Applied Soft Computing 28 (2015) 345–359 Contents lists available at ScienceDirect Applied Soft Computing j ourna l h o mepage: www.elsevier.com/locate/asoc Non-parametric particle swarm optimization for global optimization Zahra Beheshti, Siti Mariyam Shamsuddin ∗ UTM Big Data Centre, Universiti Teknologi Malaysia, Skudai, 81310 Johor, Malaysia a r t i c l e i n f o Article history: Received 30 March 2014 Received in revised form 15 October 2014 Accepted 9 December 2014 Available online 18 December 2014 Keywords: Optimization problems Particle swarm optimization Global and local optimum Non-parametric particle swarm optimization a b s t r a c t In recent years, particle swarm optimization (PSO) has extensively applied in various optimization prob- lems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several param- eters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO with- out tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlin- ear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability. © 2014 Elsevier B.V. All rights reserved. 1. Introduction PSO [1] is a population-based algorithm inspired by the social behavior of bird flocking or fish schooling. In the algorithm, a mem- ber in the swarm, particle, represents a potential solution which is a point in the search space. The global optimum is regarded as the location of food. Each particle adjusts its flying direction accord- ing to the best experiences obtained by itself and the swarm in the solution space. The algorithm has a simple concept and is easy to implement. Hence, it has received much more attention to solve real-world optimization problems [2–7], nevertheless, PSO may easily get trapped in local optima and shows a slow convergence rate when solving the complex and high dimensional multimodal objective functions [8]. A number of variant PSO algorithms have been proposed in the literature to overcome the problems. The algorithms have improved the performance of PSO in different ways using various types of topologies, selecting parameters, combining with other search techniques and so on. A local (ring) topological structure PSO (LPSO) [9] and Von Neu- mann topological structure PSO (VPSO) [10] were proposed by Kennedy and Mendes to avoid trapping into local optima. Accord- ing to Kennedy [9,11], PSO with a small neighborhood might have ∗ Corresponding author. Tel.: +60123710679. E-mail addresses: bzahra2@live.utm.my (Z. Beheshti), mariyam@utm.my (S.M. Shamsuddin). a better performance on complex problems, while PSO with a large neighborhood would perform better on simple problems. Sugan- than [12] applied a dynamically adjusted neighborhood where the neighborhood of a particle gradually increases until it includes all particles. Dynamic multi-swarm PSO (DMS-PSO) [13] was sug- gested by Liang and Suganthan where the neighborhood of a particle gradually increases until it includes all particles. Hu and Eberhart [14] applied a dynamic neighborhood where m nearest particles in the performance space is chosen to be its new neigh- borhood in each generation. Mendes et al. [15] presented the fully informed particle swarm (FIPS) algorithm that uses the informa- tion of entire neighborhood to guide the particles for finding the best solution. Parsopoulos and Vrahatis combined the global and local versions together to form the unified particle swarm opti- mizer (UPSO) [16]. Gao et al. [17] used PSO with a stochastic search technique and chaotic opposition-based population initialization to solve complex multimodal problems. The algorithm, CSPSO, finds new solutions in the neighborhoods of the previous best positions to escape from local optima. The fitness-distance-ratio-based PSO (FDR-PSO) was introduced by Peram et al. [18]. In the algorithm, each particle moves toward nearby particle with higher fitness value. Liang et al. [8] developed comprehensive learning particle swarm optimization (CLPSO) that focused on avoiding the local optima by encouraging each particle to learn its behavior from other particles on different dimensions. In another research, a selection operator was firstly proposed for PSO by Angeline [19]. Other researchers applied apart from crossover [20], and mutation [21] operations from GA into PSO. An http://dx.doi.org/10.1016/j.asoc.2014.12.015 1568-4946/© 2014 Elsevier B.V. All rights reserved.