by Kong Siu Cheung. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 114-122.

by Chong-kan Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 97-103). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Related Work --- p.2 / Chapter 1.2 --- Organizations of the Dissertation --- p.4 / Chapter 1.3 --- Notations --- p.4 / Chapter 2 --- Overview of ICLP(R) --- p.6 / Chapter 2.1 --- Basics of Interval Arithmetic --- p.6 / Chapter 2.2 --- Relational Interval Arithmetic --- p.8 / Chapter 2.2.1 --- Interval Reduction --- p.8 / Chapter 2.2.2 --- Arithmetic Primitives --- p.10 / Chapter 2.2.3 --- Interval Narrowing and Interval Splitting --- p.13 / Chapter 2.3 --- Syntax and Semantics --- p.16 / Chapter 3 --- Limitations of Interval Narrowing --- p.18 / Chapter 3.1 --- Computation Inefficiency --- p.18 / Chapter 3.2 --- Inability to Detect Inconsistency --- p.23 / Chapter 3.3 --- The Newton Language --- p.27 / Chapter 4 --- Design of CIAL --- p.30 / Chapter 4.1 --- The CIAL Architecture --- p.30 / Chapter 4.2 --- The Inference Engine --- p.31 / Chapter 4.2.1 --- Interval Variables --- p.31 / Chapter 4.2.2 --- Extended Unification Algorithm --- p.33 / Chapter 4.3 --- The Solver Interface and Constraint Decomposition --- p.34 / Chapter 4.4 --- The Linear and the Non-linear Solvers --- p.37 / Chapter 5 --- The Linear Solver --- p.40 / Chapter 5.1 --- An Interval Gaussian Elimination Solver --- p.41 / Chapter 5.1.1 --- Naive Interval Gaussian Elimination --- p.41 / Chapter 5.1.2 --- Generalized Interval Gaussian Elimination --- p.43 / Chapter 5.1.3 --- Incrementality of Generalized Gaussian Elimination --- p.47 / Chapter 5.1.4 --- Solvers Interaction --- p.50 / Chapter 5.2 --- An Interval Gauss-Seidel Solver --- p.52 / Chapter 5.2.1 --- Interval Gauss-Seidel Method --- p.52 / Chapter 5.2.2 --- Preconditioning --- p.55 / Chapter 5.2.3 --- Increment ality of Preconditioned Gauss-Seidel Method --- p.58 / Chapter 5.2.4 --- Solver Interaction --- p.71 / Chapter 5.3 --- Comparisons --- p.72 / Chapter 5.3.1 --- Time Complexity --- p.72 / Chapter 5.3.2 --- Storage Complexity --- p.73 / Chapter 5.3.3 --- Others --- p.74 / Chapter 6 --- Benchmarkings --- p.76 / Chapter 6.1 --- Mortgage --- p.78 / Chapter 6.2 --- Simple Linear Simultaneous Equations --- p.79 / Chapter 6.3 --- Analysis of DC Circuit --- p.80 / Chapter 6.4 --- Inconsistent Simultaneous Equations --- p.82 / Chapter 6.5 --- Collision Problem --- p.82 / Chapter 6.6 --- Wilkinson Polynomial --- p.85 / Chapter 6.7 --- Summary and Discussion --- p.86 / Chapter 6.8 --- Large System of Simultaneous Equations --- p.87 / Chapter 6.9 --- Comparisons Between the Incremental and the Non-Incremental Preconditioning --- p.89 / Chapter 7 --- Concluding Remarks --- p.93 / Chapter 7.1 --- Summary and Contributions --- p.93 / Chapter 7.2 --- Future Work --- p.95 / Bibliography --- p.97

by Wong Man Leung. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 227-236). / List of Figures --- p.iii / List of Tables --- p.vi / Chapter Chapter 1 : --- Introduction --- p.1 / Chapter 1.1. --- Automatic programming and program induction --- p.1 / Chapter 1.2. --- Motivation --- p.6 / Chapter 1.3. --- Contributions of the research --- p.8 / Chapter 1.4. --- Outline of the thesis --- p.11 / Chapter Chapter 2 : --- An Overview of Evolutionary Algorithms --- p.13 / Chapter 2.1. --- Evolutionary algorithms --- p.13 / Chapter 2.2. --- Genetic Algorithms (GAs) --- p.15 / Chapter 2.2.1. --- The canonical genetic algorithm --- p.16 / Chapter 2.2.1.1. --- Selection methods --- p.21 / Chapter 2.2.1.2. --- Recombination methods --- p.24 / Chapter 2.2.1.3. --- Inversion and Reordering --- p.27 / Chapter 2.2.2. --- Implicit parallelism and the building block hypothesis --- p.28 / Chapter 2.2.3. --- Steady state genetic algorithms --- p.32 / Chapter 2.2.4. --- Hybrid algorithms --- p.33 / Chapter 2.3. --- Genetic Programming (GP) --- p.34 / Chapter 2.3.1. --- Introduction to the traditional GP --- p.34 / Chapter 2.3.2. --- Automatic Defined Function (ADF) --- p.41 / Chapter 2.3.3. --- Module Acquisition (MA) --- p.44 / Chapter 2.3.4. --- Strongly Typed Genetic