Energy function minimum value search device, energy function minimum value search method, and program

Abstract

To improve a near optimum solution which can be searched for by setting a pseudo-initial solution in an Ising machine which cannot set any initial solution.SOLUTION: In order to solve the above problem, an energy function minimum value search apparatus according to the present invention has an initial solution acquiring unit, an interaction coefficient correcting unit, and a temporary solution management unit. The initial solution acquiring unit acquires a first temporary solution spin / binary variables necessary for calculation of a first energy function. The interaction coefficient correcting unit corrects an interaction coefficient of the first energy function to change it to a value which contributes to reproduction of the first temporary solution spin / binary variable, and thus generates a second energy function. The temporary solution managing unit searches for a minimum value of the second energy solution by Ising machine, and sets the spin / binary variables giving the minimum value as a second temporary solution spin / binary variable to evaluate a value of the first energy function by using the first temporary solution spin / binary variable and the second temporary solution spin / binary variable.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The disclosed technology relates to a technology for finding a suboptimal solution to a combinatorial problem using an Ising machine. [Background technology]

[0002] Combinatorial optimization is a mathematical model that selects the best combination of a specific evaluation index from a large number of combinations that satisfy certain conditions. Combinatorial optimization appears in a wide range of fields, from business decision-making such as workforce planning, route planning, and drug discovery to academic research. On the other hand, it is difficult for conventional computers to solve combinatorial optimization problems efficiently (in polynomial time relative to the problem size) (NP problem). Therefore, technology that performs high-speed combinatorial optimization using computer hardware that utilizes physical phenomena to search for optimal solutions has become an important technology.

[0003] An Ising machine (described later) is a computer that searches for the ground state of an Ising model (described later). By expressing a combinatorial optimization problem as an Ising model, an Ising machine can efficiently find a suboptimal solution to the combinatorial optimization problem. The solution obtained by an Ising machine depends on the initial state of the spin. It is known that if a relatively good solution that satisfies the constraints of the combinatorial optimization problem is set as the initial solution to the Ising machine, the solution finally obtained will be closer to the optimal solution than when no initial solution is set (Non-Patent Document 1).

[0004] <Ising model> The Ising model is a model that represents the properties of magnetic materials. An example of an Ising model is shown in Figure 1. The Ising model is a system of spins (e.g., σ3 of 101) and edges (e.g., J of 102) that connect the spins. 2,3 ), with spin σ i can take on a value of either +1 (104 is an example of +1 with an up arrow) or -1 (105 is an example of -1 with a down arrow). i (e.g., h1 in 103) is the external magnetic field coefficient, and the spin σ iIt represents the force against J i,j is the interaction coefficient, and the two spins σ i , σ j It represents the interaction between J i,j The larger the value of σ i and σ j tends to have the same value, and J i,j The smaller the value of σ i and σ j is likely to take on different values.

[0005] The energy of the Ising model is expressed as shown in equation (1).

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[0006] <qubo> QUBO (Quadratic Unconditional Binary Optimization) is a method to optimize the spin σ i Let q be a binary variable that takes the value 0 or 1. i and its energy is expressed as equation (2).

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[0007] <Ising machine> An Ising machine is a computer that searches for the ground state of the Ising model or the QUBO model. By expressing a combinatorial optimization problem as an Ising model or a QUBO model, an Ising machine can efficiently find a suboptimal solution to the combinatorial optimization problem. Ising machines include quantum annealing machines, machines based on simulated annealing, simulated bifurcation machines, and coherent Ising machines.

