EURO 2025 Leeds
Abstract Submission

495. The Evolution of Exact and Approximate Linear-Parametric Optimization and Its Connections to Multi-Objective Optimization

Invited abstract in session TB-51: Multiobjective discrete optimization, stream Multiobjective and vector optimization.

Tuesday, 10:30-12:00
Room: Parkinson B22

Authors (first author is the speaker)

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

Abstract

In linear-parametric optimization, multiple objective functions are combined into a single objective function using linear combinations with parameters as coefficients. The goal is to find a set containing an optimal solution for every possible combination of parameter values. For more than 60 years, linear-parametric optimization has been an important research area with numerous links to adjacent fields in optimization and a wide range of application areas. Among other relations, the optimal solution set of a parametric optimization problem can be characterized as the set of non-dominated extreme points of the corresponding multi-objective optimization problem. In the multi-objective literature, the parameter set is called the weight set. Hence, concepts from one field can be applied to the other. In this talk, we present our literature review of theoretical developments and exact and approximation algorithms for linear-parametric optimization problems. While existing overviews on parametric optimization are mostly concerned with parametric mixed integer linear programming, the focus of our literature review is on general, problem-agnostic approaches and results for parametric variants of specific problems, in particular, well-known combinatorial optimization problems. We compare these methods with important results from related fields to point out that some algorithms were preceded by similar algorithms from linear-parametric optimization.

Keywords

Status: accepted

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