New Approach to Constrained Shape Optimization Using Genetic Algorithms

Abstract

A robust genetic algorithm for constrained functional optimization is described. The function being sought is represented both in a piecewise-linear fashion and in two different types of orthogonal series representations, satisfying in each case specified end conditions of both Dirichlet and Neumann types. The search for the optimal function is translated to one of determining the coefficients of a series expansion, and a genetic algorithm is developed for this purpose. The method is validated in terms of test problems for which the global optimum solutions are known. The results indicate that, if the population size of the chromosome pool is held constant, the performance of the piecewise-linear-representation approach deteriorates considerably as the number of degrees of freedom increases. In contrast, the orthogonal series representations do not suffer from this drawback, and a significant reduction in the population size can be achieved. Therefore, the latter methodology offers a far more efficient approach to functional optimization than previously attempted. The developed methodology was applied to the determination of an optimal micropump shape. The genetic algorithm uncovered shapes that were nonintuitive but yielded vastly superior pump performance.