Plan determination apparatus and plan determination method

Abstract

To determine production plans of a plurality of devices more appropriately than before.SOLUTION: A plan determination apparatus (1) solves a multi-purpose optimization problem for production plans of a plurality of devices, to determine the production plans. In the multi-purpose optimization problem, a global objective function is defined based on N objective functions for a determination variable and N weighting factors. The plan determination apparatus (1) solves a provisional multi-purpose optimization problem to maximize values of the N objective functions under constraint conditions for the determination variable, using a predetermined optimization algorithm, to determine an influence order for each of the N objective functions. The plan determination apparatus (1) gradually solves the multi-purpose optimization problem for maximizing the global objective function under the constraint conditions by using the optimization algorithm while changing the N weighting factors according to the influence order, so as to derive an optimal solution of the multi-purpose optimization problem.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a plan decision device that decides production plans for a plurality of machines. [Background technology]

[0002] In various industrial fields, various methods for determining a predetermined plan using mathematical optimization techniques have been disclosed. For example, the following Patent Document 1 discloses an example of the configuration of a device that determines a plan by solving a multivariate linear programming problem. A linear programming problem is a type of multi-objective optimization problem. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2019-200695 A Summary of the Invention [Problem to be solved by the invention]

[0004] An object of one aspect of the present invention is to determine production plans for a plurality of devices more appropriately than ever before. [Means for solving the problem]

[0005] In order to solve the above-mentioned problems, a plan determination device according to one embodiment of the present invention is a plan determination device that determines a production plan by solving a multi-objective optimization problem for production plans of a plurality of machines, wherein in the multi-objective optimization problem, (i) N objective functions for decision variables are determined, and (ii) constraint conditions for the decision variables are determined, where N is an integer of 2 or more, and the N objective functions are respectively associated with N weighting coefficients, where i is an integer of 1 or more and N or less, the i-th objective function is referred to as the i-th objective function, the i-th weighting coefficient is referred to as the i-th weighting coefficient, and a product of the i-th objective function and the i-th weighting coefficient is referred to as the i-th weighting coefficient. The plan determination device solves a hypothetical multi-objective optimization problem that maximizes each of the N objective functions under the constraint conditions using a predetermined optimization algorithm, thereby determining an influence ranking for each of the N objective functions, which indicates how susceptible each of the N objective functions is to being affected by the constraint conditions, and derives an optimal solution to the multi-objective optimization problem by gradually solving the multi-objective optimization problem that maximizes the global objective function under the constraint conditions using the optimization algorithm while changing the N weighting coefficients in accordance with the influence ranking.

[0006] In order to solve the above-mentioned problems, a plan determination method according to one embodiment of the present invention is a plan determination method for determining a production plan by solving a multi-objective optimization problem for production plans of a plurality of machines, wherein in the multi-objective optimization problem, (i) N objective functions for decision variables are determined, and (ii) constraint conditions for the decision variables are determined, where N is an integer of 2 or more, and the N objective functions are associated with N weighting coefficients, respectively, where i is an integer of 1 or more and N or less, the i-th objective function is referred to as the i-th objective function, the i-th weighting coefficient is referred to as the i-th weighting coefficient, and a product of the i-th objective function and the i-th weighting coefficient is defined as A global objective function in the multi-objective optimization problem is defined as the sum of the 1st raw score to the Nth raw score, and the plan determination method uses a predetermined optimization algorithm to solve a hypothetical multi-objective optimization problem that maximizes each of the N objective functions under the constraint conditions, thereby determining an influence ranking for each of the N objective functions, which indicates how susceptible each of the N objective functions is to being affected by the constraint conditions, and then uses the optimization algorithm to progressively solve the multi-objective optimization problem that maximizes the global objective function under the constraint conditions while changing the N weighting coefficients in accordance with the influence ranking, thereby deriving an optimal solution to the multi-objective optimization problem. Effect of the Invention

[0007] According to one aspect of the present invention, production plans for a plurality of devices can be determined more appropriately than ever before. [Brief description of the drawings]

[0008] [Figure 1] 1 shows an example of the configuration of a plan determination device according to a first embodiment. [Diagram 2] An example of case data is shown below. [Diagram 3] An example of setting data is shown below. [Figure 4] An example of the initial state of a production plan is shown below. [Diagram 5] 4 shows an example of a final production plan determined by the plan determination device. [Figure 6]11 is a flowchart illustrating a process flow in the plan determination device. [Figure 7] FIG. 13 is a diagram for explaining an example of calculation of premise coefficients. [Figure 8] 1 illustrates a schematic diagram of an example of a production plan formulation process by a plan decision device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] [Embodiment 1] The plan determination device 1 of the first embodiment will be described below. For convenience of explanation, components having the same functions as the components (constituent elements) described in the first embodiment will be given the same reference numerals in the following embodiments, and the explanations thereof will not be repeated. For brevity, the explanations of well-known technical matters will also be omitted as appropriate.

[0010] Each component and each numerical value described in this specification is merely an example unless the content is inconsistent. Therefore, for example, the positional relationship and connection relationship of each component are not limited to the examples in each figure unless the content is inconsistent. In addition, each figure is not necessarily illustrated according to scale. In addition, the date illustrated in one figure does not necessarily match the date illustrated in another figure.