[0008] <Quantum Annealing> In quantum annealing, the initial state of the spins is made quantum mechanically uncertain, and each spin is made to take two values, "+1" and "-1," simultaneously (superposition state) (Fig. 2(a)). By gradually reducing the effect of quantum fluctuations from the initial state, the interaction between spins, "J i,j " and the external magnetic field "h i The influence of " is strengthened so that the values ​​of each variable are determined autonomously while approaching the ground state (Figure 2(b)). [Prior art documents] [Non-patent literature]

[0009] [Non-Patent Document 1] K. Fukada et al, "A Three-Stage Annealing Method Solving Slot-Placement Problems Using an Ising Machine," IEEE Access, vol. 9, pp. 134413-134426, 2021. [Non-Patent Document 2] S. Kawakami et al, "Giving a Quasi-Initial Solution to Ising Machines by Controlling External Magnetic Field Coefficients," IEICE TRANS on Fundamentals of Electronics, Communications and Computer Sciences, 2023KEP0004, 2023. Summary of the Invention [Problem to be solved by the invention]

[0010] In some Ising machines, due to the principles of their hardware, it is not possible to set an initial solution. For example, in an Ising machine that uses quantum annealing as the solution-finding principle, as mentioned above, the initial state of each spin must be a superposition state in which the value is undetermined, and the initial solution, which is a definite value of the spin, cannot be the initial state. The same is true for a coherent Ising machine, in which a solution is found by the phase of a random DOPO (degenerate optical parametric oscillator) pulse evolving over time and approaching the ground state. In such an Ising machine, the initial solution cannot be used to improve the suboptimal solution.

[0011] In prior research, a method has been proposed for introducing a pseudo-initial solution into an Ising machine in which an initial solution cannot be set by adjusting an external magnetic field based on an initial solution (Non-Patent Document 2). However, some Ising machines are difficult to adjust because the adjustment of the external magnetic field is independent of the interactions, and some cannot handle an external magnetic field at all. [Means for solving the problem]

[0012] In order to solve the above problem, an energy function minimum value searching device according to the disclosed technique includes an initial solution acquisition unit, an interaction coefficient correction unit, and a tentative solution management unit. The initial solution acquisition unit acquires a first tentative solution spin / binary variable required for calculating the first energy function. The interaction coefficient correcting unit corrects an interaction coefficient of the first energy function to a value that contributes to reproduction of the first tentative solution spin / binary variable, to generate a second energy function. The tentative solution management unit searches for a minimum value of the second energy function using an Ising machine, sets the spin / binary variable that gives the minimum value as a second tentative solution spin / binary variable, and evaluates the value of the first energy function using the first tentative solution spin / binary variable and the second tentative solution spin / binary variable. Effect of the Invention

[0013] According to the disclosed device and method for searching for the minimum value of an energy function, in an Ising machine in which an initial solution cannot be set and an external magnetic field cannot be adjusted, by adjusting the interaction coefficient and setting a pseudo initial solution, it is possible to obtain a solution closer to the optimum, in the same way as in the case where an initial solution is set in an Ising machine in which an initial solution can be set. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 is a diagram showing an example of an Ising model. [Diagram 2] FIG. 1 shows an example of the spin state before and after annealing. [Diagram 3] FIG. 13 is a diagram illustrating adjustment of an interaction coefficient. [Figure 4] FIG. 2 is a functional block diagram of an energy function minimum search device. [Diagram 5] FIG. 4 is a flowchart illustrating the operation of the minimum value search device according to the first embodiment. [Figure 6] FIG. 1 is a functional block diagram of a combinatorial optimization device. [Figure 7] FIG. 1 shows the results of Experiment 1 on the constrained CVRP problem. [Figure 8] FIG. 13 shows the results of Experiment 1 relating to the max-cut problem. [Figure 9] 13 shows the results of Experiment 2 on the constrained CVRP problem. [Figure 10] FIG. 13 shows the results of Experiment 2 on the max-cut problem. [Figure 11] FIG. 2 is a diagram showing an example of the functional configuration of a computer. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Hereinafter, embodiments of the disclosed technology will be described in detail. Note that components having the same functions are given the same reference numbers and duplicated explanations will be omitted. EXAMPLES

[0016] In Example 1, the interaction coefficient of a target energy function (a function for which the minimum value is to be found by an Ising machine in order to obtain an optimal solution to a combinatorial problem) is sequentially adjusted using the spin combinations searched for by the Ising machine, thereby improving a suboptimal solution.

