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In this paper we tackle the optimal portfolio selection problem (PSP). Many research has been made around this subject mainly in two ways, whether extending the Markowitz model by taking into account real-world constraints (floor-ceiling, class and cardinality) or introducing different risk measures like semivariance, value at risk, absolute desviation, etc. Here, we present the preliminary results of a new multiobjective heuristic based in the bacterial foraging optimization (BFO) which integrates the population based incremental learning (PBIL) approach. PBIL uses statistical information to guide the optimization process in the bacteria population. Furthermore, to improve the BFO heuristic we introduced a lineal decreasing function for the chemotaxis steps size, bacterias reinitialization and random weighing in the reproduction step. Our formulation include the cardinality and floorceiling constraints, both are real-world constraints needed in most of the stock markets. Based in the mean-variance model (first proposed by Markowitz) we used the well-known efficient frontier formulation which introduces a risk aversion parameter to weigh between risk and mean return, leading into a single-objective formulation problem. Applying our algorithm to solved the above mentioned model, we performed tests with a standard dataset taken from the OR-Lib. The experimental results shown our algorithm is able to find good-quality solutions uniformly distributed over the real efficient frontier.

Algoritmo de optimización mediante forrajeo de bacterias híbrido para el problema de selección de portafolios con restricción de cardinalidad