Schedule generation device, schedule generation program, and schedule generation method

Abstract

To efficiently solve a scheduling problem for equipment.SOLUTION: The schedule generation device includes a scheduling problem generator that solves a scheduling problem to generate scheduling problem data, a relaxation solution generator that solves a relaxation problem to generate relaxation solution data of a binary variable, a shortest path problem generator that solves a shortest path problem on a network flow to generate shortest path problem data, an approximate solution generator that solves the shortest path problem data to determine at least one approximate solution of the binary variable, and a continuous variable generator that generates schedule data based on parameter data and the approximate solution.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The technology disclosed in this specification relates to a schedule generation technology for devices. [Background technology]

[0002] To support optimal decision-making by system operators, scheduling using mathematical programming is implemented. One method for solving scheduling problems formulated as mixed integer programming problems is the branch-and-bound method, but since it requires a long calculation time for large-scale problems, an efficient solution method is required. For example, Patent Document 1 proposes an efficient formulation using network flow for the generator operation planning problem. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 7204696 Summary of the Invention [Problem to be solved by the invention]

[0004] In the prior art, a formulation using network flow can be used to efficiently solve a generator operation planning problem using the branch and bound method. However, even with an efficient formulation, it is still difficult to find an optimal solution using the branch and bound method for large-scale problems.

[0005] The technology disclosed in this specification has been made in consideration of the problems described above, and is a technology for efficiently solving not only generator operation planning problems but also scheduling problems involving equipment whose state transitions are modeled by network flows. [Means for solving the problem]

[0006] A schedule generation device that is a first aspect of the technology disclosed in the present specification includes a scheduling problem generation unit that generates scheduling problem data representing constraint conditions and an objective function of a scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to equipment scheduling; a relaxation solution generation unit that generates relaxation solution data of binary variables that are variables that indicate the operating state of the equipment by solving a relaxation problem generated using the scheduling problem data; a shortest path problem generation unit that generates shortest path problem data that represent constraint conditions and an objective function of a shortest path problem using the parameter data and the relaxed solution data; an approximate solution generation unit that determines at least one approximate solution of the binary variables by solving the shortest path problem data; and a continuous variable generation unit that generates schedule data that is operating data of the equipment based on the parameter data and the approximate solution. [Effects of the Invention]

[0007] According to at least the first aspect of the technology disclosed in the present specification, when solving a scheduling problem, an integer solution can be determined by a shortest path problem, which is easy to solve, thereby enabling efficient solving.

[0008] Furthermore, objects, features, aspects, and advantages associated with the technology disclosed herein will become more apparent from the detailed description and accompanying drawings set forth below. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 2 illustrates an example of a hardware configuration of a schedule generation device according to an embodiment. [Figure 2] FIG. 2 is a diagram illustrating an example of a functional configuration of a schedule generation device according to an embodiment. [Figure 3] 1 is a flowchart illustrating a schedule generating method processed by a schedule generating device according to an embodiment. [Figure 4]FIG. 2 is a diagram illustrating an example of a functional configuration of a schedule generation device according to an embodiment. [Figure 5] 1 is a flowchart illustrating a schedule generating method processed by a schedule generating device according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, embodiments will be described with reference to the accompanying drawings. In the following embodiments, detailed features are shown for the purpose of explaining the technology, but these are merely examples and are not necessarily essential features for enabling the embodiments to be implemented.

[0011] The drawings are schematic, and for the sake of convenience, components may be omitted or simplified as appropriate. The relative sizes and positions of components shown in different drawings are not necessarily accurately depicted and may be changed as appropriate. Hatching may also be used in drawings such as plan views that are not cross-sectional views to facilitate understanding of the embodiments.

[0012] In the following description, the same components are denoted by the same reference numerals, and their names and functions are also the same. Therefore, detailed descriptions of them may be omitted to avoid duplication.

[0013] Furthermore, in the description given in this specification, when a certain component is described as "comprising," "including," or "having," unless otherwise specified, this is not an exclusive expression that excludes the presence of other components.

[0014] Furthermore, although ordinal numbers such as "first" or "second" may be used in the descriptions in this specification, these terms are used for convenience to facilitate understanding of the contents of the embodiments, and the contents of the embodiments are not limited to the order that may result from these ordinal numbers.

