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An integer programming approach for the satisfiability problems.

by Lui Oi Lun Irene. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 128-132). / Abstracts in English and Chinese. / List of Figures --- p.vii / List of Tables --- p.viii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Satisfiability Problem --- p.1 / Chapter 1.2 --- Motivation of the Research --- p.1 / Chapter 1.3 --- Overview of the Thesis --- p.2 / Chapter 2 --- Constraint Satisfaction Problem and Satisfiability Problem --- p.4 / Chapter 2.1 --- Constraint Programming --- p.4 / Chapter 2.2 --- Satisfiability Problem --- p.6 / Chapter 2.3 --- Methods in Solving SAT problem --- p.7 / Chapter 2.3.1 --- Davis-Putnam-Loveland Procedure --- p.7 / Chapter 2.3.2 --- SATZ by Chu-Min Li --- p.8 / Chapter 2.3.3 --- Local Search for SAT --- p.11 / Chapter 2.3.4 --- Integer Linear Programming Method for SAT --- p.12 / Chapter 2.3.5 --- Semidefinite Programming Method --- p.13 / Chapter 2.4 --- Softwares for SAT --- p.15 / Chapter 2.4.1 --- SAT01 --- p.15 / Chapter 2.4.2 --- "SATZ and SATZ213, contributed by Chu-Min Li" --- p.15 / Chapter 2.4.3 --- Others --- p.15 / Chapter 3 --- Integer Programming --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.1.1 --- Formulation of IPs and BIPs --- p.18 / Chapter 3.1.2 --- Binary Search Tree --- p.19 / Chapter 3.2 --- Methods in Solving IP problem --- p.19 / Chapter 3.2.1 --- Branch-and-Bound Method --- p.20 / Chapter 3.2.2 --- Cutting-Plane Method --- p.23 / Chapter 3.2.3 --- Duality in Integer Programming --- p.26 / Chapter 3.2.4 --- Heuristic Algorithm --- p.28 / Chapter 3.3 --- Zero-one Optimization and Continuous Relaxation --- p.29 / Chapter 3.3.1 --- Introduction --- p.29 / Chapter 3.3.2 --- The Roof Dual expressed in terms of Lagrangian Relaxation --- p.30 / Chapter 3.3.3 --- Determining the Existence of a Duality Gap --- p.31 / Chapter 3.4 --- Software for solving Integer Programs --- p.33 / Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.35 / Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.35 / Chapter 4.2 --- From m-Constrained IP Problem to Singly-Constrained IP Problem --- p.38 / Chapter 4.2.1 --- Example --- p.39 / Chapter 5 --- A Basic Branch-and-Bound Algorithm for the Zero-One Polynomial Maximization Problem --- p.42 / Chapter 5.1 --- Reason for choosing Branch-and-Bound Method --- p.42 / Chapter 5.2 --- Searching Algorithm --- p.43 / Chapter 5.2.1 --- Branch Rule --- p.44 / Chapter 5.2.2 --- Bounding Rule --- p.46 / Chapter 5.2.3 --- Fathoming Test --- p.46 / Chapter 5.2.4 --- Example --- p.47 / Chapter 6 --- Revised Bound Rule for Branch-and-Bound Algorithm --- p.55 / Chapter 6.1 --- Revised Bound Rule --- p.55 / Chapter 6.1.1 --- CPLEX --- p.57 / Chapter 6.2 --- Example --- p.57 / Chapter 6.3 --- Conclusion --- p.65 / Chapter 7 --- Revised Branch Rule for Branch-and-Bound Algorithm --- p.67 / Chapter 7.1 --- Revised Branch Rule --- p.67 / Chapter 7.2 --- Comparison between Branch Rule and Revised Branch Rule --- p.69 / Chapter 7.3 --- Example --- p.72 / Chapter 7.4 --- Conclusion --- p.73 / Chapter 8 --- Experimental Results and Analysis --- p.80 / Chapter 8.1 --- Experimental Results --- p.80 / Chapter 8.2 --- Statistical Analysis --- p.33 / Chapter 8.2.1 --- Analysis of Search Techniques --- p.83 / Chapter 8.2.2 --- Discussion of the Performance of SATZ --- p.85 / Chapter 9 --- Concluding Remarks --- p.87 / Chapter 9.1 --- Conclusion --- p.87 / Chapter 9.2 --- Suggestions for Future Research --- p.88 / Chapter A --- Searching Procedures for Solving Constraint Satisfaction Problem (CSP) --- p.91 / Chapter A.1 --- Notation --- p.91 / Chapter A.2 --- Procedures for Solving CSP --- p.92 / Chapter A.2.1 --- Generate and Test --- p.92 / Chapter A.2.2 --- Standard Backtracking --- p.93 / Chapter A.2.3 --- Forward Checking --- p.94 / Chapter A.2.4 --- Looking Ahead --- p.95 / Chapter B --- Complete Results for Experiments --- p.96 / Chapter B.1 --- Complete Result for SATZ --- p.96 / Chapter B.1.1 --- n =5 --- p.95 / Chapter B.1.2 --- n = 10 --- p.98 / Chapter B.1.3 --- n = 30 --- p.99 / Chapter B.2 --- Complete Result for Basic Branch-and-Bound Algorithm --- p.101 / Chapter B.2.1 --- n二5 --- p.101 / Chapter B.2.2 --- n = 10 --- p.104 / Chapter B.2.3 --- n = 30 --- p.107 / Chapter B.3 --- Complete Result for Revised Bound Rule --- p.109 / Chapter B.3.1 --- n = 5 --- p.109 / Chapter B.3.2 --- n = 10 --- p.112 / Chapter B.3.3 --- n = 30 --- p.115 / Chapter B.4 --- Complete Result for Revised Branch-and-Bound Algorithm --- p.118 / Chapter B.4.1 --- n = 5 --- p.118 / Chapter B.4.2 --- n = 10 --- p.121 / Chapter B.4.3 --- n = 30 --- p.124 / Bibliography --- p.128

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323436
Date January 2001
ContributorsLui, Oi Lun Irene., Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, viii, 132 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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