Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for problems with chance constraints. Our formulation trades off the expected cost and variance of the stochastic component as well as the given deterministic constraint. We point out benefits that this 3-objective formulation has compared to a bi-objective one recently investigated for chance constraints with Normally distributed stochastic components. Our analysis shows that the 3-objective formulation allows to compute all required trade-offs using 1-bit flips only, when dealing with a deterministic cardinality constraint. Furthermore, we carry out experimental investigations for the chance constrained dominating set problem and show the benefit for this classical NP-hard problem.

翻译：进化多目标算法已成功应用于帕累托优化的场景中，即通过将特定约束松弛为一个额外目标来处理问题。本文探讨了针对机会约束问题的三目标公式化方法。该方法在期望成本、随机分量的方差以及给定的确定性约束之间进行权衡。我们指出了这一三目标公式相较于近期针对正态分布随机分量机会约束问题所研究的双目标公式的优势。分析表明，在处理确定性基数约束时，三目标公式仅需通过1位翻转即可计算所有必要的权衡方案。此外，我们针对机会约束支配集问题开展了实验研究，并展示了该经典NP困难问题的求解优势。