### Multiobjective evolutionary algorithms for complex portfolio optimization problems

Abstract

This paper investigates the ability of Multiobjective Evolutionary Algorithms (MOEAs), namely the
Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm
(PESA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), for solving complex portfolio optimization
problems. The portfolio optimization problem is a typical bi-objective optimization problem with objectives
the reward that should be maximized and the risk that should be minimized. While reward is commonly
measured by the portfolio's expected return, various risk measures have been proposed that try to better
reflect a portfolio's riskiness or to simplify the problem to be solved with exact optimization techniques
efficiently. However, some risk measures generate additional complexities, since they are non-convex,
non-differentiable functions. In addition, constraints imposed by the practitioners introduce further
difficulties since they transform the search space into a non-convex region. The results show that MOEAs,
in general, are efficient and reliable strategies for this kind of problems, and their performance is independent
of the risk function used.