On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization
Discrete Mathematics
2024-12-03 v1 Computational Complexity
Optimization and Control
Abstract
Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times.
Cite
@article{arxiv.2412.01465,
title = {On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization},
author = {José Rui Figueira and Kathrin Klamroth and Michael Stiglmayr and Julia Sudhoff Santos},
journal= {arXiv preprint arXiv:2412.01465},
year = {2024}
}