Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems
Abstract
We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. Using these properties, we give the first run-time analysis of the MOEA/D algorithm for this problem, an evolutionary algorithm that effectively optimizes by decomposing the objectives into single-objective components. We show that the MOEA/D, given an appropriate decomposition setting, finds all extreme points within expected fixed-parameter polynomial time, in the oracle model. Experiments are conducted on random bi-objective minimum spanning tree instances, and the results agree with our theoretical findings. Furthermore, compared with a previously studied evolutionary algorithm for the problem GSEMO, MOEA/D finds all extreme points much faster across all instances.
Cite
Text
Do et al. "Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems." Neural Information Processing Systems, 2023.Markdown
[Do et al. "Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems." Neural Information Processing Systems, 2023.](https://mlanthology.org/neurips/2023/do2023neurips-rigorous/)BibTeX
@inproceedings{do2023neurips-rigorous,
title = {{Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems}},
author = {Do, Anh Viet and Neumann, Aneta and Neumann, Frank and Sutton, Andrew},
booktitle = {Neural Information Processing Systems},
year = {2023},
url = {https://mlanthology.org/neurips/2023/do2023neurips-rigorous/}
}