A memetic model of evolutionary PSO for computational finance applications S.C. Chiam, K.C. Tan * , A.Al. Mamun Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore article info Keywords: Memetic algorithms Particle swarm optimization Multi-objective portfolio optimization Time series forecasting abstract Motivated by the compensatory property of EA and PSO, where the latter can enhance solutions gener- ated from the evolutionary operations by exploiting their individual memory and social knowledge of the swarm, this paper examines the implementation of PSO as a local optimizer for fine tuning in evolu- tionary search. The proposed approach is evaluated on applications from the field of computational finance, namely portfolio optimization and time series forecasting. Exploiting the structural similarity between these two problems and the non-linear fractional knapsack problem, an instance of the latter is generalized and implemented as the preliminary test platform for the proposed EA–PSO hybrid model. The experimental results demonstrate the positive effects of this memetic synergy and reveal general design guidelines for the implementation of PSO as a local optimizer. Algorithmic performance improve- ments are similarly evident when extending to the real-world optimization problems under the appro- priate integration of PSO with EA. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction The design of global optimization techniques is governed by two competing goals, namely global reliability and local refine- ment (Torn and Zilinskas, 1989). The former is required to ensure that every region of the search space is covered to provide a reli- able estimate of the global optimum and the latter to further im- prove the good solutions by concentrating search effort around their neighborhood. Many global optimization techniques achieved these two goals by adopting a combination of global and local search strategy. Although evolutionary algorithms (EA), a class of population- based stochastic search technique, have shown general success in solving complex real-world optimization problems with various conflicting specifications, they suffer from slow convergence to- wards the optimum due to their strong stochastic bias (Grimaccia, Mussetta, Pirinoli, and Zich, 2006a; Ong and Keane, 2004) and poor accuracy of the evolved solutions due to the lack of local refine- ment (Kim, Ku, Mak, and Siu, 2003). Memetic algorithms (MA), motivated by the apparent need to employ both global and local search strategy to provide an effective global optimization method, extend EA by incorporating local search operators to complement the evolutionary operators. With this synergetic combination, the evolutionary operators will perform an adaptive, global sampling of the search space that actively generates solutions in new basins of attraction (Hart, 1994) throughout the evolution, while the local optimizers will efficiently refine these solutions and identify the corresponding local optimum within each basin. Many experimen- tal studies have shown the relative advantages of MA over EA in terms of solution quality and computational efficiency (Belew, McInerney, and Schraudolph, 1992; Muhlenbein, Schomisch, and Born, 1991; Ong, 2002; Ong and Keane, 2004; Ong, Lim, Zhu, and Wong, 2006; Zhou, Ong, Nair, Keane, and Lum, 2007; Zhou, Ong, Lim, and Lim, 2007a). Motivated by the compensatory property of EA and particle swarm optimizer (PSO) (Cai, Zhang, Venayagamoorthy, and Wunsch, 2004; Cai and Wunsch, 2005; Juang, 2004; Perez and Basterrechea, 2007), where the latter can enhance individuals generated by the evolutionary operators by both sharing informa- tion between each other and their individually learned knowledge (Juang, 2004), a variety of MA that hybridize EA and PSO have been proposed in literature and applied widely in several real- world applications (Cai and Wunsch, 2005; Cai et al., 2004; Grim- aldi, Grimaccia, Mussetta, Pirinoli, and Zich, 2005; Grimaccia et al., 2006a, Grimaccia, Mussetta, Pirinoli, and Zich, 2006b; Grosan, Abraham, and Nicoara, 2005; Juang, 2004; Juang and Liou, 2004a, 2004b; Rahmat-Samii, 2003; Robinson, Sinton, and Rahmat-Samii, 2002) and experimental results have verified the superiority of such MA over the lone applications of EA and PSO. In general, EA and PSO can be hybridized in various approaches, for example, a simple two-phase approach where one algorithm is applied after the other (Grosan et al., 2005; Rahmat-Samii, 2003; Robinson et al., 2002) or interleavingly during the evolutionary search (Grimaccia et al., 2006a, 2006b; Grimaldi et al., 2005). Alter- natively, adopting one algorithm as the main evolutionary plat- form, the other can be encapsulated within, for example 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.02.048 * Corresponding author. E-mail address: eletankc@nus.edu.sg (K.C. Tan). Expert Systems with Applications 36 (2009) 3695–3711 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa