A Comparative Study on Multi-objective Evolutionary Algorithms for Tri-objective Mean-Risk-Cardinality Portfolio Optimization Problems

Abstract

In this research paper we experimentally investigate three state-of-the-art evolutionary multi-objective optimization algorithms and measure their efficiency and effectiveness in problems of multi-objective portfolio optimization. Especially we solve the mean-risk-cardinality portfolio optimization problem with six different measures of risk. Three different modern and state-of-the-art Multi-Objective Evolutionary Algorithms (MOEAs) are employed: Strength Pareto Evolutionary Algorithm (SPEA2), Multi-Objective Evolutionary Algorithm based on decomposition (MOEA/D) and S-Metric Selection Evolutionary Multi-Objective Algorithm (SMS-EMOA). Experimental results show that the best algorithm considering the C metric is MOEA/D while the best algorithm considering the hypervolume metric is SPEA2 while being the fastest approach. This suggests that the best approach for solving the problem is to run all the algorithms for a number of replicates and take the elite non-dominated solutions from the combined pool of solutions generated by the three algorithms.