[0017] First, the adjustment of the interaction coefficient will be described. The initial solution spin of the target energy function σ~(0)={σ^1(0),σ^2(0),..., σ^ N (0)} is given. For example, set the interaction coefficient and external magnetic field coefficient in accordance with the target energy function in the Ising machine, run the Ising machine for a certain period of time to obtain a solution, and set this as the initial solution spin. Figure 3 shows an example of an Ising model with three spins. Figure 3(a) shows the interaction coefficient J 1,2 ,J 1,3 ,J 2,3 By setting the external magnetic field coefficients h1, h2, and h3 and running the Ising machine, it appears that the initial solution spins σ1 = +1, σ2 = -1, and σ3 = -1 were obtained.

[0018] As mentioned above, in the Ising model, the interaction coefficient J i,j The larger the value of the two corresponding spins σ i ,σ j is σ i = σ j The interaction coefficient J i,j The smaller is, the more σ i ≠σ j It is easy to become.

[0019] Here, in the initial solution of the combinatorial optimization problem represented by the Ising model, sets E1 and E2 are defined as equations (4) and (5), respectively.

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[0020] For a pair of integers (i, j) ∈ E1, the interaction coefficient J in the Ising model i,j The value of J' i,j >J i,j A real number J' that satisfies i,j , the value of the interaction coefficient becomes larger, and the spin σ i ,σ j In addition, for a pair of integers (i, j) ∈ E2, the interaction coefficient J in the Ising model i,j The value of J" i,j <J i,j A real number J" that satisfies i,j , the value of the interaction coefficient becomes smaller and the spin σ i ,σ j The value of is likely to be different. Figure 3(b) shows the J 1,2 and J. 1,3 A smaller J" 1,2 and J" 1,3 To, J 2,3 to a larger J' 2,3 It is expected that by running the Ising machine again, the spin combinations indicated by the dotted arrows will be reproduced.

[0021] Similarly, the tentative solution t~={σ^1(t),σ^2(t),..., σ^ N (t)}, the sets E1 and E2 are defined as equations (6) and (7).

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[0022] Here, the function g shown in equation (8) ctl Introduce the following.

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[0023] From equation (10), H wi For a pair (i, j) of integers that satisfies (i, j) ∈ E1, the interaction coefficient is J' i,j In addition, for a pair (i, j) of integers that satisfies (i, j) ∈ E2, the interaction coefficient is J" i,j where,c i,j ≧0, λ>0, so from equation (11), J' i,j ≧J i,j For a pair (i, j) of integers that satisfies (i, j)∈E1, σ i = σ j The force of forcing the i,j ≦0, λ>0, so from equation (12), J" i,j ≦J i,j For integers (i, j) that satisfy (i, j)∈E2, σ i ≠σ j The coercive force will become stronger. In other words, it is expected that by modifying the mutual adoption coefficient in the energy function as in equation (10), it is possible to introduce a pseudo initial solution.

[0024] In addition, in the initial solution of the combinatorial optimization problem represented by QUBO, the sets E1 and E2 are defined as in the Ising model, respectively, as in (13) and (14), and the interaction adjustment term g ctl By defining as in equation (15), the interaction coefficient J i,j You can adjust the value of .

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[0025] FIG. 4 is a functional block diagram of a minimum value search device 301 according to a first embodiment of the disclosed technique. The minimum value search device 301 includes an Ising machine 302, an initial solution acquisition unit 303, an interaction coefficient correction unit 304, a tentative solution management unit 305, and a termination determination unit 306, and receives an energy function as input and outputs the minimum value of the energy function. Below, we will use the Ising model as an example, but if you replace "spin" with "binary variable," it will explain the minimum value search device using the QUBO model.

