Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization
Abstract
We explore how warm-starting strategies can be integrated into scalarization-based approaches for multi-objective optimization in (mixed) integer linear programming. Scalarization methods remain widely used classical techniques to compute Pareto-optimal solutions in applied settings. They are favored due to their algorithmic simplicity and broad applicability across continuous and integer programs with an arbitrary number of objectives. While warm-starting has been applied in this context before, a systematic methodology and analysis remain lacking. We address this gap by providing a theoretical characterization of warm-starting within scalarization methods, focusing on the sequencing of subproblems. However, optimizing the order of subproblems to maximize warm-start efficiency may conflict with alternative criteria, such as early identification of infeasible regions. We quantify these trade-offs through an extensive computational study.
Cite
@article{arxiv.2507.21933,
title = {Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization},
author = {Stephanie Riedmüller and Janina Zittel and Thorsten Koch},
journal= {arXiv preprint arXiv:2507.21933},
year = {2025}
}