Paper:

# A Hybrid Particle Swarm Optimization Approach and its Application to Solving Portfolio Selection Problems

## Shamshul Bahar Yaakob^{*,**} and Junzo Watada^{*}

^{*}Graduate School of IPS, Waseda University, 2-7 Hibikino, Wakamatsu, Kitakyushu 808-0135, Japan

^{**}School of Electrical Systems Engineering, Universiti Malaysia Perlis, 02600 Perlis Malaysia

In modern portfolio theory, the basic topic is how to construct a diversified portfolio of financial securities to improve trade-offs between risk and return. The objective of this paper is to apply a heuristic algorithm using Particle Swarm Optimization (PSO) to the portfolio selection problem. PSO makes the search algorithm efficient by combining a local search method through self-experience with the global search method through neighboring experience. PSO attempts to balance the exploration-exploitation tradeoff that achieves efficiency and accuracy of optimization. In this paper, a newly obtained approach is proposed by making simple modifications to the standard PSO: the velocity is controlled and the mutation operator of Genetic Algorithms (GA) is added to solve a stagnation problem. Our adaptation and implementation of the PSO search strategy are applied to portfolio selection. Results of typical applications demonstrate that the Velocity Control Hybrid PSO (VC-HPSO) proposed in this study effectively finds optimum solution to portfolio selection problems. Results also show that our proposed method is a viable approach to portfolio selection.

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