  The Markowitz-based portfolio selection turns to an NP-hard problem when
considering cardinality constraints. In this case, existing exact solutions
like quadratic programming may not be efficient to solve the problem. Many
researchers, therefore, used heuristic and metaheuristic approaches in order to
deal with the problem. This work presents Asexual Reproduction Optimization
(ARO), a model free metaheuristic algorithm inspired by the asexual
reproduction, in order to solve the portfolio optimization problem including
cardinality constraint to ensure the investment in a given number of different
assets and bounding constraint to limit the proportions of fund invested in
each asset. This is the first time that this relatively new metaheuristic is in
the field of portfolio optimization, and we show that ARO results in better
quality solutions in comparison with some of the well-known metaheuristics
stated in the literature. To validate our proposed algorithm, we measured the
deviation of obtained results from the standard efficient frontier. We report
our computational results on a set of publicly available benchmark test
problems relating to five main market indices containing 31, 85, 89, 98, and
225 assets. These results are used in order to test the efficiency of our
proposed method in comparison to other existing metaheuristic solutions. The
experimental results indicate that ARO outperforms Genetic Algorithm(GA), Tabu
Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) in
most of test problems. In terms of the obtained error, by using ARO, the
average error of the aforementioned test problems is reduced by approximately
20 percent of the minimum average error calculated for the above-mentioned
algorithms.
