

[0093] As described above, according to the first embodiment, the solution search device 1 includes the aspiration level / ideal point setting unit 12 that sets the first aspiration level Q1, which is a target value for multiple objective functions in a multi-objective optimization problem, the first optimal solution calculation unit 13 that calculates a first optimal solution R using the first aspiration level Q1 set by the aspiration level / ideal point setting unit 12 and a frontier, which is a solution set for optimizing the multiple objective functions, and the first optimal solution adjustment unit 15 that, when receiving an instruction from a user not to adopt the first optimal solution R calculated by the first optimal solution calculation unit 13, receives an input of an adjustment amount for adjusting the first optimal solution R from the user and adjusts the first optimal solution R within the range of the frontier based on the received adjustment amount. As a result, the solution search device 1 according to the first embodiment can shorten the time required to obtain an optimal solution that satisfies a decision maker compared to the conventional art.

[0094] Furthermore, the first optimal solution adjustment unit 15 adjusts the first optimal solution R within the range of the frontier based on the adjustment amount, thereby calculating a second optimal solution R' different from the first optimal solution R. This allows the solution search device 1 according to the first embodiment to accurately calculate the second optimal solution R'.

[0095] Furthermore, when the solution space in the multi-objective optimization problem is a two-dimensional space, the first optimal solution calculation unit 13 calculates the intersection point between a line connecting the first aspiration level Q1 set by the aspiration level / ideal point setting unit 12 and an ideal point P1 indicating the optimal solution in all of the objective functions among the multiple objective functions, and a line indicating the frontier in the solution space, as the first optimal solution R, and the first optimal solution adjustment unit 15 adjusts the first optimal solution R calculated by the first optimal solution calculation unit 13 by moving the adjustment amount on the line indicating the frontier. As a result, the solution search device 1 according to the first embodiment can accurately calculate the first optimal solution R and the second optimal solution R' when the solution space is a two-dimensional space.

[0096] Furthermore, when the first optimal solution R is located between two current solutions that are solutions existing on a line indicating the frontier, the adjustment amount is given by the ratio between the length of the line segment connecting the two current solutions and the length of the line segment connecting one of the two current solutions and the adjusted first optimal solution R'. This allows the solution search device 1 according to the first embodiment to accurately calculate the second optimal solution R' based on the adjustment amount.

[0097] Furthermore, when the solution space in the multi-objective optimization problem is a three-dimensional space, the first optimal solution calculation unit 13 calculates the intersection of a line connecting the first aspiration level Q1 set by the aspiration level / ideal point setting unit 12 and the ideal point P1 indicating the optimal solution in all of the objective functions among the multiple objective functions, and a plane indicating the frontier in the solution space, as the first optimal solution R, and the first optimal solution adjustment unit 15 adjusts the first optimal solution R calculated by the first optimal solution calculation unit 13 by moving the adjustment amount on the plane indicating the frontier. As a result, the solution search device 1 according to the first embodiment can accurately calculate the first optimal solution R and the second optimal solution R' when the solution space is a three-dimensional space.

[0098] Furthermore, when the first optimal solution R is located on a plane that indicates the frontier and that includes the three current solutions that are solutions included in the frontier, the adjustment amount is given by a coefficient to be multiplied with each second vector when the first vector from the ideal point P1 to the adjusted first optimal solution R' is expressed as the sum of three second vectors from the ideal point P1 to each of the three current solutions. This allows the solution search device 1 according to the first embodiment to accurately calculate the second optimal solution R' based on the adjustment amount.

[0099] The solution search device 1 also includes a second aspiration level calculation unit 16 that calculates a second aspiration level Q2, which is an aspiration level different from the first aspiration level Q1, based on the first optimal solution R' adjusted by the first optimal solution adjustment unit 15 and an ideal point P1 that indicates the optimal solutions in all of the objective functions among the multiple objective functions. This allows the solution search device 1 according to the first embodiment to accurately calculate the second aspiration level Q2, which is an aspiration level different from the first aspiration level Q1.

[0100] Embodiment 2 In the first embodiment, a solution search device 1 is described that calculates a second optimal solution R' different from the first optimal solution R by adjusting the first optimal solution R within the range of the frontier based on an adjustment amount received from a decision maker. In the second embodiment, a solution search device 1 is described that has a GUI function for supporting the decision maker in inputting the adjustment amount.

[0101] A configuration example of the solution search device 1 according to the second embodiment is the same as the configuration example of the solution search device 1 according to the first embodiment shown in Fig. 1. In the second embodiment, the screen generator 24 generates data (hereinafter also referred to as "screen data") showing a support screen for supporting the decision maker in inputting an adjustment amount. The display controller 23 causes the display unit 22 to display the support screen shown by the screen data generated by the screen generator 24.

[0102] An example of the support screen is shown in Fig. 10. Here, as an example, a case where the objective functions in the multi-objective optimization problem are rent and age of the building will be described.

[0103] The support screen is configured to include, for example, as shown in FIG. 10, an ideal point etc. input area A1, a first optimal solution display area A2, an adjustment amount input area A3, a solution space display area A4, and a current solution display area A5.

