Logic, optimization, and constraint programming

Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use logical inference in different ways, and how these ways can be combined. It sketches the intellectual background for recent efforts at integration. It traces the history of logic-based methods in optimization and the development of constraint programming in artificial intelligence. It concludes with a review of recent research, with emphasis on schemes for integration, relaxation methods, and practical applications.