Modified Bacterial Foraging Optimization for Fuzzy Mean-Semivariance-Skewness Portfolio Selection

Abstract

In this paper, a novel bacterial foraging optimization with decreasing chemotaxis step combined with sine function is employed to solve a fuzzy portfolio optimization with a modified mean-semivariance-skewness model which includes the transaction fee and no short sales. First of all, a decreasing chemotaxis step combined with sine function (BFO-SDC) takes the place of constant chemotaxis step size. It is a nonlinear decreasing strategy at every iteration of the algorithm. And then, the variance is replaced by semivariance and skewness is taken into account in order to generate asymmetry of return distributions to overcome the inadequacy of the standard mean-variance model. Finally, fuzzy variables are used to express the uncertain and imprecise elements in the decision-making process. The results of the simulation show that the model can be solved more reasonably and effectively by BFO-SDC than the original bacterial foraging optimization.