[0104] The ideal point etc. input area A1 is an area for the decision maker to input the ideal point P1 and the first aspiration level Q1 to the solution search device 1. In the ideal point etc. input area A1, the item "rent_hope" indicates the first aspiration level for the rent, and the item "age of the building_hope" indicates the first aspiration level for the age of the building. The item "rent_ideal" indicates the ideal point for the rent, and the item "age of the building_ideal" indicates the ideal point for the age of the building. In the example of FIG. 10, the first aspiration level for the rent is "50,000 (yen)", the first aspiration level for the age of the building is "10 (years)", the ideal point for the rent is "28,000.00 (yen)", and the ideal point for the age of the building is "1.00 (years)".

[0105] In addition, an adjustment section (here, a slide button) for adjusting the ideal point P1 and the first aspiration level Q1 is displayed adjacent to each item. By appropriately operating this adjustment section, the decision maker can arbitrarily adjust the ideal point P1 and the first aspiration level Q1 while continuously changing the ideal point P1 and the first aspiration level Q1.

[0106] The first optimum solution display area A2 is an area where the first optimum solution R (displayed as "virtual solution" in the figure) calculated by the first optimum solution calculation unit 13 is displayed.

[0107] The adjustment amount input area A3 is an area for the decision maker to input the adjustment amount, that is, the coefficient t. Note that, although the coefficient t is set to "0.70" in the example of Fig. 10, this value may be set in advance in the solution search device 1 as an initial value.

[0108] Also, an adjustment section (here, a slide button) for adjusting the coefficient t is displayed adjacent to the item. By appropriately operating this adjustment section, the decision maker can adjust the coefficient t as desired while continuously changing the value of the coefficient t. Note that the adjustment amount input area A3 also displays the optimal solution after adjustment (i.e., the second optimal solution R') and the desired solution after adjustment (i.e., the second aspiration level Q2).

[0109] The solution space display area A4 is an area for displaying the solution space. In the example of FIG. 10, a two-dimensional solution space defined by the building age on the horizontal axis and the rent on the vertical axis is displayed. The solution space displayed in the solution space display area A4 displays the Pareto frontier extracted by the solution extraction unit 11, the solutions on the Pareto frontier, the ideal point P1, the first aspiration level Q1, the second aspiration level Q2, the first optimal solution R, the second optimal solution R', and the like. The decision maker can intuitively grasp each of the above values ​​through this solution space display area A4.

[0110] The current solution display area A5 is an area for displaying the current solutions. Here, among the solutions constituting the Pareto frontier, two solutions (current solutions 1 and 2) that are particularly close to the first aspiration level Q1 are displayed as the current solutions.

[0111] Next, a transition example of the support screen will be described. First, when the Pareto frontier is extracted by the solution extractor 11, the screen generator 24 generates screen data in which the Pareto frontier is displayed on the solution space in the solution space display area A4. The display controller 23 causes the display unit 22 to display the support screen indicated by the generated screen data.

[0112] Next, the decision maker inputs an ideal point P1 and a first aspiration level Q1 from the ideal point etc. input area A1 of the displayed support screen. In response to this input, the first optimal solution calculation unit 13 calculates a first optimal solution R. At this time, the screen generation unit 24 updates the previously generated screen data. The updated screen data is screen data in a state in which the first optimal solution R is displayed in the first optimal solution display area A2, the first optimal solution R is displayed on the solution space in the solution space display area A4, and the current solution is displayed in the current solution display area A5. Then, the display control unit 23 causes the display unit 22 to display the support screen indicated by the updated screen data.

[0113] Next, the decision maker determines whether or not to adopt the first optimal solution R. If the decision is made not to adopt the first optimal solution R and not to optimize the first optimal solution R based on the first aspiration level Q1, the decision maker inputs a coefficient t as an adjustment amount from the adjustment amount input area A3.

[0114] Upon receiving this input, the first optimal solution adjustment unit 15 adjusts the first optimal solution R within the range of the Pareto frontier based on the coefficient t. As a result, the first optimal solution adjustment unit 15 calculates the second optimal solution R'. In addition, the second aspiration level calculation unit 16 calculates the second aspiration level Q2.

[0115] At this time, the screen generation unit 24 re-updates the previously updated screen data. The re-updated screen data is screen data in a state in which the adjusted optimal solution (i.e., the second optimal solution R') and the adjusted desired solution (i.e., the second aspiration level Q2) are displayed in the adjustment amount input area A3, and the second optimal solution R' and the second aspiration level Q2 are displayed on the solution space in the solution space display area A4. The display control unit 23 causes the display unit 22 to display the support screen indicated by the re-updated screen data.

[0116] In this way, in the second embodiment, a support screen for supporting the decision maker in inputting the adjustment amount can be generated and displayed. This allows the decision maker to easily input the adjustment amount, reducing the operational burden. In addition, the decision maker can easily input the ideal point P1 and the first aspiration level Q1 via the support screen.

[0117] Note that the configuration example of the support screen shown in Fig. 10 is merely one example. For example, the layout of the above-mentioned areas A1 to A5 may be other than the above. In addition, in the above description, an example has been described in which the adjustment units displayed in the ideal point input area A1 and the adjustment amount input area A3 are configured with slide buttons, but the adjustment units are not limited to this and may be configured with elements other than slide buttons.

[0118] As described above, according to the second embodiment, the solution search device 1 includes the screen generation unit 24 that generates data showing a support screen for supporting the decision maker in inputting an adjustment amount, and the display control unit 23 that causes the display unit 22 to display the support screen shown by the data generated by the screen generation unit 24. Thus, the solution search device 1 according to the second embodiment can reduce the operational burden on the decision maker in addition to the effects of the first embodiment.

