Global+Optimization+Algorithms+Theory+and+Application_Part8

Global+Optimization+Algorithms+Theory+and+Application_Part8...

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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 [742] began to apply computer-aided simulations in order to gain more insight into genetic processes and the natural evolution and selection. Bremermann [287] 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 [219]. At the end of that decade, important research on such search spaces was contributed by Bagley [116] (who introduced the term genetic algorithm ), Rosenberg [1760], Cavicchio, Jr. [354, 355], and Frantz [741] – 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 [1681] that can be tackled with genetic algorithms. Therefore, various forms of genetic algorithms [423] 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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