Particle swarm optimization with dynamic random population topology strategies for a generalized portfolio selection problem

Population topology of particle swarm optimization (PSO) has an important impact on solving performance of PSO. The more commonly used population topology is with static structure, such as fully connected structure and ring structure. In the process of evolution, the static population topology is always the same, which affects the information exchange between individuals of the population to a certain extent. In this paper, several feasible dynamic random population topologies are proposed based on the study of random population topology. In the PSO algorithm with dynamic random population topology, the neighborhood particles of a particle will evolve according to certain rules. In detail, a population topology is abstracted into an undirected connected graph which could be randomly generated according to predefined rule and degree. By tuning the rule and degree, the communication mechanisms evolve in the evolutionary process and the solving performance of PSO will be enhanced significantly. Furthermore, for the generalized portfolio selection model in the financial engineering field, the proposed several PSO algorithms are employed to solve the problems related to the generalized portfolio selection model, and the performance of them have been compared with the classic PSO variant in detail. The data of experiment is the weekly prices in a certain period which include the indices of HangSeng, DAX 100, FTSE 100, S&P 100 and Nikkei 225. The computational results demonstrate that the proposed dynamic random population topology could obviously improve the performance of PSO. It is especially worth noting that one proposed dynamic random population topology strategy shows an excellent performance on most data sets which could find good solutions to the generalized portfolio selection problems.