JP2014142849A - Solution search device, solution search method and solution search program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a solution search device capable of calculating a solution within a designated calculation time while reducing memory usage in a solution search using a simulation, a solution search method and a solution search program.SOLUTION: The solution search device includes a contraction part 101 for removing a node from a search tree when the node that does not have a plurality of child nodes in the search tree exists in the search tree in solution search using a simulation, and executing contraction processing for connecting child nodes to a master node of the child nodes when the removed node has the child nodes.

Description

  The present invention relates to a solution search apparatus, a solution search method, and a solution search program applied to solution search in optimization calculation and the like.

  The optimization problem is often a problem in which an objective function and constraint conditions are set, and an optimal solution with the best objective function is derived. In the field of artificial intelligence, a search method using simulation, such as MCTS (Monte-Carlo Tree Search) described in Non-Patent Document 1, is attracting attention. These search methods are positioned as an advanced form of a method for solving MBP (Multi-armed Bandit Problem), which is attracting attention in the fields of data mining and machine learning. Moreover, those search methods are being put into practical use, and computer Go is an example that has already been successfully put into practical use. In optimization used in OR (Operations Research) or the like, practical use of these search methods is expected, but practical application is difficult.

  The most different point between computer go and optimization is that in the solution space tree (hereinafter referred to as the solution space tree), computer go etc. finds the best node in the next step in each step of the solution space tree. The purpose of optimization is to find the best node among the solution nodes at the lowest level. Extending the search tree to the bottom of the solution space tree is an unprecedented goal in MCTS.

  There is a technique of pruning so as to reduce the size of the search tree and reach the bottom of the solution space tree within a given calculation time. By pruning, the search range can be appropriately narrowed within a range where calculation time is possible, so that the number of simulations of the node determined to be important based on the simulation result can be increased. Therefore, it is possible to increase the possibility of improving the accuracy of the solution of a search method such as MCTS that calculates an evaluation value by simulation.

C. Browne, E .; Powley, D.W. Whitehouse, S.W. Lucas, P.M. I. Cowling, P.M. Rolfshagen, S .; Travener, D.M. Perez, S.M. Samothrakis and S. Colton, A Survey of Monto, Carlo Tree Search Methods, IEEE Transactions on Computational Intelligence and AI in Games, Vol. 4, no. 1, March 2012. P. Auer, N.A. Cesa-Bianchi, and P.M. Fischer, Fine-time Analysis of the Multi-banded Problem, Machine Learning, Vol. 47, p. 235-256, 2002

  In a tree in a solution search aiming to search the bottom node like MCTS, when there is only one node for expansion or when the child node becomes 1 or less by pruning, a node without a branch is generated To do. In the search tree, it is useless to follow a node having no branch.

  Therefore, the present invention provides a solution search apparatus, a solution search method, and a solution search program that can calculate a solution within a specified calculation time while reducing memory usage in solution search using simulation. For the purpose.

  In the solution search apparatus according to the present invention, in a solution search using simulation, if there is a node that does not have a plurality of child nodes in the search tree, the node is removed from the search tree, and the removed node indicates a child node. In the case of having, a contraction unit that executes contraction processing for connecting the child node to the parent node of the node is included.

  In the solution search method according to the present invention, in a solution search using simulation, when a node having no plurality of child nodes exists in the search tree, the node is removed from the search tree, and the removed node is replaced with a child node. If so, the child node is connected to the parent node of the node.

  In the solution search program according to the present invention, when there is a node that does not have a plurality of child nodes in the search tree in the solution search using simulation, the node is removed from the search tree, and the removed node is When there is a child node, a process of connecting the child node to the parent node of the node is executed.

  According to the present invention, in a solution search using simulation, a solution can be calculated within a designated calculation time while reducing memory usage.

It is a block diagram which shows the structure of 1st Embodiment of an optimization system. It is a flowchart which shows operation | movement of the calculation part in 1st Embodiment. It is explanatory drawing which shows a mode that the search tree is shrunk | reduced in 1st Embodiment. It is a block diagram which shows an example of a structure of the optimization system provided with the optimization apparatus containing two pruning parts. It is explanatory drawing which shows a mode that the search tree is shrunk | reduced in 2nd Embodiment. It is a block diagram which shows the minimum structure of the solution search apparatus by this invention. It is a block diagram which shows the other minimum structure of the solution search apparatus by this invention.

Embodiment 1. FIG.
A first embodiment of the present invention will be described below with reference to the drawings.