[0119] The support screen also includes an adjustment amount input area A3 in which the decision maker can input an adjustment amount and in which the first optimal solution R' adjusted by the first optimal solution adjustment unit 15 based on the input adjustment amount can be displayed. This allows the solution search device 1 according to the second embodiment to reduce the burden on the decision maker of inputting the adjustment amount. Furthermore, the decision maker can easily check the adjusted first optimal solution R'.

[0120] The support screen also includes an ideal point etc. input area A1 in which the decision maker can input the first aspiration level Q1 and an ideal point P1 indicating the optimal solution for all of the objective functions among the multiple objective functions. This allows the solution search device 1 according to the second embodiment to reduce the burden on the decision maker of inputting the ideal point P1 and the first aspiration level Q1.

[0121] Embodiment 3 In the first embodiment, the case where the frontier is the Pareto frontier has been described as an example. In the third embodiment, the case where the frontier is the efficient frontier will be described as an example.

[0122] A configuration example of the solution search device 1 according to the third embodiment is the same as the configuration example of the solution search device 1 according to the first embodiment shown in Fig. 1. In the third embodiment, the solution extraction unit 11 extracts the efficient frontier by using Data Envelopment Analysis (DEA) instead of the Pareto Frontier.

[0123] Data Envelopment Analysis (DEA) is a tool for measuring the management efficiency of a business entity (DMU: Decision Making Unit) with a multi-input multi-output system. It is assumed that the production activity of a business entity involves some input (input) and some revenue (output), and evaluates the conversion efficiency with a one-dimensional scale called the efficiency value.

[0124] For example, a case of calculating efficiency values ​​of eight business entities (A to J) having two objective functions g1 and g2 will be described with reference to Fig. 11. In Fig. 11, the horizontal axis indicates the first objective function (g1), and the vertical axis indicates the second objective function (g2).

[0125] In Figure 11, the further down to the left (the origin) the business entity is, the more productive its activities are. In data envelopment analysis (DEA), the efficient frontier in Figure 11 is taken as the Pareto optimal solution, and each business entity is evaluated by measuring how far it is from this efficient frontier.

[0126] In this case, business entities that are on the frontier are judged to be conducting efficient activities and are given an evaluation value of 1 (=100%). Conversely, business entities that are not on the frontier are judged to be conducting inefficient activities and are given an evaluation value of less than 1. In this case, the standard for evaluating each business entity is given as a frontier rather than a single point (any one of the Pareto solutions), making it possible to perform evaluations that take into account the characteristics of each business entity.

[0127] When extracting the efficient frontier, the solution extraction unit 11 calculates the efficiency value of each solution (each business entity in the above example) existing in the solution space. At this time, the efficiency value calculation method includes, for example, the CCR (Chames Cooper Rhodes) model and the ultra-CCR model.

[0128] The CCR model is a method for quantitatively evaluating efficiency values ​​that was proposed by Chames Cooper Rhodes in 1978. This method is well known, so a detailed explanation will be omitted, but in this method, the upper limit of the efficiency value is set to 1, and the efficient frontier is found.

[0129] For example, in the example of Fig. 12, the efficiency value θ of business entity H is calculated by θ = OP / OH. Then, based on the following formula (9), business entities that maximize this θ (θ = 1) are extracted, and the efficient frontier is obtained from the extraction results. In formula (9), x indicates input, y indicates output, and u and v indicate weights. TIFF0007621575000009.tif44166

[0130] On the other hand, the Ultra CCR model is a model in which each business entity is removed from the constraints of the CCR model, and efficiency values ​​are allowed to exceed 1. The frontier surface that serves as the basis for evaluation collapses, but business entities that were on the frontier in the CCR model can now calculate efficiency values ​​of 1 or more.

[0131] For example, in the example of Fig. 13, the efficiency value θ of business entity D is calculated by θ = OP / OD. Then, based on the following formula (10), business entities that maximize this θ (θ can be 1 or more) are extracted, and the efficient frontier is found from the extraction results. TIFF0007621575000010.tif44166

[0132] Although the CCR (Chames Cooper Rhodes) model and the ultra-CCR model have been described as examples of methods for calculating the efficiency value here, the method for calculating the efficiency value is not limited to these, and other methods may also be used.

[0133] In this way, the solution extraction unit 11 in the third embodiment extracts an efficient frontier by using data envelopment analysis (DEA) instead of the Pareto frontier. As a result, in the third embodiment, solutions with an efficiency value of 1 or more can be extracted as the frontier, and the number of solutions to be used as the frontier can be reduced compared to the first embodiment in which the Pareto frontier is extracted. Also, in the third embodiment, since the number of solutions to be used as the frontier can be reduced compared to the first embodiment, interpretation of the solutions becomes easier.

[0134] As described above, according to the third embodiment, the solution search device 1 includes the solution extraction unit 11 that uses data envelope analysis to extract an efficient frontier as a frontier from a solution set existing in a solution space for a multi-objective optimization problem, and the first optimal solution calculation unit 13 calculates a first optimal solution R using the first aspiration level Q1 set by the aspiration level / ideal point setting unit 12 and the efficient frontier extracted by the solution extraction unit 11. As a result, the solution search device 1 according to the third embodiment can reduce the number of solutions to be used as a frontier compared to the first embodiment, in addition to the effects of the first embodiment.

