A general stochastic approach to solving problems with hard and soft constraints

Abstract

Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable | in general, one is interested in a set of \preferred" solutions (for example, solutions that minimize some cost function). Preferences can be encoded by incorporating \soft" constraints in the problem instance. We show how both hard and soft constraints can be handled by encoding problems as instances of weighted MAX-SAT ((nd-ing a model that maximizes the sum of the weights of the satissed clauses that make up a problem instance). We generalize a local-search algorithm for satissability to handle weighted MAX-SAT. To demonstrate the eeec-tiveness of our approach, we present experimental results on encodings of a set of well-studied network Steiner-tree problems. This approach turns out to be competitive with some of the best current specialized algorithms developed in operations research.