[0011] (Configuration example of the plan determination device 1) FIG. 1 shows a schematic configuration example of the plan determination device 1. The plan determination device 1 is configured to be able to determine a production plan by solving a multi-objective optimization problem for a production plan of a plurality of machines. The multi-objective optimization problem in the first embodiment may be a problem for finding an optimal solution under a plurality of objective functions. Therefore, the multi-objective optimization problem in the first embodiment includes a linear programming problem and a non-linear programming problem. As an example, each of the plurality of objective functions may have a trade-off relationship with each other. In the first embodiment, a case in which the production plans of four machines from a first machine to a fourth machine are determined using the plan determination device 1 is illustrated.

[0012] The plan determination device 1 has a control unit 10, an output unit 80, and a storage unit 90. The control unit 10 comprehensively controls each unit of the plan determination device 1. The control unit 10 executes a series of calculations for determining a production plan. The control unit 10 has a data acquisition unit 11, a coefficient calculation unit 12, an influence ranking determination unit 13, a calculation order determination unit 14, a plan formulation unit 15, and a final solution determination unit 16. The data acquisition unit 11 includes a case data acquisition unit 11-1 and a setting data acquisition unit 11-2. The coefficient calculation unit 12 includes a premise coefficient calculation unit 12-1 and an adjustment coefficient calculation unit 12-2.

[0013] The output unit 80 outputs the production plan determined by the control unit 10 to the outside. An example of the output unit 80 will be described later. The storage unit 90 may store a program executed by the control unit 10 and various data used in the program. In the example of Fig. 1, the storage unit 90 stores case data DT1 and setting data DT2.

[0014] FIG. 2 shows an example of the project data DT1. In the example of the first embodiment, it is assumed that multiple projects are associated with each device in the production plan. In the first embodiment, it is assumed that K projects from project 1 to project K are taken into consideration. K is a natural number equal to or greater than 2. The project data DT1 in the example of FIG. 2 includes a project list DT1-1, a project type list DT1-2, and calendar data DT1-3. In the example of FIG. 2, the start date of the production schedule for a certain project is abbreviated as "start date", and the end date of the production schedule for that project is abbreviated as "end date".

[0015] The case list DT1-1 shows the correspondence between each case and "start date, end date, deadline, case type, and equipment." The "end deadline and case type" corresponding to each case are input in advance as given data. The "start date, end date, and equipment" columns corresponding to each case are blank before a specific optimization algorithm is executed.

[0016] The project type list DT1-2 indicates the correspondence between a certain project type and the required production schedule of the equipment for that project type. In the example of the first embodiment, four types of project types A to D are set. As shown in Fig. 2, the required production schedule of the equipment differs depending on the project type. The project type is used as an index indicating the difficulty of the production work for a certain project.

[0017] The calendar data DT1-3 indicates whether or not non-productive work is performed on each machine on each day. In this specification, non-productive work generally refers to "repair, inspection, and adjustment" of machines. The flag value "0" indicates "non-productive work: no", and the flag value "1" indicates "non-productive work: yes".

[0018] In the multi-objective optimization problem in the first embodiment, (i) N objective functions for decision variables are defined, and (ii) constraint conditions for the decision variables are defined. N is an integer equal to or greater than 2. In this specification, the decision variables are collectively denoted as x.

[0019] In the multi-objective optimization problem in the first embodiment, the N objective functions are associated with N weighting coefficients, respectively. In this specification, the i-th objective function is referred to as the i-th objective function, and the i-th weighting coefficient is referred to as the i-th weighting coefficient, where i is an integer between 1 and N.

[0020] In the first embodiment, the case where N = 3 is mainly illustrated. Therefore, in the first embodiment, unless otherwise specified in the context, it is assumed that three objective functions, a first objective function f1 to a third objective function f3, are defined.

[0021] In the first embodiment, one global objective function F in a multi-objective optimization problem is determined based on N objective functions and N weighting coefficients. In this specification, the product of the i-th objective function and the i-th weighting coefficient is referred to as the i-th raw score. In the first embodiment, F is determined as the sum of the first raw score to the N-th raw score.

[0022] Therefore, the global objective function F in the N=3 example is: F = w1 f1 + w2 f2 + w3 f3 = w T f …(1) It is expressed as:

[0023] The vector f in equation (1) is

number

[0024] In formula (2), w1 to w3 are weighting coefficients corresponding to f1 to f3, respectively. w1 to w3 are the first weighting coefficient to the third weighting coefficient, respectively. The vector w in formula (1) is expressed as formula (8) described later. w is also called a weight vector.

[0025] In the first embodiment, a predetermined optimization algorithm is executed to maximize F. The maximization of F is given by: Max[F(x)]=Max[w T f(x)] …(3) Therefore, the optimization algorithm in the first embodiment is performed to find x that gives the maximum value of F.

[0026] In the multi-objective optimization problem in the example of the first embodiment, a constraint condition for x is defined. The constraint condition is as follows: st Ax≧b,x≧0 …(4) This can be formulated as follows:

[0027] In equation (4), A is a coefficient matrix for x,

number

[0028] In equation (4), x is a vector,

number

[0029] In the formula (4), b is

number

[0030] As described later, the weighting coefficient vector w can change through a series of processes in the plan determination device 1. In the first embodiment, w is expressed as follows:

number

[0031] In formula (8), α1 to α3 and β1 to β3 are coefficients corresponding to f1 to f3, respectively. α1 to α3 may be referred to as the first priority coefficient to the third priority coefficient, respectively. β1 to β3 may be referred to as the first adjustment coefficient to the third adjustment coefficient, respectively. In this specification, α1 to α3 may be collectively referred to as the priority coefficient α, and β1 to β3 may be collectively referred to as the adjustment coefficient β.

