Anytime lower bounds for constraint violation minimization problems

Abstract

Constraint Violation Minimization Problems arise when dealing with over-constrained CSPs. Unfortunately, experiments and practice show that they quickly become too large and too difficult to be optimally solved. In this context, multiple methods (limited tree search, heuristic or stochastic local search) are available to produce non-optimal, but good quality solutions, and thus to provide the user with anytime upper bounds of the problem optimum. On the other hand, few methods are available to produce anytime lower bounds of this optimum. In this paper, we explore some ways of producing such bounds. All of them are algorithmic variants of a Branch and Bound search. More specifically, we show that a new algorithm, resulting from a combination of the Russian Doll Search and Iterative Deepening algorithms, clearly outperforms five known algorithms and allows high lower bounds to be rapidly produced.