{"ID":2889274,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.21933","arxiv_id":"2507.21933","title":"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.","short_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 algor...","url_abs":"https://arxiv.org/abs/2507.21933","url_pdf":"https://arxiv.org/pdf/2507.21933v1","authors":"[\"Stephanie Riedmüller\",\"Janina Zittel\",\"Thorsten Koch\"]","published":"2025-07-29T15:47:51Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}