[0026] FIG. 5 is a flowchart illustrating the operation of the minimum value search device according to the first embodiment. The initial solution acquisition unit 303 obtains the number of spins N of the Ising machine and the interaction coefficient J according to the target energy function (a function that formulates the combinatorial optimization problem to be solved using the Ising model; Equation (1)). i,j and the external magnetic field coefficient h i is set (initial setting) (step S401). The initial solution acquisition unit 303 operates the Ising machine to search for a combination of spins (initial solution spins) that minimizes the target energy function under the initial settings, and obtains the result σ~(0). The tentative solution management unit 305 also obtains σ~(0) from the initial solution acquisition unit 303 and sets it as the tentative solution spin t~ (step S402).

[0027] The interaction coefficient correction unit 304 generates a modified energy function H(σ~) given by equations (10), (11), and (12) based on the spin combinations given by t~, and among the settings of the Ising machine, updates the interaction coefficient J with J' in equation (11) and J" in equation (12) (step S403). wi (σ~) is generated, and among the settings of the Ising machine, the interaction coefficient J i,j is set to J' in equation (11) i,j and J" in equation (12) i,j for updating (step S403). The interaction coefficient correction unit 304 operates the Ising machine to search for a combination of spins that minimizes the modified energy function H(σ~) and obtains the result σ~(1). wi (σ~) and obtains the result σ~(1). The tentative solution management unit 305 acquires σ~(1) from the interaction coefficient correction unit 304 and sets it as s~ (step S404).

[0028] The tentative solution management unit 305 compares the values of H(s~) and H(t~) for the objective energy function H. If H(s~) < H(t~) (Yes in step S405), since s~ gives a better solution than t~, s~ is substituted into t~ to update the tentative solution spin t~ (step S406). If H(s~) ≥ H(t~) (No in step S405), the process proceeds to step S407 without updating the tentative solution spin.

[0029] The end determination unit 306 determines whether the minimum value search procedure satisfies the end condition. If the end condition is satisfied (Yes in step S407), the minimum value search device 301 ends the procedure and outputs the obtained minimum value. The end condition can be indicated by, for example, the number of loop iterations from step S407 to S403, the number of updates of the tentative solution spin t~, the degree of improvement of H(t~) with respect to H(σ~(0)), or the case where the solution does not improve even after looping a predetermined number of times. If the end condition is not satisfied (No in step S407), the process returns to step S403, performs grouping according to equations (6) and (7) based on the latest tentative solution spin t~, and updates J' in equation (11) i,j and J" in equation (12) i,j for updating.

[0030] The above is a description of the minimum value search device according to the first embodiment. EXAMPLES

[0031] In the first embodiment, in step S403, all the spin-spin interaction coefficients are adjusted based on the tentative solution spin t~. However, if the interaction coefficients are adjusted for all spin interactions as in equations (11) and (12), the initial solution spin σ~(0) may affect the entire annealing, and a good solution may not be obtained. Therefore, in Example 2, only a portion of the spin interactions (a total of N(N-1) / 2) are subject to adjustment (called "adjustment interactions"), and the rest (called "non-adjustment interactions") are not adjusted.

[0032] The adjustment interaction can be determined in various ways, for example, by the interaction adjustment ratio r ctl Define (N(N-1) / 2)×r ctl The number of pieces should be selected randomly. Note that (N(N-1) / 2)×r ctl If is not an integer, a value converted to an integer by rounding up or down may be used. For moderating interactions, c i,j >0, d i,j < 0. For non-coordinated interactions, c i,j =0, d i,j =0.

[0033] The functional block diagram of the minimum value search device according to the second embodiment is the same as that of the first embodiment. In the flowchart of the minimum value search device according to the second embodiment, step 403 in the first embodiment is changed as follows. The interaction coefficient correction unit 304 selects the interaction coefficient to be adjusted. The interaction coefficient correction unit 304 corrects the modified energy function H given by the equations (10), (11), and (12) based on the combination of spins given by t. wi (σ~) is generated, and the interaction coefficient J i,j J' in equation (11) i,j and J" in equation (12) i,j (Step S403). However, for the adjustment interaction, i,j >0, d i,j < 0, and for non-coordinated interactions, c i,j =0, d i,j =0. The remaining steps are similar to those in Example 1.

