Constrained single-objective problems have been frequently tackled by evolutionary multi-objective algorithms where the constraint is relaxed into an additional objective. Recently, it has been shown that Pareto optimization approaches using bi-objective models can be significantly sped up using sliding windows (Neumann and Witt, ECAI 2023). In this paper, we extend the sliding window approach to $3$-objective formulations for tackling chance constrained problems. On the theoretical side, we show that our new sliding window approach improves previous runtime bounds obtained in (Neumann and Witt, GECCO 2023) while maintaining the same approximation guarantees. Our experimental investigations for the chance constrained dominating set problem show that our new sliding window approach allows one to solve much larger instances in a much more efficient way than the 3-objective approach presented in (Neumann and Witt, GECCO 2023).

翻译：约束单目标问题常通过将约束松弛为额外目标的进化多目标算法求解。近期研究表明，采用滑动窗口技术可显著加速基于双目标模型的帕累托优化方法（Neumann与Witt，ECAI 2023）。本文将该滑动窗口方法扩展至三目标模型以处理机会约束问题。在理论层面，我们证明新滑动窗口方法在保持相同近似保证的同时，改进了（Neumann与Witt，GECCO 2023）中获得的原有运行时界。针对机会约束支配集问题的实验研究表明，相较于（Neumann与Witt，GECCO 2023）提出的三目标方法，新滑动窗口方法能以更高效率求解更大规模的问题实例。