A collaboration-based particle swarm optimizer for global optimization problems

  • Leilei Cao
  • Lihong Xu
  • Erik D. Goodman
Original Article


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.


Collaboration Global learning Particle swarm optimization Learning probability Worst replacement 



This work was supported in part by the National Natural Science Foundation of China under Grant 61573258, in part by the National High-Technology Research and Development Program (863 Program) of China under Grant 2013AA103006-2, in part by the US National Science Foundation’s BEACON Center for the Study of Evolution in Action, funded under Cooperative Agreement no. DBI-0939454, and by the China Scholarship Council under Grant 201506260093.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Control Science and EngineeringTongji UniversityShanghaiChina
  2. 2.BEACON Center for the Study of Evolution in ActionMichigan State UniversityEast LansingUSA

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