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

Anh Viet Do · Aneta Neumann · Frank Neumann · Andrew Sutton

Great Hall & Hall B1+B2 (level 1) #1120
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[ Paper [ Poster [ OpenReview
Tue 12 Dec 8:45 a.m. PST — 10:45 a.m. PST


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.

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