Self-adaptation procedures in genetic algorithms applied to the optimal design of composite structures
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Self-adaptation procedures in genetic algorithms applied to the optimal design of composite structures Carlos Conceic¸a˜o Anto´nio
Received: 23 February 2009 / Accepted: 5 March 2009 / Published online: 17 March 2009 Ó Springer Science+Business Media, B.V. 2009
Abstract It is recognized that the efficiency of Genetic Algorithms improves if some adaptive rules are included. In this work, adaptive properties in Genetic Algorithms applied to structural optimization are studied. The adaptive rules work by using additional information related to the behavior of state and design variables of the structural problem. At each generation, the self-adaptation of the genetic parameters to evolutionary conditions attempts to improve the efficiency of the genetic search. The introduction of adaptive rules occurs at three levels: (i) when defining the search domain in each generation; (ii) considering a crossover operator based on commonality and local improvements; and (iii) by controlling mutation, including behavioral data. Selfadaptation has proved to be highly beneficial in automatically and dynamically adjusting evolutionary parameters. Numerical examples showing these benefits are presented. Keywords Genetic algorithms Self-adaptation Adaptive rules Local improvement Controlled mutation
C. C. Anto´nio (&) Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal e-mail: [email protected]
1 Introduction Since the pioneering works of Holland (1975) and Goldberg (1989), the objective of research in Genetic Algorithms (GAs) has been to increase the efficiency of algorithms. The two most relevant conclusions that can be extracted from the literature are: (1) the importance of randomness of the main operators, namely selection, crossover, and mutation, and (2) the referred randomness improves the population initial fitness, inducing its evolution towards the global optimum. However, some aspects of GAs have not been explained, and the optimality conditions of the method remain unknown. Most of the remaining information on the efficiency of algorithms has a heuristic nature or is deduced from numerical tests applied to simple examples. Although GAs have been used successfully in solving structural optimization problems, the performance of this method depends on the choice of GA parameters, which can be a timeconsuming task. Some experimental (Schaffer et al. 1989) or theoretical (Goldberg and Deb 1991; Back and Schwefel 1993) approaches have been proposed to determine the appropriate parameters. Other approaches, such as Parameter Adaptation, have tried to eliminate the dependence on parameter setting processes by adapting parameters during the evolutionary algorithm (Davis 1989; Tuson and Ross 1998). It has been recognized that the efficiency of GAs improves if some adaptive rules are included (Yoon and Moon 2002; Conceic¸a˜o Anto´nio 2006). In the
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present work, the adaptive properties of GAs applied to structural optimization are studied. The adaptive rules work by using additio
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