面向机会约束问题的滑动窗口三目标帕累托优化
Sliding Window 3-Objective Pareto Optimization for Problems with Chance Constraints
AI总结：
本文将滑动窗口技术从双目标帕累托优化扩展到三目标形式以求解机会约束问题，在保持近似保证的同时改进了理论运行时间上界，并在机会约束支配集问题上实现了对更大规模实例的高效求解。
摘要：
约束单目标问题经常通过进化多目标算法来处理，其中约束被松弛为一个额外目标。最近的研究表明，使用双目标模型的帕累托优化方法可以通过滑动窗口显著加速（Neumann 和 Witt，ECAI 2023）。在本文中，我们将滑动窗口方法扩展到三目标形式，以处理机会约束问题。在理论方面，我们证明了新的滑动窗口方法改进了（Neumann 和 Witt，GECCO 2023）中先前获得的运行时间上界，同时保持了相同的近似保证。我们对机会约束支配集问题的实验研究表明，与（Neumann 和 Witt，GECCO 2023）中提出的三目标方法相比，新的滑动窗口方法能够以更高效的方式求解规模大得多的实例。
英文摘要：
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).
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