[0135] Embodiment 4 In the first embodiment, an example was described in which a second optimal solution R' different from the first optimal solution R is calculated by adjusting the first optimal solution R within the range of the frontier based on the adjustment amount received from the decision maker. In the fourth embodiment, an example is described in which, when the decision maker is not satisfied with the second optimal solution R' obtained by the above adjustment, a new aspiration level (second aspiration level) is presented to the decision maker and the second optimal solution R' is calculated from this new aspiration level.

[0136] Fig. 14 is a diagram showing a configuration example of the solution search device 1 according to embodiment 4. The solution search device 1 according to embodiment 4 additionally includes an aspiration level frontier calculation unit 31, a first aspiration level adjustment unit 32, and a second optimal solution calculation unit 33, in comparison with the solution search device 1 according to embodiment 1 shown in Fig. 1. The other configuration of the solution search device 1 according to embodiment 4 is the same as that of the solution search device 1 according to embodiment 1 shown in Fig. 1, so the same reference numerals are used and the description thereof will be omitted.

[0137] When the aspiration-level frontier calculation unit 31 receives an instruction from a decision maker not to adopt the first optimal solution (i.e., the second optimal solution) R' adjusted by the first optimal solution adjustment unit 15, it uses the above frontier and the first aspiration level Q1 set by the aspiration-level / ideal point setting unit 12 to calculate an aspiration-level frontier, which is a set of aspiration-level candidates including the first aspiration level Q1.

[0138] Here, an example of the calculation of the aspiration-level frontier by the aspiration-level frontier calculation unit 31 is shown in Fig. 15. When the solution space in a multi-objective optimization problem is a two-dimensional space, for example as shown in Fig. 15, the aspiration-level frontier calculation unit 31 calculates the aspiration-level frontier shown by a line obtained by enlarging the line showing the Pareto frontier by a predetermined magnification.

[0139] For example, the aspiration level frontier calculation unit 31 draws a line that passes through the first aspiration level Q1 and shows the Pareto frontier, projected at a predetermined magnification in the right-back direction (the direction of the first aspiration level Q1) on the solution space. The line QF drawn at this time is the line showing the aspiration level frontier. At this time, the curvature of the bent part of the line QF is approximately equal to the curvature of the bent part of the line showing the Pareto frontier.

[0140] The first aspiration level adjustment unit 32 receives input of an adjustment amount for adjusting the first aspiration level Q1 from the decision maker, and calculates the second aspiration level Q2 by adjusting the first aspiration level Q1 within the range of the aspiration level frontier based on the received adjustment amount.

[0141] The second optimal solution calculation unit 33 calculates a second optimal solution R' different from the first optimal solution R, using the second aspiration level Q2 calculated by the first aspiration level adjustment unit 32 and the above-mentioned frontier.

[0142] Next, a calculation example of the second optimal solution R' and the second aspiration level Q2 in the fourth embodiment will be described with reference to Fig. 16. In Fig. 16, the horizontal axis indicates the first objective function (g1), and the vertical axis indicates the second objective function (g2). Also in Fig. 16, point P1 indicates the ideal point, point Q1 indicates the first aspiration level, and point R indicates the first optimal solution. Also in Fig. 16, point Q2 indicates the second aspiration level, and point R' indicates the second optimal solution.

[0143] 16, points C and D indicate solutions (current solutions) on the Pareto frontier. In the example of FIG. 16, the first optimal solution R exists on the line segment connecting the current solution C and the current solution D. In addition, in FIG. 16, the line segment connecting points Q1 and Q2 is a part of the line indicating the aspiration level frontier calculated by the aspiration level frontier calculation unit 31.

[0144] In FIG. 16, the coordinates of each point in the solution space K are defined as follows: First optimal solution R:(x, y) Second optimal solution R´:(x´, y´) Ideal point P1: (x1, y1) First aspiration level Q1:(x0, y0) The second aspiration level Q2: (x´0, y´0) Current solution C: (x2, y2) Current solution D:(x3, y3)

[0145] Here, the first aspiration level adjustment unit 32 adjusts the first aspiration level Q1 by moving the first aspiration level Q1 on the line segment indicating the aspiration level frontier, and calculates a second aspiration level Q2 different from the first aspiration level Q1. At this time, the decision maker inputs, via the interface unit 20, one of the values ​​(x, y) of the two objective functions that determine the second aspiration level Q2, as the adjustment amount of the first aspiration level Q1.

[0146] For example, the decision maker inputs the value of the x-coordinate as an adjustment amount among the x-coordinate and y-coordinate that define the second aspiration level Q2. At this time, since the slope of the line segment connecting the current solution C and the current solution D is equal to the slope of the line segment connecting the points Q1 and Q2 (both are (y3-y2) / (x3-x2)), if the decision maker only inputs the value of the x-coordinate of the second aspiration level Q2, the first aspiration level adjustment unit 32 can calculate the value of the y-coordinate of the second aspiration level Q2 using the following formula (11). TIFF0007621575000011.tif36166

[0147] Alternatively, the decision maker may input the value of the y coordinate of the second aspiration level Q2 as the adjustment amount. In this case, the first aspiration level adjustment unit 32 can calculate the x coordinate of the second aspiration level Q2 using the following formula (12). TIFF0007621575000012.tif12166

[0148] In this way, the decision maker only needs to input at least one of the x and y coordinates that define the second aspiration level Q2, i.e., the value of at least one of the two objective functions, as an adjustment amount, and the first aspiration level adjustment unit 32 can calculate the second aspiration level Q2. Therefore, the burden of input operations on the decision maker is reduced.