[0032] As shown in formula (8), one weighting coefficient corresponding to one objective function is expressed as the product of one priority coefficient α and one adjustment coefficient β. For example, w1 is expressed as the product of α1 and β1.

[0033] Each objective function in the example of the first embodiment is set with the intention of adjusting the production schedule of each project. In the first embodiment, f1 is a function formulated to minimize the downtime of a certain machine. In this specification, the downtime means the days excluding the production days and non-production work days in the production plan of the machine. On the other hand, f2 is a function formulated to position the production date of a certain project as far ahead as possible from the end date of the project. In this specification, for the sake of clarity, the explanation of the example of f3 is omitted.

[0034] In the example of the first embodiment, two constraint conditions, a first constraint condition and a second constraint condition, are defined as constraint conditions for x. The first constraint condition is a conditional expression that formulates that the production date of a certain project must be located before the deadline for the project. On the other hand, the second constraint condition is a conditional expression that formulates that the production date of a certain project must not overlap with a non-production work day. The constraint condition in the above formula (4) collectively represents the first constraint condition and the second constraint condition.

[0035] Fig. 3 shows an example of the setting data DT2. Various parameters related to a series of calculations in the plan determination device 1 are preset in the setting data DT2. The priority coefficient α in the first embodiment is preset in the setting data DT2. In the example of Fig. 3, α1=10, α2=5, and α3=1.

[0036] Therefore, in embodiment 1, w1=10·β1 w2=5·β2 w3=β3 As is clear from this, w can be adjusted by adjusting β.

[0037] The optimization algorithm executed by the plan determination device 1 may be any algorithm as long as it can solve a multi-objective optimization problem with constraint conditions. In the first embodiment, a genetic algorithm (GA) is exemplified as the optimization algorithm. For this reason, the setting data DT2 in the example of FIG. 3 sets values ​​of the number of generations, the number of solution candidates, the crossover probability, and the mutation probability, which are parameters of the GA.

[0038] In the example of the first embodiment, the theoretical maximum and minimum values ​​of each objective function are set in the setting data DT2. In addition, the maximum number of loops (described later) for determining the production plan is also set in the setting data DT2.

[0039] In the first embodiment, N thresholds corresponding to the N objective functions are set. In this specification, the threshold corresponding to the i-th objective function is referred to as the i-th threshold. In the setting data DT2 in the example of FIG. 3, a first threshold to a third threshold are set. In this specification, the first threshold to the third judgment threshold are represented as th1 to th3, respectively. An example of processing using these thresholds will be described later.

[0040] Fig. 4 shows an example of the initial state of a production plan in embodiment 1. As shown in Fig. 4, in the example of embodiment 1, the positions of non-production work days are assumed to be fixed. In Fig. 4, for example, the fact that the case type of case 1 is A is shown as "case 1 (A)".

[0041] 5 shows an example of a final production plan (final production plan) determined by the plan determination device 1 through a series of processes described below. The plan determination device 1 may generate calculation result data DT1-1New by writing various values ​​corresponding to a final solution described below in the blank columns of the project list DT1-1 in FIG.

[0042] (Example of process flow in the plan determination device 1) 6 is a flowchart illustrating a process flow in the plan determination device 1. In S1, the case data acquisition unit 11-1 acquires case data DT1 from the storage unit 90. In S2, the setting data acquisition unit 11-2 acquires setting data DT2 from the storage unit 90.

[0043] In S3, the premise coefficient calculation unit 12-1 calculates premise coefficients. That is, the premise coefficient calculation unit 12-1 calculates the coefficient matrix A shown in equation (5) and the right-hand side vector b shown in equation (7).

[0044] FIG. 7 is a diagram for explaining an example of calculation of the premise coefficient. FIG. 7 shows an example of the first constraint condition for case 1. The first constraint condition in the example of FIG. 7 is as follows: a11·D01+a12·s(M)≦b1 …(9) It is expressed as:

[0045] D01 and D11 in FIG. 7 respectively represent the start date and end deadline of project 1. D01 and D11 in FIG. 7 are assumed to be defined in project data DT1. When calculating the premise coefficients, D01 and D11 are converted into numerical data according to formula (9). s(M) represents the number of days required for production of project 1 in the Mth device. Since the first device is illustrated in FIG. 7, M=1.

[0046] In the example of formula (9), D01 and s(M)=s(1) correspond to the decision variables. That is, D01 in the example of formula 9 is an example of x1, and s(1) is an example of x2. In the example of FIG. 7, the premise coefficient calculation unit 12-1 may calculate a11, a12, and b1 in formula (9) using any algorithm. As an example, the calculation results of the premise coefficient calculation unit 12-1 are a11=1, a12=1, and b1=D11.

[0047] 6 again. In S4, adjustment coefficient calculation unit 12-2 calculates β based on the premise coefficient calculated in S3. First, adjustment coefficient calculation unit 12-2 sets the weighting coefficient of only one of the multiple objective functions to 1, and sets the weighting coefficients of the remaining objective functions to 0.

