On the Structure of a Best Possible Crossover Selection Strategy in Genetic Algorithms
The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover to find a solution with high fitness for a given optimization problem. Many different schemes have been described in the literature as possible strategies for this task but so far comparisons have been predominantly empirical. It is shown that if one wishes to maximize any linear function of the final state probabilities, e.g. the fitness of the best individual in the final population of the algorithm, then a best probability distribution for selecting an individual in each generation is a rectangular distribution over the individuals sorted in descending sequence by their fitness values. This means uniform probabilities have to be assigned to a group of the best individuals of the population but probabilities equal to zero to individuals with lower fitness, assuming that the probability distribution to choose individuals from the current population can be chosen independently for each iteration and each individual. This result is then generalized also to typical practically applied performance measures, such as maximizing the expected fitness value of the best individual seen in any generation.
KeywordsGenetic Algorithm Crossover Operator Good Individual Rectangular Distribution Frequency Assignment Problem
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- 1.S. Boettcher and A. G. Percus. Extremal Optimization: Methods derived from Co-Evolution. In GECCO-99, Proceedings of the Genetic and Evolutionary Computation Conference, pages 825–832, Orlando, Florida, July 1999.Google Scholar
- 3.M. Chakraborty and U. K. Chakraborty. An Analysis of Linear Ranking and Binary Tournament Selection in Genetic Algorithms. In Proceedings of the International Conference on Information, Communications and Signal Processing, pages 407–411, Singapore, September 1997.Google Scholar
- 9.T. Friedrich, P. S. Oliveto, D. Sudholt, and C. Witt. Theoretical Analysis of Diversity Mechanisms for Global Exploration. In Interational Genetic and Evolutionary Computation Conference 2008, pages 945–952, Atlanta, Georgia, July 2008. ACM Press.Google Scholar
- 10.E. Happ, D. Johannsen, C. Klein, and F. Neumann. Rigorous Analyses of Fitness-Proportional Selection for Optimizing Linear Functions. In Interational Genetic and Evolutionary Computation Conference 2008, pages 953–960, Atlanta, Georgia, July 2008. ACM Press.Google Scholar
- 15.J. Lässig, K. H. Hoffmann, and M. Enăachescu. Threshold Selecting: Best Possible Probability Distribution for Crossover Selection in Genetic Algorithms. In Interational Genetic and Evolutionary Computation Conference 2008, pages 2181–2185, Atlanta, Georgia, July 2008. ACM Press.Google Scholar
- 16.A. Moraglio and R. Poli. Inbreeding Properties of Geometric Crossover and Non-geometric Recombinations. In C. R. Stephens, M. Toussaint, D. Whitley, and P. F. Stadler, editors, Foundations of Genetic Algorithms: 9th International Workshop, pages 1–14, Mexico City, Mexico, June 2007. Springer Berlin.Google Scholar
- 18.D. Srinivasan and L. Rachmawati. An Efficient Multi-objective Evolutionary Algorithm with Steady-State Replacement Model. In Proceedings of the 8th annual conference on Genetic and evolutionary computation, pages 715–722, Seattle, Washington, USA, July 2006.Google Scholar