[0149] Then, when the second aspiration level Q2 is calculated as described above, the second optimal solution calculation unit 33 calculates the second optimal solution R' by the following formula (13). TIFF0007621575000013.tif16166

[0150] In addition, in formula (13), 1-s is the ratio of the length of the line segment connecting the ideal point P1 and the current solution D to the length of the line segment connecting the ideal point P1 and point U. Note that point U can be uniquely determined as the intersection point of the line segment connecting the ideal point P1 and the current solution D and the line segment indicating the aspiration level frontier. In other words, the second optimal solution calculation unit 33 calculates the second optimal solution R' by applying the relationship of the ratio of the line segments that holds between the ideal point P1, the current solution D, and point U to the relationship between the ideal point P1, the second optimal solution R', and the second aspiration level Q2.

[0151] In this way, in the fourth embodiment, an aspiration level frontier is generated, and the first aspiration level Q1 is adjusted within the range of this aspiration level frontier to calculate the second aspiration level Q2. Then, the second optimal solution R' is calculated from this second aspiration level Q2. This means that the second optimal solution R' is calculated using an approach different from that of the first embodiment. As a result, even if a satisfactory solution cannot be obtained even if the first optimal solution R is adjusted within the range of the frontier, the decision maker can obtain the second optimal solution R' using a different approach, that is, by adjusting the first aspiration level Q1 within the range of the aspiration level frontier. In addition, at this time, the decision maker only needs to input at least one of the x-coordinate and y-coordinate values ​​that determine the second aspiration level Q2 as the adjustment amount of the first aspiration level Q1, so the load of the input operation is light.

[0152] In the above explanation, it is assumed that the decision maker adjusts the first optimal solution R within the range of the frontier. However, the decision maker is not limited to this, and may generate the aspiration level frontier and adjust the first aspiration level Q1 without adjusting the first optimal solution R within the range of the frontier.

[0153] As described above, according to the fourth embodiment, the solution search device 1 includes an aspiration-level frontier calculation unit 31 that, when receiving an instruction from a decision maker not to adopt the first optimal solution R' adjusted by the first optimal solution adjustment unit 15, calculates an aspiration-level frontier, which is a set of aspiration-level candidates including the first aspiration level Q1, using the above frontier and the first aspiration level Q1 set by the aspiration-level / ideal point setting unit 12; a first aspiration-level adjustment unit 32 that receives an input of an adjustment amount for adjusting the first aspiration level Q1 from the decision maker and calculates a second aspiration level Q2 by adjusting the first aspiration level Q1 within the range of the aspiration-level frontier based on the received adjustment amount; and a second optimal solution calculation unit 33 that calculates a second optimal solution R' different from the first optimal solution R, using the second aspiration level Q2 calculated by the first aspiration-level adjustment unit 32 and the above frontier. As a result, the solution search device 1 according to the fourth embodiment has the same effect as the first embodiment, and further has the following effect by adjusting the first aspiration level Q1: Then, a second aspiration level Q2 can be obtained. Also, a new optimal solution R' can be calculated based on the obtained second aspiration level Q2.

[0154] Furthermore, when the solution space in the multi-objective optimization problem is a two-dimensional space, the aspiration level frontier calculation unit 31 calculates the aspiration level frontier indicated by the line QF obtained by enlarging the line indicating the frontier by a predetermined magnification. This allows the solution search device 1 according to the fourth embodiment to easily generate the aspiration level frontier.

[0155] Moreover, the adjustment amount is given by the value of one of the two objective functions that determine the second aspiration level Q2. This enables the solution search device 1 according to the fourth embodiment to reduce the burden of input operations on the decision maker.

[0156] Embodiment 5. In the fifth embodiment, a specific method of optimization calculation by the first optimization calculation unit 14 and the second optimization calculation unit 17 will be described. A configuration example of the solution search device 1 according to the fifth embodiment is the same as the configuration example of the solution search device 1 according to the first embodiment shown in FIG.

[0157] When a decision maker determines to optimize the first optimal solution R based on the first aspiration level Q1, the first optimization calculation unit 14 searches for a solution that is in the vicinity of the first optimal solution R in the solution space K and is different from the first optimal solution R. At this time, the first optimization calculation unit 14 converts the multi-objective optimization problem into a single-objective optimization problem based on the ideal point P1, the first aspiration level Q1, and the first optimal solution R, thereby determining a search area for a solution and performing a focused search for a solution in the search area.

[0158] Similarly, when a decision maker determines to optimize the second optimal solution R' based on the second aspiration level Q2, the second optimization calculation unit 17 searches for a solution that is in the vicinity of the second optimal solution R' in the solution space K and is different from the second optimal solution R'. At this time, the second optimization calculation unit 17 converts the multi-objective optimization problem into a single-objective optimization problem based on the ideal point P1, the second aspiration level Q2, and the second optimal solution R', thereby determining a search area for a solution and performing an intensive search for a solution in the search area.

[0159] The basic solution search method used by the first optimization calculation unit 14 and the second optimization calculation unit 17 is similar, so the basic solution search method used by the second optimization calculation unit 17 will be described here as an example.

[0160] First, the second optimization calculation unit 17 sets a region (hereinafter also referred to as a "reference region") in the solution space K that includes the second optimal solution R', and sets a region (hereinafter also referred to as an "extended region") in the solution space K that is an extension of this reference region to a predetermined range. Then, the second optimization calculation unit 17 randomly samples multiple solutions included in this extended region, and calculates an evaluation value for each of the obtained solutions.

