Zugl.: Düsseldorf, Universiẗat, Diss., 1999.

Techn. Hochsch., Diss., 2000--Aachen.

published_or_final_version / Mathematics / Master / Master of Philosophy

by Anthony Yiu-Cheung Tang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 145-152). / ACKNOWLEDGMENTS --- p.i / ABSTRACT --- p.ii / LIST OF FIGURES --- p.vii / LIST OF TABLES --- p.ix / Chapter 1. --- INTRODUCTION --- p.1 / Chapter 1.1 --- Introducing evolutionary computation --- p.2 / Chapter 1.2 --- Adaptation and learning --- p.7 / Chapter 1.3 --- Comparing the efficency of evolutionary computation and sequential computation --- p.8 / Chapter 1.4 --- The place of evolutionary computation in computer science --- p.9 / Chapter 1.4.1 --- Mathematical foundation --- p.9 / Chapter 1.4.2 --- Scalability --- p.10 / Chapter 1.4.3 --- Parallelism --- p.11 / Chapter 1.5 --- Enhancing genetic search by local search --- p.11 / Chapter 1.6 --- Thesis Overview --- p.12 / Chapter 2. --- A REVIEW OF GENETIC ALGORITHMS --- p.14 / Chapter 2.1 --- Introduction --- p.14 / Chapter 2.2 --- The canonical genetic algorithm --- p.14 / Chapter 2.3 --- Optimal allocation of trials and schemata analysis --- p.17 / Chapter 2.4 --- Applications --- p.23 / Chapter 2.4.1 --- Function optimizations --- p.23 / Chapter 2.4.2 --- Machine Learning --- p.24 / Chapter 2.4.3 --- Combinatorial optimizations --- p.25 / Chapter 2.5 --- Criticisms --- p.25 / Chapter 2.5.1 --- Parameter settings --- p.25 / Chapter 2.5.2 --- Convergence and divergence --- p.26 / Chapter 2.5.3 --- Genetic algorithms for function optimizations --- p.27 / Chapter 2.5.4 --- The role of crossover and build blocks --- p.28 / Chapter 2.6 --- Future directions --- p.29 / Chapter 2.6.1 --- Is the schemata theorem wrong ？ --- p.29 / Chapter 2.6.2 --- Artificial life --- p.29 / Chapter 2.6.3 --- Parallel genetic algorithms --- p.31 / Chapter 2.6.4 --- Non-binary alphabets --- p.31 / Chapter 2.6.5 --- Investigations on problems that are hard for GA --- p.33 / Chapter 3. --- THE GENERAL STRUCTURE OF TOLKIEN --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- Class Description --- p.39 / Chapter 3.2.1 --- Collection classes --- p.39 / Chapter 3.2.2 --- Vector classes --- p.39 / Chapter 3.2.3 --- GA-related classes --- p.40 / Chapter 3.2.4 --- Utility classes --- p.42 / Chapter 3.3 --- The TOLKIEN Genetic Algorithm --- p.43 / Chapter 3.3.1 --- Binary and Gray Code Representations --- p.44 / Chapter 3.3.2 --- Crossover Operators --- p.44 / Chapter 3.3.3 --- Haploids and Diploids --- p.47 / Chapter 3.3.4 --- Population --- p.50 / Chapter 3.3.5 --- Selection scheme --- p.50 / Chapter 3.3.6 --- Scaling scheme...: --- p.51 / Chapter 3.4 --- The TOLKIEN Classifier System --- p.52 / Chapter 3.4.1 --- Classifiers --- p.52 / Chapter 3.4.2 --- Messages and Message Lists --- p.53 / Chapter 3.4.3 --- Producing New Messages --- p.55 / Chapter 3.4.4 --- The Bucket Brigade Algorithm --- p.55 / Chapter 3.5 --- Where to obtain TOLKIEN --- p.56 / Chapter 4. --- ILLUSTRATING THE CAPABILITIES OF TOLKIEN --- p.57 / Chapter 4.1 --- de Jong's Test Bed : Function Optimization using GA --- p.57 / Chapter 4.2 --- Royal road function experiments --- p.63 / Chapter 4.2.1 --- RRMF --- p.64 / Chapter 4.2.2 --- RRJH --- p.65 / Chapter 4.2.3 --- Testing royal road functions using TOLKIEN --- p.68 / Chapter 4.2.4 --- Results --- p.71 / Chapter 4.2.5 --- Adding hillclimbing algorithm to solve royal road functions --- p.72 / Chapter 4.2.6 --- Discussions --- p.73 / Chapter 4.3 --- A classifier system to learn a multiplexer --- p.74 / Chapter 4.4 --- A classifier system maze traveller --- p.83 / Chapter 4.4.1 --- Framework of the Animat --- p.84 / Chapter 4.4.2 --- Constructing the maze navigation classifier system --- p.85 / Chapter 4.4.3 --- Results --- p.86 / Chapter 4.5 --- Future Enhancements on TOLKIEN --- p.88 / Chapter 4.6 --- Chapter Summary --- p.88 / Chapter 5. --- SOLVING TSP USING GENETIC ALGORITHMS --- p.89 / Chapter 5.1 --- Introduction --- p.89 / Chapter 5.2 --- Recombination operators for TSP --- p.91 / Chapter 5.2.1 --- PMX Crossover --- p.91 / Chapter 5.2.2 --- Order Crossover --- p.92 / Chapter 5.2.3 --- Edge Recombination operator --- p.93 / Chapter 5.3 --- Simulated Annealing --- p.95 / Chapter 5.4 --- Simulation Comparisons --- p.96 / Chapter 5.4.1 --- The Test Bed --- p.96 / Chapter 5.4.2 --- The Experimental Setup --- p.97 / Chapter 5.4.3 --- Results --- p.97 / Chapter 5.4.4 --- Discussions --- p.100 / Chapter 6. --- AN IMPROVED EDGE RECOMBINATION OPERATOR FOR TSP --- p.101 / Chapter 6.1 --- EDGENN ： a new edge recombination operator --- p.102 / Chapter 6.2 --- Experimental results --- p.104 / Chapter 6.2.1 --- Comparing EdgeNN and Edge-2 --- p.104 / Chapter 6.2.2 --- Comparing EdgeNN and Edge-3 --- p.106 / Chapter 6.3 --- Further improvement : a heuristic genetic algorithm using EdgeNN --- p.106 / Chapter 6.4 --- Discussion --- p.108 / Chapter 7. --- CONCLUSIONS --- p.111 / Chapter 7.1 --- Evaluation on TOLKIEN --- p.111 / Chapter 7.2 --- EdgeNN as a useful recombination operator for solving TSP --- p.112 / Chapter 7.3 --- Genetic algorithm and hillclimbing --- p.112 / EPILOGUE --- p.113 / APPENDIX : PROGRAM LISTINGS --- p.114 / Function optimizations --- p.114 / Maze Navigator --- p.122 / Multiplexer --- p.135 / Royal road functions --- p.141 / BIBLIOGRAPHY --- p.145 / INDEX --- p.153

