On the Analysis of HPSO Improvement by Use of the Volitive Operator of Fish School Search

Swarm Intelligence algorithms have been extensively applied to solve optimization problems. However, in some domains even well-established techniques such as Particle Swarm Optimization (PSO) may not present the necessary ability to generate diversity during the process of the swarm convergence. Indeed, this is the major difficulty to use PSO to tackle dynamic problems. Many efforts to overcome this weakness have been made. One of them is through the hybridization of the PSO with other algorithms. For example, the Volitive PSO is a hybrid algorithm that presents as good performance on dynamic problems by applying a very interesting feature, the collective volitive operator, which was extracted from the Fish School Search algorithm and embedded into PSO. In this paper, the authors investigated further hybridizations in line with the Volitive PSO approach. This time they used the Heterogeneous PSO instead of the PSO, and named this novel approach Volitive HPSO. In the paper, the authors investigate the influence of the collective volitive operator (of FSS) in the HPSO. The results show that this operator significantly improves HPSO performance when compared to the non-hybrid approaches of PSO and its variations in dynamic environments. DOI: 10.4018/jsir.2013010103 International Journal of Swarm Intelligence Research, 4(1), 62-77, January-March 2013 63 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. algorithms; all of them conceived based on collective behaviors of simple entities. In general, swarm algorithms are inspired in groups of animals, such as flocks of birds, schools of fish, hives of bees, colonies of ants, etc. Even though a lot of swarm-based algorithms were already proposed, just a few designed to tackle dynamic problems. Particle Swarm Optimization (PSO) is among the most used swarm intelligence algorithms. Despite the fast convergence capability, the standard version of the PSO cannot tackle dynamic optimization problems. This occurs because the entire swarm often increases the exploitation around a good region of the search space, reducing the overall diversity of the population. In order to remedy that, some variations of the PSO have been created in order to increase the capacity of escaping from regions of the search space where the global optimum is not located anymore or where the previous global optimum is now a local optimum (Bentley et al., 2002; Ebadzadeh et al., 2008; Engelbrecht et al., 2008). Another swarm intelligence algorithm proposed in 2008 by Bastos-Filho and Lima Neto, the Fish School Search algorithm (FSS) (Bastos-Filho et al., 2008; Bastos-Filho et al., 2009a; Bastos-Filho et al., 2009b), presents a very interesting feature that is thought to be very useful for dynamic environments. That is, among its operators, FSS presents one, called volitive operator, which is capable of auto-regulating the exploration-exploitation trade-off during execution. Since the PSO algorithm has a fast convergence and the FSS algorithm, as explained, can self-adapt the granularity of the search, Cavalcanti-Junior, Bastos-Filho and Lima-Neto (2011) proposed of joining these features to tackle dynamic problems. Then, they develop a hybrid algorithm based on PSO and the FSS operator, which was called Volitive PSO. This approach presented good capacity of dealing with dynamic problems and overcomes results produced by PSO, FSS and Charged PSO (Blackwell & Bentley, 2002) that is a PSO variation proposed for dealing with dynamic optimization tasks. The Volitive PSO uses the standard PSO with inertia factor (Inertia PSO), which is one of the formers PSO approaches, proposed by Shi and Eberhart (1998). But, other PSO variations were proposed since the inertia PSO, one of them is HPSO (Heterogeneous PSO) (Engelbrecht, 2010) than overcame many PSO variations in static problems optimization because it was initially thought as a mechanism to generate diversity. Based on the good performance of the HPSO, we propose in this paper to substitute the inertia PSO (as the basis for the hybridization in the Volitive PSO) with the HPSO, calling this approach Volitive HPSO. Following that we investigate the improvement of the volitive operator on PSO and HPSO in benchmark dynamic optimization problems. This paper is organizer as follows. The second section provides the background on PSO, FSS, Charged PSO, HPSO and Volitive PSO. The third section compares the dynamics of the PSO and the Volitive PSO in dynamic environment, and shows the difficulties of PSO to tackle dynamic problems. The fourth section describes our proposal: the FSS-HPSO hybrid algorithm. The fifth and sixth sections present simulation setup and results, respectively. Finally, in the last section we produce our conclusions and present some ideas for future works.