Programming (STGP) --- p.49 / Chapter 2.4. --- Evolution Strategies (ES) --- p.50 / Chapter 2.5. --- Evolutionary Programming (EP) --- p.55 / Chapter Chapter 3 : --- Inductive Logic Programming --- p.59 / Chapter 3.1. --- Inductive concept learning --- p.59 / Chapter 3.2. --- Inductive Logic Programming (ILP) --- p.62 / Chapter 3.2.1. --- Interactive ILP --- p.64 / Chapter 3.2.2. --- Empirical ILP --- p.65 / Chapter 3.3. --- Techniques and methods of ILP --- p.67 / Chapter Chapter 4 : --- Genetic Logic Programming and Applications --- p.74 / Chapter 4.1. --- Introduction --- p.74 / Chapter 4.2. --- Representations of logic programs --- p.76 / Chapter 4.3. --- Crossover of logic programs --- p.81 / Chapter 4.4. --- Genetic Logic Programming System (GLPS) --- p.87 / Chapter 4.5. --- Applications --- p.90 / Chapter 4.5.1. --- The Winston's arch problem --- p.91 / Chapter 4.5.2. --- The modified Quinlan's network reachability problem --- p.92 / Chapter 4.5.3. --- The factorial problem --- p.95 / Chapter Chapter 5 : --- The logic grammars based genetic programming system (LOGENPRO) --- p.100 / Chapter 5.1. --- Logic grammars --- p.101 / Chapter 5.2. --- Representations of programs --- p.103 / Chapter 5.3. --- Crossover of programs --- p.111 / Chapter 5.4. --- Mutation of programs --- p.126 / Chapter 5.5. --- The evolution process of LOGENPRO --- p.130 / Chapter 5.6. --- Discussion --- p.132 / Chapter Chapter 6 : --- Applications of LOGENPRO --- p.134 / Chapter 6.1. --- Learning functional programs --- p.134 / Chapter 6.1.1. --- Learning S-expressions using LOGENPRO --- p.134 / Chapter 6.1.2. --- The DOT PRODUCT problem --- p.137 / Chapter 6.1.2. --- Learning sub-functions using explicit knowledge --- p.143 / Chapter 6.2. --- Learning logic programs --- p.148 / Chapter 6.2.1. --- Learning logic programs using LOGENPRO --- p.148 / Chapter 6.2.2. --- The Winston's arch problem --- p.151 / Chapter 6.2.3. --- The modified Quinlan's network reachability problem --- p.153 / Chapter 6.2.4. --- The factorial problem --- p.154 / Chapter 6.2.5. --- Discussion --- p.155 / Chapter 6.3. --- Learning programs in C --- p.155 / Chapter Chapter 7 : --- Knowledge Discovery in Databases --- p.159 / Chapter 7.1. --- Inducing decision trees using LOGENPRO --- p.160 / Chapter 7.1.1. --- Decision trees --- p.160 / Chapter 7.1.2. --- Representing decision trees as S-expressions --- p.164 / Chapter 7.1.3. --- The credit screening problem --- p.166 / Chapter 7.1.4. --- The experiment --- p.168 / Chapter 7.2. --- Learning logic program from imperfect data --- p.174 / Chapter 7.2.1. --- The chess endgame problem --- p.177 / Chapter 7.2.2. --- The setup of experiments --- p.178 / Chapter 7.2.3. --- Comparison of LOGENPRO with FOIL --- p.180 / Chapter 7.2.4. --- Comparison of LOGENPRO with BEAM-FOIL --- p.182 / Chapter 7.2.5. --- Comparison of LOGENPRO with mFOILl --- p.183 / Chapter 7.2.6. --- Comparison of LOGENPRO with mFOIL2 --- p.184 / Chapter 7.2.7. --- Comparison of LOGENPRO with mFOIL3 --- p.185 / Chapter 7.2.8. --- Comparison of LOGENPRO with mFOIL4 --- p.186 / Chapter 7.2.9. --- Comparison of LOGENPRO with mFOIL5 --- p.187 / Chapter 7.2.10. --- Discussion --- p.188 / Chapter 7.3. --- Learning programs in Fuzzy Prolog --- p.189 / Chapter Chapter 8 : --- An Adaptive Inductive Logic Programming System --- p.192 / Chapter 8.1. --- Adaptive Inductive Logic Programming --- p.192 / Chapter 8.2. --- A generic top-down ILP algorithm --- p.196 / Chapter 8.3. --- Inducing procedural search biases --- p.200 / Chapter 8.3.1. --- The evolution process --- p.201 / Chapter 8.3.2. --- The experimentation setup --- p.202 / Chapter 8.3.3. --- Fitness calculation --- p.203 / Chapter 8.4. --- Experimentation and evaluations --- p.204 / Chapter 8.4.1. --- The member predicate --- p.205 / Chapter 8.4.2. --- The member predicate in a noisy environment --- p.205 / Chapter 8.4.3. --- The multiply predicate --- p.206 / Chapter 8.4.4. --- The uncle predicate --- p.207 / Chapter 8.5. --- Discussion --- p.208 / Chapter Chapter 9 : --- Conclusion and Future Work --- p.210 / Chapter 9.1. --- Conclusion --- p.210 / Chapter 9.2. --- Future work --- p.217 / Chapter 9.2.1. --- Applying LOGENPRO to discover knowledge from databases --- p.217 / Chapter 9.2.2. --- Learning recursive programs --- p.218 / Chapter 9.2.3. --- Applying LOGENPRO in engineering design --- p.220 / Chapter 9.2.4. --- Exploiting parallelism of evolutionary algorithms --- p.222 / Reference --- p.227 / Appendix A --- p.237