[0034] The above is a description of the minimum value search device according to the second embodiment.

[0035] [Example 2: Experiment for solving combinatorial optimization problems] 6 is a functional block diagram of a combinatorial optimization device 601 including a minimum search device 301. A calculation unit 602 performs calculations such as converting a combinatorial optimization problem into an energy function of an Ising model or a QUBO model, and converting the output of the minimum search device 301 into a solution to the combinatorial optimization problem. Below, we explain the two combinatorial optimization problems used in the experiment, the two experimental contents, and their results.

[0036] <Problem 1: Vehicle routing problem with capacity constraints and additional constraints> The Capacitated Vehicle Routing Problem (CVRP) is a problem of finding a truck route that satisfies the capacity constraints of each truck and minimizes the total route length when multiple trucks deliver packages to multiple customers. The total route length is found under the following four constraints: (1) no overlapping visits, (2) no simultaneous visits, (3) truck loading capacity, and (4) designated starting and ending points. In Problem 1, in addition to the above constraints, we added the "(5) Delivery vehicle designation constraint" that certain customers are visited by a designated truck. The CVRP problem with the fifth constraint added is hereafter called the CVRP with added constraint.

[0037] This disclosure does not go into the details of converting the CVRP problem to a QUBO model. For more information on CVRP and quantum annealing, see, for example, S. Feld et al., "A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer", Frontiers in ICT, Volume 6, Article 13, June 2019 (Reference 1).

[0038] Now, the energy function H CVRP For example, is defined as follows:

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[0039]

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[0040] <Problem 2: Maximum cut problem> The max-cut problem is the problem of dividing a set of vertices V of a polygon into two parts such that the sum of the weights of the edges to be cut is maximized, given a set of vertices V and a set of weighted edges E connecting the vertices. Now, suppose that the set of vertices is divided into sets S and T, and each vertex corresponds to a spin.

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[0041] <Experiment 1: Interaction adjustment ratio r ctl Optimization > We used CVRPLIB (Reference 2) and G-set (Reference 3) as instances of the CVRP and max-cut problems, respectively. Reference 2: Capacitated Vehicle Routing Problem Library, http: / / vrp.atd-lab.inf.puc-rio.br / index.php / en / Reference 3: http: / / web.stanford.edu / ~yyye / yyye / Gset / In addition, for each instance of CVRP, as a delivery vehicle selection constraint, six customers in total were randomly selected, two for each of the three trucks (k = 0, 1, 2), and the customer-truck pair (j, k) was made an element of set F in equation (18), resulting in a constrained CVRP.

[0042] Using an energy function that does not include an interaction adjustment term, a solution search is performed 100 times using an Ising machine, and the best feasible solution obtained (the one with the smallest total path length in the constrained CVRP problem, and the one with the largest total weight of the cut edges in the max-cut problem) is set as the initial solution in Example 2. The values ​​of the hyperparameters in the constrained CVRP are α, β, δ, and λ, which are the maximum distances between customers, and γ, which is 1. In the max-cut problem, λ=1. In addition, according to Example 2, r ctl The interaction coefficient J i,j Select and press c i,j =1, d i,j For non-coordinated interactions, c i,j =0, d i,j =0. The number of loops from step 407 to 403 in FIG. 5 was set to 100, and the execution time of one execution of the Ising machine was set to 1000 ms. In the constrained CVRP, r ctl Experiments were conducted with five different values: r = 0.005, 0.01, 0.015, 0.02, and 0.025. For the maximum cut problem, ctl =0.5×10 -4 , 1×10 -4 , 1.5× 10 -4 , 2×10 -4 , 2.5×10 -4 The experiment was conducted in five ways.