[0161] An example of this case is shown in Fig. 17. For example, in Fig. 17, R' is the second optimal solution, K1 is the reference region, and K2 is the extended region. Also, gi is a sampled solution included in the extended region K2.

[0162] The second optimization calculation unit 17 calculates an evaluation value Vn,i of the sampled solution g i by using, for example, the following equation (14). TIFF0007621575000014.tif28166

[0163] That is, the second optimization calculation unit 17 calculates an evaluation value Vn,i for each solution gi based on how far each solution gi is from the second aspiration level Q2 in the solution space K. Here, the farther a solution gi is from the second aspiration level Q2 (the closer a solution gi is to the ideal point P1), the higher the evaluation value Vn,i that is calculated.

[0164] Then, the second optimization calculation unit 17 selects a predetermined number of solutions gi with top evaluation values ​​Vn,i. Then, as shown in Fig. 18, the second optimization calculation unit 17 sets a predetermined region in the solution space including each selected solution gi as a new search region K3, and randomly samples a plurality of solutions gi' included in this search region K3. Then, the solutions gi' sampled from the search region K3 are presented to a decision maker via the interface unit 20, and the decision maker judges whether or not to adopt each of the presented solutions gi'.

[0165] Thus, in the fifth embodiment, the second optimization calculation unit 17 converts the multi-objective optimization problem into a single-objective optimization problem by calculating the evaluation value Vn,i based on the ideal point P1 and the second aspiration level Q2 for the solutions gi sampled from the extended region K2 including the second optimal solution R'. Then, the second optimization calculation unit 17 selects a predetermined number of solutions gi with the highest evaluation values ​​Vn,i, sets a predetermined region in the solution space including each of the selected solutions gi as a new search region K3, and focuses on searching for the solutions gi' included in this search region K3. As a result, in the fifth embodiment, it is possible to focus on searching for solutions close to the decision maker's preferences.

[0166] The solution search method by the first optimization calculation unit 14 is basically the same as the solution search method by the above-mentioned second optimization calculation unit 17. In the case of the first optimization calculation unit 14, in the above explanation, the second optimal solution R' should be read as the first optimal solution R, and the second aspiration level Q2 should be read as the first aspiration level Q1.

[0167] As described above, according to the fifth embodiment, the solution search device 1 includes the second optimization calculation unit 17 that searches for solutions present in the peripheral area of ​​the adjusted first optimal solution R' in the solution space K of the multi-objective optimization problem when an instruction not to adopt the first optimal solution R' adjusted by the first optimal solution adjustment unit 15 is received from a decision maker. In this way, the solution search device 1 according to the fifth embodiment can focus on searching for solutions close to the preferences of the decision maker, in addition to the effects of the first embodiment.

[0168] Furthermore, the second optimization calculation unit 17 calculates evaluation values ​​of solutions existing in a peripheral area of ​​the adjusted first optimal solution R' based on the second aspiration level Q2 and the ideal point P1, and further searches around a predetermined number of solutions having the highest calculated evaluation values. In this way, the solution search device 1 according to the fifth embodiment can convert a multi-objective optimization problem into a single-objective optimization problem using the evaluation values, and can focus on searching for solutions close to the decision maker's preferences.

[0169] Embodiment 6 In the sixth embodiment, a description will be given of another example of a specific technique for optimization calculation by the first optimization calculation unit 14 and the second optimization calculation unit 17. The configuration example of the solution search device 1 according to the sixth embodiment is the same as the configuration example of the solution search device 1 according to the first embodiment shown in FIG.

[0170] When a decision maker determines to optimize the first optimal solution R based on the first aspiration level Q1, the first optimization calculation unit 14 searches for a solution that is in the vicinity of the first optimal solution R in the solution space K and is different from the first optimal solution R. At this time, the first optimization calculation unit 14 determines a search area for solutions using the first aspiration level Q1 as a reference point, and performs an intensive search for solutions in the search area.

[0171] Similarly, when a decision maker determines to optimize the second optimal solution R' based on the second aspiration level Q2, the second optimization calculation unit 17 searches for a solution that is in the vicinity of the second optimal solution R' but different from the second optimal solution R' in the solution space K. At this time, the second optimization calculation unit 17 determines a search area for solutions using the second aspiration level Q2 as a reference point, and performs an intensive search for solutions in the search area.

[0172] The basic solution search method used by the first optimization calculation unit 14 and the second optimization calculation unit 17 is similar, so the basic solution search method used by the second optimization calculation unit 17 will be described here as an example.

[0173] First, the second optimization calculation unit 17 sets the second aspiration level Q2 as a reference point in the solution space. Then, the second optimization calculation unit 17 sets a region in the solution space that can include the region (reference region) containing the second optimal solution R' and that is within a predetermined distance from the reference point as a new search region K4, and focuses on searching for solutions g i ' contained in this search region K4. Then, the searched solutions g i ' are presented to the decision maker via the interface unit 20, and the decision maker judges whether or not to adopt each of the presented solutions g i '.

[0174] Thus, in the sixth embodiment, the second optimization calculation unit 17 sets the second aspiration level Q2 as a reference point in the solution space, sets a search area K4 based on the distance from this reference point, and searches with a focus on solutions gi' included in this search area K4. This makes it possible to search with a focus on solutions close to the decision maker's preferences in the sixth embodiment.

