Pareto solution calculation device and pareto solution calculation method

Abstract

This Pareto solution calculation device is configured to comprise: an aspiration level reception unit (1) that receives an aspiration level related to each of a plurality of objective functions; a Pareto solution calculation unit (3) that calculates a Pareto solution for each of the objective functions on the basis of the aspiration level received by the aspiration level reception unit (1); an objective function reception unit (4) that receives, from among the plurality of objective functions, an objective function for which an adjacent solution adjacent to the Pareto solution is to be calculated; and an adjacent solution calculation unit (5) that calculates an evaluation value of the objective function while changing the aspiration level related to the objective function received by the objective function reception unit (4), and calculates the adjacent solution on the basis of the evaluation value of the objective function.

Description

Pareto solution calculation device and Pareto solution calculation method

[0001] This disclosure relates to a Pareto solution calculation device and a Pareto solution calculation method.

[0002] There is a Pareto solution calculation device that calculates a Pareto solution for each of multiple objective functions based on the desired level for each of those objective functions. As such a Pareto solution calculation device, for example, Patent Document 1 discloses a Pareto solution calculation device comprising an interface unit that accepts desired levels for each objective function, and an optimization unit that calculates a Pareto solution for each objective function based on the desired levels accepted by the interface unit. If the user is not satisfied with the Pareto solution calculated by the optimization unit, they can change the desired level by operating the interface unit. The optimization unit then calculates a Pareto solution for each objective function based on the changed desired level.

[0003] Japanese Patent Publication No. 2009-30476

[0004] The Pareto solution calculation device disclosed in Patent Document 1 has the problem that, although the optimization unit can calculate Pareto solutions for each objective function based on the modified desired level, it cannot calculate adjacent solutions that are adjacent to the previously calculated Pareto solution.

[0005] This disclosure was made to solve the above-mentioned problems, and aims to provide a Pareto solution calculator that can calculate adjacent solutions that are adjacent to Pareto solutions for some of the objective functions among multiple objective functions.

[0006] The Pareto solution calculation device according to this disclosure includes: a desired level receiving unit that receives desired levels for each of a plurality of objective functions; a Pareto solution calculation unit that calculates a Pareto solution for each objective function based on the desired levels received by the desired level receiving unit; an objective function receiving unit that receives an objective function from among a plurality of objective functions for which adjacent solutions to be calculated are adjacent to the Pareto solution; and an adjacent solution calculation unit that calculates an evaluation value of the objective function while changing the desired level for the objective function received by the objective function receiving unit, and calculates an adjacent solution based on the evaluation value of the objective function.

[0007] According to this disclosure, it is possible to calculate adjacent solutions that are adjacent to the Pareto solution for some of the objective functions among multiple objective functions.

[0008] This is a configuration diagram showing a Pareto solution calculation device according to Embodiment 1. This is a hardware configuration diagram showing the hardware of the Pareto solution calculation device according to Embodiment 1. This is a hardware configuration diagram of a computer when the Pareto solution calculation device is implemented by software or firmware, etc. This is a flowchart showing the Pareto solution calculation method, which is the processing procedure of the Pareto solution calculation device. A certain objective function f among multiple objective functions ｉ This is an explanatory diagram showing an example of a Pareto solution for the desired level f. ｏ ａｓｐ The evaluation value v of solution s after the change ｓ This is an explanatory diagram showing the changes. This is an explanatory diagram showing an example of the Pareto solution before and after the change acceptance. This is a configuration diagram showing the Pareto solution calculation device according to Embodiment 2. This is a hardware configuration diagram showing the hardware of the Pareto solution calculation device according to Embodiment 2. This is an explanatory diagram showing an example in which three Pareto solution candidates are selected from among multiple Pareto solution candidates as the Pareto solution for a certain objective function.

[0009] To provide a more detailed explanation of this disclosure, the forms for implementing this disclosure will be described below with reference to the attached drawings.

[0010] Embodiment 1. Figure 1 is a configuration diagram showing a Pareto solution calculation device according to Embodiment 1. Figure 2 is a hardware configuration diagram showing the hardware of the Pareto solution calculation device according to Embodiment 1. The Pareto solution calculation device shown in Figure 1 comprises a desired level receiving unit 1, an ideal solution receiving unit 2, a Pareto solution calculation unit 3, an objective function receiving unit 4, an adjacent solution calculation unit 5, and a display processing unit 6.

