Static Polynomial Approximation Using Set-based Particle Swarm Optimisation

Abstract

Recently, a set-based particle swarm optimisation (SBPSO) algorithm was developed to find optimal polynomials for univariate polynomial approximation problems. This SBPSO algorithm employed a computational costly adaptive coordinate descent (ACD) algorithm to find optimal monomial coefficients. In addition, the ACD algorithm prematurely converged in coefficient space. This paper presents a variation of the SBPSO polynomial approximation algorithm where the ACD algorithm is replaced with a standard particle swarm optimisation (PSO) algorithm, which is applied to find optimal monomial coefficients only after an optimal polynomial architecture has been found. This results in a significant reduction in computational costs and prevents premature stagnation in coefficient space. The results show that the new SBPSO algorithm for polynomial approximation performs well on univariate, static polynomial approximation problems.