by Lee, Ka-wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 61-67). / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Traveling Salesman Problem --- p.6 / Chapter 1.2 --- Genetic Algorithms --- p.8 / Chapter 1.3 --- Solving TSP using Genetic Algorithms --- p.10 / Chapter 1.4 --- Outline of Work --- p.12 / Chapter Part I --- Algorithm Development --- p.14 / Chapter 2 --- A Local DP Crossover Operator 一 LDPX --- p.15 / Chapter 2.1 --- Review of DP for Solving TSP --- p.15 / Chapter 2.2 --- On the Original LDPX --- p.18 / Chapter 2.2.1 --- Gene Representation --- p.18 / Chapter 2.2.2 --- The Original Crossover Procedure --- p.19 / Chapter 2.3 --- Analysis --- p.21 / Chapter 2.3.1 --- Ring TSP --- p.21 / Chapter 2.3.2 --- Computational Results of Solving Ring TSP and Other TSP using LDPX --- p.22 / Chapter 2.4 --- Augmentation of the Gene Set Representation --- p.24 / Chapter 2.5 --- Enhancement of Crossover Procedure --- p.25 / Chapter 2.6 --- Computational Comparison of the new proposed LDPX with the orig- inal LDPX --- p.26 / Chapter 2.7 --- SPIR ´ؤ An Operator for Single Parent Improved Reproduction --- p.26 / Chapter 3 --- A New TSP Solver --- p.29 / Chapter 4 --- Performance Analysis of the TSP Solver --- p.33 / Chapter 4.1 --- Computational results --- p.34 / Chapter 4.2 --- "Comparison between SPIR/LDPX, PMX and ER" --- p.35 / Chapter 4.3 --- Convergence Test of SPIR/LDPX --- p.37 / Chapter Part II --- Application --- p.43 / Chapter 5 --- Flowshop Scheduling Problem --- p.44 / Chapter 5.1 --- Brief Review of the Flowshop Scheduling Problem --- p.44 / Chapter 5.2 --- Flowshop Scheduling with travel times between machines --- p.45 / Chapter 6 --- A New Approach to Solve FSTTBM --- p.47 / Chapter 7 --- Computational Results of the New Algorithm for CPFSTTBM --- p.53 / Chapter 7.1 --- Comparison with Global Optimum --- p.54 / Chapter 7.2 --- The Algorithm of SPIRIT --- p.55 / Chapter 7.3 --- Comparison with SPIRIT --- p.57 / Chapter 8 --- Conclusion --- p.59 / Bibliography --- p.61 / Chapter A --- Random CPFSTTBM problem Generation Algorithm --- p.68

No description available.