  FIG. 1 is a block diagram showing the configuration of the first embodiment of the optimization system.

  As shown in FIG. 1, the optimization system in the first embodiment includes a user terminal 1 and an optimization device 2. The user terminal 1 and the optimization device 2 are connected so as to communicate with each other. Although one user terminal is illustrated in FIG. 1, any number of user terminals may be connected to the optimization device 2.

  The user terminal 1 is an information processing terminal such as a personal computer. The user terminal 1 includes an operation unit 11 and a display unit 12.

  The operation unit 11 inputs information necessary for the optimization calculation to be executed (hereinafter referred to as optimization calculation input information). In addition, the operation unit 11 inputs an execution instruction. The operation unit 11 outputs an execution instruction to the optimization device 2 together with the optimization calculation input information.

  The display unit 12 receives the solution of the optimization calculation result from the optimization device 2 and displays it.

  The optimization apparatus 2 includes a GUI (Graphical User Interface) unit 21, a calculation unit 22, and a storage unit 23.

  The GUI unit 21 receives optimization calculation input information from the operation unit 11 of the user terminal 1. The GUI unit 21 transmits optimization calculation input information to the calculation unit 22. The GUI unit 21 receives the solution of the optimization calculation result from the calculation unit 22 and transmits it to the display unit 12 of the user terminal 1.

  The calculation unit 22 includes a selection unit 221, an enlargement unit 222, a simulation unit 223, an evaluation value update unit 224, a pruning unit 225, and a shrinkage unit 226.

  The selection unit 221 selects a node to be played out from among the expanded nodes. Hereinafter, a node that is a playout execution target is referred to as a selection node.

  The expansion unit 222 expands the search tree (tree). Specifically, the enlargement unit 222 determines whether it is necessary to expand the node selected by the selection unit 221 according to a predetermined criterion, and expands the node further one step lower if necessary. To expand the search tree. When expanding the node, the enlarging unit 222 reselects the selected node as the next lower node.

  The simulation unit 223 executes a simulation. Specifically, the simulation unit 223 searches for one solution by a simple method such as playout, that is, random simulation, and acquires an evaluation value of the solution.

  The evaluation value update unit 224 updates the evaluation value of the solution of each node according to the result of the playout performed by the simulation unit 223. Specifically, the evaluation value of each node stored in the storage unit 23 is updated. The evaluation value of each node includes a statistical value obtained by collecting evaluation values obtained by repeated simulations, and the evaluation value update unit 224 updates the statistical value. In the present embodiment, the evaluation value update unit 224 calculates the evaluation function values (index values) of best, mean, and kbest as the evaluation value of the solution.

  The pruning unit 225 performs pruning. Specifically, the pruning unit 225 connects a node with a poor evaluation value to the node in order to reduce the memory usage or guide the search to the bottom of the solution space tree within a given calculation time. Remove branches (edges).

  The contraction unit 226 removes nodes from which no branching has occurred due to pruning or the like from the search tree.

  The storage unit 23 stores an objective function and constraint conditions. When the optimization system is applied to a scheduling problem, the storage unit 23 stores data necessary for solving the problem, such as task information and person-in-charge information (hereinafter referred to as problem data). In addition, the storage unit 23 stores information that changes such as an evaluation value of a node when the calculation process in the calculation unit 22 proceeds. In the present embodiment, the storage unit 23 stores the number of node searches and evaluation values obtained by the calculation unit 22 during each calculation. The storage unit 23 stores a solution that needs to be held among the solutions obtained by the calculation unit 22.

  The GUI unit 21 and the calculation unit 22 are realized by a computer that operates according to a solution search program, for example. In this case, the CPU provided in the optimization apparatus 2 reads the solution search program and operates as the GUI unit 21 and the calculation unit 22 according to the program. Moreover, each part of the GUI part 21 and the calculation part 22 may be implement | achieved by separate hardware.

  The storage unit 23 is realized by a storage device such as a RAM (Random Access Memory) included in the optimization device 2.

  Next, the operation of this embodiment will be described.

  FIG. 2 is a flowchart showing the operation of the calculation unit 22 in the first embodiment.

  Here, a case where the optimization system shown in FIG. 1 is applied to a scheduling problem is taken as an example.