[0011] The desired level receiving unit 1 is implemented, for example, by the desired level receiving circuit 11 shown in Figure 2. The desired level receiving unit 1 receives desired levels for each of the multiple objective functions. The desired level receiving unit 1 outputs the desired level for each objective function to the Pareto solution calculation unit 3 and the adjacent solution calculation unit 5, respectively. When the Pareto solution calculation device shown in Figure 1 is applied to a search device for properties such as apartments, the objective functions may include, for example, the rent of the apartment, the area of ​​the apartment, the age of the apartment, and the walking time from the station to the apartment. The desired level represents the limit value that the user can consider satisfactory. For example, when the objective function is the rent of the apartment, if the affordable rent is 70,000 yen, the desired level is 70,000 yen. For example, when the objective function is the area of ​​the apartment, if the minimum required area is 20 m² ２ In that case, the desired level is 20m ２ Furthermore, the desired level receiving unit 1 accepts changes to the desired levels for each objective function. The desired level receiving unit 1 outputs the changed desired levels to the Pareto solution calculation unit 3.

[0012] The ideal solution receiving unit 2 is implemented, for example, by the ideal solution receiving circuit 12 shown in Figure 2. The ideal solution receiving unit 2 receives ideal solutions for each objective function. The ideal solution receiving unit 2 outputs the ideal solution for each objective function to the Pareto solution calculation unit 3 and the adjacent solution calculation unit 5, respectively. The ideal solution is an ideal value for the objective function. For example, if the objective function is the rent of an apartment, and the ideal rent is 20,000 yen, then the ideal solution is 20,000 yen. For example, if the objective function is the area of ​​an apartment, and the ideal area is 100 m², then the ideal solution is 100 m². ２ In that case, the ideal solution is 100m２ That is the case.

[0013] The Pareto solution calculation unit 3 is implemented, for example, by the Pareto solution calculation circuit 13 shown in Figure 2. The Pareto solution calculation unit 3 obtains desired levels for each objective function from the desired level reception unit 1 and obtains ideal solutions for each objective function from the ideal solution reception unit 2. The Pareto solution calculation unit 3 calculates the Pareto solution for each objective function based on the desired levels received by the desired level reception unit 1 and the ideal solutions received by the ideal solution reception unit 2. The Pareto solution calculation unit 3 also calculates the Pareto solution for each objective function based on the desired levels after modification received by the desired level reception unit 1. For example, the satisfyating trade-off method is used for the Pareto solution calculation process by the Pareto solution calculation unit 3. However, the Pareto solution calculation process is not limited to the satisfyating trade-off method, and a multi-objective optimization method such as the linear weighted sum method may also be used. The Pareto solution calculation unit 3 outputs the Pareto solution for each objective function to the display processing unit 6.

[0014] The objective function receiving unit 4 is implemented, for example, by the objective function receiving circuit 14 shown in Figure 2. The objective function receiving unit 4 receives objective functions from among a plurality of objective functions that are adjacent to the Pareto solution and are to be used for the calculation of adjacent solutions. The objective function receiving unit 4 outputs the objective functions to be used for the calculation of adjacent solutions to the adjacent solution calculation unit 5.

[0015] The adjacent solution calculation unit 5 is implemented, for example, by the adjacent solution calculation circuit 15 shown in Figure 2. The adjacent solution calculation unit 5 obtains the objective function for which adjacent solutions are to be calculated from the objective function receiving unit 4. The adjacent solution calculation unit 5 obtains information about the objective function for which adjacent solutions are to be calculated from the desired level receiving unit 1 and obtains an ideal solution for the objective function for which adjacent solutions are to be calculated from the ideal solution receiving unit 2. The adjacent solution calculation unit 5 calculates an evaluation value of the objective function while changing the desired level for the objective function for which adjacent solutions are to be calculated, and calculates adjacent solutions based on the evaluation value of the objective function. For example, the satisfactori trade-off method is used for the adjacent solution calculation process by the adjacent solution calculation unit 5. However, the adjacent solution calculation process is not limited to the satisfactori trade-off method, and a multi-objective optimization method such as the linear weighted sum method may also be used. The adjacent solution calculation unit 5 outputs the adjacent solutions to the display processing unit 6.

[0016] The display processing unit 6 is implemented, for example, by the display processing circuit 16 shown in Figure 2. The display processing unit 6 obtains the Pareto solution for each objective function from the Pareto solution calculation unit 3 and obtains the adjacent solutions for the objective function for which adjacent solutions are to be calculated from the adjacent solution calculation unit 5. The display processing unit 6 displays the Pareto solution and adjacent solutions for the objective function to be calculated on a display, for example (not shown). The display processing unit 6 also displays on the display the Pareto solution calculated by the Pareto solution calculation unit 3 based on the desired level received by the desired level reception unit 1, and the Pareto solution calculated based on the desired level after the change received by the desired level reception unit 1.