[0048] As an example, the adjustment coefficient calculation unit 12-2 sets only w1 to 1, and sets w2 and w3 to 0. In this case, F is expressed as follows: F=w1·f1+w2·f2+w3·f3=1·f1+0·f2+0·f3 =f1 It is expressed as:

[0049] In this way, by setting only w1 to 1 and the other weighting coefficients to 0, a provisional F equal to f1 is obtained. In this specification, the provisional F equal to the i-th objective function is referred to as the i-th provisional global function. F in the above example represents the first provisional global function.

[0050] Deriving the maximum value of the i-th temporary global function under a certain constraint condition is equivalent to deriving the maximum value of the i-th objective function under the same constraint condition. Therefore, the adjustment coefficient calculation unit 12-2 derives the maximum value of the first temporary global function under the constraint condition of the above-mentioned formula (4) by executing GA. That is, the adjustment coefficient calculation unit 12-2 derives the maximum value of f1 under the above-mentioned constraint condition by executing GA. In the example of the first embodiment, the adjustment coefficient calculation unit 12-2 derives the maximum value of f1 under the above-mentioned constraint condition by executing GA with, for example, 50 generations and 100 solution candidates.

[0051] In the example of the first embodiment, the number of generations and the number of solution candidates of the GA in S4 are set smaller than the number of generations and the number of solution candidates set in the setting data DT2. For this reason, the multi-objective optimization problem solved in S4 is called a tentative multi-objective optimization problem.

[0052] The adjustment coefficient calculation unit 12-2 acquires the maximum value of f1 for each generation in the GA. Then, the adjustment coefficient calculation unit 12-2 calculates the amount of change in the maximum value of f1 for each generation. Next, the adjustment coefficient calculation unit 12-2 calculates the average value of the amount of change in the maximum value of f1. In this specification, the average value of the amount of change in the maximum value of f1 is represented as f1(Max_mean).

[0053] In the example of the first embodiment, the adjustment coefficient calculation unit 12-2 calculates β1 based on f1Max_mean and the maximum and minimum values ​​of f1 defined in the setting data DT2. In this specification, the maximum and minimum values ​​of f1 defined in the setting data DT2 are denoted as f1Max and f1min, respectively.

[0054] As an example, the adjustment coefficient calculation unit 12-2 β1=f1Max_mean / (f1Max-f1min) …(10) As shown in FIG. 3, f1Max=3 and f1min=0. Therefore, for example, when f1Max_mean=0.1, β1 = 0.1 / 3 = 1 / 30 ≒ 0.033 It is.

[0055] In formula (10), (f1Max-f1min) represents the theoretical maximum value of the change in f1 for each generation in GA. Therefore, β1 determined by formula (10) is a value obtained by normalizing the average value of the change in the maximum value of f1 by the theoretical maximum value of the change. Such normalization can facilitate the work of adjusting the values ​​of each weighting coefficient in the subsequent steps. For this reason, β in this specification is referred to as an adjustment coefficient.

[0056] Next, the adjustment coefficient calculation unit 12-2 calculates β2 by deriving the maximum value of f2 under the constraint condition of the above-mentioned formula (4) using GA in the same manner as the above example for β1. Then, the adjustment coefficient calculation unit 12-2 calculates β3 by deriving the maximum value of f3 under the same constraint condition using GA. In the example of the first embodiment, β2=0.5 and β3=0.1.

[0057] In S5, the influence ranking determination unit 13 uses β calculated in S4 as a provisional weighting coefficient in F to update (reset) F. In the example of the first embodiment, the influence ranking determination unit 13: F = β1 f1 + β2 f2 + β3 f3 =0.033 f1 + 0.5 f2 + 0.1 f3 Update F as follows.

[0058] Then, the influence ranking determination unit 13 derives the maximum value of F after updating under the constraint condition of the above-mentioned formula (4). In the example of the first embodiment, the influence ranking determination unit 13 derives the maximum value of F after updating under the above-mentioned constraint condition by executing a GA with 50 generations and 100 solution candidates. In the example of the first embodiment, the number of generations and the number of solution candidates of the GA in S5 are also set smaller than the number of generations and the number of solution candidates set in the setting data DT2. For this reason, the multi-objective optimization problem solved in S5 is also called a tentative multi-objective optimization problem.

[0059] The influence ranking determination unit 13 refers to the result of the GA and obtains the amount of increase in the value of f1 from the first generation to the final generation. Then, the influence ranking determination unit 13 multiplies the amount of increase by β1 to calculate the increase width of f1. Similarly, the influence ranking determination unit 13 calculates the increase width of f2 and f3. In this specification, the increase widths of f1 to f3 are referred to as the first increase width to the third increase width.

[0060] For example, when the first increase amount is larger than the second increase amount, f1 is considered to be a function that is more likely to increase than f2 under the above constraint conditions. In other words, when the first increase amount is larger than the second increase amount, f1 is considered to be a function that is more likely to be affected by the same constraint conditions than f2.

[0061] Therefore, the influence rank determination unit 13 may determine the influence rank of each objective function with respect to the constraint condition of formula (4) based on the calculated increase range of each objective function. The influence rank in this specification is an example of an index indicating the susceptibility to the influence from the constraint condition. Therefore, the jth influence rank in this specification indicates that an objective function among the N objective functions is the jth most susceptible to the influence from the constraint condition. j is an integer not less than 1 and not more than N. From the above, the influence rank determination unit 13 assigns a smaller influence rank number to an objective function as the increase range of the objective function increases.

