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A Velocity-Combined Local Best Particle Swarm Optimization Algorithm for Nonlinear Equations

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  • Zhigang Lian
  • Songhua Wang
  • Yangquan Chen

Abstract

Many people use traditional methods such as quasi-Newton method and Gauss–Newton-based BFGS to solve nonlinear equations. In this paper, we present an improved particle swarm optimization algorithm to solve nonlinear equations. The novel algorithm introduces the historical and local optimum information of particles to update a particle’s velocity. Five sets of typical nonlinear equations are employed to test the quality and reliability of the novel algorithm search comparing with the PSO algorithm. Numerical results show that the proposed method is effective for the given test problems. The new algorithm can be used as a new tool to solve nonlinear equations, continuous function optimization, etc., and the combinatorial optimization problem. The global convergence of the given method is established.

Suggested Citation

  • Zhigang Lian & Songhua Wang & Yangquan Chen, 2020. "A Velocity-Combined Local Best Particle Swarm Optimization Algorithm for Nonlinear Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, August.
    • Handle: RePEc:hin:jnlmpe:6284583
    DOI: 10.1155/2020/6284583
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    Cited by:

    1. Alireza Falahiazar & Arash Sharifi & Vahid Seydi, 2022. "An efficient spread-based evolutionary algorithm for solving dynamic multi-objective optimization problems," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 794-849, August.

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