[0017] In Figure 1, it is assumed that the components of the Pareto solution calculation device—the desired level receiving unit 1, the ideal solution receiving unit 2, the Pareto solution calculation unit 3, the objective function receiving unit 4, the adjacent solution calculation unit 5, and the display processing unit 6—are each implemented by dedicated hardware as shown in Figure 2. Specifically, it is assumed that the Pareto solution calculation device is implemented by a desired level receiving circuit 11, an ideal solution receiving circuit 12, a Pareto solution calculation circuit 13, an objective function receiving circuit 14, an adjacent solution calculation circuit 15, and a display processing circuit 16. Each of the desired level receiving circuit 11, ideal solution receiving circuit 12, Pareto solution calculation circuit 13, objective function receiving circuit 14, adjacent solution calculation circuit 15, and display processing circuit 16 can be, 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 thereof.

[0018] The components of a Pareto solution calculator are not limited to those implemented by dedicated hardware; the calculator may also be implemented by software, firmware, or a combination of software and firmware. The software or firmware is stored as a program in the computer's memory. A computer refers to the hardware that executes the program, and includes, for example, a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a processor, or a DSP (Digital Signal Processor).

[0019] Figure 3 is a hardware configuration diagram of a computer when the Pareto solution calculation device is implemented by software or firmware. When the Pareto solution calculation device is implemented by software or firmware, a program that causes the computer to execute the respective processing procedures in the desired level receiving unit 1, the ideal solution receiving unit 2, the Pareto solution calculation unit 3, the objective function receiving unit 4, the adjacent solution calculation unit 5, and the display processing unit 6 is stored in memory 21. The computer's processor 22 then executes the program stored in memory 21.

[0020] Furthermore, Figure 2 shows an example in which each component of the Pareto solution calculation device is implemented by dedicated hardware, and Figure 3 shows an example in which the Pareto solution calculation device is implemented by software or firmware, etc. However, this is only one example, and some components of the Pareto solution calculation device may be implemented by dedicated hardware, while the remaining components may be implemented by software or firmware, etc.

[0021] Next, the operation of the Pareto solution calculation device shown in Figure 1 will be explained. Figure 4 is a flowchart showing the Pareto solution calculation method, which is the processing procedure of the Pareto solution calculation device. Multiple objective functions are set for the Pareto solution calculation device shown in Figure 1. When the Pareto solution calculation device is applied to a search device for properties such as apartments, for example, the objective functions may include the rent of the apartment, the area of ​​the apartment, the age of the apartment, and the walking time from the station to the apartment. When the Pareto solution calculation device is applied to a search device for used cars, for example, the objective functions may include the car's body type, engine displacement, color, year of manufacture, and price.

[0022] When the desired level reception unit 1 is realized by, for example, a man-machine interface, the user can set the desired level for each objective function by operating the desired level reception unit 1. The desired level reception unit 1 receives the desired level for each objective function set by the user (step ST1 in FIG. 4). The desired level reception unit 1 outputs the desired level for each objective function to each of the Pareto solution calculation unit 3 and the adjacent solution calculation unit 5.

[0023] When the objective function is, for example, the rent of an apartment, if the affordable rent is 70,000 yen, the desired level is 70,000 yen. When the objective function is, for example, the area of an apartment, if the minimum required area is 20 m ２ then the desired level is 20 m ２ When the objective function is, for example, the age of construction of an apartment, if the allowable age of construction is 30 years, the desired level is 30 years. When the objective function is, for example, the travel time on foot, if the allowable travel time is 30 minutes, the desired level is 30 minutes.

[0024] When the ideal solution reception unit 2 is realized by, for example, a man-machine interface, the user can set the ideal solution for each objective function by operating the ideal solution reception unit 2. The ideal solution reception unit 2 receives the ideal solution for each objective function set by the user (step ST2 in FIG. 4). The ideal solution reception unit 2 outputs the ideal solution for each objective function to each of the Pareto solution calculation unit 3 and the adjacent solution calculation unit 5.

[0025] When the objective function is, for example, the rent of an apartment, if the ideal rent is 20,000 yen, the ideal solution is 20,000 yen. When the objective function is, for example, the area of an apartment, if the ideal area is 100 m ２ then the ideal solution is 100 m ２ When the objective function is, for example, the age of construction of an apartment, if the ideal age of construction is 1 year, the ideal solution is 1 year. When the objective function is, for example, the travel time on foot of an apartment, if the ideal travel time is 1 minute, the ideal solution is 1 minute.

[0026] The Pareto solution calculation unit 3 obtains desired levels for each objective function from the desired level reception unit 1 and obtains ideal solutions for each objective function from the ideal solution reception unit 2. Based on the desired levels for each objective function and the ideal solutions for each objective function, the Pareto solution calculation unit 3 calculates the Pareto solution for each objective function (step ST3 in Figure 4). The Pareto solution calculation unit 3 outputs the Pareto solution for each objective function to the display processing unit 6. The calculation process of the Pareto solution by the Pareto solution calculation unit 3 will be described in detail below.

