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

No description available.

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.

Microaggregation is a method of statistical disclosure control that attempts to reconcile the need to release information to researchers with the need to protect privacy of individual records in a dataset. Under microaggregation, records are divided into groups containing at least k members. Actual data values of the members are replaced by the mean value of the group, such that each record in the group is indistinguishable from at least k-1 other records. The goal of microaggregation is to create groups of similar records such that information loss is minimized, where information loss is the sum squared deviation between the actual data values and the group means. Optimal multivariate microaggregation is an NP-hard problem, and heuristics have been proposed to generate solutions in reasonable running time. New heuristics are desirable for either producing groups with lower information loss, or for producing groups with similar information loss but lower computational complexity. Some of the best performing existing microaggregation heuristics are based on record ordering, since it has been proven that for a given ordering of records, the optimal set of groups for that particular ordering can be efficiently computed. This dissertation improves on previous heuristics that order records in a dataset and subsequently use this record ordering to generate high quality microaggregated k- partitions. This was accomplished by using heuristics from the traveling salesman problem (TSP) literature in order to more effectively order the records. In particular, two tour construction heuristics - the Greedy heuristic and the Quick Boruvka heuristic - that are comparable in complexity to extant microaggregation methods were investigated. Next, three tour improvement heuristics - 2-opt, 3-opt, and Lin-Kernighan - were used on the tours constructed to investigate whether further reduction in information loss could be achieved. The tour improvement heuristics - particularly the 3-opt and Lin-Kernighan heuristics - provided microaggregation solutions better than the best previous known solutions across several datasets and values of k.

Genetic algorithms are an evolutionary technique that use crossover and mutation operators to solve optimization problems using a survival of the fittest idea. They have been used successfully in a variety of different problems, including the traveling salesman problem. In the traveling salesman problem we wish to find a tour of all nodes in a weighted graph so that the total weight is minimized. The traveling salesman problem is NP-hard but has many real world applications so a good solution would be useful. Many different crossover and mutation operators have been devised for the traveling salesman problem and each give different results. We compare these results and find that operators that use heuristic information or a matrix representation of the graph give the best results.

The Time-Dependent Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem, where the cost for travel between two nodes is dependent on the nodes and their position in the tour. Inequalities for the Asymmetric TSP can be easily extended to the TDTSP, but the added time information can be used to strengthen these inequalities. We look at extending the Lifted Cycle Inequalities, a large family of inequalities for the ATSP. We define a new inequality, the Extended Cycle (X-cycle) Inequality, based on cycles in the graph. We extend the results of Balas and Fischetti for Lifted Cycle Inequalities to define Lifted X-cycle Inequalities. We show that the Lifted X-cycle Inequalities include some inequalities which define facets of the submissive of the TDTS Polytope.

The Time-Dependent Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem, where the cost for travel between two nodes is dependent on the nodes and their position in the tour. Inequalities for the Asymmetric TSP can be easily extended to the TDTSP, but the added time information can be used to strengthen these inequalities. We look at extending the Lifted Cycle Inequalities, a large family of inequalities for the ATSP. We define a new inequality, the Extended Cycle (X-cycle) Inequality, based on cycles in the graph. We extend the results of Balas and Fischetti for Lifted Cycle Inequalities to define Lifted X-cycle Inequalities. We show that the Lifted X-cycle Inequalities include some inequalities which define facets of the submissive of the TDTS Polytope.

No description available.

The traveling salesperson (or, salesman) problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NP-complete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. Typical applications in operations research include vehicle routing, computer wiring, cutting wallpaper and job sequencing. The main application in statistics is combinatorial data analysis, e.g., reordering rows and columns of data matrices or identifying clusters. In this paper, we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available. (authors' abstract)

Smith, T.H.C., Prof.