Use of heuristic rules in evolutionary methods for the selection of optimal investment portfolios

Abstract

A novel hybrid algorithm that combines evolutionary algorithms, quadratic programming, and a specially devised pruning heuristic is proposed for the selection of cardinality- constrained optimal portfolios. The framework used is the standard Markowitz mean-variance formulation for portfolio selection with constraints of practical interest, such as minimum and maximum investments per asset and/or on groups of assets. The use of cardinality constraints transforms portfolio selection into an NP-hard mixed-integer quadratic optimization problem that is difficult to solve by standard methods. An implementation of the algorithm that employs a genetic algorithm with a set representation, an appropriately defined mutation operator and Random Assortment Recombination for crossover (RAR-GA) is compared with implementations using various estimation of distribution algorithms (EDAs). Without the pruning heuristic, RAR-GA is superior to the implementations with EDAs in terms of both accuracy and efficiency. The incorporation of the pruning heuristic leads to a significant decrease in computation times and makes EDAs competitive with RAR-GA.