Abstract
In real-world applications, it is often desired that a solution is not only of high performance, but also of high robustness. In this context, a solution is usually called robust, if its performance only gradually decreases when design variables or environmental parameters are varied within a certain range. In evolutionary optimization, robust optimal solutions are usually obtained by averaging the fitness over such variations. Frequently, maximization of the performance and increase of the robustness are two conflicting objectives, which means that a trade-off exists between robustness and performance. Using the existing methods to search for robust solutions, this trade-off is hidden and predefined in the averaging rules. Thus, only one solution can be obtained. In this paper, we treat the problem explicitly as a multiobjective optimization task, thereby clearly identifying the trade-off between performance and robustness in the form of the obtained Pareto front. We suggest two methods for estimating the robustness of a solution by exploiting the information available in the current population of the evolutionary algorithm, without any additional fitness evaluations. The estimated robustness is then used as an additional objective in optimization. Finally, the possibility of using this method for detecting multiple optima of multimodal functions is briefly discussed. © Springer-Verlag Berlin Heidelberg 2003.