S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization

Seyedali Mirjalili, Andrew Lewis

Research output: Contribution to journalArticlepeer-review

798 Citations (Scopus)


Particle Swarm Optimization (PSO) is one of the most widely used heuristic algorithms. The simplicity and inexpensive computational cost makes this algorithm very popular and powerful in solving a wide range of problems. The binary version of this algorithm has been introduced for solving binary problems. The main part of the binary version is a transfer function which is responsible to map a continuous search space to a discrete search space. Currently there appears to be insufficient focus on the transfer function in the literature despite its apparent importance. In this study six new transfer functions divided into two families, s-shaped and v-shaped, are introduced and evaluated. Twenty-five benchmark optimization functions provided by CEC 2005 special session are employed to evaluate these transfer functions and select the best one in terms of avoiding local minima and convergence speed. In order to validate the performance of the best transfer function, a comparative study with six recent modifications of BPSO is provided as well. The results prove that the new introduced v-shaped family of transfer functions significantly improves the performance of the original binary PSO.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalSwarm and Evolutionary Computation
Publication statusPublished - 1 Apr 2013
Externally publishedYes


  • BPSO
  • Evolutionary algorithm
  • Heuristic algorithm
  • Particle swarm
  • PSO
  • Transfer function


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