[0015] First Embodiment A schedule generating device, a schedule generating program, and a schedule generating method according to this embodiment will be described below.

[0016] <Configuration of the schedule generation device> Fig. 1 is a diagram showing an example of the hardware configuration of a schedule generation device according to this embodiment. As shown in Fig. 1, the schedule generation device is configured using, for example, a PC (Personal Computer) 010. The PC 010 includes a CPU (Central Processing Unit) 01, a main memory device 02, an auxiliary memory device 03, an external memory device 04, an input device 05, and an output device 06.

[0017] The external storage device 04 may be connected via a network 07. The PC 010 may also be connected to an external computer 08 via a network. The main storage device 02 is, for example, a memory device such as a DRAM (Dynamic Random Access Memory). The auxiliary storage device 03 is, for example, a magnetic disk. The external storage device 04 is, for example, an optical disk such as a CD-R or DVD-R, or a flash memory storage device such as a USB memory or an SD card. The input device 05 is, for example, a mouse or a keyboard. The output device 06 is, for example, a display or a printer. The network 07 is composed of optical communication equipment.

[0018] Fig. 2 is a diagram showing an example of the functional configuration of a schedule generation device according to this embodiment. As shown in Fig. 2, the schedule generation device includes a scheduling problem generation unit 2 that generates scheduling problem data 3 from scheduling problem parameter data 1, a relaxed solution generation unit 4 that generates relaxed solution data 5 from the generated scheduling problem data 3, a shortest path problem generation unit 6 that generates shortest path problem data 7 from the scheduling problem parameter data 1 and the relaxed solution data 5, a binary approximation solution determination unit 8 that generates binary approximation solution data 9 from the shortest path problem data 7, and a continuous variable determination unit 10 that generates schedule data 11 from the scheduling problem parameter data 1 and the binary approximation solution data 9.

[0019] The scheduling problem generator 2 uses a network flow to generate scheduling problem data 3 based on the scheduling problem parameter data 1. The scheduling problem parameter data 1 is data related to the target period of the schedule, time intervals, equipment specifications, constraints on equipment operation, and objective functions. The scheduling problem data 3 is a mathematical expression that represents the constraints and objective functions of a scheduling problem formulated as a mathematical optimization problem. An example of generating scheduling problem data 3 for a power generator operation planning problem is shown below.

[0020] The minimum output of generator g is X g MIN and the maximum output is X g MAX The minimum operation time is T g MUT The minimum stopping time is T g MDT In addition, the quadratic coefficient of the fuel cost characteristic function is F g Q and the linear coefficient is F g L and the constant term is F g G and the startup cost is F g ONIn addition, the group of generators to be planned is G, the group of time is T = {1, 2, , |T|}, and the power demand D at time t ∈ T is t Also, let x be the variable that represents the output of generator g at time t. gt Let u be the variable that indicates the start / stop state (1 is start, 0 is stop). g,t Let e ​​be the variable that is 1 if the activation / deactivation state transitions from s1 to s2, and 0 otherwise. g,t,s1,s2 In addition, the initial start / stop state of the generator is defined as E g In addition, the symbol δ is 1 when t1=t2 and 0 when t1≠t2. t1,t2 Define

[0021] In this case, the generator operation planning problem can be expressed as the following equations (1) to (7). g,t,s1,s2 For , if the index is not included in T, it is assumed to be 0.

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[0029] Equation (1) is the sum of fuel cost and startup cost, which is to be minimized. Equation (2) is the upper and lower output constraints of the generator. Equation (3) is the variable e g,t,s1,s2 Then, the variable u that indicates the start / stop state g,t Equations (4) and (5) are flow conservation laws in the network flow, imposing minimum operating time constraints and minimum stop time constraints. Equation (6) is the supply and demand balance constraint. Equation (7) represents the domain of each decision variable.

[0030] The relaxation solution generation unit 4 generates a relaxation problem from the scheduling problem data 3, and obtains relaxation solution data 5 by solving the relaxation problem. The relaxation solution data 5 is a relaxation solution of the decision variables of the scheduling problem. To explain the process using a generator operation planning problem as an example, the problem shown in equations (1) to (7) is solved by the binary variable u g,t and e g,t,s1,s2 The relaxed problem is generated by successively relaxing the above equation. The solution obtained by solving the generated relaxed problem using an interior point method or the like is stored as the relaxed solution data 5.

