Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many problems of interest to AI and operations research cannot be conveniently encoded as simple satisfiability, because they involve both hard and soft constraints -- that is, any solution may have to violate some of the less important constraints. We show how both kinds of constraints can be handled by encoding problems as instances of weighted MAX-SAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize our local-search algorithm for satisfiability (GSAT) to handle weighted MAX-SAT, and present experimental results on encodings of the Steiner tree problem, which is a well-studied hard combinatorial search problem. On many...

. 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 (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize a local-search algorithm for satisfiability to handle weighted MAX-SAT. To demonstrate the effectiveness 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. 1. Introduction Traditi...