A review of particle swarm optimization for multimodal problems

A review of particle swarm optimization for multimodal problems

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Particle swarm optimizations (PSOs) are population-based methods inspired from the flight of a flock of birds seeking food. After the development of over 20 years, PSOs have become a major branch of evolutionary algorithms (EAs) and have been successfully applied to solve many science and engineering optimization problems. Most of PSOs are designed to search one solution of a problem. However, many science and engineering optimization problems are complex and multimodal in nature. More and more researches are aiming to identify multiple global and local solutions of complex multimodal problems, and several competitions in recent international conferences had been set up to encourage researchers to develop more effective and efficient algorithms for exploring multiple solutions. There are several techniques in the literature which can be used by combining with an existing EA to solve multimodal optimization problems. Those techniques are called niching. The most commonly used niching techniques are crowding, fitness share, clustering and species conserving. PSO-related methods for multimodal problems are reviewed in this chapter, including hybrid PSO with other EAs. Additionally, the multimodal functions, including some challenge composition multimodal functions, are listed as references for researchers to test their new algorithms. The species conserving PSO is described in detail and used to solve some multimodal engineering optimization problems to demonstrate the power of niching in exploring multiple solutions.

Chapter Contents:

  • Abstract
  • 16.1 Introduction
  • 16.2 Particle swarm optimization
  • 16.3 Niching PSOs
  • 16.3.1 Crowding PSO
  • 16.3.2 Fitness share/NichePSO
  • NichePSO
  • Sub-niches/swarms
  • 16.3.3 Clustering PSO
  • 16.3.4 Species PSO
  • 16.3.5 Hybrid PSO
  • 16.4 Species-conserving PSO
  • 16.4.1 Identifying species
  • 16.4.2 Conserving species
  • 16.4.3 Updating particle position through a velocity function
  • 16.4.4 Identifying local and global solutions
  • 16.4.5 Procedures of the SCPSO
  • 16.5 Multimodal testing functions
  • 16.5.1 Simple multimodal functions
  • 16.5.2 Composition multimodal function
  • 16.6 Engineering applications
  • 16.6.1 Example 1: design of torsion rods
  • 16.6.2 Example 2: gear train design
  • 16.6.3 Example 3: topology of 15-members, 6-node truss
  • Problem description
  • Optimal solutions
  • 16.7 Conclusion
  • References

Inspec keywords: evolutionary computation; particle swarm optimisation

Other keywords: evolutionary algorithms; complex multimodal problems; particle swarm optimization; science; PSOs; multimodal engineering optimization problems; multiple global solutions; population-based methods; local solutions; multimodal optimization problems; EAs

Subjects: Optimisation; Optimisation techniques; Optimisation techniques

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