Thesis(B.Sc.(Hons. ))--University of Adelaide, dept. of Mathematics, 1968.

Thesis (M.Phil.)--University of Hong Kong, 2003. / Includes bibliographical references (leaves 49-50) Also available in print.

M.Sc. (Computer Science) / The STSP (symmetric travelling salesman problem) involves finding the cheapest tour through a number of cities. It is a difficult problem and until recently algorithms for the TSP could not find the optimal tour in a reasonable time if the number of cities exceeded 100. In 1987 Padberg and Rinaldi published their computational experience with a new branch-and-cut algorithm. They were able to solve problems with up to 2392 cities on a CDC CYBER 205 supercomputer. Padberg and Rinaldi used a standard LP (linear programming) solver in their implementation of the branch-and-cut algorithm. The algorithm first solves the continuous 2-matching problem (RMP2) using the LP solver. It then repeatedly identifies constraints of the TSP which are not satisfied by the current RMP2-solution and solve RMP2 with the identified TSP-constraints as side constraints. However, RMP2 is a linear programming problem with a very special structure which we exploited in an implementation of the primal simplex algorithm for RMP2. Our computational experience with this implementation indicates that it is almost 400 times faster than a commercial LP solver on problems with 200 cities. We developed an implementation of the dual simplex algorithm which exploits the special structure of both RMP2 and the side constraints identified in the branch-and-cut algorithm. An existing set of side constraints for solving a 48-eity problem was used to test our implementation of the dual simplex algorithm. We implemented the procedure described by Padberg & Rinaldi to identify subtour elimination side constraints (one type of side constraint) for the 48-eity problem. Our implementation of the identification procedure was then used in conjunction with our implementation of the dual simplex algorithm. The maximum flow problem has to be solved in the algorithm for identification of subtour elimination constraints. We implemented the Sleator-Tarjan algorithm for this purpose.

M.Sc. (Computer Science) / The Travelling Salesman Problem (TSP) comprises the following: A salesman is required, by definition of his job description, to visit a set of cities. He leaves from a base city, visits each of the other cities exactly once and then returns to his base city. In travelling between city pairs, he incurs certain costs. It is a travelling salesman's constant endeavour, therefore, to find the cheapest route. A combinatorial optimisation problem involves the selection of the best alternative from a finite set of alternatives. The TSP is one of the best known and most studied combinatorial optimisation problems. At present, the branch-and-cut algorithm of Padberg and Rinaldi is the most successful algorithm for solving large-scale instances of the TSP. Padberg and Rinaldi used a general LP solver to solve the subproblem P(L, F0 , F1 ), where L is a set of side constraints, F0 is the set of variables fixed at 0 and F1 is the set of variables fixed at 1. As noted by Smith and Leenen, however, this subproblem has a special structure that was exploited by them to solve the subproblem more efficiently. In this dissertation, we would like to present improvements on Leenen's contribution. For this purpose, we compared our results with those of a commercial LP solver. It was found that our program on average executed in half the time of that of the commercial LP solver. The problem P(L, F0 , F1;) has to be solved many times in the branch-and-cut algorithm before a solution to the TSP is obtained. For large-scale instances of the TSP, a substantial portion of the execution time of the entire branch-and-cut algorithm is spent in the linearprogram optimiser. The branch-and-cut algorithm could,• therefore, be potentially more efficient if the special structure were utilised. We constructed a full implementation of the branch-and-cut algorithm, utilising the special structure. We did not, however, implement all the refinements discussed by Padberg and Rinaldi. Padberg and Rinaldi used four classes of TSP constraints: subtour elimination, 2-matching, comb and clique-tree inequalities. Owing to time constraints and the complexity of identifying the other classes of constraints, we decided to implement subtour elimination constraints only. We subsequently compared our results with those of Padberg and Rinaldi, and realised that we totally underestimated the importance of using more classes of constraints. Our search trees had become extremely huge. We realised, therefore, that more classes of constraints were essential for solving large instances of the TSP. Even though numerical errors still posed a problem, they might disappear if the size of the search tree were reduced to that obtained by Padberg and Rinaldi.