Operations Research 2025
Abstract Submission

2181. Modern Algorithms in Old Literature: What Can Multi-Objective Optimization Learn from Parametric Optimization?

Invited abstract in session FA-5: Multiobjective Optimization 4: Complex Systems, Scalarizations, and Related Problems, stream Decision Theory and Multi-criteria Decision Making.

Friday, 8:45-10:15
Room: H7

Authors (first author is the speaker)

1. Levin Nemesch
Mathematics, RPTU in Kaiserslautern
2. Stefan Ruzika
Mathematik, Rheinland-Pfälzische Technische Universität Kaiserslautern
3. Clemens Thielen
TUM Campus Straubing for Biotechnology and Sustainability, Technical University of Munich
4. Alina Wittmann
TUM Campus Straubing for Biotechnology and Sustainability, Technical University of Munich

Abstract

In multi-objective optimization, the goal is to optimize several, often conflicting, objectives at once. Instead of one single optimal solution, a whole set of efficient solutions is usually needed to achieve this. In parametric optimization, the goal is to optimize a problem that depends on one or more parameters. Again, solving a parametric optimization problem requires finding a set of solutions.

For many applications, the perspectives of multi-objective optimization and parametric optimization are inherently interwoven. Throughout the literature, similar strategies appear in each field. Surprisingly, however, literature from one is often unaware of literature from the other. Instead, approaches have been developed independently from each other several times. In many cases, strategies used in parametric optimization predate the ones used in multi-objective optimization by decades.

In this talk, we highlight parallel developments of algorithms in parametric and multi-objective optimization. Exemplary, we look at algorithms for the so-called weight set decomposition. The purpose of this talk is two-fold:
First, we want to highlight some results that are rather unknown in modern literature, but deserve to be better known, as they can be seen as precursors to modern algorithms. Second, our talk should motivate researchers in all fields to be aware of fields with similar settings to theirs, such as parametric optimization, robust optimization, computational geometry and others for multi-objective optimization.

Keywords

Status: accepted

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