[0043] The experimental results are shown in Figures 7 and 8. Figures 7 and 8 show the experimental results for the constrained CVRP problem and the max-cut problem, respectively. The values ​​in the "Initial solution" and "Best solution" columns are the "total path length" (the shorter the better) and the "edge weight" (the heavier the better), respectively. From Figure 7, in the constrained CVRP, r ctl =0.015 or r ctl When r = 0.02, the improvement rate from the initial solution was the highest in each instance. The average improvement rate was r ctl When r = 0.015, the maximum was 6.30%. ctl <0.015, the solution is worse, and r ctl >0.015, r ctl As the value of increases, the average improvement rate becomes smaller and smaller. Also, from Figure 8, in the maximum cut problem, r ctl =1×10 -4 Or r ctl =1.5×10 -4 When , the improvement rate from the initial solution was the highest in each instance. The average improvement rate was 1×10 -4 The maximum was 0.37% when ctl In the range of >1×10-4, r ctl The improvement rate tends to decrease as the value of r increases. ctl =0.5×10 -4 When , the solution got worse in all instances.

[0044] <Experiment 2: Optimization of hyperparameter λ> We prepared instances of the constrained CVRP and max-cut problems in the same way as in Experiment 1. We also used the same initial solutions as those generated in Experiment 1. ctl The value of r was set to the value at which the average improvement rate was maximized in Experiment 1. That is, from Figures 7 and 8, in the constrained CVRP, ctl = 0.015, and for the max-cut problem, r ctl =1.0×10 -4 It was set as follows. The number of loops from step 407 to 403 in Fig. 5 was set to 100, and the execution time of one Ising machine was set to 1000 ms. In the constrained CVRP, experiments were performed with λ = l × (maximum value of the distance between customers), with five settings of l = 1, 2, 3, 4, and 5. In addition, in the max-cut problem, experiments were performed with seven settings of λ = 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, and 1.4.

[0045] The experimental results are shown in Fig. 9 and Fig. 10. Fig. 9 and Fig. 10 show the experimental results for the constrained CVRP and the max-cut problem, respectively. The l=1 column in Figure 9 is the r ctl = 0.015. In constrained CVRP, when l = 2 or l = 4, the improvement rate from the initial solution was the highest in each instance. The average improvement rate was the highest when l = 2, at 10.41%. Since the best solution is obtained when l > 1 in all instances, it is considered better to set the value of λ in constrained CVRP larger than the other hyperparameters α, β, γ, and δ. Also, from Figure 10, in the max-cut problem, the improvement rate from the initial solution in each instance was the highest when λ = 0.4 or λ = 1.0. The average improvement rate was the highest when λ = 0.4, at 0.56%. Also, (c i,j =1, d i,j = -1), when λ>1, the solution was hardly improved, so in the max-cut problem, the interaction adjustment value λc i,j , λd i,j It is considered good to set the absolute value of to be less than 1.

[0046] [Programs, recording media] The various processes described above can be implemented by loading a program for executing each step of the above method into the recording unit 2020 of the computer 2000 shown in FIG. 11, and operating the control unit 2010, input unit 2030, output unit 2040, display unit 2050, etc.

[0047] The program describing the processing contents can be recorded on a computer-readable recording medium, which may be, for example, a magnetic recording device, an optical disk, a magneto-optical recording medium, a semiconductor memory, or any other type of recording medium.

[0048] The program may be distributed, for example, by selling, transferring, lending, etc. portable recording media such as DVDs and CD-ROMs on which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of a server computer and transferring the program from the server computer to other computers via a network.

[0049] A computer that executes such a program, for example, first stores the program recorded on a portable recording medium or the program transferred from a server computer in its own storage device. Then, when executing a process, the computer reads the program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from the portable recording medium and execute a process according to the program, or may execute a process according to the received program each time a program is transferred from the server computer to the computer. The above-mentioned process may be executed by a so-called ASP (Application Service Provider) type service that realizes a processing function only by issuing an execution instruction and obtaining a result, without transferring a program from the server computer to the computer. Note that the program in this embodiment includes information used for processing by an electronic computer and equivalent to a program (data that is not a direct command to the computer but has a nature that specifies the processing of the computer, etc.).