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Finding integer solutions to linear equations has various real world applications. In the thesis, we investigate its application to the reachability analysis of Petri nets. Introduced by Petri in 1962, Petri net has been a powerful mathematical formalism for modeling, analyzing and designing discrete event systems. In the research community of Petri nets, finding a feasible path from the initial state to the target state in Petri net, known as reachability analysis, is probably one of the most important and challenging subjects. The reachability algebraic analysis is equivalent to finding the nonnegative integer solutions to a fundamental equation constructed from the Petri net. We apply our algorithm in this thesis to reachability analysis of Petri net by finding the nonnegative integer solutions to the fundamental equation. / Finding the optimal binary solution to a quadratic object function is known as the Binary Quadratic Programming problem (BQP), which has been studied extensively in the last three decades. In this thesis, by investigating geometric features of the ellipse contour of a concave quadratic function, we derive new upper and lower bounding methods for BQP. Integrating these new bounding schemes into a proposed solution algorithm of a branch-and-bound type, we propose an exact solution method in solving general BQP with promising preliminary computational results. Meanwhile, by investigating some special structures of the second order matrix and linear term in BQP, several polynomial time algorithms are discussed to solve some special cases of BQP. / In the realm of integer programming, finding integer solutions to linear equations is another important research direction. The problem is proved to be NP-Complete, and several algorithms have been proposed such as the algorithm based on linear Diophantine equations as well as the method based on Groebner bases. Unlike the traditional algorithms, the new efficient method we propose in this thesis is based on our results on zero duality gap and the cell enumeration of an arrangement of hyperplanes in discrete geometry. / Integer programming plays an important role in operations research and has a wide range of applications in various fields. There are a lot of research directions in the area of integer programming. In this thesis, two main topics will be investigated in details. One is to find the optimal binary solution to a quadratic object function, and the other is to find integer solutions to linear equations. / Gu, Shenshen. / Adviser: Wang Jun. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 98-103). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Sin Man Cheang. / "March 2005." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 219-233) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Cheung, Sin Shuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 55-59). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.5 / Chapter 2.1 --- Heuristics by Hoeffding and Janson --- p.5 / Chapter 2.2 --- Facts in Matrix Theory --- p.10 / Chapter 2.3 --- Facts in Probability --- p.11 / Chapter 3 --- General Chance-Constrained LMIs --- p.18 / Chapter 3.1 --- Probability Inequalities --- p.18 / Chapter 3.2 --- Safe Tractable Approximations --- p.22 / Chapter 4 --- Chance-Constrained Quadratically Perturbed LMIs --- p.27 / Chapter 4.1 --- Exact Proper Fractional Covers --- p.27 / Chapter 4.2 --- Bounding the Matrix Moment Generating Functions --- p.32 / Chapter 5 --- Computational Study --- p.39 / Chapter 5.1 --- Update Procedures for Safe Tractable Approximations --- p.39 / Chapter 5.2 --- A Numerical Example and Comparisons --- p.44 / Chapter 6 --- Conclusion --- p.54 / Bibliography --- p.55