A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization

Real-world optimization problems are often subject to uncertainties, which can arise regarding stochastic model parameters, objective functions and decision variables. These uncertainties can take different forms in terms of distribution, bound and central tendency. In the multiobjective context, several studies have been proposed to take uncertainty into account, and most of them propose an extension of Pareto dominance to the stochastic case. In this paper, we pursue a slightly different approach where the optimization goal is defined in terms of a quality indicator, i.e., an objective function on the set of Pareto set approximations. We consider the scenario that each solution is inherently associated with a probability distribution over the objective space, without assuming a ’true’ objective vector per solution. We propose different algorithms which optimize the quality indicator, and preliminary simulation results indicate advantages over existing methods such as averaging, especially with many objective functions.