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Unformatted text preview: 3 Genetic Algorithms 3.1 Introduction Genetic algorithms 1 (GAs) are a subclass of evolutionary algorithms where the elements of the search space G are binary strings ( G = B ∗ ) or arrays of other elementary types. As sketched in Figure 3.1 , the genotypes are used in the reproduction operations whereas the values of the objective functions f ∈ F are computed on basis of the phenotypes in the problem space X which are obtained via the genotype-phenotype mapping “gpm”. [821, 940, 916, 2208] The roots of genetic algorithms go back to the mid-1950s, where biologists like Barricelli [150, 151, 152, 153] and the computer scientist Fraser  began to apply computer-aided simulations in order to gain more insight into genetic processes and the natural evolution and selection. Bremermann  and Bledsoe [216, 215, 217, 218] used evolutionary approaches based on binary string genomes for solving inequalities, for function optimization, and for determining the weights in neural networks in the early 1960s . At the end of that decade, important research on such search spaces was contributed by Bagley  (who introduced the term genetic algorithm ), Rosenberg , Cavicchio, Jr. [354, 355], and Frantz  – all based on the ideas of Holland at the University of Michigan. As a result of Holland’s work [937, 939, 940, 938] genetic algorithms as a new approach for problem solving could be formalized finally became widely recognized and popular. Today, there are many applications in science, economy, and research and development  that can be tackled with genetic algorithms. Therefore, various forms of genetic algorithms  have been developed to. Some genetic algorithms 2 like the human-based genetic algorithms 3 (HBGA), for instance, even require human beings for evaluating or selecting the solution candidates [1884, 1997, 1998, 1178, 883] It should further be mentioned that, because of the close relation to biology and since ge- netic algorithms were originally applied to single-objective optimization, the objective func- tions f here are often referred to as fitness functions . This is a historically grown misnaming which should not be mixed up with the fitness assignment processes discussed in Section 2.3 on page 111 and the fitness values v used in the context of this book. 1 http://en.wikipedia.org/wiki/Genetic_algorithm [accessed 2007-07-03] 2 http://en.wikipedia.org/wiki/Interactive_genetic_algorithm [accessed 2007-07-03] 3 http://en.wikipedia.org/wiki/HBGA [accessed 2007-07-03] 142 3 Genetic Algorithms Population Pop genotype g mutation crossover phenotype x genotype g Population objective function f i G P M Reproduction create new individuals from the mating pool by crossover and mutation Selection select the fittest indi- viduals for reproduction Evaluation compute the objective values of the solution candidates Fitness Assignment use the objective values to determine fitness values Initial Population create an initial...
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This document was uploaded on 08/10/2011.
- Spring '11