Keywords: structural optimization, genetic algorithm, population dynamics, reliability analysis.

Competition is introduced among the populations of a number of Genetic Algorithms (GAs). The aim is to calibrate the size of the populations of the GAs by altering the resources of the system i.e. the allocated computing time. The evolution of the different populations is controlled on the level of metapopulation, i.e. the union of populations, on the basis of statistics and trends of the evolution of every population. The method is applied to the reliability based optimal design of a simple truss. Numerical results are presented and the robustness of the proposed algorithm is discussed.

Genetic Algorithms are search algorithms based on the concepts of natural selection and survival of the fittest. They guide the evolution of a set of randomly selected individuals towards good near optimal solutions. This is accomplished through a number of generations that are subjected to successive reproduction, crossover and mutation, based on the statistics of the generation. The efficiency of the process is problem dependent and relies heavily on the successful selection of the number of parameters, such as population size, probabilities of crossover and mutation, type of crossover etc. In this work, a method is proposed, that attempts to automate the evolution of population size through an adaptive process. This is based on the competition of populations, with different sets of GA parameters, struggling for the available resources of the system.

Competition among different populations is common in natural systems. Populations evolve by adapting themselves to the environment where the resources are limited. By coupling GAs with a scheme of Competing Populations (CP) a number of populations are produced in every generation. They evolve in the space of solutions guided by every GA. The CP scheme alters the population size in an adaptive manner based on the overall fitness of the populations of the metapopulation. By altering the available resources competition is activated thus, forcing the system to organize better its overall search strategy in every generation. The ability of every population to adapt to the artificial habitat is used to calculate the overall fitness at a particular generation. Competition arises when the resources are insufficient to sustain the metapopulation. The proposed method is applied to the reliability based optimal design of a simple truss.

From the above analysis and the parametric studies performed it becomes evident that the proposed competitive algorithm controls satisfactorily the evolution process favouring the expansion of "promising" populations and the contraction of "weak" ones in a statistical sense. The descriptive statistics at the metapopulation level together with the rules of conflict guide the utilization of resources towards the most competent GAs. With regard to the algorithm's capacity of producing good solutions in all cases, the proposed algorithm was able to trace better designs than the given best design obtained from the standard GA. In conclusion, the proposed method succeeds in finding good "near" optimal solutions in a robust way and in most cases faster than a standard GA, for the same number of repetitions of a standard GA for the simple example under investigation.

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