[0027] Here, we will explain an example in which the Pareto solution calculation unit 3 calculates the Pareto solution using the satisfactori trade-off method. The Pareto solution calculation unit 3 calculates the set of objective functions F = [f １ , f ２ , ..., f ｎ This is done by performing multi-objective optimization on [s], and the set of solutions S = [s] is obtained. １ ,s ２ , , s ｎ The objective function f is obtained as shown in equation (1) below. ｉ The desired level f of ∈F ｉ ａｓｐ And the objective function f ｉ The ideal solution f for ∈F ｉ ｄｅａｌ This method calculates a preferred solution s from the given set of solutions S. A preferred solution s is one of the solutions included in the set of solutions S.

[0028] In equation (1), g ｓ，ｉ The objective function f for the solution s∈S is ｉ ∈ the value of F. Equation (1) is the value of the objective function g. ｓ，ｉ and desired level f ｉ ａｓｐ The difference between this and the desired level f ｉ ａｓｐ and the ideal solution f ｉ ｄｅａｌ By dividing by the difference with, the desired level f ｉ ａｓｐ This indicates that a preference solution s is obtained that minimizes the maximum value of the distance from the target.

[0029] The Pareto solution calculation unit 3 outputs the preferred solution s as the Pareto solution to the display processing unit 6. The Pareto solution calculation unit 3 calculates an evaluation value v for each solution s∈S, as shown in equation (2) below. ｓ The following can be calculated: the evaluation value v for each solution s∈S. ｓ By comparing them with each other, it is also possible to determine the ranking of the solutions s.

[0030]

[0031] The display processing unit 6 obtains the Pareto solutions for each objective function from the Pareto solution calculation unit 3. The display processing unit 6 displays the Pareto solutions for each objective function on a display (not shown), for example (step ST4 in Figure 4). Figure 5 shows a certain objective function f among several objective functions. ｉ This is an explanatory diagram showing an example of a Pareto solution for [the given problem]. In Figure 5, the horizontal axis represents the value s of a certain objective function, and the vertical axis represents the evaluation value v. ｓ This indicates that.

[0032] The user checks the Pareto solution displayed on the screen and identifies a certain objective function f ｉ If we are not satisfied with the Pareto solution for , then there is a certain objective function f ｉ The calculation of adjacent solutions for a given objective function can be requested. If the objective function receiving unit 4 is implemented, for example, by a human-machine interface, the user can set the objective function for which adjacent solutions will be calculated by operating the objective function receiving unit 4. In this case, the objective function receiving unit 4 accepts the objective function for which adjacent solutions will be calculated from among multiple objective functions. The user can also change the desired level for each objective function by operating the desired level receiving unit 1. In this case, the desired level receiving unit 1 accepts the change in the desired level for each objective function.

[0033] When the objective function to be calculated for adjacent solutions is received by the objective function receiving unit 4 (step ST5 in Figure 4: YES), the adjacent solution calculation unit 5 obtains the objective function to be calculated from the objective function receiving unit 4. The adjacent solution calculation unit 5 also obtains information about the objective function to be calculated for adjacent solutions from the desired level receiving unit 1 and obtains an ideal solution for the objective function to be calculated from the ideal solution receiving unit 2. The adjacent solution calculation unit 5 calculates an evaluation value of the objective function while changing the desired level for the objective function to be calculated, and calculates adjacent solutions based on the evaluation value of the objective function (step ST6 in Figure 4). The adjacent solution calculation unit 4 outputs the adjacent solutions for the objective function to be calculated to the display processing unit 6. The adjacent solution calculation process by the adjacent solution calculation unit 5 will be described in detail below.

[0034] Here, we will explain an example in which the adjacent solution calculation unit 5 calculates adjacent solutions using the satisfactori trade-off method. When calculating adjacent solutions for the objective function o ∈ F, the remaining objective function f ｉ The desired level of ∈F\{o} is fixed. The desired level f of the objective function o being calculated. ｏ ａｓｐ If this is changed, what is the evaluation value v of the solution s∈S? ｓ The value changes as shown in Figure 6. Figure 6 shows the desired level f. ｏ ａｓｐ The evaluation value v of solution s after the change ｓ This is an explanatory diagram showing the change. The evaluation value v of solution s shown in equation (3) below. ｓ In the calculation formula, the variable is the desired level f. ｏ ａｓｐ Only this is true; all others can be treated as constants.

[0035]

[0036] Therefore, when the following equation (4) holds, the evaluation value v ｓ It is constant. In Figure 6, it is the straight line portion of the graph. On the other hand, when the following equation (5) holds, the desired level f ｏ ａｓｐ As the evaluation value v changes, ｓ This changes. In Figure 6, this is the curved portion of the graph.

