No description available.

No description available.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 51-52). Also available in electronic version. Access restricted to campus users.

No description available.

No description available.

No description available.

Thesis (M.S.)--Ohio University, November, 1995. / Title from PDF t.p.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, December 2002. / Thesis advisor(s): R. Kevin Wood, Matthew Carlyle. Includes bibliographical references (p. 35). Also available online.

by Mei Long. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 93-98). / Abstracts in English and Chinese. / Table of Contents --- p.v / Abstract --- p.viii / Acknowledgements --- p.x / 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 --- Satisfiability Problem --- p.4 / Chapter 2.1 --- Satisfiability Problem --- p.5 / Chapter 2.1.1 --- Basic Definition --- p.5 / Chapter 2.1.2 --- Phase Transitions --- p.5 / Chapter 2.2 --- History --- p.6 / Chapter 2.3 --- The Basic Search Algorithm --- p.8 / Chapter 2.4 --- Some Improvements to the Basic Algorithm --- p.9 / Chapter 2.4.1 --- Satz by Chu-Min Li --- p.9 / Chapter 2.4.2 --- Heuristics and Local Search --- p.12 / Chapter 2.4.3 --- Relaxation --- p.13 / Chapter 2.5 --- Benchmarks --- p.14 / Chapter 2.5.1 --- Specific Problems --- p.14 / Chapter 2.5.2 --- Randomly Generated Problems --- p.14 / Chapter 2.6 --- Software and Internet Information for SAT solving --- p.16 / Chapter 2.6.1 --- Stochastic Local Search Algorithms (incomplete) --- p.16 / Chapter 2.6.2 --- Systematic Search Algorithms (complete) --- p.16 / Chapter 2.6.3 --- Some useful Links to SAT Related Sites --- p.17 / Chapter 3 --- Integer Programming Formulation for Logic Problem --- p.18 / Chapter 3.1 --- SAT Problem --- p.19 / Chapter 3.2 --- MAXSAT Problem --- p.19 / Chapter 3.3 --- Logical Inference Problem --- p.19 / Chapter 3.4 --- Weighted Exact Satisfiability Problem --- p.20 / Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.22 / Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.22 / Chapter 4.2 --- Integer Programming Model for 3-SAT --- p.23 / Chapter 4.3 --- The Equivalence of the SAT and the IP --- p.23 / Chapter 4.4 --- Example --- p.24 / Chapter 5 --- Integer Solvability of Linear Programs --- p.27 / Chapter 5.1 --- Unimodularity --- p.27 / Chapter 5.2 --- Totally Unimodularity --- p.28 / Chapter 5.3 --- Some Results on Recognition of Linear Solvability of IP --- p.32 / Chapter 6 --- TU Based Matrix Research Results --- p.33 / Chapter 6.1 --- 2x2 Matrix's TU Property --- p.33 / Chapter 6.2 --- Extended Integer Programming Model for SAT --- p.34 / Chapter 6.3 --- 3x3 Matrix's TU Property --- p.35 / Chapter 7 --- Totally Unimodularity Based Branching-and-Bound Algorithm --- p.38 / Chapter 7.1 --- Introduction --- p.38 / Chapter 7.1.1 --- Enumeration Trees --- p.39 / Chapter 7.1.2 --- The Concept of Branch and Bound --- p.42 / Chapter 7.2 --- TU Based Branching Rule --- p.43 / Chapter 7.2.1 --- How to sort variables based on 2x2 submatrices --- p.43 / Chapter 7.2.2 --- How to sort the rest variables --- p.45 / Chapter 7.3 --- TU Based Bounding Rule --- p.46 / Chapter 7.4 --- TU Based Branch-and-Bound Algorithm --- p.47 / Chapter 7.5 --- Example --- p.49 / Chapter 8 --- Numerical Result --- p.57 / Chapter 8.1 --- Experimental Result --- p.57 / Chapter 8.2 --- Statistical Results of ILOG CPLEX --- p.59 / Chapter 9 --- Conclusions --- p.61 / Chapter 9.1 --- Contributions --- p.61 / Chapter 9.2 --- Future Work --- p.62 / Chapter A --- The Coefficient Matrix A for Example in Chapter 7 --- p.64 / Chapter B --- The Detailed Numerical Information of Solution Process for Exam- ple in Chapter 7 --- p.66 / Chapter C --- Experimental Result --- p.67 / Chapter C.1 --- "# of variables: 20, # of clauses: 91" --- p.67 / Chapter C.2 --- "# of variables: 50, # of clauses: 218" --- p.70 / Chapter C.3 --- # of variables: 75，# of clauses: 325 --- p.73 / Chapter C.4 --- "# of variables: 100, # of clauses: 430" --- p.76 / Chapter D --- Experimental Result of ILOG CPLEX --- p.80 / Chapter D.1 --- # of variables: 20´ة # of clauses: 91 --- p.80 / Chapter D.2 --- # of variables: 50，#of clauses: 218 --- p.83 / Chapter D.3 --- # of variables: 75，# of clauses: 325 --- p.86 / Chapter D.4 --- "# of variables: 100, # of clauses: 430" --- p.89 / Bibliography --- p.93

The objective of this thesis is to develop and computationally test a new algorithm for the class of network models with generalized upper bound (GUB) side constraints. Various algorithms have been developed to solve the network with arbitrary side constraints problem; however, no algorithm that exploits the special structure of the GUB side constraints previously existed. The proposed algorithm solves the network with GUB side constraints problem using two sequences of problems. One sequence yields a lower bound on the optimal value for the problem by using a Lagrangean relaxation based on relaxing copies of some subset of the original variables. This is achieved by first solving a pure network subproblem and then solving a set of single constraint bounded variable linear programs. Because only the cost coefficients change from one pure network subproblem to another, the optimal solution for one subproblem is at least feasible, if not optimal, for the next pure network subproblem. The second sequence yields an upper bound on the optimal value by using a decomposition of the problem based on changes in the capacity vector. Solving for the decomposed problem corresponds to solving for pure network subproblems that have undergone changes in lower and/or upper bounds. Recently developed reoptimization techniques are incorporated in the algorithm to find an initial (artificial) feasible solution to the pure network subproblem. A program is developed for solving the network with GUB side constraints problem by using the relaxation and decomposition techniques. The algorithm has been tested on problems with up to 200 nodes, 2000 arcs and 100 GUB constraints. Computational experience indicates that the upper bound procedure seems to perform well; however, the lower bound procedure has a fairly slow convergence rate. It also indicates that the lower bound step size, the initial lower bound value, and the lower and upper bound iteration strategies have a significant effect on the convergence rate of the lower bound algorithm. / Graduation date: 1990