Multiobjective Memetic Algorithm for the Markowitz Model Based on Informed Decisions

Abstract

This paper deals with the selection of investment portfolios with cardinality constraints in the context of the Markowitz model. To this end, a multiobjective memetic algorithm (MA) featuring a novel hybrid combination of population variation based on elite memory and local search is introduced. These heuristic add-ons revolve around the use of the Sharpe index, a return/risk measure used to evaluate the efficiency of the portfolios generated, allowing to focus the search on relevant areas in the nondominated front. The elite memory exploits this indicator to maintain a record of the most effective solutions found and is used as a tunable intensification mechanism. A sensitivity analysis of the algorithm to determine a suitable parameterization is first performed, and then a comparison is made with seven multiobjective evolutionary algorithms. Data from the equity financial market of the Colombian Stock Exchange between 2010 and 2016 are taken as a benchmark and confirm the great potential of the MA for this problem.