[0062] As an example, consider a case where the first increase amount>the second increase amount>the third increase amount. In this case, the influence rank determination unit 13 determines the influence rank of f1 as the first influence rank, the influence rank of f2 as the second influence rank, and the influence rank of f3 as the third influence rank.

[0063] In S6, the calculation order determination unit 14 determines the order in which the weight coefficients of each objective function are enabled (returned to a non-zero value) based on the influence ranking of each objective function set in S5. In addition, the calculation order determination unit 14 divides the number of generations of the GA set in the setting data DT2 into generation intervals equal to the total number of objective functions. In the example of the first embodiment, the total number of objective functions is 3, and the number of generations of the GA is 900. Therefore, the calculation order determination unit 14 sets the 1st to 300th generations as the first generation interval, the 301st to 600th generations as the second generation interval, and the 601st to 900th generations as the third generation interval.

[0064] The calculation order determination unit 14 associates a generation section with a smaller number with an influence order with a smaller number. In the example of the first embodiment, the calculation order determination unit 14 associates the first generation section with the first influence order, the second generation section with the second influence order, and the third generation section with the third influence order. In other words, the calculation order determination unit 14 associates the first generation section with f1, the second generation section with f2, and the third generation section with f3.

[0065] The calculation order determination unit 14 validates only w1 in the first generation interval. Specifically, the calculation order determination unit 14 sets w1 in the first generation interval as w1=α1·β1. In the example of the first embodiment, α1=10, and β1 is calculated as 1 / 30 in the above-mentioned S4. Therefore, the calculation order determination unit 14 sets w1 in the first generation interval as w1=1 / 3≈0.333. This w1 is also maintained in the subsequent second generation interval and third generation interval.

[0066] Next, the calculation order determination unit 14 newly validates w2 in the second generation interval. Specifically, the calculation order determination unit 14 sets w2 in the second generation interval as w2=α2·β2. In the example of the first embodiment, α2=5, and β1=0.5 is calculated in S4 above. Therefore, the calculation order determination unit 14 sets w2 in the second generation interval as w2=2.5. This w2 is also maintained in the subsequent third generation interval.

[0067] Next, the calculation order determination unit 14 newly validates w3 in the third generation interval. Specifically, the calculation order determination unit 14 sets w3 in the third generation interval as w3=α3·β3. In the example of the first embodiment, α3=1, and β3 is calculated as 0.1 in S4 described above. Therefore, the calculation order determination unit 14 sets w3 in the third generation interval as w3=0.1.

[0068] Thus, in S6, In the first generation section, "w1=0.333, w2=0, w3=0", In the second generation section, "w1=0.333, w2=2.5, w3=0" In the third generation section, "w1=0.333, w2=2.5, w3=0.1" As such, w1 to w3 are set as follows: In this manner, the calculation order determination unit 14 increases the number of weighting coefficients to be activated as the generation interval progresses.

[0069] As described above, the plan determination device 1 may determine the influence ranking for each of the N objective functions by using GA to solve a hypothetical multi-objective optimization problem that maximizes each value of the N objective functions under the constraint condition of formula (4). For example, as described above, the plan determination device 1 may determine the j-th influence ranking by solving the hypothetical multi-objective optimization problem under the constraint condition.

[0070] In S7, the planning unit 15 uses each generation interval and the weighting coefficient for each generation interval determined in S6 to create a production plan. Specifically, the planning unit 15 applies the weighting coefficient for each generation interval to F. Then, the planning unit 15 uses GA to derive the maximum value of F under the above constraint conditions. The planning unit 15 derives x that gives the maximum value of the global function F in all generations as an optimal solution x_opt of the multi-objective optimization problem in embodiment 1.

[0071] As described above, the plan determination device 1 can derive x_opt by gradually solving the multi-objective optimization problem of maximizing F under the constraints of equation (4) using GA while changing the N weighting coefficients according to the influence rank.

[0072] For example, the plan determination device 1 may set the jth stage corresponding to the jth influence rank in a multi-objective optimization problem of maximizing F under the above constraint conditions. The jth generation section in the above example is an example of the jth stage. As described above, the plan determination device 1 may set the weight coefficients corresponding to the 1st influence rank to the jth influence rank among the N weight coefficients to non-zero in the jth stage, and set the weight coefficients corresponding to the (j+1)th influence rank to the Nth influence rank to 0.

[0073] In S8, the final solution determination unit 16 judges whether or not x_opt derived in S7 satisfies a predetermined termination condition. In the first embodiment, the termination condition is set as the condition that the value of each objective function in x_opt is equal to or greater than the threshold value of each objective function.

[0074] Therefore, in the first embodiment, the final solution determination unit 16 calculates f1(x_opt), f2(x_opt), and f3(x_opt). Next, the final solution determination unit 16 calculates f1(x_opt) ≧ th1 … (11-1) f2(x_opt) ≧ th2 … (11-2) f3(x_opt) ≧ th3 … (11-3) Determine whether or not the following is satisfied.

[0075] If the answer is YES in S8, that is, if all of the conditional expressions (11-1) to (11-3) are satisfied, the final solution determination unit 16 determines x_opt as the final solution x_final, and then proceeds to S10.

[0076] As described above, for all i from 1 to N, when the value of the i-th objective function in x_opt is equal to or greater than the i-th threshold, the plan determination device 1 may determine x_opt as x_final.

