EURO 2025 Leeds
Abstract Submission

1499. Warm-Starting Strategies in Scalarization Methods for Multi-Objective Optimization

Invited abstract in session MA-51: Recent advances in multiobjective optimization, stream Multiobjective and vector optimization.

Monday, 8:30-10:00
Room: Parkinson B22

Authors (first author is the speaker)

1. Stephanie Riedmüller
Applied Algorithmic Intelligence Methods, Zuse Institute Berlin
2. Janina Zittel
Applied Algorithmic Intelligence Methods Department, Zuse Institute Berlin
3. Thorsten Koch
Applied Algorithmic Intelligence Methods, ZIB / TU Berlin

Abstract

In this talk, we explore the integration of warm-starting techniques within scalarization methods for multi-objective optimization for mathematical programming problems. Particularly in applied settings, scalarization methods remain the most commonly employed classical optimization techniques for computing a subset of Pareto-optimal solutions, specifically the weighted sum and epsilon-constraint methods. Despite the availability of more involved and specialized algorithms (which often use scalarization methods as subroutines), these scalarization methods are favored due to their straightforward implementation and universal applicability to both linear and integer programs across an arbitrary number of objectives. Although warm-starting has been integrated into scalarization methods in previous studies, a detailed methodology and comprehensive analysis have yet to be provided. Therefore, we present a theoretical overview of its advantages and limitations. An effective warm-starting strategy for scalarization methods is primarily determined by the sequence in which subproblems are solved. However, optimizing the sequence of subproblems in terms of warm-starting can directly conflict with other desirable properties based on the order of subproblems, such as the early detection of infeasible subregions. We illustrate their impact by an extensive computational study.

Keywords

Status: accepted

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