## Logic-based methods for optimization: combining optimization and constraint satisfactionA pioneering look at the fundamental role of logic in optimization and constraint satisfaction While recent efforts to combine optimization and constraint satisfaction have received considerable attention, little has been said about using logic in optimization as the key to unifying the two fields. Logic-Based Methods for Optimization develops for the first time a comprehensive conceptual framework for integrating optimization and constraint satisfaction, then goes a step further and shows how extending logical inference to optimization allows for more powerful as well as flexible modeling and solution techniques. Designed to be easily accessible to industry professionals and academics in both operations research and artificial intelligence, the book provides a wealth of examples as well as elegant techniques and modeling frameworks ready for implementation. Timely, original, and thought-provoking, Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques in problem solving * Offers tutorials in constraint satisfaction/constraint programming and logical inference * Clearly explains such concepts as relaxation, cutting planes, nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developers seeking to combine the two techniques * Features extensive references to important computational studies * And much more |

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0-1 inequality algorithm appears in Figure augmenting path Benders cut Benders decomposition branching cardinality clauses Chapter checkable constraints clausal computed consistency constraint logic programming constraint programming constraint satisfaction constraint set contains continuous relaxation convex hull cutting planes deﬁned dependency graph discrete disjunction domain reduction duality dynamic programming empty clause equivalent falsiﬁed feasible set feasible solution ﬁnd ﬁnite ﬁrst ﬁxed formulation global constraints heuristic Horn clauses implies induced width infeasible inference integer programming Joblist Lagrangean leaf node Lemma linear programming literals logic programming lower bound master problem maximize minimize mixed integer programming no-good nonlinear objective function obtained optimal solution optimal value optimization problem original problem parallel resolution partial assignment procedure programming problem projection propositional logic recursion reduced resolution algorithm resolvent rule satisﬁability problem search tree search variables Section soluble constraints solved solvers straint strengthenings subproblem subset Theorem unit resolution unsatisﬁable vector