Logic-Based Methods for Optimization

. This paper proposes a logic-based approach to optimization that combines solution methods from mathematical programming and logic programming. From mathematical programming it borrows strategies for exploiting structure that have logic-based analogs. From logic programming it borrows methods for extracting information that are unavailable in a traditional mathematical programming framework. Logicbased methods also provide a unified approach to solving optimization problems with both quantitative and logical constraints. 1 Introduction The theory and practice of integer and mixed integer programming are based primarily on polyhedral methods. The thesis of this paper is that one can develop a parallel theory and practice using logic-based methods. The basic idea is to replace the essential elements of optimization methods with logical analogs. The integer variables are regarded as atomic propositions, and inequality constraints involving them are rewritten as logical formulas..