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ORIGINAL ARTICLE

A collaboration-based particle swarm optimizer for global optimization problems Leilei Cao1   · Lihong Xu1 · Erik D. Goodman2 Received: 30 May 2017 / Accepted: 17 March 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract This paper introduces a collaboration-based particle swarm optimizer (PSO) by incorporating three new strategies: a global learning strategy, a probability of learning, and a “worst replacement” swarm update rule. Instead of learning from the personal historical best position and the global (or local) best position which was used by the classical PSO, a target particle learns from another randomly chosen particle and the global best one in the swarm. Instead of accepting a new velocity directly, the velocity updates according to a learning probability, according to which the velocity of the target particle in each dimension updates via learning from other particles or simply inherits its previous velocity component. Since each particle has the same chance to be selected as a leader, the worst particle might influence the whole swarm’s performance. Therefore, the worst particle in the swarm in each update is moved to a new better position generated from another particle. The proposed algorithm is shown to be statistically significantly better than six other state-of-the-art PSO variants on 20 typical benchmark functions with three different dimensionalities. Keywords  Collaboration · Global learning · Particle swarm optimization · Learning probability · Worst replacement

1 Introduction Since Particle Swarm Optimization (PSO) was developed in 1995 [1], it has been actively studied and widely applied on many academic and real-world problems—e.g., multiobjective optimization [2], artificial neural network evolution [3], image processing [4], data clustering [5], diagnosis of neuromuscular disorders [6], PID parameter tuning [7], and many others. PSO simulates the swarm behavior of birds flocking, where each member in the swarm searches for food by learning from its own experience and other members’ experiences, which is called a collaborative manner [1]. In the particle swarm algorithm, a particle which represents * Lihong Xu [email protected] Leilei Cao [email protected] Erik D. Goodman [email protected] 1



Department of Control Science and Engineering, Tongji University, Shanghai 201804, China



BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI 48824, USA

2

a potential solution learns from its own and from others’ experiences as observed through its personal best and the global best positions [1]. Under appropriate parameter settings, PSO performs well on some problems, often with an especially fast convergence speed [8]. However, this basic algorithm easily gets trapped in a local optimum when solving some complex multimodal problems, and sometimes even converges prematurely when solving some complex unimodal problems [10]. Some local versions of PSO have been proposed to improve this weakness [8]. Instea