Improving multi-objective robust optimization under interval uncertainty using worst possible point constraint cuts

Many real-world engineering design optimization problems are multi-objective and have uncertainty in their parameters. For such problems it is useful to obtain design solutions that are both multi-objectively optimum and robust. A robust design is one whose objective and constraint function variations under uncertainty are within an acceptable range. While the literature reports on many techniques in robust optimization for single objective optimization problems, very few papers report on methods in robust optimization for multiobjective optimization problems. The Multi-Objective Robust Optimization (MORO) technique with interval uncertainty proposed in this paper is a significant improvement, with respect to computational effort, over a previously reported MORO technique. In the proposed technique, a master problem solves a relaxed optimization problem whose feasible domain is iteratively confined by constraint cuts determined by the solutions from a sub-problem. The proposed approach and the synergy between the master problem and sub-problem are demonstrated by three examples. The results obtained show a general agreement between the solutions from the proposed MORO and the previous MORO technique. Moreover, the number of function calls for obtaining solutions from the proposed technique is an order of magnitude less than that from the previous MORO technique.