Multi-objective robust optimization based on NSGA-II and degree of robustness¯

This paper presents an approach to search robust optimal solutions with the concept of degree of robustness in multi-objective optimization problems. The definition of the degree of robustness is used in the calculation of the mean effective objective function(f^eff(X)) and in the evolutionary process, degree of robustness is considered as a factor to select robust solutions which can meet the demand for better robustness. Some simulation results are shown to prove that this approach can control the distribution of objective value and help system improve robustness by finding solutions with better robustness. Also, the decision maker(DM) can modulate some robust parameters according to the actual robust demands which makes this approach have more practical significance.

I. INTRODUCTION

In the past decade or more, multi-objective optimization problems were concerned in many researches which focused on the convergence and diversity of Pareto front. These Pareto-optimal solutions are non-dominated to each other and in the entire search space there is no other solution which dominates any of these solutions. Such solutions are of utmost importanc e in multi-objective optimization problems in theory. However, in practice, a solution often can not be implemented with an arbitrary accuracy and even the implemented solution such as a global optimal solution which is sensitiv e to some variable perturbation in its vicinity may be somewhat different from the theoretical global optimal solution. Thus, such solutions are not so important for practical applications that the emphasis must be made in finding robust solutions which are to a certain extent immune to some perturbation in the vicinity ^[1].