[0031] The shortest path problem generator 6 generates shortest path problem data 7 that represents the shortest path problem on the network flow from the scheduling problem parameter data 1 and the relaxed solution data 5. The shortest path problem data 7 is a mathematical expression that represents the constraints and objective function of the shortest path problem formulated as a mathematical optimization problem. An example of generating shortest path problem data 7 for a generator operation planning problem is shown below.

[0032] The relaxed solution for activation and shutdown obtained by the relaxed solution generating unit 4 is set as follows:

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[0034] In this case, regarding activation and deactivation, u is set so that the amount of separation from the relaxed solution is minimized while satisfying the constraints in the network flow. g,t The problem of determining can be expressed as a problem with equation (8) as the objective function and equations (4), (5) and (9) as constraints.

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[0037] Equation (8) shows the deviation from the relaxed solution, e g,t,s1,s2 The objective function e g,t,s1,s2 If we consider the coefficients of as the lengths of the paths, we can see that this problem is equivalent to the shortest path problem on the network flow expressed by equations (4), (5), and (9).

[0038] The binary approximate solution determination unit 8 generates binary approximate solution data 9 by solving a shortest path problem in which the decision variables are integer solutions of binary variables held as shortest path problem data 7. The binary approximate solution data 9 is an approximate solution of a binary variable that represents the operating state of equipment. The binary approximate solution data 9 is generated by directly solving the shortest path problem data 7 using Dijkstra's algorithm, or by solving a continuous relaxation problem of the shortest path problem data 7 using a continuous value optimization method such as the simplex method. Note that although the shortest path problem data 7 is a combinatorial optimization problem, it is generally known that an integer solution can be obtained as a solution to the continuous relaxation problem because the coefficient matrix representing the constraint conditions is a completely unimodular matrix.

[0039] The continuous variable determination unit 10 determines a solution of the continuous variables from the scheduling problem parameter data 1 and the binary approximation solution data 9, and generates schedule data 11 using the solution of the continuous variables. The schedule data 11 is operation data of the equipment for each time, and includes the operation state or output of the equipment. To explain the process using the generator operation planning problem as an example, the binary variable e g,t,s1,s2 The value of is fixed to the approximate solution obtained by the binary approximate solution determination unit 8, and the problem expressed by equations (1) to (7) is solved. Here, the approximate solution is set as follows.

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[0041] This problem is a quadratic programming problem and can be solved using the interior point method. g、t , startup / shutdown state u g,t and its transition e g,t,s1,s2 is stored as the schedule data 11.

[0042] FIG. 3 is a flowchart showing a schedule generation method that is processed by the schedule generation device according to this embodiment.

[0043] First, the scheduling problem generation unit 2 executes a scheduling problem generation process (step ST101), and stores the scheduling problem data 3 output as a result in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0044] Next, the relaxation solution generating unit 4 executes the relaxation solution generating process (step ST102), and stores the resulting relaxation solution data 5 in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0045] Next, the shortest path problem generation unit 6 executes the shortest path problem generation process on the CPU 01 (step ST103), and stores the shortest path problem data 7 output as a result in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0046] Next, the binary approximate solution determination unit 8 executes a binary approximate solution determination process on the CPU 01 (step ST104), and stores the binary approximate solution data 9 output as a result in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0047] Finally, the continuous variable determination unit 10 executes the continuous variable determination process on the CPU 01 (step ST105), and the resulting output schedule data 11 is stored in the main storage device 02, the auxiliary storage device 03, or the external storage device 04. The schedule data 11 may be output by the output device 06.

[0048] According to this embodiment, in solving a scheduling problem, an integer solution can be determined by a shortest path problem, which is easy to solve, and there is no need to search for integer variables using a branch and bound method. Therefore, efficient solution is possible.

[0049] The schedule generation device may be realized by a hardware configuration such as that shown in Fig. 1, or may be realized as software such as a program that embodies each function of the schedule generation device on a computer, or as a recording medium on which the software is recorded. The recording medium may be any type, such as a hard disk, an optical disk, or a magneto-optical disk.

