Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems

Reviewer: Edward Sava-Segal

Repair heuristics have already proven successful for solving combinatorial search problems. The authors try to underline their importance for constraint satisfaction problems (CSPs), where a constructive, backtracking approach is customary. The trigger for their work and this well- written paper was the performance of a neural network developed for a complex task: scheduling the Hubble Space Telescope. The analysis of this problem has led the authors to suggest that repair-based methods can perform better than constructive methods because a complete assignment, although inconsistent, provides more information in guiding a search than a partial assignment. They identify a powerful heuristic, namely selecting the repair that minimizes the number of conflicts, but admit that its usefulness is domain-dependent and affected by several factors, such as the expected distance between the initial assignment and the solution. These conjectures are sustained by a statistical model for CSP repair. The authors have implemented their ideas in a symbolic CSP that offers the opportunity of employing different search strategies and hence opens another area for future research. Hill-climbing seems to be more appropriate than other search methods to at least capture the essential characteristics of the original network. Other experiments the authors report and analyze include the N-queens problem and graph coloring. The paper's main achievement is that it enforces open-mindedness with respect to applying repair heuristics. “Min-conflicts” performance on such a well-studied case as the N-queens problem is certainly an argument. The possibility of using the heuristic in combination with informed backtracking algorithms is another.