LEADER 05508nam 2200673 450 001 9910830712103321 005 20230422033039.0 010 $a1-283-28261-5 010 $a9786613282613 010 $a1-118-03128-8 010 $a1-118-03303-5 035 $a(CKB)3460000000080821 035 $a(EBL)695094 035 $a(OCoLC)815646185 035 $a(SSID)ssj0000613346 035 $a(PQKBManifestationID)11406606 035 $a(PQKBTitleCode)TC0000613346 035 $a(PQKBWorkID)10584761 035 $a(PQKB)10277019 035 $a(MiAaPQ)EBC695094 035 $a(EXLCZ)993460000000080821 100 $a20160816h20002000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLogic-based methods for optimization $ecombining optimization and constraint satisfaction /$fJohn Hooker 210 1$aNew York, New York :$cJohn Wiley & Sons, Inc.,$d2000. 210 4$dİ2000 215 $a1 online resource (520 p.) 225 1 $aWiley-Interscience Series in Discrete Mathematics and Optimization 300 $a"A Wiley-Interscience Publication." 311 $a0-471-38521-2 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aLogic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction; Preface; Contents; 1 Introduction; 1.1 Logic and Optimization; 1.1.1 Optimization and Constraint Satisfaction; 1.1.2 Constraint Programming; 1.1.3 Development of Logic-Based Methods; 1.1.4 Recent Applications and Software; 1.2 Organization of the Book; 1.2.1 How Much to Read; 1.2.2 Background Material; 1.2.3 A Practical Logic-Based System; 1.2.4 A Deeper Analysis; 2 Some Examples; 2.1 Logic-Based Modeling; 2.1.1 The Traveling Salesman Problem; 2.1.2 The Assignment Problem 327 $a2.1.3 The Quadratic Assignment Problem2.1.4 A Job Shop Scheduling Problem; 2.2 A Knapsack Problem; 2.2.1 An Integer Programming Model; 2.2.2 An Integer Programming Solution; 2.2.3 A Logic-Based Solution; 2.3 Processing Network Design; 2.3.1 An Integer Programming Approach; 2.3.2 A Logic-Based Approach; 2.4 Lot Sizing; 2.4.1 An Integer Programming Model; 2.4.2 A Logic-Based Model; 3 The Logic of Propositions; 3.1 The Idea of Propositional Logic; 3.1.1 Formulas; 3.1.2 Clauses; 3.1.3 Conversion to Clausal Form; 3.1.4 Horn Clauses; 3.1.5 Renamable Horn Clauses; 3.2 Resolution 327 $a3.2.1 The Resolution Algorithm3.2.2 Projection; 3.2.3 Unit Resolution; 3.2.4 Constraint-Based Search; 4 The Logic of Discrete Variables; 4.1 Formulas of Discrete-Variable Logic; 4.1.1 Formulas and Semantics; 4.1.2 Multivalent Clauses; 4.2 Multivalent Resolution; 4.2.1 Full Resolution; 4.2.2 Projection; 4-2.3 Unit Resolution; 4.2.4 Constraint Generation; 4.3 Defined Predicates; 5 The Logic of 0-1 Inequalities; 5.1 Inequalities and Implication; 5.2 Resolution for 0-1 Inequalities; 5.2.1 The Algorithm; 5.2.2 Completeness of 0-1 Resolution; 5.2.3 Resolution and Cutting Planes 327 $a5.3 Equivalent Inequalities5.3.1 Characterizing an Equivalence Class; 5.3.2 A Polar Approach to Checking Equivalence; 5.3.3 Polar Characterization of Equivalence Classes; 5.3.4 Canonical Inequalities; 6 Cardinality Clauses; 6.1 Resolution for Cardinality Clauses; 6.1.1 The Classical Resolution Step; 6.1.2 The Diagonal Summation Step; 6.2 Generating Cardinality Clauses; 6.2.1 Implied Cardinality Clauses; 6.2.2 Generating Nonredundant Implications; 6.2.3 Implied Contiguous Clauses; 7 Classical Boolean Methods; 7.1 Pseudoboolean Optimization; 7.1.1 The Basic Method 327 $a7.1.2 The Basic Algorithm Revisited7.2 Roof Duality; 7.2.1 Roofs; 7.2.2 The Roof Dual; 7.3 Implied Constraints; 7.3.1 Implications of a Linear 0-1 Inequality; 7.3.2 Implications of a Nonlinear 0-1 Inequality; 7.4 Matching Problems; 8 Logic-Based Modeling; 8.1 A Modeling Framework; 8.1.1 The Basic Framework; 8.1.2 A Growing Lexicon of Global Constraints; 8.1.3 Element Constraints and Variable Subscripts; 8.1.4 Sum Constraints and Variable Index Sets; 8.1.5 Integer and Mixed Integer Modeling; 8.1.6 The Objective Function; 8.2 Some Modeling Examples Revisited 327 $a8.2.1 Traveling Salesman, Assignment, and Job Shop Problems 330 $aA pioneering look at the fundamental role of logic in optimization and constraint satisfactionWhile recent efforts to combine optimization and constraint satisfaction have received considerable attention, little has been said about using logic in optimization as the key to unifying the two fields. Logic-Based Methods for Optimization develops for the first time a comprehensive conceptual framework for integrating optimization and constraint satisfaction, then goes a step further and shows how extending logical inference to optimization allows for more powerful as well as flexible modeling 410 0$aWiley-Interscience series in discrete mathematics and optimization. 606 $aLinear programming 606 $aMathematical optimization 606 $aLogic, Symbolic and mathematical 615 0$aLinear programming. 615 0$aMathematical optimization. 615 0$aLogic, Symbolic and mathematical. 676 $a519.3 676 $a519.72 700 $aHooker$b John$f1949-$0860609 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830712103321 996 $aLogic-based methods for optimization$91920469 997 $aUNINA