  First, the user inputs optimization calculation input information to the operation unit 11 of the user terminal 1. A user inputs problem data such as a task for which optimization calculation is desired, a person in charge who can be engaged, and cost and effectiveness when each person in charge engages in each task as optimization calculation input information. At this time, the user inputs an execution instruction to the operation unit 11 together with the optimization calculation input information. The operation unit 11 outputs optimization calculation input information and an execution instruction to the optimization device 2.

  When the GUI unit 21 of the optimization device 2 receives an execution instruction from the user terminal 1 together with the optimization calculation input information, the GUI unit 21 transmits the optimization calculation input information to the calculation unit 22. The calculation unit 22 inputs optimization calculation input information as preprocessing (step S201).

  After step S201, the selection unit 221 of the calculation unit 22 selects a node to be simulated from among the expanded nodes (step S202). Since there is only one node in the initial state, that node is a selection target. In this embodiment, the node is selected using the index value calculated by the evaluation value update unit 224. In addition, when selecting a node, the selection unit 221 uses an index value that is different from the index value used by the pruning unit 225 to determine whether or not to execute pruning. In this embodiment, the index used for node selection is mean, and the index used for pruning is best. That is, each node in the search tree has both a meanValue that is an evaluation value for node selection and a bestValue that is an evaluation value for pruning. Specifically, the evaluation value update unit 224 stores the meanValue and the bestValue in the storage unit 23 in association with each node in the search tree.

  The enlargement unit 222 expands the search tree to a node one level lower when the number of playouts of the node selected by the selection unit 221 satisfies a predetermined condition (step S203). In the present embodiment, the enlargement unit 222 expands when the number of playouts exceeds a predetermined number. When there is only one node in the initial state, it is expanded regardless of this condition. In the case of expansion, the enlargement unit 222 sets one of the expanded nodes as a selection node.

  The simulation unit 223 searches for one solution by executing playout, that is, random simulation, from the selected node (step S204). Although it is possible to execute a plurality of simulations for one selected node and search for a plurality of solutions, here, as a simplest example, one simulation is executed for one selected node, A method for searching for one solution will be described. The technical scope of the present invention is not limited to the form of executing one simulation for one selected node. Therefore, a form of executing a plurality of simulations for one selected node can also be included in the technical scope of the present invention.

  The evaluation value update unit 224 uses the solution obtained by the simulation unit 223 to update the evaluation value of the solution such as best, mean, kbest. In this embodiment, the evaluation value update unit 224 updates the evaluation value of the solution of mean and best (step S205). The evaluation value of the best solution is the optimum among the results of simulations executed from the selected node so far. The evaluation value of the mean solution is an average of the results of simulations executed from the selected node so far. The evaluation value of the kbest solution is an average of the k-th best solution among the results of simulations executed from the selected node so far.

  The evaluation value update unit 224 performs the following normalization process on the evaluation values of the solutions of mean and best, which are index values.

When the index values in the selected node and its sibling nodes (nodes having a common parent node with the selected node) are v ₁ , v ₂ , v ₃ ,... V _L , the maximum value M and the minimum value m are as follows: Can be expressed as Note that L is the total number of child nodes having a common parent node.

Here, it is assumed that v _i is determined to be a good value when it is close to the minimum value m according to a predetermined criterion. Further, it is assumed that a bad value is determined when the value is close to the maximum value M. The evaluation value updating unit 224 normalizes v _i so that the minimum value m, which is a good value, is 0, and the maximum value M, which is a bad value, is 1. Specifically, the evaluation value update unit 224 converts v _i as follows. Value _i is a value after normalization of v _i .

Note that v _i may be further normalized so that the value _i falls within a certain variance.

Value _i corresponding to mean and best is calculated by the evaluation value update unit 224 executing the above processing for mean and best. Hereinafter, Value _i corresponding to best, mean, and kbest are expressed as bestValue, meanValue, and kbestValue (k), respectively. “(K)” represents that the top k solutions are to be averaged.

  The evaluation value update unit 224 calculates meanValue and bestValue at each of the selected node and its upper nodes, and updates the evaluation value of each node based on the calculation result.

  The pruning unit 225 performs pruning when it determines that pruning is necessary because the size of the search tree, for example, the number of nodes of the entire search tree or the number of leaf nodes of the search tree is large. Further, when it is determined that the space to be searched needs to be narrowed so that the search tree reaches the bottom of the solution space tree within the given designated time, pruning is executed (step S206). In the present embodiment, the pruning unit 225 evaluates each node with the bestValue updated by the evaluation value update unit 224 in step S205. The pruning unit 225 prunes nodes with poor evaluation values from the search tree. Thereafter, no simulation is performed from that node or its lower nodes.

