Dynamic Neighborhood Particle Swarm Optimization Algorithm Based on Euclidean Distance for Solving the Nonlinear Equation System

Locating all roots of nonlinear equation of systems (NESs) in a single computational procedure remains a fundamental challenge in computational mathematics. The Dynamic Neighborhood Particle Swarm Optimization algorithm based on Euclidean Distance (EDPSO) is proposed to address this issue. First, a dynamic neighborhood strategy based on Euclidean distance is proposed, to facilitate particles within the population with forming appropriate neighborhoods. Secondly, the Levy flight strategy is integrated into the particle velocity-update mechanism to balance the global search capability and local search capability of particles. Furthermore, integrating a discrete crossover strategy into the PSO algorithm enhances its capability in solving high-dimensional nonlinear equations. Finally, to validate the effectiveness and feasibility of the proposed algorithms, the EDPSO algorithm, along with its comparative counterparts, is applied to solve 20 NESs problems and the forward kinematics equations of a 3-RPS parallel mechanism. Experimental results demonstrate that for the 20 NESs, the EDPSO algorithm achieved the highest success rate (SR = 0.992) and root rate (RR = 0.999) among all compared methods, followed by LSTP, NSDE, KSDE, NCDE, HNDE, and DR-JADE. In solving the forward kinematics of the 3-RPS parallel mechanism, the EDPSO algorithm achieved the highest SR of = 0.9975 and RR = 0.9800, followed by LSTP, KSDE, DR-JADE, NCDE, NSDE, and HNDE, based on these metrics.

• Publication year

  2025

• Venue

  Symmetry

• Publication date

  2025-09-10

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.3390/sym17091500
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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