[0050] Furthermore, in this embodiment, the generator operation planning problem has been described as an example, but the operation schedule can be optimized in a similar manner for any scheduling problem for equipment in which state transitions are modeled using network flows.

[0051] Below are examples of scheduling problem data 3 and shortest path problem data 7 for the economic load dispatch control problem. The scheduling problem data 3 for the economic load dispatch control problem for a generator with three bands (output bands) is expressed as equations (10) to (19).

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[0062] Here, T is the set of planning time periods, G is the set of generators, and S={0,1,2} is the set of bands.

[0063] F g,s Q and F g,s L are the quadratic and linear coefficients of the fuel cost characteristic function of generator g in band s, respectively. X g,s MIN and X g,s MAX are the lower and upper limits of the output of generator g in band s, respectively. x g,t,s is a continuous variable that represents the output value when generator g operates in band s at time t, and is 0 otherwise. g,t,s1,s2 trans is a binary variable that is 1 when generator g transitions from band s1 to band s2 at time t, and 0 otherwise. T g,s1,s2 trans is the time required for the band transition. C(S,2) is a set created by selecting any two distinct elements from the set S.

[0064] Equation (10) represents the fuel cost. Equations (11), (12), and (13) represent the upper and lower output constraints for each band. Equation (14) is the equation for calculating the band. Equations (15), (16), and (17) are the flow conservation laws in the network flow, and impose retention constraints when transitioning between bands. Equation (18) is the supply and demand balance constraint. Equation (19) represents the domain of each decision variable. Here, β g,t The relaxed solution of is given as follows:

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[0066] Then, the shortest path problem data 7 becomes equations (20), (15), (16), and (17).

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[0068] <Second embodiment> A schedule generation device, a schedule generation program, and a schedule generation method according to the present embodiment will be described. In the following description, components similar to those described in the above embodiments will be denoted by the same reference numerals, and detailed descriptions thereof will be omitted as appropriate.

[0069] <Configuration of the schedule generation device> Fig. 4 is a diagram showing an example of the functional configuration of a schedule generation device according to this embodiment. In Fig. 4, the binary approximate solution determiner 8, binary approximate solution data 9, and continuous variable determiner 10 of the configuration shown in Fig. 2 are replaced by a binary approximate solution candidate generator 12, binary approximate solution candidate data 13, and continuous variable candidate generator 14, respectively.

[0070] The binary approximate solution candidate generation unit 12 generates binary approximate solution candidate data 13 based on the shortest path problem data 7. The binary approximate solution candidate data 13 is a collection of multiple patterns of binary approximate solution data. The binary approximate solution data is an approximate solution of a binary variable that represents the operating state of the equipment. The shortest path problem data 7 can generally be expressed by equations (21), (22), and (23).

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[0074] Here, E is the set of branches, N is the set of nodes, and C(e) is the cost of branch e. ​​IN(n,e) is a function that is 1 if branch e ends at node n, and 0 otherwise. OUT(n,e) is a function that is 1 if branch e starts at node n, and 0 otherwise. Equation (21) represents the length of the path, equation (22) represents the conservation of flow, and equation (23) represents the domain of the branch, which is the decision variable.

[0075] The binary approximate solution candidate generation unit 12 generates multiple patterns of binary approximate solution data based on equations (21), (22), and (23), and stores them as binary approximate solution candidate data 13. For example, it transforms equations (21), (22), and (23) into unconstrained binary quadratic optimization problems shown in equations (24) and (25) using a weight W. Then, it solves the unconstrained binary quadratic optimization problem multiple times to obtain multiple patterns of binary approximate solution data, and stores them as binary approximate solution candidate data 13. The unconstrained binary quadratic optimization problem may be solved using annealing on a quantum computer, a quantum approximate optimization algorithm, simulated annealing, or the like.

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[0078] Alternatively, the binary approximate solution candidate generation unit 12 may obtain multiple patterns of binary approximate solution data and store them as binary approximate solution candidate data 13 by performing the process of solving the problem multiple times by adding a random number to the cost C(e) of branch e in equations (21), (22), and (23).