  The contraction unit 226 removes a node having no branch among the nodes in the search tree by pruning by the pruning unit 225 or the like (step S207). Then, the contraction unit 226 directly connects the parent node and the child node of the removed node. At that time, the contraction unit 226 copies the statistical value used for the evaluation function for node selection from the parent node to the child node. Specifically, the contraction unit 226 stores the statistical value stored in the storage unit 23 in association with the parent node in association with the child node. The statistical value used for the evaluation function for pruning is not copied, but the value of the child node is used as it is.

  FIG. 3 is an explanatory diagram illustrating how the search tree is contracted in the first embodiment. The search tree shown in FIG. 3A is a search tree having the node A as a root node. Below node A, nodes B to K exist. In addition, node G has three expansion candidate nodes (nodes L, M, and N). The “x” mark indicates that the node F, the node J, and the node K are pruning execution targets.

  FIG. 3B shows a state after pruning is performed on the search tree shown in FIG. FIG. 3C illustrates a state after the contraction process is performed on the search tree illustrated in FIG. In FIG. 3C, nodes B and D that have no branches due to pruning are removed. Node A and node E are directly connected. FIG. 3D shows a state after node expansion is performed on the search tree shown in FIG.

  The calculation unit 22 performs the processing in steps S202 to S207 (selection processing, node expansion processing, simulation execution processing, evaluation value update processing, pruning processing, and contraction until the calculation time in the calculation unit 22 reaches a predetermined upper limit. Process) is repeated. That is, when the calculation time has not reached the upper limit (Yes in step S208), the calculation unit 22 returns to the process in step S202. When the calculation time reaches the upper limit (No in step S208), the calculation unit 22 ends the calculation, and passes the optimization calculation result, that is, solution information indicating the solution obtained by the search, to the GUI unit 21 ( Step S209). Note that the calculation unit 22 may repeatedly execute the processes of steps S202 to S207 until the solution value given as a requirement is calculated instead of the calculation time.

  In the calculation process of steps S202 to S207, the calculation unit 22 stores information including the number of node searches and evaluation values obtained during each calculation in the storage unit 23. Further, the calculation unit 22 stores information including the solution obtained by searching in the storage unit 23. The calculation unit 22 can recognize the number of searches for each node and the evaluation value during the calculation by acquiring information stored in the storage unit 23.

  In this embodiment, the case where problem data is input as optimization calculation input information from the user terminal 1 to the calculation unit 22 is taken as an example. However, the calculation unit 22 acquires the problem data stored in the storage unit 23. You may do it. In order to realize such a form, a user or the like may store problem data in the storage unit 23 in advance.

  Further, the timing for executing the contraction process in step S207 is not limited to after the pruning process in step S206. The contraction part may be included in the pruning part. When the calculation unit includes a plurality of pruning units, each pruning unit may include a contraction unit. FIG. 4 is a block diagram illustrating an example of a configuration of an optimization system including an optimization device including two pruning units. In the example illustrated in FIG. 4, the calculation unit 22 solves the search tree in the first calculation unit 2251 that performs a pruning process for the purpose of suppressing the size of the search tree and the specified calculation time. A second pruning unit 2252 that performs a pruning process for the purpose of reaching the bottom of the tree. Each of the first pruning unit 2251 and the second pruning unit 2252 includes a contraction unit 226. That is, the calculation unit 22 illustrated in FIG. 4 executes the contraction process twice in the calculation process for one selected node.

  As described above, according to the present embodiment, when pruning is executed, a search tree is shrunk to remove a useless node having no branch generated by pruning. be able to. Therefore, the number of nodes in the search tree can be further reduced. In the present embodiment, the parent node and the child node of the removed node are directly connected. Thereby, it is possible to reduce the time taken from the root node of the search tree to the leaf node, and to reduce the calculation time in the solution search. Therefore, according to the present embodiment, in the solution search using simulation, the solution can be calculated within the designated calculation time while reducing the memory usage.

  In the present embodiment, the statistical value used for the evaluation function for node selection and the statistical value used for the evaluation function for pruning are separately held in each node. Further, when a node having no branch is removed, a statistical value used for an evaluation function for node selection held by the parent node of the node is copied to a child node of the node. As a result, the evaluation function value for node selection can be appropriately maintained as compared with a system that simply removes a node, so that the accuracy of the solution is unlikely to deteriorate.