[0077] On the other hand, if the result in S8 is NO, that is, if at least one of the conditional expressions (11-1) to (11-3) is not satisfied, the process proceeds to S9.

[0078] In S9, the calculation order determination unit 14 selects an objective function that does not satisfy the termination condition. As an example, consider a case where conditional formula (11-1) is not satisfied and conditional formulas (11-2) to (11-3) are satisfied. In this case, the calculation order determination unit 14 selects f1 as the objective function that does not satisfy the termination condition.

[0079] Then, the calculation order determination unit 14 updates the generation interval of the selected objective function. In the above example, the calculation order determination unit 14 updates the first generation interval. As an example, the calculation order determination unit 14 may update the first generation interval by extending the length of the first generation interval that was initially set by a predetermined percentage (e.g., 10%).

[0080] As an example, the calculation order determination unit 14 updates the length of the first generation interval from 300 generations to 330 generations. That is, the calculation order determination unit 14 resets the first generation interval to 1 to 330 generations. With the resetting of the first generation interval, the calculation order determination unit 14 resets the second generation interval to 331 to 630 generations and resets the third generation interval to 631 to 930 generations. Then, the process returns to S7.

[0081] As described above, if the result in S8 is NO, then in S7, the optimal solution x_opt is derived again using the generation interval reset in S9. Therefore, the processes of S9 and S7 are repeated until all the objective functions satisfy the termination condition. However, if the number of times that the result in S8 is NO has reached the maximum number of loops set in the setting data DT2, the process of FIG. 6 may be terminated.

[0082] In S10, the final solution determination unit 16 determines a final production plan based on the final solution x_final. That is, the final solution determination unit 16 determines a final production plan corresponding to x_final.

[0083] In S11, the output unit 80 acquires the final production plan from the final solution determination unit 16, and outputs the final production plan to the outside of the plan determination device 1. As an example, the output unit 80 may be a display unit. In this case, the output unit 80 may display the final production plan. This allows the final production plan to be visually presented to the user of the plan determination device 1.

[0084] (Comparative Example) Before describing the effects of the plan determination device 1, a comparative example will be described. In the comparative example, a current production plan (a new production plan) is determined using a conventional technology (e.g., the technology of Patent Document 1). Specifically, in the comparative example, a weighting factor for the current production plan is searched for by a grid search based on past production plans.

[0085] In this way, in the comparative example, the current production plan is determined on the basis of the past production plan. However, the conditions in the current production plan do not necessarily match the conditions in the past production plan. As an example, the current production plan may determine non-production work days under conditions different from those in the past production plan. As a result, the current production plan may determine constraint conditions different from those in the past production plan.

[0086] In the comparative example, the weighting coefficient in the current production plan is strongly dependent on the past production plan, and therefore, in the comparative example, when the current production plan has constraint conditions different from those in the past production plan, the weighting coefficient may not be set appropriately for the current production plan.

[0087] Therefore, in the comparative example, the contribution rate of one objective function to the global function may be significantly larger than the contribution rate of another objective function to the global function. As a result, it is considered that the comparative example has a relatively high tendency to fall into a local optimum solution in a multi-objective optimization problem. For this reason, in the comparative example, there is a risk that the current production plan cannot be set appropriately.

[0088] (Effect of planning decision device 1) According to the plan determination device 1, unlike the comparative example, it is possible to set the weight coefficient of each objective function after considering the influence of the constraint conditions on each objective function. In addition, according to the plan determination device 1, it is possible to set the weight coefficient without needing past production plans, unlike the comparative example. Therefore, according to the plan determination device 1, it is possible to reduce the risk of falling into a locally optimal solution, compared to the comparative example.

[0089] From the above, according to the plan determination device 1, it is possible to determine the current production plan more flexibly than in the comparative example. In this way, according to the plan determination device 1, it is possible to determine the production plan more appropriately than in the past.

[0090] Fig. 8 shows a schematic example of a production plan formulation process by the plan determination device 1. Fig. 8 shows an example of the calculation process in S7 described above. For the sake of clarity, the example in Fig. 8 illustrates a case where N=2. Therefore, in the example in Fig. 8, the number of generations of the GA is divided into a first generation section and a second generation section.

[0091] In the first generation section in the example of Fig. 8, only w1 is enabled. Therefore, the global function F in the first generation section depends only on f1. In the first generation section in the example of Fig. 8, (i) the case 8(A) is exchanged with the case 10(B) in the first device, and (ii) the case 7(D) is exchanged with the case 6(A) in the second device, in response to f1.

[0092] In the second generation section in the example of FIG. 8, w1 and w2 are enabled. Therefore, the global function F in the first generation section depends on f1 and f2. In the second generation section in the example of FIG. 8, (i) the case 3 (D) is exchanged with the case 2 (B) in the second device, and (ii) the case 13 (B) is exchanged with the case 9 (D) in the fourth device, in response to f1. In addition, in the second generation section in the example of FIG. 8, the end dates of some cases are brought forward in response to f2 compared to the end dates of the cases in the first generation section.

[0093] [Embodiment 2] (1) As described in the first embodiment, the optimization algorithm executed by the plan determination device 1 is not limited to GA. Other examples of the optimization algorithm include local search, ant colony optimization (ACO), artificial bee colony optimization (ABC), partial swarm optimization (PSO), and differential evolution (DE).

