Local Search with a SAT Oracle for Combinatorial Optimization

NP-hard combinatorial optimization problems are pivotal in science and business. There exists a variety of approaches for solving such problems, but for problems with complex constraints and objective functions, local search algorithms scale the best. Such algorithms usually assume that finding a non-optimal solution with no other requirements is easy. However, what if it is NP-hard? In such case, a SAT solver can be used for finding the initial solution, but how can one continue solving the optimization problem? We offer a generic methodology, called Local Search with SAT Oracle (LSSO), to solve such problems. LSSO facilitates implementation of advanced local search methods, such as variable neighbourhood search, hill climbing and iterated local search, while using a SAT solver as an oracle. We have successfully applied our approach to solve a critical industrial problem of cell placement and productized our solution at Intel.