Sliding Window 3-Objective Pareto Optimization for Problems with Chance Constraints

TL;DR

This paper extends the sliding window method to three-objective Pareto optimization for chance constrained problems, improving runtime bounds and enabling more efficient solutions for larger instances.

Contribution

It introduces a 3-objective sliding window approach that enhances previous methods by improving theoretical runtime bounds and practical efficiency.

Findings

Improved runtime bounds for 3-objective sliding window approach.

Enhanced ability to solve larger chance constrained problems.

Experimental results show significant efficiency gains over previous methods.

Abstract

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).