[0094] (2) In the first embodiment, the weight coefficient in a certain generation interval is constant. However, the weight coefficient in a certain generation interval does not necessarily have to be set to a constant value. For example, the plan determination device 1 may gradually change w1 in the first generation interval as the generation progresses. Therefore, as an example, the plan determination device 1 may have a function that determines the manner of change in w1 as the generation progresses.

[0095] (3) In the first embodiment, a case where different influence ranks are assigned to each of the multiple objective functions has been exemplified. However, in one aspect of the present invention, the same influence rank may be assigned to each of the multiple objective functions.

[0096] For example, when the absolute value of the difference between the second and third increase ranges is equal to or less than a predetermined value (e.g., 0.001), the influence of the constraint condition of formula (4) on f2 is considered to be substantially equal to the influence of the constraint condition on f3. Therefore, when the absolute value is equal to or less than a predetermined value, the influence ranking determination unit 13 may determine the influence rankings of both f2 and f3 as the second influence ranking.

[0097] In this case, the calculation order determination unit 14 associates the first generation section with the first influence priority, and the second and third generation sections with the second influence priority. In other words, the calculation order determination unit 14 associates the first generation section with f1, and the second and third generation sections with f2 and f3.

[0098] In this case, the calculation order determination unit 14 newly validates both w2 and w3 in the second generation section. These w2 and w3 are also maintained in the subsequent third generation section. Therefore, In the first generation section, "w1=0.333, w2=0, w3=0", In the second and third generation sections, "w1=0.333, w2=2.5, w3=0", As such, w1 to w3 are set as follows: In this manner, the calculation order determination unit 14 may newly activate two or more weighting coefficients as one generation interval progresses.

[0099] [Software implementation example] The functions of the plan determination device 1 (hereinafter referred to as the "device") can be realized by a program for causing a computer to function as the device, and a program for causing a computer to function as each control block of the device (particularly each part included in the control unit 10).

[0100] In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the program. The control device and storage device execute the program to realize each function described in each of the above embodiments.

[0101] The program may be non-transitory and may be recorded in one or more computer-readable recording media. The recording media may or may not be included in the device. In the latter case, the program may be provided to the device via any wired or wireless transmission medium.

[0102] In addition, some or all of the functions of each of the control blocks can be realized by a logic circuit. For example, an integrated circuit in which a logic circuit that functions as each of the control blocks is formed is also included in the scope of the present invention. In addition, the functions of each of the control blocks can be realized by, for example, a quantum computer.

[0103] Furthermore, each process described in each of the above embodiments may be executed by AI (Artificial Intelligence). In this case, the AI ​​may be executed by the control device or another device (for example, an edge computer or a cloud server).

[0104] 〔summary〕 A plan determination device according to a first aspect of the present invention is a plan determination device that determines a production plan by solving a multi-objective optimization problem for production plans of a plurality of machines, wherein in the multi-objective optimization problem, (i) N objective functions for decision variables are defined, and (ii) constraint conditions for the decision variables are defined, where N is an integer of 2 or more, the N objective functions are associated with N weighting coefficients, respectively, where i is an integer of 1 or more and N or less, the i-th objective function is referred to as the i-th objective function, the i-th weighting coefficient is referred to as the i-th weighting coefficient, and a product of the i-th objective function and the i-th weighting coefficient is referred to as the i-th raw score, A global objective function in the multi-objective optimization problem is defined as the sum of a first raw score to an Nth raw score, and the plan determination device solves a hypothetical multi-objective optimization problem that maximizes each of the N objective functions under the constraint conditions using a predetermined optimization algorithm, thereby determining an influence ranking for each of the N objective functions, which indicates how susceptible each of the N objective functions is to being influenced by the constraint conditions, and derives an optimal solution to the multi-objective optimization problem by gradually solving the multi-objective optimization problem that maximizes the global objective function under the constraint conditions using the optimization algorithm while changing the N weighting coefficients in accordance with the influence ranking.

[0105] In the plan determination device according to aspect 2 of the present invention, in aspect 1, j is an integer greater than or equal to 1 and less than or equal to N, and the plan determination device may determine a j-th influence ranking indicating that a certain objective function among the N objective functions is the jth most susceptible to being influenced by the constraint condition by solving the virtual multi-objective optimization problem under the constraint condition, and may set a j-th stage corresponding to the j-th influence ranking in the multi-objective optimization problem that maximizes the global objective function under the constraint condition, and in the j-th stage, may set the weighting coefficients corresponding to the 1st influence ranking to the j-th influence ranking among the N weighting coefficients to non-zero, and set the weighting coefficients corresponding to the (j+1)th influence ranking to the Nth influence ranking to 0.

[0106] In the plan determination device according to aspect 3 of the present invention, in aspect 1 or 2, N thresholds corresponding to the N objective functions may be set, and among the N thresholds, the threshold corresponding to the i-th objective function may be referred to as the i-th threshold, and the plan determination device may determine the optimal solution as a final solution when the value of the i-th objective function in the optimal solution is equal to or greater than the i-th threshold for all i from 1 to N.

[0107] In the plan determination device according to a fourth aspect of the present invention, in the third aspect, the plan determination device may determine the production plan corresponding to the final solution.

[0108] In the plan determination device according to a fifth aspect of the present invention, in any one of the first to fourth aspects, the optimization algorithm may be a genetic algorithm.