[0079] The continuous variable candidate generation unit 14 generates multiple patterns of solutions for continuous variables based on the scheduling problem parameter data 1 and the binary approximate solution candidate data 13. Specifically, multiple continuous value optimization problems are generated by fixing the binary variables of the scheduling problem data 3 with binary approximate solutions of each pattern, and multiple patterns of solutions for continuous variables are generated by independently solving these. Then, multiple schedules are generated by treating the continuous variable solutions and the corresponding binary approximate solutions as one tentative schedule, and the one with the best objective function value (the largest objective function value for a maximization problem, or the smallest objective function value for a minimization problem) is stored as schedule data 11.

[0080] FIG. 5 is a flowchart showing a schedule generating method that is processed by the schedule generating device according to this embodiment.

[0081] First, the scheduling problem generation unit 2 executes a scheduling problem generation process (step ST101), and stores the scheduling problem data 3 output as a result in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0082] Next, the relaxation solution generating unit 4 executes the relaxation solution generating process (step ST102), and stores the resulting relaxation solution data 5 in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0083] Next, the shortest path problem generation unit 6 executes the shortest path problem generation process on the CPU 01 (step ST103), and stores the shortest path problem data 7 output as a result in the main storage device 02, the auxiliary storage device 03, or the external storage device 04.

[0084] Next, the binary approximate solution candidate generating unit 12 executes a binary approximate solution candidate generating process (step ST201), and the continuous variable candidate generating unit 14 executes a continuous variable candidate generating process and a schedule selecting process (step ST202).

[0085] According to this embodiment, an optimal solution can be obtained by calculating a plurality of patterns of integer solutions.

[0086] <Effects Produced by the Multiple Embodiments Described Above> Next, examples of effects obtained by the above-described embodiments will be described. Note that in the following description, the effects will be described based on the specific configurations exemplified in the above-described embodiments, but these may be replaced with other specific configurations exemplified in the present specification as long as the same effects are obtained. In other words, for convenience, only one of the associated specific configurations may be described as a representative below, but the representatively described specific configuration may be replaced with another associated specific configuration.

[0087] Furthermore, the replacement may be made across multiple embodiments, i.e., configurations illustrated in different embodiments may be combined to produce the same effect.

[0088] According to the embodiment described above, the schedule generation device includes a scheduling problem generation unit 2, a relaxation solution generation unit 4, a shortest path problem generation unit 6, an approximate solution generation unit, and a continuous variable generation unit. Here, the approximate solution generation unit corresponds to, for example, the binary approximate solution determination unit 8 or the binary approximate solution candidate generation unit 12. Furthermore, the continuous variable generation unit corresponds to, for example, the continuous variable determination unit 10 or the continuous variable candidate generation unit 14. The scheduling problem generation unit 2 solves a scheduling problem generated using a network flow based on parameter data related to equipment scheduling. Here, the parameter data corresponds to, for example, scheduling problem parameter data 1. In this way, the scheduling problem generation unit 2 generates scheduling problem data 3 representing the constraints and objective function of the scheduling problem. The relaxation solution generation unit 4 solves the relaxation problem generated using the scheduling problem data 3. In this way, the relaxation solution generation unit 4 generates relaxation solution data 5 of binary variables, which are variables indicating the operating states of the equipment. The shortest path problem generation unit 6 solves the shortest path problem on the network flow generated using the scheduling problem parameter data 1 and the relaxation solution data 5. By doing so, the shortest path problem generation unit 6 generates shortest path problem data 7 that represents the constraints and objective function of the shortest path problem. The approximate solution generation unit determines at least one approximate solution of binary variables by solving the shortest path problem data 7. Here, the approximate solution corresponds to, for example, binary approximate solution data 9. The continuous variable generation unit generates schedule data, which is operation data for equipment, based on the scheduling problem parameter data 1 and the binary approximate solution data 9.

[0089] Furthermore, according to the embodiment described above, the schedule generation device includes a processing circuit (CPU 01) that executes a program and storage devices (main storage device 02, auxiliary storage device 03) that store the program to be executed. The processing circuit (CPU 01) executes the program to realize the following operations.