[0037]

[0038] Desired level f ｏ ａｓｐ When the variable is changed in a predetermined direction, the Pareto solution is the preference solution s. ＊ The solutions relating to the graphs that intersect with the graph are the adjacent solutions. In the example in Figure 6, of the three graphs (one adjacent solution graph and two other solution graphs in the figure), the preferred solution s ＊ The solution relating to the graph that first intersects with the graph is the adjacent solution. The seeking level relating to the intersection point where the graphs intersect is the new seeking level relating to the adjacent solution.

[0039] The following describes in detail the process for calculating a new preference level related to adjacent solutions. The preferred solution s is a Pareto solution. ＊ Find all the intersection points between the graph of and the graphs of the other solutions (three graphs in the example in Figure 6), and select a preferred solution s from among one or more intersection points. ＊ Desired level f related to the graph ｏ ａｓｐ By selecting the closest intersection point, we can find the adjacent solution for the graph containing the selected intersection point.

[0040] To find the intersection points of the graphs, we need the evaluation value v of the solution s. ｓ When expressed by equation (3), and the evaluation value v of solution s ｓ However, we consider the cases that can be expressed on the right side of equation (4) or on the right side of equation (5) separately. Specifically, the preference solution s ＊ Evaluation value v ｓ This is expressed by the following equation (6), and the evaluation value v of the other solution s' ｓ’ Case (1) is represented by the following equation (7), and the preference solution s ＊ Evaluation value v ｓ This is expressed by the following equation (8), and the evaluation value v of the other solution s' ｓ’ There are two cases, one where the answer is expressed by the following equation (9) (2). Also, the preference solution s ＊ Evaluation value v ｓ This is expressed by equation (6), and the evaluation value v of the other solution s'. ｓ’ Case (3) is represented by the following equation (9), and the preference solution s ＊ Evaluation value v ｓ This is expressed by the following equation (8), and the evaluation value v of the other solution s' ｓ’There is a case (4) represented by the following formula (7).

[0041]

[0042] In the case of case (1), the intersection occurs only when g ｓ＊，ｏ = g ｓ，ｏ , and the two graphs coincide. In the case of case (2), the intersection occurs when the evaluation value v ＊ of the preferred solution s represented by formula (8) ｓ coincides with the evaluation value v ｓ’ of another solution s' represented by formula (9), and the two graphs coincide.

[0043] In the case of case (3), since the evaluation value v ｓ’ of another solution s' represented by formula (9) is a constant, from the linear equation in which only the aspiration level f ｏ ａｓｐ shown in the following formula (10) becomes a variable, the aspiration level f ｏ ａｓｐ at the intersection can be obtained.

[0044]

[0045] In the case of case (4), the aspiration level f ｏ ａｓｐ at the intersection can be calculated in the same way as in the case of case (3). However, if it is smaller than the aspiration level f ｏ ａｓｐ before the change, then the evaluation value v ｓ’ of another solution s' is better than the evaluation value v ＊ of the preferred solution s ｓ by nature, which contradicts the assumption that s ＊ is the preferred solution. Therefore, the aspiration level f ｏ ａｓｐ obtained at the intersection is larger than the aspiration level f ｏ ａｓｐ before the change, so case (4) is excluded from the current target.

[0046] The display processing unit 6 obtains the Pareto solution for the objective function for which adjacent solutions are to be calculated from the Pareto solution calculation unit 3, and obtains the adjacent solutions for the objective function for which adjacent solutions are to be calculated from the adjacent solution calculation unit 5. As shown in Figure 6, the display processing unit 6 displays the Pareto solution and adjacent solutions for the objective function for which solutions are to be calculated on a display (not shown), for example (step ST7 in Figure 4). The operation of the Pareto solution calculation device shown in Figure 1 returns to the process of step ST5.

[0047] Next, if the objective function receiving unit 4 has not received an objective function for which adjacent solutions are to be calculated (step ST5 in Figure 4: NO), and the desired level receiving unit 1 has received a change in the desired level for each objective function (step ST8 in Figure 4: YES), the Pareto solution calculation unit 3 obtains the changed desired level from the desired level receiving unit 1. The Pareto solution calculation unit 3 calculates the Pareto solution for each objective function based on the changed desired level received by the desired level receiving unit 1 (step ST9 in Figure 4). The Pareto solution calculation process itself is the same as the Pareto solution calculation process in step ST3. The Pareto solution calculation unit 3 outputs the Pareto solution for each objective function to the display processing unit 6.

[0048] The display processing unit 6 obtains from the Pareto solution calculation unit 3 the Pareto solution calculated based on the desired level before the change was accepted (hereinafter referred to as the "Pareto solution before the change was accepted") and the Pareto solution calculated based on the desired level after the change was accepted (hereinafter referred to as the "Pareto solution after the change was accepted"). As shown in Figure 7, the display processing unit 6 displays the Pareto solution before the change was accepted and the Pareto solution after the change was accepted, for example, on a display (step ST10 in Figure 4). The operation of the Pareto solution calculation device shown in Figure 1 returns to the process of step ST5.