  In the present embodiment, the case has been described in which the index value used when the selection unit 221 selects a node and the index value used when the pruning unit 225 performs pruning are different. The index value used when selecting a node and the index value used when the pruning unit 225 executes pruning may be the same. That is, the index used for node selection and the index used for pruning may be the same.

Embodiment 2. FIG.
Hereinafter, a second embodiment of the present invention will be described with reference to the drawings.

  The configuration of the optimization system in the second embodiment is the same as the configuration of the first embodiment.

  Here, as in the first embodiment, a case where the optimization system is applied to a scheduling problem is taken as an example.

  The operation of the calculation unit 22 in the second embodiment is the same as the operation of the first embodiment shown in FIG.

  However, the operation of the selection unit 221 in step S202, the operation of the evaluation value update unit 224 in step S205, and the operation of the contraction unit 226 in step S207 are different. Here, operations in steps S202, S205, and S206 will be described.

  In step S202, the selection unit 221 uses an index value held by a branch (edge) when selecting a node. Specifically, the index value held by the edge is an index value stored in the storage unit 23 by the evaluation value update unit 224 in association with each edge.

  In step S205, when the normalization process is performed, the evaluation value update unit 224 normalizes not only the index values at the selected node and its sibling nodes but also the index values at the edges of those nodes as follows. To do.

  The evaluation value update unit 224 calculates the index value meanValue at the selected node and its sibling node using Equations 1 to 3. Then, the evaluation value update unit 224 updates the evaluation value of each of the selected node and its higher nodes based on the calculation result.

  Similarly, the evaluation value update unit 224 calculates meanValue for each edge connected to the selected node and its sibling nodes using Equations 1 to 3. Then, the evaluation value update unit 224 updates the evaluation value of each edge on the route connecting the selected node and the higher-order node based on the calculation result. For example, in the search tree shown in FIG. 3D, when the node L is the selected node, each of the edge connecting the nodes L and G, the edge connecting the nodes G and C, and the edge connecting the nodes C and A, respectively. The evaluation value of is updated.

  In step S206, when the contraction unit 226 removes a node having no branch, the contraction unit 226 directly connects the parent node and the child node of the node. At that time, the contraction unit 226 removes the node and an edge connecting the node and the child node. The contraction unit 226 connects an edge connecting the node and the parent node to a child node of the node.

  FIG. 5 is an explanatory diagram showing how the search tree is contracted in the second embodiment. As shown in FIG. 5 (c), in this embodiment, an edge connecting node A and node B that no longer has a branch due to pruning represents node A and a child node (node E) of node B. It becomes an edge to connect.

  As described above, in this embodiment, as in the first embodiment, it is possible to remove a useless node that does not have a branch and is generated by pruning. Therefore, the same effect as the first embodiment can be obtained.

  In each embodiment, the case where the optimization apparatus is applied to the scheduling problem is taken as an example, but the scope of application of the present invention is not limited thereto. The present invention can be applied to optimization problems in general, focusing on combinatorial optimization problems such as scheduling problems for assigning tasks to persons in charge. It can also be applied to solution searches other than optimization problems.

  FIG. 6 is a block diagram showing the minimum configuration of the solution search apparatus according to the present invention. FIG. 7 is a block diagram showing another minimum configuration of the solution search apparatus according to the present invention.

  As shown in FIG. 6, the solution search device (corresponding to the optimization device 2 shown in FIG. 1), in the solution search using simulation, when there are nodes that do not have a plurality of child nodes in the search tree. When the node is removed from the search tree and the removed node has a child node, the contraction unit 101 (the optimization apparatus shown in FIG. 1) executes a contraction process for connecting the child node to the parent node of the node. 2 corresponds to the contraction portion 226 in FIG.

  According to such a configuration, the number of nodes in the search tree can be further reduced. Therefore, it is possible to reduce the time for tracing from the root node of the search tree to the leaf node, that is, the calculation time for solution search. Therefore, in the solution search using simulation, the solution can be calculated within the designated calculation time while reducing the memory usage.

  In the above embodiment, the following solution search apparatus is also disclosed.

(1) The contraction unit 101 is a solution search apparatus that executes contraction processing in a Monte Carlo tree search using simulation.

  According to such a configuration, the number of nodes in the search tree can be further reduced in the Monte Carlo tree search.

