Comparing Solutions under Uncertainty in Multiobjective Optimization

Due to various reasons the solutions in real-world optimization problems cannot always be exactly evaluated but are sometimes represented with approximated values and confidence intervals. In order to address this issue, the comparison of solutions has to be done differently than for exactly evaluated solutions. In this paper, we define new relations under uncertainty between solutions in multiobjective optimization that are represented with approximated values and confidence intervals. The new relations extend the Pareto dominance relations, can handle constraints, and can be used to compare solutions, both with and without the confidence interval. We also show that by including confidence intervals into the comparisons, the possibility of incorrect comparisons, due to inaccurate approximations, is reduced. Without considering confidence intervals, the comparison of inaccurately approximated solutions can result in the promising solutions being rejected and the worse ones preserved. The effect of new relations in the comparison of solutions in a multiobjective optimization algorithm is also demonstrated.