[0049] Figure 7 is an explanatory diagram showing an example of the Pareto solution before and after the change was accepted. In Figure 7, the dashed line shows the Pareto solution before the change was accepted, and the solid line shows the Pareto solution after the change was accepted. The thick line connecting the two dots is a slider component that indicates the range for each objective function. The range for the objective function is from the desired level to the ideal solution. The user can change the range for the objective function by moving the slider component using the human-machine interface.

[0050] In the diagram, the left-pointing triangle and the right-pointing triangle are change buttons that accept changes to the desired level for each objective function. Users can change the desired level for each objective function by touching these change buttons using the human-machine interface. On the right side of Figure 7, a list of searched apartments is displayed. In Figure 7, for example, Apartment A, Apartment B, and Apartment C are displayed as searched apartments.

[0051] Next, if the objective function receiving unit 4 has not received an objective function for which adjacent solutions are to be calculated (step ST5 in Figure 4: NO), and the desired level receiving unit 1 has not received a change in the desired level for each objective function (step ST8 in Figure 4: NO), the series of operations of the Pareto solution calculation device shown in Figure 1 is terminated.

[0052] In the above embodiment 1, the Pareto solution calculation device is configured to include: a desire level receiving unit 1 that receives desire levels for each of a plurality of objective functions; a Pareto solution calculation unit 3 that calculates Pareto solutions for each objective function based on the desire levels received by the desire level receiving unit 1; an objective function receiving unit 4 that receives objective functions from among the plurality of objective functions for which adjacent solutions to be calculated that are adjacent to the Pareto solution are to be calculated; and an adjacent solution calculation unit 5 that calculates an evaluation value of the objective function while changing the desire level for the objective function received by the objective function receiving unit 4, and calculates adjacent solutions based on the evaluation value of the objective function. Therefore, the Pareto solution calculation device can calculate adjacent solutions that are adjacent to the Pareto solutions for some of the objective functions among the plurality of objective functions.

[0053] In Embodiment 1, the Pareto solution calculation device is configured to include a display processing unit 6 that displays the Pareto solution for the objective function received by the objective function receiving unit 4 and the adjacent solutions calculated by the adjacent solution calculation unit 5. Therefore, the Pareto solution calculation device can allow the user to confirm the Pareto solution and adjacent solutions for some objective functions.

[0054] In Embodiment 1, the desired level receiving unit 1 accepts desired levels for each objective function, as well as changes to the desired levels for each objective function. The Pareto solution calculation unit 3 then calculates the Pareto solution for each objective function based on the desired levels after the changes have been accepted by the desired level receiving unit 1. Thus, the Pareto solution calculation unit can obtain the Pareto solution based on the desired levels after the changes have been accepted.

[0055] In Embodiment 1, the Pareto solution calculation device is configured to include a display processing unit 6 that displays the Pareto solution calculated based on the desired level received by the desired level receiving unit 1, and the Pareto solution calculated based on the desired level after the change acceptance by the desired level receiving unit 1, using a Pareto solution calculation unit 3. Therefore, the Pareto solution calculation device allows the user to confirm the desired level before and after the change acceptance.

[0056] Embodiment 2. Embodiment 2 describes a Pareto solution calculation device that includes a Pareto solution calculation unit 7 which calculates a plurality of Pareto solution candidates for each objective function based on the desired levels received by the desired level receiving unit 1, and also calculates an evaluation value for each Pareto solution candidate.

[0057] Figure 8 is a configuration diagram showing a Pareto solution calculation device according to Embodiment 2. In Figure 8, the same reference numerals as in Figure 1 indicate the same or corresponding parts, so a detailed explanation is omitted. Figure 9 is a hardware configuration diagram showing the hardware of the Pareto solution calculation device according to Embodiment 2. In Figure 9, the same reference numerals as in Figure 2 indicate the same or corresponding parts, so a detailed explanation is omitted. The Pareto solution calculation device shown in Figure 8 includes a desired level receiving unit 1, an ideal solution receiving unit 2, a Pareto solution calculation unit 7, an objective function receiving unit 4, an adjacent solution calculation unit 5, and a display processing unit 6.

[0058] The Pareto solution calculation unit 7 is implemented, for example, by the Pareto solution calculation circuit 17 shown in Figure 9. The Pareto solution calculation unit 7 obtains desired levels for each objective function from the desired level receiving unit 1 and obtains ideal solutions for each objective function from the ideal solution receiving unit 2. Based on the desired levels received by the desired level receiving unit 1 and the ideal solutions received by the ideal solution receiving unit 2, the Pareto solution calculation unit 7 calculates multiple Pareto solution candidates for each objective function and calculates an evaluation value for each Pareto solution candidate. Based on the evaluation value for each Pareto solution candidate, the Pareto solution calculation unit 7 selects one or more Pareto solution candidates from the multiple candidates as the Pareto solution for each objective function. Furthermore, similar to the Pareto solution calculation unit 3 shown in Figure 1, the Pareto solution calculation unit 7 calculates the Pareto solution for each objective function based on the desired levels after modification received by the desired level receiving unit 1. The Pareto solution calculation unit 7 outputs the Pareto solution for each objective function to the display processing unit 6.

