Trade-off between Optimality and Robustness: An Evolutionary Multiobjective Approach

In real-world applications, it is often desired that a solution is not only of high performance, but also of strong robustness. In evolutionary optimization, robust optimal solutions can be obtained either by averaging the fitness in the neighborhood or by perturbing the design variables in fitness evaluations. Unfortunately, only one solution can usually be obtained from one run of optimization using the existing methods for searching robust solutions. Besides, the user knows little about the performance degradation due to the improvement of robustness of a solution using these methods. This paper suggests 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. Thus, a trade-off between optimality and robustness can be realized with the help of evolutionary multiobjective optimization. Simulation studies have been conducted to verify the proposed method. Finally, the possibility of using this method for detecting multiple optima of multimodal functions is briefly discussed.