  Portfolio optimization is a financial task which requires the allocation of
capital on a set of financial assets to achieve a better trade-off between
return and risk. To solve this problem, recent studies applied multi-objective
evolutionary algorithms (MOEAs) for its natural bi-objective structure. This
paper presents a method injecting a distribution-based mutation method named
L\'evy Flight into a decomposition based MOEA named MOEA/D. The proposed
algorithm is compared with three MOEA/D-like algorithms, NSGA-II, and other
distribution-based mutation methods on five portfolio optimization benchmarks
sized from 31 to 225 in OR library without constraints, assessing with six
metrics. Numerical results and statistical test indicate that this method can
outperform comparison methods in most cases. We analyze how Levy Flight
contributes to this improvement by promoting global search early in the
optimization. We explain this improvement by considering the interaction
between mutation method and the property of the problem.