[0175] The solution search method by the first optimization calculation unit 14 is basically the same as the solution search method by the above-mentioned second optimization calculation unit 17. In the case of the first optimization calculation unit 14, in the above explanation, the second optimal solution R' should be read as the first optimal solution R, and the second aspiration level Q2 should be read as the first aspiration level Q1.

[0176] As described above, according to the sixth embodiment, the second optimization calculation unit 17 uses the second aspiration level Q2 as a reference point, and searches for an area in the vicinity of the adjusted first optimal solution R', in which the distance from the reference point in the solution space K is within a predetermined value. Thus, in the sixth embodiment, in addition to the effect of the first embodiment, it is possible to focus on searching for solutions close to the decision maker's preferences.

[0177] Finally, a description will be given of an application example of the solution searching device 1 according to the present disclosure. The solution searching device 1 according to the present disclosure can be applied to, for example, an air conditioning optimization system.

[0178] For example, a building manager may change the temperature setting of the air conditioning system based on past power consumption data, and manage daily power consumption so as not to exceed the target value. In this case, the manager may be concerned that suppressing power consumption may reduce the comfort (=thermal comfort) of the office. Therefore, the manager may set an appropriate desired level for the air conditioning optimization system, taking into account thermal comfort and allowable power consumption.

[0179] On the other hand, an air-conditioning optimization system calculates an optimal solution based on an aspiration level set by a manager in a multi-objective optimization problem in which thermal comfort is a first objective function and power consumption is a second objective function, and presents the solution to the manager. The solution search device 1 according to the present disclosure can be applied to an air-conditioning optimization system used in such a situation.

[0180] Furthermore, the solution searching device 1 according to the present disclosure can be applied to, for example, a surveillance camera placement optimization system.

[0181] For example, surveillance cameras (hereinafter also referred to as "cameras") are installed everywhere, such as in commercial facilities, inside train stations, and throughout the city. In general, cameras are installed to capture signs of crimes, accidents, fights, and other incidents to prevent them before they occur, or to check whether an incident has occurred and grasp the situation at the scene. Therefore, cameras need to be placed so that they can reliably capture the situation, such as what has happened when an incident occurs, or what is currently happening. On the other hand, increasing the number of cameras not only increases costs, but also may increase the burden of maintaining and managing the cameras.

[0182] Therefore, the administrator of the camera placement optimization system takes into consideration the areas that need to be monitored with priority (for example, areas that are prone to blind spots) and the acceptable number of cameras, and sets an appropriate desired level for the camera placement optimization system.

[0183] On the other hand, a camera placement optimization system calculates an optimal solution based on an aspiration level set by an administrator in a multi-objective optimization problem in which the surveillance range of the cameras is a first objective function and the number of cameras is a second objective function, and presents the solution to the administrator. The solution search device 1 according to the present disclosure can be applied to a camera placement optimization system used in such a situation.

[0184] In addition, the present disclosure allows free combination of the respective embodiments, modification of any of the components of each embodiment, or omission of any of the components of each embodiment. [Industrial Applicability]

[0185] The present disclosure makes it possible to reduce the time required to obtain an optimal solution that satisfies a decision maker, and is suitable for use in a solution search device and a solution search method. [Explanation of symbols]

[0186] 1 Solution search device, 10 Population generation unit, 11 Solution extraction unit, 12 Aspiration level / ideal point setting unit, 13 First optimal solution calculation unit, 14 First optimization calculation unit, 15 First optimal solution adjustment unit, 16 Second aspiration level calculation unit, 17 Second optimization calculation unit, 18 Judgment unit, 20 Interface unit, 21 Input unit, 22 Display unit, 23 Display control unit, 24 Screen generation unit, 31 Aspiration level frontier calculation unit, 32 First aspiration level adjustment unit, 33 Second optimal solution calculation unit, 51 Processing circuit, 52 CPU, 53 Memory, A1 Ideal point etc. input area, A2 First optimal solution display area, A3 Adjustment amount input area, A4 Solution space display area, A5 Solution display area, C Current solution, D Current solution, g1 Objective function, g2 Objective function, gi Solution, gi´ Solution, K Solution space, K2 expansion region, K3 search region, K4 search region, P1 ideal point, PF line or surface representing the frontier, Q1 first aspiration level, Q2 second aspiration level, R first optimal solution, R´ second optimal solution.

Claims

1. a setting unit that sets a first aspiration level, which is a target value for a plurality of objective functions in a multi-objective optimization problem; a first optimal solution calculation unit that calculates a first optimal solution by using the first aspiration level set by the setting unit and a frontier that is a solution set for optimizing the plurality of objective functions; a first optimal solution adjustment unit that, when receiving an instruction from a user not to adopt the first optimal solution calculated by the first optimal solution calculation unit, receives an input of an adjustment amount for adjusting the first optimal solution from the user, and adjusts the first optimal solution within a range of the frontier based on the received adjustment amount; A solution search device comprising:

2. The first optimal solution adjustment unit A second optimal solution different from the first optimal solution is calculated by adjusting the first optimal solution within the range of the frontier based on the adjustment amount.