[0090] That is, a scheduling problem generated using a network flow based on scheduling problem parameter data 1 related to equipment scheduling is solved. By doing so, scheduling problem data 3 representing the constraints and objective function of the scheduling problem is generated. Then, a relaxed problem generated using the scheduling problem data 3 is solved. By doing so, relaxed solution data 5 of binary variables, which are variables indicating the operating state of the equipment, is generated. Then, a shortest path problem on the network flow generated using the scheduling problem parameter data 1 and the relaxed solution data 5 is solved. By doing so, shortest path problem data 7 representing the constraints and objective function of the shortest path problem is generated. Then, by solving the shortest path problem data 7, at least one binary approximation solution data 9 of the binary variables is determined. Then, schedule data, which is operation data of the equipment, is generated based on the scheduling problem parameter data 1 and the binary approximation solution data 9.

[0091] With this configuration, when solving a scheduling problem, an integer solution can be determined by a shortest path problem, which is easy to solve, and there is no need to search for integer variables using a branch and bound method. This allows for efficient solution.

[0092] Furthermore, even if other configurations shown as examples in this specification are appropriately added to the above configuration, that is, even if other configurations in this specification that were not mentioned as the above configuration are appropriately added, the same effect can be achieved.

[0093] Furthermore, according to the embodiment described above, the binary approximate solution candidate generation unit 12 determines a plurality of approximate solutions. With this configuration, an optimal solution can be obtained by calculating a plurality of patterns of integer solutions.

[0094] Furthermore, according to the embodiment described above, the relaxation solution generation unit 4 generates a relaxation problem by continuously relaxing binary variables. Then, the continuous variable generation unit determines a solution for the continuous variables based on the scheduling problem parameter data 1 and the binary approximate solution data 9, and generates schedule data using the solution for the continuous variables. With this configuration, the relaxation problem is generated by continuously relaxing binary variables, and schedule data can be generated using the solution for the continuous variables, enabling efficient solution generation.

[0095] Furthermore, according to the embodiment described above, the shortest path problem generation unit 6 generates shortest path problem data 7 by solving a shortest path problem in which integer solutions of binary variables are decision variables. Then, the approximate solution generation unit determines binary approximate solution data 9, which is an integer solution, by solving the shortest path problem data 7. With this configuration, it is possible to determine integer solutions of binary variables by using the shortest path problem, thereby enabling efficient solution generation.

[0096] Furthermore, according to the embodiment described above, the device is a device whose state transition is modeled by a network flow. With this configuration, for the device (facility) whose state transition is modeled by a network flow, an integer solution can be determined by a shortest path problem that is easy to solve, thereby enabling efficient solution.

[0097] According to the embodiment described above, the schedule generation program is a schedule generation program having a plurality of computer-executable instructions to be executed by one or more processors. The instructions executed by the processor cause the computer to generate scheduling problem data 3 representing constraints and an objective function of the scheduling problem by solving a scheduling problem generated using a network flow based on scheduling problem parameter data 1 related to equipment scheduling. The computer then generates relaxation solution data 5 of binary variables, which are variables indicating the operating state of the equipment, by solving a relaxation problem generated using the scheduling problem data 3. The computer then generates shortest path problem data 7 representing constraints and an objective function of the shortest path problem by solving a shortest path problem on the network flow generated using the scheduling problem parameter data 1 and the relaxation solution data 5. The computer then determines at least one binary approximation solution data 9 of the binary variables by solving the shortest path problem data 7. The computer then generates schedule data, which is operation data for the equipment, based on the scheduling problem parameter data 1 and the binary approximation solution data 9.

[0098] With this configuration, when solving a scheduling problem, an integer solution can be determined by a shortest path problem, which is easy to solve, and there is no need to search for integer variables using a branch and bound method. This allows for efficient solution.

[0099] Furthermore, the same effect can be achieved even if at least one of the other configurations for which examples are shown in this specification is appropriately added to the above configuration, i.e., even if another configuration for which examples are shown in this specification that was not mentioned as the above configuration is appropriately added.

[0100] The above program may be recorded on a computer-readable portable recording medium such as a magnetic disk, a flexible disk, an optical disk, a compact disk, a Blu-ray Disc (registered trademark), or a DVD. Portable recording media on which the program for realizing the above functions is recorded may be commercially distributed.