[0059] In Figure 8, it is assumed that each of the components of the Pareto solution calculation device—the desired level receiving unit 1, the ideal solution receiving unit 2, the Pareto solution calculation unit 7, the objective function receiving unit 4, the adjacent solution calculation unit 5, and the display processing unit 6—is implemented by dedicated hardware as shown in Figure 9. That is, it is assumed that the Pareto solution calculation device is implemented by a desired level receiving circuit 11, an ideal solution receiving circuit 12, a Pareto solution calculation circuit 17, an objective function receiving circuit 14, an adjacent solution calculation circuit 15, and a display processing circuit 16. Each of the desired level receiving circuit 11, the ideal solution receiving circuit 12, the Pareto solution calculation circuit 17, the objective function receiving circuit 14, the adjacent solution calculation circuit 15, and the display processing circuit 16 can be, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0060] The components of the Pareto solution calculation device are not limited to those implemented by dedicated hardware; the Pareto solution calculation device may also be implemented by software, firmware, or a combination of software and firmware. When the Pareto solution calculation device is implemented by software or firmware, a program for causing a computer to execute the respective processing procedures in the desired level receiving unit 1, the ideal solution receiving unit 2, the Pareto solution calculation unit 7, the objective function receiving unit 4, the adjacent solution calculation unit 5, and the display processing unit 6 is stored in the memory 21 shown in Figure 3. Then, the processor 22 shown in Figure 3 executes the program stored in the memory 21.

[0061] Furthermore, Figure 9 shows an example in which each component of the Pareto solution calculation device is implemented by dedicated hardware, while Figure 3 shows an example in which the Pareto solution calculation device is implemented by software or firmware. However, this is merely one example, and some components of the Pareto solution calculation device may be implemented by dedicated hardware, while the remaining components may be implemented by software or firmware.

[0062] Next, the operation of the Pareto solution calculation device shown in Figure 8 will be explained. However, it is the same as the Pareto solution calculation device shown in Figure 1, except for the Pareto solution calculation unit 7. Therefore, here we will mainly explain the operation of the Pareto solution calculation unit 7. The Pareto solution calculation unit 3 shown in Figure 1 calculates only one Pareto solution for each objective function, whereas the Pareto solution calculation unit 7 differs in that it calculates multiple Pareto solution candidates for each objective function.

[0063] The Pareto solution calculation unit 7 obtains desired levels for each objective function from the desired level receiving unit 1 and obtains ideal solutions for each objective function from the ideal solution receiving unit 2. The Pareto solution calculation unit 7 calculates multiple candidate Pareto solutions for each objective function based on the desired levels for each objective function and the ideal solutions for each objective function, for example, using the satisfactori trade-off method. For example, equation (1) is used in the calculation process of candidate Pareto solutions by the Pareto solution calculation unit 7. However, g in equation (1) ｓ，ｉ The value of differs for each Pareto solution candidate. The Pareto solution calculation unit 7 calculates the evaluation value for each Pareto solution candidate. For example, equation (2) is used in the calculation of the evaluation value by the Pareto solution calculation unit 7. However, g in equation (2) ｓ，ｉ The value of differs for each candidate Pareto solution.

[0064] The Pareto solution calculation unit 7 selects one or more Pareto solution candidates from among multiple Pareto solution candidates as Pareto solutions for each objective function, based on the evaluation value of each Pareto solution candidate. Figure 10 is an explanatory diagram showing an example in which three Pareto solution candidates are selected from among multiple Pareto solution candidates as Pareto solutions for a certain objective function. In the example in Figure 10, the evaluation values ​​of multiple Pareto solution candidates are compared with each other, and the top three Pareto solution candidates with the highest evaluation values ​​are selected.

[0065] When the objective function receiving unit 4 receives the objective function to be calculated for adjacent solutions adjacent to each Pareto solution candidate, the adjacent solution calculation unit 5 obtains the objective function to be calculated from the objective function receiving unit 4 and obtains the ideal solution for the objective function to be calculated from the ideal solution receiving unit 2. The adjacent solution calculation unit 5 calculates an evaluation value of the objective function while changing the desired level for the objective function to be calculated, and calculates adjacent solutions based on the evaluation value of the objective function. These adjacent solutions are adjacent solutions for each Pareto solution candidate. The adjacent solution calculation unit 5 outputs the adjacent solutions for each Pareto solution candidate to the display processing unit 6.