[0050] In addition, in this embodiment, the present device is configured by executing a predetermined program on a computer, but at least a part of the processing contents may be realized by hardware. [Industrial Applicability]

[0051] The disclosed energy function minimum search device and method can be used to quickly search for suboptimal solutions to combinatorial optimization problems known as NP problems. [Explanation of symbols]

[0052] 301 Minimum value search device 302 Ising Machine 303 Initial solution acquisition part 304 Interaction coefficient correction unit 305 Temporary solution management department 306 Termination Judgment Section 601 Combinatorial Optimization Device 602 Arithmetic section 2000 Computer 2010 Control Unit 2020 Records Department 2030 Input section 2040 Output section 2050 Display section< / qubo>

Claims

1. An energy function minimum value search device that searches for a minimum value of an energy function expressed by an Ising model / QUBO model using an Ising machine, an initial solution acquisition unit that acquires a first tentative solution spin / binary variable necessary for calculating a first energy function; an interaction coefficient correcting unit that corrects an interaction coefficient of the first energy function to a value that contributes to reproduction of the first tentative solution spin / binary variable, to generate a second energy function; a tentative solution management unit that searches for a minimum value of the second energy function by an Ising machine, defines a spin / binary variable that gives the minimum value as a second tentative solution spin / binary variable, and evaluates a value of the first energy function by using the first tentative solution spin / binary variable and the second tentative solution spin / binary variable; An apparatus for searching for a minimum value of an energy function, comprising:

2. 2. The energy function minimum search device according to claim 1, the interaction coefficient correction unit performs a correction for the first energy function to increase an interaction coefficient at an edge where a product of the pair of the first tentative solution spin / binary variable is 1 / 1, and performs a correction for decreasing the interaction coefficient at an edge where a product of the pair is -1 / 0. A device for searching the minimum value of an energy function.

3. 2. The energy function minimum search device according to claim 1, the interaction coefficient correction unit selects the interaction coefficients to be corrected at a predetermined ratio; A device for searching the minimum value of an energy function.

4. 2. An apparatus for searching for a minimum value of an energy function according to claim 1, A termination determination unit is further provided, the tentative solution management unit calculates a first tentative minimum value and a second tentative minimum value from the first energy function using the first tentative solution spin / binary variable and the second tentative solution spin / binary variable, and if the second tentative minimum value is smaller than the first tentative minimum value, updates the first tentative solution with the second tentative solution; repeating the correction of the interaction coefficient, the search for the minimum value of the second energy function, and the update of the first tentative solution until the end determination unit determines that the search is ended. A device for searching the minimum value of an energy function.

5. A method for searching for a minimum value of an energy function expressed by an Ising model / QUBO model using an Ising machine, comprising: The initial solution acquisition unit acquires a first tentative solution spin / binary variable necessary for calculating the first energy function; an interaction coefficient correcting unit corrects an interaction coefficient of the first energy function to a value that contributes to reproduction of the first tentative solution spin / binary variable to generate a second energy function; A tentative solution management unit searches for a minimum value of the second energy function using an Ising machine, defines a spin / binary variable that gives the minimum value as a second tentative solution spin / binary variable, and evaluates a value of the first energy function using the first tentative solution spin / binary variable and the second tentative solution spin / binary variable. A method for searching the minimum of the energy function.

6. 6. A method for searching for a minimum value of an energy function according to claim 5, comprising the steps of: the interaction coefficient correction unit performs a correction for the first energy function to increase an interaction coefficient at an edge where a product of the pair of the first tentative solution spin / binary variable is 1 / 1, and performs a correction for decreasing the interaction coefficient at an edge where a product of the pair is -1 / 0. A method for searching the minimum of the energy function.

7. 6. A method for searching for a minimum value of an energy function according to claim 5, comprising the steps of: the interaction coefficient correction unit selects the interaction coefficients to be corrected at a predetermined ratio; A method for searching the minimum of the energy function.

8. 5. A program for causing a computer to function as the device for searching for a minimum value of an energy function according to claim 1.

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