[0101] According to the embodiment described above, in the schedule generation method, a scheduling problem generated using a network flow is solved based on scheduling problem parameter data 1 related to equipment scheduling. By doing so, scheduling problem data 3 representing the constraints and objective function of the scheduling problem is generated. Then, a relaxed problem generated using the scheduling problem data 3 is solved. By doing so, relaxed solution data 5 of binary variables, which are variables indicating the operating state of the equipment, is generated. Then, a shortest path problem on the network flow generated using the scheduling problem parameter data 1 and the relaxed solution data 5 is solved. By doing so, shortest path problem data 7 representing the constraints and objective function of the shortest path problem is generated. Then, by solving the shortest path problem data 7, at least one binary approximation solution data 9 of the binary variables is determined. Then, schedule data, which is operation data of the equipment, is generated based on the scheduling problem parameter data 1 and the binary approximation solution data 9.

[0102] With this configuration, when solving a scheduling problem, an integer solution can be determined by a shortest path problem, which is easy to solve, and there is no need to search for integer variables using a branch and bound method. This allows for efficient solution.

[0103] Furthermore, even if other configurations shown as examples in this specification are appropriately added to the above configuration, that is, even if other configurations in this specification that were not mentioned as the above configuration are appropriately added, the same effect can be achieved.

[0104] <Modifications of the above-described embodiments> In the multiple embodiments described above, the dimensions, shapes, relative positional relationships, and implementation conditions of each component may also be described, but these are merely examples in all aspects and are not limiting.

[0105] Therefore, countless modifications and equivalents not shown as examples are contemplated within the scope of the technology disclosed in the present specification, including, for example, modifying, adding, or omitting at least one component, and further, extracting at least one component in at least one embodiment and combining it with a component in another embodiment.

[0106] Furthermore, unless a contradiction arises, when it is stated in the above-described embodiments that "one" component is provided, "one or more" of that component may also be provided.

[0107] Furthermore, each component in the embodiments described above is a conceptual unit, and the scope of the technology disclosed in this specification includes cases where one component is made up of multiple structures, cases where one component corresponds to part of a structure, and even cases where multiple components are provided in one structure.

[0108] Furthermore, each of the components in the embodiments described above includes structures having other structures or shapes as long as they perform the same function.

[0109] Furthermore, the descriptions in this specification are incorporated by reference for all purposes related to the present technology, and none of them are admitted to be prior art.

[0110] Various aspects of the present disclosure are summarized below as appendices.

[0111] (Appendix 1) a scheduling problem generation unit for generating scheduling problem data representing constraints and an objective function for a scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to device scheduling; a relaxation solution generation unit for generating relaxation solution data of binary variables that are variables indicating the operating states of the equipment by solving a relaxation problem generated using the scheduling problem data; a shortest path problem generator for generating shortest path problem data representing constraints and an objective function of a shortest path problem using the parameter data and the relaxation solution data; an approximate solution generating unit for determining at least one approximate solution of the binary variables by solving the shortest path problem data; a continuous variable generation unit for generating schedule data, which is operation data of the equipment, based on the parameter data and the approximate solution; Schedule generator.

[0112] (Appendix 2) 2. A schedule generation device according to claim 1, the approximate solution generation unit determines a plurality of the approximate solutions; Schedule generator.

[0113] (Appendix 3) 3. A schedule generation device according to claim 1 or 2, the relaxation solution generation unit generates the relaxation problem by successively relaxing the binary variables; the continuous variable generation unit determines a solution for a continuous variable based on the parameter data and the approximate solution, and generates the schedule data using the solution for the continuous variable. Schedule generator.

[0114] (Appendix 4) 4. A schedule generation device according to any one of Supplementary Notes 1 to 3, the shortest path problem generation unit generates shortest path problem data in which integer solutions of the binary variables are decision variables; the approximate solution generation unit determines the approximate solution, which is an integer solution, by solving the shortest path problem data; Schedule generator.

[0115] (Appendix 5) 5. A schedule generation device according to any one of Supplementary Notes 1 to 4, the device is a device whose state transition is modeled by the network flow; Schedule generator.

[0116] (Appendix 6) a schedule generation program having computer-executable instructions for execution by one or more processors, The instructions executed by the processor include: causing the computer to generate scheduling problem data representing constraints and an objective function for the scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to equipment scheduling; causing the computer to generate relaxation solution data for binary variables that are variables indicating the operating states of the equipment by solving a relaxation problem generated using the scheduling problem data; causing the computer to generate shortest path problem data representing constraints and an objective function of the shortest path problem by solving a shortest path problem on a network flow generated using the parameter data and the relaxed solution data; causing the computer to determine at least one approximate solution for the binary variables by solving the shortest path problem data; causing the computer to generate schedule data, which is operation data for the equipment, based on the parameter data and the approximate solution; Schedule generator.

