Genetic algorithm optimization of multi-peak problems: studies in convergence and robustness

Engineering design studies can often be cast in terms of optimization problems. However, for such an approach to be worthwhile, designers must be content that the optimization techniques employed are fast, accurate and robust. This paper describes recent studies of convergence and robustness problems found when applying genetic algorithms (GAS) to the constrained, multi-peak optimization problems often found in design. It poses a two-dimensional test problem which exhibits a number of features designed to cause difficulties with standard GAS and other optimizers. The application of the GA to this problem is then posed as a further, essentially recursive problem, where the control parameters of the GA must be chosen to give good performance on the test problem over a number of optimization attempts. This overarching problem is dealt with both by the GA and also by the technique of simulated annealing. It is shown that, with the appropriate choice of control parameters, sophisticated niche forming techniques can significantly improve the speed and performance of the GA for the original problem when combined with the simple rejection strategy commonly employed for handling constraints. More importantly, however, it also shows that more sophisticated multi-pass, constraint penalty functions, culled from the literature of classical optimization theory, can render such methods redundant, yielding good performance with traditional GA methods.