2. The solution search device according to claim 1.

3. When the solution space in the multi-objective optimization problem is a two-dimensional space, The first optimal solution calculation unit calculating, as a first optimal solution, an intersection point between a line connecting the first aspiration level set by the setting unit and an ideal point indicating an optimal solution for all of the objective functions among the plurality of objective functions, and a line indicating the frontier in the solution space; The first optimal solution adjustment unit The adjustment is performed by moving the first optimal solution calculated by the first optimal solution calculation unit by the adjustment amount on the line indicating the frontier.

3. The solution search device according to claim 1 or 2.

4. The first optimal solution is When the solution is located between two current solutions that are on the line indicating the frontier, The adjustment amount is given by the ratio between the length of a line segment connecting the two current solutions and the length of a line segment connecting one of the two current solutions and the first optimal solution after the adjustment.

4. The solution search device according to claim 3.

5. When the solution space in the multi-objective optimization problem is a three-dimensional space, The first optimal solution calculation unit calculating, as a first optimal solution, an intersection point between a line connecting the first aspiration level set by the setting unit and an ideal point indicating an optimal solution for all of the objective functions among the plurality of objective functions, and a surface indicating the frontier in the solution space; The first optimal solution adjustment unit The adjustment is performed by moving the first optimal solution calculated by the first optimal solution calculation unit by the adjustment amount on a plane indicating the frontier.

3. The solution search device according to claim 1 or 2.

6. The first optimal solution is When the solution is located on a surface that represents the frontier and includes three current solutions that are included in the frontier, The adjustment amount is When a first vector leading from the ideal point to the first optimal solution after the adjustment is expressed as a sum of three second vectors leading from the ideal point to each of the three current solutions, the coefficient is given by multiplying each of the second vectors.

6. The solution search device according to claim 5.

7. a first optimal solution adjusted by the first optimal solution adjustment unit; and and a second aspiration level calculation unit that calculates a second aspiration level that is different from the first aspiration level, based on an ideal point that indicates an optimal solution for all of the objective functions among the plurality of objective functions.

3. The solution search device according to claim 1 or 2.

8. a screen generating unit that generates data showing a support screen for supporting the user in inputting the adjustment amount; a display control unit that causes a support screen indicated by the data generated by the screen generation unit to be displayed on a display unit; 3. The solution search device according to claim 1, further comprising:

9. The support screen includes: a region in which the user can input the adjustment amount and in which a first optimal solution adjusted by the first optimal solution adjustment unit based on the input adjustment amount can be displayed; 9. The solution searching device according to claim 8.

10. The support screen includes: an area in which the user can input the first aspiration level and an ideal point that indicates an optimal solution for all of the objective functions among the plurality of objective functions; 9. The solution searching device according to claim 8.

11. a solution extraction unit that extracts an efficient frontier as the frontier from a solution set existing in a solution space of the multi-objective optimization problem by using a data envelopment analysis method; The first optimal solution calculation unit calculates a first optimal solution by using the first aspiration level set by the setting unit and the efficient frontier extracted by the solution extraction unit.

3. The solution search device according to claim 1 or 2.

12. When an instruction not to adopt the first optimal solution adjusted by the first optimal solution adjustment unit is received from a user, an aspiration level frontier calculation unit that calculates an aspiration level frontier, which is a set of aspiration level candidates including the first aspiration level, by using the frontier and the first aspiration level set by the setting unit; a first aspiration level adjustment unit that receives an input of an adjustment amount for adjusting the first aspiration level from a user, and calculates a second aspiration level by adjusting the first aspiration level within the range of the aspiration level frontier based on the received adjustment amount; a second optimal solution calculation unit that calculates a second optimal solution different from the first optimal solution by using the second aspiration level calculated by the first aspiration level adjustment unit and the frontier; 3. The solution search device according to claim 1, further comprising:

13. When the solution space in the multi-objective optimization problem is a two-dimensional space, The aspiration level frontier calculation unit The aspiration level frontier is calculated by enlarging the line showing the frontier by a predetermined factor.

13. The solution search device according to claim 12.

14. The adjustment amount is The second aspiration level is given by one of the two objective function values.

14. The solution search device according to claim 13.

15. When an instruction not to adopt the first optimal solution adjusted by the first optimal solution adjustment unit is received from a user, An optimization calculation unit that searches for solutions existing in a peripheral area of ​​the adjusted first optimal solution in a solution space of the multi-objective optimization problem.

8. The solution search device according to claim 7.

16. The optimization calculation unit is Calculating evaluation values ​​of solutions present in a peripheral area of ​​the adjusted first optimal solution based on the second aspiration level and an ideal point that indicates an optimal solution for all of the objective functions among the plurality of objective functions, and further searching for solutions surrounding a predetermined number of solutions having the highest calculated evaluation values.

16. The solution search device according to claim 15.

17. The optimization calculation unit is Using the second aspiration level as a reference point, a region in a solution space that is a distance from the reference point within a predetermined value is searched for within a peripheral region of the adjusted first optimal solution.

16. The solution search device according to claim 15.

18. A solution search method by a solution search device, comprising: A setting unit sets a first aspiration level which is a target value for a plurality of objective functions in a multi-objective optimization problem; A step in which a first optimal solution calculation unit calculates a first optimal solution by using a first aspiration level set by the setting unit and a frontier that is a solution set for optimizing the plurality of objective functions; a first optimal solution adjustment unit receiving an input of an adjustment amount for adjusting the first optimal solution from the user when an instruction not to adopt the first optimal solution calculated by the first optimal solution calculation unit is received from the user, and adjusting the first optimal solution within the range of the frontier based on the received adjustment amount; A solution search method having the following structure.

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