Two Improved Constraint-Solving Algorithms Based on lmaxRPC3rm

Abstract

The Constraint Satisfaction Problem (CSP) is a significant research area in artificial intelligence, and includes a large number of symmetric or asymmetric structures. A backtracking search combined with constraint propagation is considered to be the best CSP-solving algorithm, and the consistency algorithm is the main algorithm used in the process of constraint propagation, which is the key factor in constraint-solving efficiency. Max-restricted path consistency (maxRPC) is a well-known and efficient consistency algorithm, whereas the lmaxRPC3rm algorithm is a classic lightweight algorithm for maxRPC. In this paper, we leverage the properties of symmetry to devise an improved pruning strategy aimed at efficiently diminishing the problem’s search space, thus enhancing the overall solving efficiency. Firstly, we propose the maxRPC3sim algorithm, which abandons the two complex data structures used by lmaxRPC3rm. We can render the algorithm to be more concise and competitive compared to the original algorithm while ensuring that it maintains the same average performance. Secondly, inspired by the RCP3 algorithm, we propose the maxRPC3simR algorithm, which uses the idea of residual support to cut down the redundant operation of the lmaxRPC3rm algorithm. Finally, combining the domain/weighted degree (dom/wdeg) heuristic with the activity-based search (ABS) heuristic, a new variable ordering heuristic, ADW, is proposed. Our heuristic prioritizes the selection of variables with symmetry for pruning, further enhancing the algorithm’s pruning capabilities. Experiments were conducted on both random and structural problems separately. The results indicate that our two algorithms generally outperform other algorithms in terms of performance on both problem classes. Moreover, the new heuristic algorithm demonstrates enhanced robustness across different problem types when compared to various existing algorithms.