  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.