[0117] (Appendix 7) generating scheduling problem data representing constraints and an objective function for a scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to equipment scheduling; generating relaxation solution data for a binary variable that is a variable indicating an operating state of the equipment by solving a relaxation problem generated using the scheduling problem data; generating shortest path problem data representing constraints and an objective function of the shortest path problem by solving a shortest path problem on a network flow generated using the parameter data and the relaxed solution data; determining at least one approximate solution for the binary variables by solving the shortest path problem data; generating schedule data, which is operation data of the equipment, based on the parameter data and the approximate solution; Schedule generation method. [Explanation of symbols]

[0118] 01 CPU, 1 scheduling problem parameter data, 2 scheduling problem generation unit, 02 main memory, 3 scheduling problem data, 03 auxiliary memory, 4 relaxation solution generation unit, 04 external memory, 5 relaxation solution data, 05 input device, 6 shortest path problem generation unit, 06 output device, 07 network, 7 shortest path problem data, 08 external computer, 8 binary approximation solution determination unit, 9 binary approximation solution data, 010 PC, 10 continuous variable determination unit, 11 schedule data, 12 binary approximation solution candidate generation unit, 13 binary approximation solution candidate data, 14 continuous variable candidate generation unit.

Claims

1. a scheduling problem generation unit for generating scheduling problem data representing constraints and an objective function for a scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to device scheduling; a relaxation solution generation unit for generating relaxation solution data of binary variables that are variables indicating the operating states of the equipment by solving a relaxation problem generated using the scheduling problem data; a shortest path problem generator for generating shortest path problem data representing constraints and an objective function of a shortest path problem using the parameter data and the relaxation solution data; an approximate solution generating unit for determining at least one approximate solution of the binary variables by solving the shortest path problem data; a continuous variable generation unit for generating schedule data, which is operation data of the equipment, based on the parameter data and the approximate solution; Schedule generator.

2. 2. The schedule generation device according to claim 1, the approximate solution generation unit determines a plurality of the approximate solutions; Schedule generator.

3. 3. A schedule generation device according to claim 1, the relaxation solution generation unit generates the relaxation problem by successively relaxing the binary variables; the continuous variable generation unit determines a solution for a continuous variable based on the parameter data and the approximate solution, and generates the schedule data using the solution for the continuous variable. Schedule generator.

4. 3. A schedule generation device according to claim 1, the shortest path problem generation unit generates shortest path problem data in which integer solutions of the binary variables are decision variables; the approximate solution generation unit determines the approximate solution, which is an integer solution, by solving the shortest path problem data; Schedule generator.

5. 3. A schedule generation device according to claim 1, the device is a device whose state transition is modeled by the network flow; Schedule generator.

6. a schedule generation program having computer-executable instructions for execution by one or more processors, The instructions executed by the processor include: causing the computer to generate scheduling problem data representing constraints and an objective function for the scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to equipment scheduling; causing the computer to generate relaxation solution data for binary variables that are variables indicating the operating states of the equipment by solving a relaxation problem generated using the scheduling problem data; causing the computer to generate shortest path problem data representing constraints and an objective function of the shortest path problem by solving a shortest path problem on a network flow generated using the parameter data and the relaxed solution data; causing the computer to determine at least one approximate solution for the binary variables by solving the shortest path problem data; causing the computer to generate schedule data, which is operation data for the equipment, based on the parameter data and the approximate solution; Schedule generator.

7. generating scheduling problem data representing constraints and an objective function for a scheduling problem by solving the scheduling problem generated using a network flow based on parameter data related to equipment scheduling; generating relaxation solution data for a binary variable that is a variable indicating an operating state of the equipment by solving a relaxation problem generated using the scheduling problem data; generating shortest path problem data representing constraints and an objective function of the shortest path problem by solving a shortest path problem on a network flow generated using the parameter data and the relaxed solution data; determining at least one approximate solution for the binary variables by solving the shortest path problem data; generating schedule data, which is operation data of the equipment, based on the parameter data and the approximate solution; Schedule generation method.

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