[0066] The display processing unit 6 obtains multiple Pareto solution candidates for the objective function for which adjacent solutions are to be calculated from the Pareto solution calculation unit 7, and obtains adjacent solutions related to each Pareto solution candidate from the adjacent solution calculation unit 5. As shown in Figure 10, the display processing unit 6 displays the multiple Pareto solution candidates and the adjacent solutions related to each Pareto solution candidate on a display, for example.

[0067] In the above embodiment 2, the Pareto solution calculation unit 7 calculates multiple Pareto solution candidates for each objective function based on the desired level received by the desired level receiving unit 1, and also calculates an evaluation value for each Pareto solution candidate. The Pareto solution calculation device is configured such that the Pareto solution calculation unit 7 selects one or more Pareto solution candidates from among the multiple Pareto solution candidates as the Pareto solution for each objective function based on the evaluation value for each Pareto solution candidate. Therefore, the Pareto solution calculation device can calculate adjacent solutions that are adjacent to the Pareto solutions for some of the objective functions among the multiple objective functions, and can also calculate one or more Pareto solutions.

[0068] Furthermore, this disclosure allows for free combination of each embodiment, modification of any component in each embodiment, or omission of any component in each embodiment.

[0069] The Pareto solution calculation device according to this disclosure can calculate adjacent solutions that are adjacent to the Pareto solution for some of the objective functions among a plurality of objective functions, and is suitable for use in Pareto solution calculation devices and the like.

[0070] 1. Desired level receiving unit, 2. Ideal solution receiving unit, 3. Pareto solution calculation unit, 4. Objective function receiving unit, 5. Adjacent solution calculation unit, 6. Display processing unit, 7. Pareto solution calculation unit, 11. Desired level receiving circuit, 12. Ideal solution receiving circuit, 13. Pareto solution calculation circuit, 14. Objective function receiving circuit, 15. Adjacent solution calculation circuit, 16. Display processing circuit, 17. Pareto solution calculation circuit, 21. Memory, 22. Processor.

Claims

1. A Pareto solution calculation device comprising: a desired level receiving unit that receives desired levels for each of a plurality of objective functions; a Pareto solution calculation unit that calculates a Pareto solution for each objective function based on the desired levels received by the desired level receiving unit; an objective function receiving unit that receives an objective function from among the plurality of objective functions for which an adjacent solution to be calculated is adjacent to the Pareto solution; and an adjacent solution calculation unit that calculates an evaluation value of the objective function while changing the desired level for the objective function received by the objective function receiving unit, and calculates the adjacent solution based on the evaluation value of the objective function.

2. The Pareto solution calculation device according to claim 1, further comprising a display processing unit that displays the Pareto solution for the objective function received by the objective function receiving unit and the adjacent solutions calculated by the adjacent solution calculation unit.

3. The Pareto solution calculation device according to claim 1, wherein the desired level receiving unit accepts desired levels for each objective function, as well as changes to the desired levels for each objective function, and the Pareto solution calculation unit calculates the Pareto solution for each objective function based on the desired levels after the changes have been accepted by the desired level receiving unit.

4. The Pareto solution calculation device according to claim 3, further comprising a display processing unit that displays the Pareto solution calculated by the Pareto solution calculation unit based on the desired level received by the desired level receiving unit, and the Pareto solution calculated based on the desired level after the change has been accepted by the desired level receiving unit.

5. The Pareto solution calculation device according to any one of claims 1 to 4, characterized in that the Pareto solution calculation unit calculates a plurality of Pareto solution candidates for each objective function based on the desired level received by the desired level receiving unit, calculates an evaluation value for each Pareto solution candidate, and selects one or more Pareto solution candidates from the plurality of Pareto solution candidates as the Pareto solution for each objective function based on the evaluation value for each Pareto solution candidate.

6. The Pareto solution calculation device according to any one of claims 1 to 5, characterized in that the Pareto solution calculation unit calculates Pareto solutions for each objective function using the satisfactory trade-off method.

7. The Pareto solution calculation device according to any one of claims 1 to 6, characterized in that the adjacent solution calculation unit calculates the adjacent solution using the satisfactory trade-off method.

8. A Pareto solution calculation method comprising: a desired level receiving unit receiving desired levels for each of a plurality of objective functions; a Pareto solution calculation unit calculating a Pareto solution for each objective function based on the desired levels received by the desired level receiving unit; an objective function receiving unit receiving an objective function from among the plurality of objective functions for which an adjacent solution to be calculated is adjacent to the Pareto solution; and an adjacent solution calculation unit calculating an evaluation value of the objective function while changing the desired level for the objective function received by the objective function receiving unit, and calculating the adjacent solution based on the evaluation value of the objective function.

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