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. 2016 Apr 28;11(4):e0154191.
doi: 10.1371/journal.pone.0154191. eCollection 2016.

Lagrange Interpolation Learning Particle Swarm Optimization

Zhang Kai  1 , Song Jinchun  1 , Ni Ke  1 , Li Song  1
Affiliations

Lagrange Interpolation Learning Particle Swarm Optimization

Zhang Kai et al. PLoS One. .

Abstract

In recent years, comprehensive learning particle swarm optimization (CLPSO) has attracted the attention of many scholars for using in solving multimodal problems, as it is excellent in preserving the particles' diversity and thus preventing premature convergence. However, CLPSO exhibits low solution accuracy. Aiming to address this issue, we proposed a novel algorithm called LILPSO. First, this algorithm introduced a Lagrange interpolation method to perform a local search for the global best point (gbest). Second, to gain a better exemplar, one gbest, another two particle's historical best points (pbest) are chosen to perform Lagrange interpolation, then to gain a new exemplar, which replaces the CLPSO's comparison method. The numerical experiments conducted on various functions demonstrate the superiority of this algorithm, and the two methods are proven to be efficient for accelerating the convergence without leading the particle to premature convergence.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. ForI ≠ 0, the different cases of the solution.
Fig 2
Fig 2. The flowchart of LSLI.
Fig 3
Fig 3. Selection of the exemplar dimensions for particle i.
(a)CLPSO (b)CLPSO-LIL.
Fig 4
Fig 4. The flowchart of LILPSO.
Fig 5
Fig 5. The comparison on convergence.
(a) Sphere (b) Rosenbrock (c) Noise Quadric (d) Penalized (e) Griewank (f) Schwefel.
See this image and copyright information in PMC

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