Bacterial Foraging Optimization Based on Levy Flight for Fuzzy Portfolio Optimization

In this paper, a new kind of bacterial foraging optimization that combines with levy flight (LBFO) is employed to solve a novel portfolio optimization (PO) problem with fuzzy variables and modified mean-semivariance model which includes the transaction fee (including the purchase fee and sell fee), no short sales and the original proportion of the different assets. First of all, a chemotaxis step size using levy distribution takes the place of fixed chemotaxis step size, which makes a good balance between local search and global search through frequent short-distance search and occasional long-distance search. Moreover, fuzzy variables are used to signify the uncertainty of future risks and returns on assets and some constrained conditions are taken into consideration. The results of the simulation show that the model can be solved more reasonably and effectively by LBFO algorithm than the original bacterial foraging optimization (BFO).