Learning variable ordering heuristics for solving constraint satisfaction problems
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP), which is widely applied in various domains such as automated planning and scheduling. The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commo...
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sg-ntu-dr.10356-1627262022-11-07T06:39:58Z Learning variable ordering heuristics for solving constraint satisfaction problems Song, Wen Cao, Zhiguang Zhang, Jie Xu, Chi Lim, Andrew School of Computer Science and Engineering Engineering::Computer science and engineering Constraint Satisfaction Problem Variable Ordering Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP), which is widely applied in various domains such as automated planning and scheduling. The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are hand-crafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances, without the need of relying on hand-crafted features and heuristics. We show that directly optimizing the search tree size is not convenient for learning, and propose to optimize the expected cost of reaching a leaf node in the search tree. To capture the complex relations among the variables and constraints, we design a representation scheme based on Graph Neural Network that can process CSP instances with different sizes and constraint arities. Experimental results on random CSP instances show that on small and medium sized instances, the learned policies outperform classical hand-crafted heuristics with smaller search tree (up to 10.36% reduction). Moreover, without further training, our policies directly generalize to instances of larger sizes and much harder to solve than those in training, with even larger reduction in the search tree size (up to 18.74%). Agency for Science, Technology and Research (A*STAR) This study is supported under the RIE2020 Industry Alignment Fund–Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from Singapore Telecommunications Limited (Singtel), through Singtel Cognitive and Artificial Intelligence Lab for Enterprises (SCALE@NTU). This study is also supported by the National Natural Science Foundation of China under Grant 62102228 and 61803104, and in part by Shandong Provincial Natural Science Foundation under Grant ZR2021QF063, and in part by the A*STAR Cyber-Physical Production System (CPPS) – Towards Contextual and Intelligent Response Research Program, under the RIE2020 IAF-PP Grant A19C1a0018. 2022-11-07T06:39:58Z 2022-11-07T06:39:58Z 2022 Journal Article Song, W., Cao, Z., Zhang, J., Xu, C. & Lim, A. (2022). Learning variable ordering heuristics for solving constraint satisfaction problems. Engineering Applications of Artificial Intelligence, 109, 104603-. https://dx.doi.org/10.1016/j.engappai.2021.104603 0952-1976 https://hdl.handle.net/10356/162726 10.1016/j.engappai.2021.104603 2-s2.0-85121424180 109 104603 en A19C1a0018 Engineering Applications of Artificial Intelligence © 2021 Elsevier Ltd. All rights reserved. |
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Engineering::Computer science and engineering Constraint Satisfaction Problem Variable Ordering Song, Wen Cao, Zhiguang Zhang, Jie Xu, Chi Lim, Andrew Learning variable ordering heuristics for solving constraint satisfaction problems |
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Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP), which is widely applied in various domains such as automated planning and scheduling. The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are hand-crafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances, without the need of relying on hand-crafted features and heuristics. We show that directly optimizing the search tree size is not convenient for learning, and propose to optimize the expected cost of reaching a leaf node in the search tree. To capture the complex relations among the variables and constraints, we design a representation scheme based on Graph Neural Network that can process CSP instances with different sizes and constraint arities. Experimental results on random CSP instances show that on small and medium sized instances, the learned policies outperform classical hand-crafted heuristics with smaller search tree (up to 10.36% reduction). Moreover, without further training, our policies directly generalize to instances of larger sizes and much harder to solve than those in training, with even larger reduction in the search tree size (up to 18.74%). |
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School of Computer Science and Engineering |
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School of Computer Science and Engineering Song, Wen Cao, Zhiguang Zhang, Jie Xu, Chi Lim, Andrew |
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Article |
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Song, Wen Cao, Zhiguang Zhang, Jie Xu, Chi Lim, Andrew |
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Song, Wen |
title |
Learning variable ordering heuristics for solving constraint satisfaction problems |
title_short |
Learning variable ordering heuristics for solving constraint satisfaction problems |
title_full |
Learning variable ordering heuristics for solving constraint satisfaction problems |
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Learning variable ordering heuristics for solving constraint satisfaction problems |
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Learning variable ordering heuristics for solving constraint satisfaction problems |
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learning variable ordering heuristics for solving constraint satisfaction problems |
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2022 |
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https://hdl.handle.net/10356/162726 |
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