Surrogate constraint analysis-new heuristics and learning schemes for satisfiability problems

Surrogate constraint analysis has been applied effectively to a variety of combinatorial optimization problems, as a foundation for both exact and heuristic methods. In the heuristic domain, surrogate constraint methods are particularly suited to the creation of associated learning procedures and to the application of probabilistic decisions. We show that these approaches are natural and effective for satisfiability (SAT) problems. Added motivation comes from observing that the current best exact and heuristic procedures for multidimensional knapsack problems are provided independently by surrogate constraint methods and probabilistic methods that use memory and learning structures (derived from tabu search). We show that the SAT problem can be formulated as a special instance of a binary-choice multidimensional knapsack problem (or equivalently, a binary-choice generalized covering problem), and demonstrate how surrogate constraint analysis can be specialized in a particularly convenient way to exploit the structure of this problem. Our approach incorporates simple (first order) instances of adaptive memory structures characteristic of tabu search implementations, to give a learning effect to guide the search. This use of memory adds a dimension to the solution process that has not adequately been examined in the past. We find that the combination of surrogate constraint analysis and simple learning proves more effective than probabilistic search designs, including those that encompass probabilistic rules that have been highly favored in previous SAT approaches. These outcomes motivate a closer look at surrogate strategies and more advanced ways of integrating them with adaptive memory and learning procedures.