Geometric particle swarm optimization for the sudoku puzzle

Geometric particle swarm optimization (GPSO) is a recently introduced generalization of traditional particle swarm optimization (PSO) that applies to all combinatorial spaces. The aim of this paper is to demonstrate the applicability of GPSO to non-trivial combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic ideas because it is entertaining and instructive as well as a nontrivial constrained combinatorial problem. We apply GPSO to solve the sudoku puzzle

04081 Abstracts Collection -- Theory of Evolutionary Algorithms

From 15.02.04 to 20.02.04, the Dagstuhl Seminar 04081 ``Theory of Evolutionary Algorithms\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Population-based runtime optimisation in static and dynamic environments

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Self adaptation in evolutionary algorithms

Evolutionary Algorithms are search algorithms based on the Darwinian metaphor of “Natural Selection”. Typically these algorithms maintain a population of individual solutions, each of which has a fitness attached to it, which in some way reflects the quality of the solution. The searchproceeds via the iterative generation, evaluation and possible incorporation of new individuals based on the current population, using a number of parameterisedgenetic operators. In this thesis the phenomenon of Self Adaptation of the genetic operators is investigated.A new framework for classifying adaptive algorithms is proposed, based on the scope of the adaptation, and on the nature of the transition function guiding the search through the space of possible configurations of the algorithm. Mechanisms are investigated for achieving the self adaptation of recombination and mutation operators within a genetic algorithm, and means of combining them are investigated. These are shown to produce significantly better results than any of the combinations of fixed operators tested, across a range of problem types. These new operators reduce the need for the designer of an algorithm to select appropriate choices of operators and parameters, thus aiding the implementation of geneticalgorithms. The nature of the evolving search strategies are investigated and explained in terms of the known properties of the landscapes used, and it is suggested how observations of evolving strategies on unknown landscapes may be used to categorise them, and guide further changes in other facets of the genetic algorithm.This work provides a contribution towards the study of adaptation in Evolutionary Algorithms, and towards the design of robust search algorithms for “real world” problems

Considerations for Rapidly Converging Genetic Algorithms Designed for Application to Problems with Expensive Evaluation Functions

A genetic algorithm is a technique designed to search large problem spaces using the Darwinian concepts of evolution. Solution representations are treated as living organisms. The procedure attempts to evolve increasingly superior solutions. As in natural genetics, however, there is no guarantee that the optimum organism will be produced. One of the problems in producing optimal organisms in a genetic algorithm is the difficulty of premature convergence. Premature convergence occurs when the organisms converge in similarity to a pattern which is sub-optimal, but insufficient genetic material is present to continue the search beyond this sub-optimal level, called a local maximum. The prevention of premature convergence of the organisms is crucial to the success of most genetic algorithms. In order to prevent such convergence, numerous operators have been developed and refined. All such operators, however, rely on the property of the underlying problem that the evaluation of individuals is a computationally inexpensive process. In this paper, the design of genetic algorithms which intentionally converge rapidly is addressed. The design considerations are outlined, and the concept is applied to an NP-Complete problem, known as a Crozzle, which does not have an inexpensive evaluation function. This property would normally make the Crozzle unsuitable for processing by a genetic algorithm. It is shown that a rapidly converging genetic algorithm can successfully reduce the effective complexity of the problem

A Genetic Algorithm for the Vehicle Routing Problem

The purpose of this research was to develop a version of a genetic algorithm (GA ) which would provide near optimal solutions for Vehicle Routing Problems (VRP) with both time and weight constraints. The genetic algorithm used for the experimentation was adapted from a GA which had been developed by James Bean at the University of Michigan to solve machine scheduling problems. The VRP data sets used in this research were obtained from the literature. Various aspects of the GA were experimented with in order to develop a version which would perform consistently well for all the data sets. The results of the final version of the genetic algorithm were then compared to the results presented in the original papers. The results from this research indicated that the genetic algorithm seems to perform relatively well for smaller problems with 50 or fewer customers. However, the results seem to become progressively worse as the problem becomes larger