Artificial Bee Colony Algorithm Hybridized with Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Selection Problem

Portfolio selection (optimization) problem is a very important and widely researched problem in the areas of finance and economy. Literature review shows that many methods and heuristics were applied to this hard optimization problem, however, there are only few implementations of swarm intelligence metaheuristics. This paper presents artificial bee colony (ABC) algorithm applied to the cardinality constrained mean-variance (CCMV) portfolio optimization model. By analyzing ABC metaheuristic, some deficiencies such as slow convergence to the optimal region, were noticed. In this paper ABC algorithm improved by hybridization with the firefly algorithm (FA) is presented. FA's search procedure was incorporated into the ABC algorithm to enhance the process of exploitation. We tested our proposed algorithm on standard test data used in the literature. Comparison with other state-of-the-art optimization metaheuristics including genetic algorithms, simulated annealing, tabu search and particle swarm optimization (PSO) shows that our approach is superior considering quality of the portfolio optimization results, especially mean Euclidean distance from the standard efficiency frontier.