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

Abstract

This paper describes a simple heuristic approach to solving large-scale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a v alue-ordering heuristic, the min-con icts heuristic, that attempts to minimize the number of constraint violations after each step. The heuristic can be used with a variety of di erent search strategies.We demonstrate empirically that on the n-queens problem, a technique based on this approach performs orders of magnitude better than traditional backtracking techniques. We also describe a scheduling application where the approach has been used successfully. A theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most e ective.

Distance-constrained grid colouring

“…This problem was a benchmark for a long time, because it was hard to solve, since it contained many constraints: the figures cannot be in the same row, nor in the same column, and neither in the same diagonal. Suddenly, this problem became easy, a 10 6 -queens problem could be solved within seconds with the method of minimal conflicts [6]. This method counts the violations of the constraints (conflict), and selects randomly chosen variables with such values for which the number of conflict is minimal.…”

“…The method of minimal conflicts was introduced in [6]. To solve the 4-colouring of USA map, this method needs about 60 steps too.…”

Hybridization of Estimation of Distribution Algorithms with a Repair Method for Solving Constraint Satisfaction Problems

“…In addition, the class of CSPs in which each constraint in the problems is related only to two variables is called binary CSPs. In this paper, we treat a class of discrete binary CSPs, where the [10], a binary CSP which is one of the benchmark CSP is delineated in Fig. 1.…”

“…Recently, CSP solvers from genetic and evolutionary algorithms have been broadly studied by many researchers [2]- [9]. These studies showed that the uses of the domain knowledge in the CSPs, that is, the hybridization with local search method (repair method) based upon the notion of Min-Conflict Hill Climbing (MCHC) [10], and the utilization of constraint networks [6], are quite effective.…”

Adaptation using constraint satisfaction techniques

“…Conflicting variable values continue to be repaired until there are no more conflicts, at which point we have found a solution to the new problem. The empirical results for the algorithm showed that since the number of required repairs remains approximately constant as n grows, the algorithm's empirical time is approximately linear 20 , as opposed to the exponential complexity of traditional constructive backtracking techniques. The effectiveness of the algorithm stems from using information about the current assignment to guide the search that is not available to standard backtracking algorithms.…”