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

Anh Viet Do, Aneta Neumann, Frank Neumann, Andrew M. Sutton

Keywords: minimum weight base problem, multi-objective optimization, approximation, evolutionary algorithm

TL;DR: The paper studies the multi-objective minimum weight base problem and analyzes the run-time of MOEA/D in finding an approximation.

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.

Submission Number: 11291