Lagrange Interpolation Learning Particle Swarm Optimization

<div><p>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.</p></div

results for D = 50, N = 100, FEs = 500,000.

<p>results for D = 50, N = 100, FEs = 500,000.</p

PID Results optimized by some algorithms.

<p>PID Results optimized by some algorithms.</p

Results for D = 10, N = 50, FEs = 100,000.

<p>Results for D = 10, N = 50, FEs = 100,000.</p

Selection of the exemplar dimensions for particle i.

<p>(a)CLPSO (b)CLPSO-LIL.</p

Iterative forms of each algorithms.

<p>Iterative forms of each algorithms.</p

Details of benchmarks.

<p>Details of benchmarks.</p

The comparison on convergence.

<p>(a) Sphere (b) Rosenbrock (c) Noise Quadric (d) Penalized (e) Griewank (f) Schwefel.</p

results for D = 50, N = 100, FEs = 500,000.

<p>results for D = 50, N = 100, FEs = 500,000.</p

Results for D = 30, N = 40, FEs = 200,000.

<p>Results for D = 30, N = 40, FEs = 200,000.</p