Polynomial Approximation Using Set-Based Particle Swarm Optimization

Abstract

This paper introduces a new approach to solving regression problems by using a particle swarm optimization algorithm to find optimal polynomial regressions to these problems. Polynomial regression is defined as a multi-objective optimization problem, with the goals to find both an optimal combination of terms in the polynomial and optimal values of the coefficients of the terms, in order to minimize the approximation error. This paper shows that a set-based PSO works well to find the optimal term structure of the target polynomials in low dimensions, and holds promise for improved performance in higher dimensions. The results of the set-based PSO are compared to the results of a Binary PSO on the same problems. Finally, this paper explores possible solutions to create a hybrid algorithm that can find both the optimal term structure and the coefficients of the found terms.