An n-state switching PSO algorithm for scalable optimization
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An n-state switching PSO algorithm for scalable optimization Izaz Ur Rahman1
· Muhammad Zakarya1
· Mushtaq Raza2 · Rahim Khan1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Particle swarm optimization (PSO) is an optimization method that is most widely used to solve a number of problems in various fields such as engineering, economics and computer systems. However, due to its scalability and unsatisfying performance particularly for large-scale optimization problems; numerous PSO variants have been suggested so far, in the literature. This paper also proposes a new variant of the canonical PSO algorithm (‘N -state switching PSO—NS-SPSO’) that uses the evolutionary factor information to update particles velocities and, therefore, further enhance its performance. The evolutionary factor is derived by using the population distribution and the mean distance of each particle from the global best. The population distribution and the mean distance are determined through Euclidean distance. Moreover, algorithmic parameters such as inertia weight, and acceleration coefficients are assigned appropriate values at N stages (derived from exploration, exploitation, convergence and jumping out states) that improves the search efficiency and convergence speed. The proposed algorithm is applied to 12 widely used mathematical benchmark functions that demonstrate its best performance in terms of minimum evaluation error, fast convergence and low computational time. Besides these, seven high-dimensional functions and few other algorithms for large-scale optimization were considered to test the scalability of NS-SPSO algorithm. Our comparative results show that NS-SPSO performs well on low-dimensional problems and is promising for solving largescale optimization problems. Furthermore, the proposed NS-PSO algorithm almost outperforms its closest rivals for various benchmarks. Keywords Particle swarm optimization · Evolutionary factor · Large-scale optimization · scalability
1 Introduction Optimization is a real-world problem that is illustrated as the minimization or maximization of an objective function according to some constraints. In order to optimize real-world problems, they must be mathematically formulated, first. Mathematically, all optimization problems can Communicated by A. Di Nola.
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Izaz Ur Rahman [email protected] Muhammad Zakarya [email protected] Mushtaq Raza [email protected] Rahim Khan [email protected]
1
Department of Computer Science, Abdul Wali Khan University, Mardan, Pakistan
2
Faculty of Engineering, University of Porto, Porto, Portugal
be divided into two types based on the derived cost function, i.e. linear and nonlinear. In the literature, three different approaches have been adopted to solve optimization problems, i.e. deterministic, analytical and stochastic (Elijah 2012). Moreover, all deterministic approaches are based on a given initial condition and/or assumption, whereas analytical approaches have some pre-defined targets for a particu
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