[0109] A plan determination method according to a sixth aspect of the present invention is a plan determination method for determining a production plan by solving a multi-objective optimization problem for production plans of a plurality of machines, wherein in the multi-objective optimization problem, (i) N objective functions for decision variables are determined, and (ii) constraint conditions for the decision variables are determined, N is an integer of 2 or more, the N objective functions are respectively associated with N weighting coefficients, i is an integer of 1 or more and N or less, the i-th objective function is referred to as the i-th objective function, the i-th weighting coefficient is referred to as the i-th weighting coefficient, and a product of the i-th objective function and the i-th weighting coefficient is referred to as the i-th raw score, A global objective function in the multi-objective optimization problem is determined as the sum of a first raw score to an Nth raw score, and the plan determination method uses a predetermined optimization algorithm to solve a hypothetical multi-objective optimization problem that maximizes each of the N objective functions under the constraint conditions, thereby determining an influence ranking for each of the N objective functions, which indicates how susceptible each of the N objective functions is to being affected by the constraint conditions, and derives an optimal solution to the multi-objective optimization problem by gradually solving the multi-objective optimization problem that maximizes the global objective function under the constraint conditions using the optimization algorithm while changing the N weighting coefficients in accordance with the influence ranking.

[0110] [Additional Notes] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention. [Explanation of symbols]

[0111] 1. Planning and decision-making device 10 Control section 11 Data Acquisition Section 11-1 Case data acquisition section 11-2 Setting data acquisition section 12 Coefficient calculation section 12-1 Prerequisite coefficient calculation section 12-2 Adjustment coefficient calculation section 13. Influence Priority Determination Division 14 Calculation order determination part 15 Planning Department 16 Final Solution Determination Section 90 Memory section DT1 Project Data DT2 setting data

Claims

1. A plan determination device that determines a production plan by solving a multi-objective optimization problem for a production plan of a plurality of machines, comprising: In the multi-objective optimization problem, (i) N objective functions for decision variables are defined, and (ii) constraints for the decision variables are defined; N is an integer of 2 or more, The N objective functions are respectively associated with N weighting coefficients, i is an integer greater than or equal to 1 and less than or equal to N, The i-th objective function is referred to as the i-th objective function, The i-th weighting factor is referred to as the i-th weighting factor, The product of the i-th objective function and the i-th weighting coefficient is called the i-th raw score, A global objective function in the multi-objective optimization problem is defined as a sum of a first raw score to an Nth raw score, The plan determination device includes: determining an influence ranking indicating the susceptibility of each of the N objective functions to an influence from the constraint condition by solving a virtual multi-objective optimization problem for maximizing each of the N objective functions under the constraint condition using a predetermined optimization algorithm; a planning decision device which derives an optimal solution to the multi-objective optimization problem by gradually solving the multi-objective optimization problem, which maximizes the global objective function under the constraint conditions, using the optimization algorithm while changing the N weighting coefficients according to the influence ranking.

2. j is an integer greater than or equal to 1 and less than or equal to N, The plan determination device includes: determining a j-th influence rank indicating that an objective function among the N objective functions is the j-th most susceptible to being influenced by the constraint condition by solving the virtual multi-objective optimization problem under the constraint condition; In the multi-objective optimization problem for maximizing the global objective function under the constraint condition, a jth stage corresponding to the jth influence rank is set; 2. The plan determination device according to claim 1, wherein, in the jth stage, among the N weighting coefficients, weighting coefficients corresponding to the first influence rank through the jth influence rank are set to non-zero, and weighting coefficients corresponding to the (j+1)th influence rank through the Nth influence rank are set to 0.

3. N thresholds corresponding to the N objective functions are set, Among the N thresholds, a threshold corresponding to the i-th objective function is referred to as an i-th threshold, 3. The plan determination device according to claim 1, wherein, for all i from 1 to N, when a value of the i-th objective function in the optimal solution is equal to or greater than the i-th threshold, the plan determination device determines the optimal solution as a final solution.

4. The plan determination device according to claim 3 , further comprising: a production plan determination unit configured to determine the production plan corresponding to the final solution.

5. The plan determination device according to claim 1 , wherein the optimization algorithm is a genetic algorithm.

6. A plan determination method for determining a production plan by solving a multi-objective optimization problem for a production plan of a plurality of machines, the method comprising: In the multi-objective optimization problem, (i) N objective functions for decision variables are defined, and (ii) constraints for the decision variables are defined; N is an integer of 2 or more, The N objective functions are respectively associated with N weighting coefficients, i is an integer greater than or equal to 1 and less than or equal to N, The i-th objective function is referred to as the i-th objective function, The i-th weighting factor is referred to as the i-th weighting factor, The product of the i-th objective function and the i-th weighting coefficient is called the i-th raw score, A global objective function in the multi-objective optimization problem is defined as a sum of a first raw score to an Nth raw score, In the plan determination method, determining an influence ranking indicating the susceptibility of each of the N objective functions to an influence from the constraint condition by solving a virtual multi-objective optimization problem for maximizing each of the N objective functions under the constraint condition using a predetermined optimization algorithm; a multi-objective optimization problem for maximizing the global objective function under the constraint conditions, the multi-objective optimization problem being solved progressively using the optimization algorithm while varying the N weighting coefficients according to the influence ranking, thereby deriving an optimal solution to the multi-objective optimization problem.

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