(2) As shown in FIG. 7, an execution unit 102 that selects a node to be simulated from among the nodes that are options in the search tree and executes the simulation from the selected node (optimum shown in FIG. 1) Equivalent to the selection unit 221, the enlargement unit 222, and the simulation unit 223 in the conversion apparatus 2), and an evaluation value is calculated based on the simulation result, and the evaluation value is selected based on the evaluation value Update unit 103 (equivalent to evaluation value update unit 224 in optimization apparatus 2 shown in FIG. 1) that updates the evaluation value of the node and its upper node, and a node having an evaluation value that does not satisfy a predetermined criterion A pruning unit 104 to be removed from the tree (corresponding to the pruning unit 225 in the optimization apparatus 2 shown in FIG. 1). After executing the processing of removing de, solution search apparatus for performing contraction processing.

  According to such a configuration, it is possible to eliminate a useless node having no branch generated by pruning by performing shrinkage after performing pruning.

(3) The updating unit 103 calculates an evaluation value for node selection used when the execution unit 102 selects a node by using the evaluation function for node selection, and uses the evaluation function for pruning to A solution search device that calculates an evaluation value for pruning that is used when the pruning unit 104 removes a node from the search tree.

  According to such a configuration, each node can separately hold a statistical value used for an evaluation function for node selection and a statistical value used for an evaluation function for pruning.

(4) When the node removed from the search tree by the contraction unit 101 has a child node, the update unit 103 uses the evaluation value calculated using the node selection evaluation function of the parent node of the node. A solution search apparatus for updating an evaluation value for node selection of the child node.

  According to such a configuration, the evaluation function value for node selection can be appropriately maintained as compared with a system that simply removes a node and does not perform contraction processing, so that the accuracy of the solution is unlikely to deteriorate.

(5) When the node removed from the search tree by the contraction unit 101 has a child node, the update unit 103 uses the evaluation value calculated by using the evaluation function for pruning the child node. A solution search device that updates an evaluation value for pruning a child node.

  According to such a configuration, the evaluation function value for pruning can be appropriately maintained as compared with a system that simply removes a node and does not perform contraction processing, so that the accuracy of the solution is unlikely to deteriorate.

DESCRIPTION OF SYMBOLS 1 User terminal 2 Optimization apparatus 11 Operation part 12 Display part 21 GUI part 22 Calculation part 23 Storage part 101,226 Shrinkage part 102 Execution part 103 Update part 104,225 Pruning part 221 Selection part 222 Expansion part 223 Simulation part 224 Evaluation Value updating unit 225 Pruning unit 2251 First pruning unit 2252 Second pruning unit 226 Contracting unit

Claims (8)

In solution search using simulation, if a node that does not have multiple child nodes exists in the search tree, the node is removed from the search tree, and if the removed node has child nodes, the child node A solution search apparatus comprising: a contraction unit that executes contraction processing for connecting a node to a parent node of the node. The solution search apparatus according to claim 1, wherein the contraction unit performs contraction processing in a Monte Carlo tree search using simulation. An execution unit that selects a node to be simulated from among the nodes that are options in the search tree, and executes the simulation from the selected node;
Based on the simulation result, an evaluation value is calculated using an evaluation function, and based on the evaluation value, an update unit that updates the evaluation value of the selected node and its upper node,
A pruning unit that removes a node having an evaluation value that does not satisfy a predetermined criterion from the search tree,
The solution search apparatus according to claim 1, wherein the contraction unit performs contraction processing after the pruning unit executes processing for removing a node from the search tree. The update unit calculates an evaluation value for node selection used when the execution unit selects a node using the evaluation function for node selection, and uses the evaluation function for pruning, and the pruning unit selects the node The solution search apparatus according to claim 3, wherein an evaluation value for pruning used when removing from the search tree is calculated. When the node removed from the search tree by the contraction unit has a child node, the update unit, based on the evaluation value calculated using the node selection evaluation function of the parent node of the node, The solution search apparatus according to claim 4, wherein the evaluation value for node selection is updated. When the node removed from the search tree by the contraction unit has a child node, the updating unit prunes the child node based on the evaluation value calculated using the evaluation function for pruning the child node. The solution search device according to claim 4, wherein the evaluation value for use is updated. In solution search using simulation, if a node that does not have multiple child nodes exists in the search tree, the node is removed from the search tree, and if the removed node has child nodes, the child node A solution search method characterized by connecting to the parent node of the node. On the computer,
In solution search using simulation, if a node that does not have multiple child nodes exists in the search tree, the node is removed from the search tree, and if the removed node has child nodes, the child node A solution search program for executing the process of connecting to the parent node of the node.

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