Multi-objective Robust Optimization Using Probabilistic Indices

In the multi-objective optimizations, it is quite crucial to obtain a set of solutions which make the objective functions robust to the system parameters uncertainties. In this paper, two probability-based indices violation probability and cumulative satisfaction probability are introduced to evaluate the multi-objective probabilistic robustness at a specified acceptance performance level. The first index is minimized as the multi-objective function (instead of the original non-robust multi-objective function) to obtain a set of Pareto-optimal solutions, which guarantees the maximum probability of acceptable performance when system parameters vary in a stochastic manner. The second index is used to get an insight and distinct observation of above Pareto-optimal solutions at all performance levels, which facilitate the users to make a decision. An example of probabilistic robust multi-objective optimization problem is solved to illustrate the optimization and analysis method.