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arXiv · 2306.03409

Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems

Anh Viet Do·Aneta Neumann·Frank Neumann·Andrew M. Sutton
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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, the parameter being the number of objectives. 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.

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Anh Viet Do, Aneta Neumann, Frank Neumann, Andrew M. Sutton. 2023-06-06. Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems. https://arxiv.org/abs/2306.03409

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