Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization

TL;DR

This paper investigates how warm-starting strategies can be systematically integrated into scalarization methods for multi-objective optimization, analyzing trade-offs and providing theoretical insights and computational results.

Contribution

It offers a theoretical characterization of warm-starting in scalarization methods and examines the trade-offs involved in sequencing subproblems.

Findings

Warm-starting can significantly improve solution times in scalarization methods.

Optimizing subproblem order involves trade-offs between efficiency and early infeasibility detection.

Computational experiments quantify the benefits and limitations of different warm-start strategies.

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.