Searching for Robust Pareto-Optimal Solutions in Multi-objective Optimization

In optimization studies including multi-objective optimization, the main focus is usually placed in finding the global optimum or global Pareto-optimal frontier, representing the best possible objective values. However, in practice, users may not always be interested in finding the global best solutions, particularly if these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the so-called

robust

solutions which are less sensitive to small changes in variables. Although robust optimization has been dealt in detail in single-objective optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find the robust optimal frontier, instead of the global Pareto-optimal front. The first procedure is a straightforward extension of a technique used for single-objective robust optimization and the second procedure is a more practical approach enabling a user to control the extent of robustness desired in a problem. To demonstrate the subtle differences between global and robust multi-objective optimization and the differences between the two robust optimization procedures, we define four test problems and show simulation results using NSGA-II. The results are useful and should encourage further studies considering robustness in multi-objective optimization.