A robust genetic algorithm for constrained functional optimization is
described, The function being sought is represented both in a piecewis
e-linear fashion and in two different types of orthogonal series repre
sentations, satisfying in each case specified end conditions of both D
irichlet and Neumann types. The search for the optimal function is tra
nslated to one of determining the coefficients of a series expansion,
and a genetic algorithm is developed for this purpose, The method is v
alidated in terms of test problems for which the global optimum soluti
ons are known, The results indicate that, if the population size of th
e chromosome pool is held constant, the performance of the piecewise-l
inear-representation approach deteriorates considerably as the number
of degrees of freedom increases, In contrast, the orthogonal series re
presentations do not suffer from this drawback, and a significant redu
ction in the population size can be achieved. Therefore, the latter me
thodology offers a far more efficient approach to functional optimizat
ion than previously attempted, The developed methodology was applied t
o the determination of an optimal micropump shape. The genetic algorit
hm uncovered shapes that were nonintuitive but yielded vastly superior
pump performance.