期刊
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
卷 109, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.engappai.2021.104603
关键词
Constraint Satisfaction Problem; Variable ordering; Deep reinforcement learning; Graph Neural Network
类别
资金
- RIE2020 Industry Alignment Fund -Industry Collaboration Projects (IAF-ICP) Funding Initiative
- Singapore Telecommunications Limited (Singtel), through Singtel Cognitive and Artificial Intelligence Lab for Enterprises (SCALE@NTU)
- National Natural Science Foundation of China [62102228, 61803104]
- Shandong Provincial Natural Science Foundation [ZR2021QF063]
- A*STAR Cyber-Physical Production System (CPPS) -Towards Contextual and Intelligent Response Research Program, under the RIE2020 IAF-PP Grant [A19C1a0018]
This paper proposes a deep reinforcement learning based approach to automatically discover new variable ordering heuristics for a given class of CSP instances. Experimental results show that the learned policies outperform classical hand-crafted heuristics in small and medium-sized instances, and also effectively reduce the search tree size in larger and harder instances.
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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