A fixed point evolution algorithm based on expanded Aitken rapid iteration method for global numeric optimization

Abstract

Evolution algorithms based on mathematical models that their reproduction operators are derived from mathematical models are a promising branch of metaheuristic algorithms. Aitken rapid iteration method, as a fixed point iteration technique for solving nonlinear equations, performs a procedure of progressive display of a root. Inspired by the idea of viewing the progressive display procedure of a fixed point iteration as an evolutionary optimization process, a fixed point evolution algorithm based on expanded Aitken rapid iteration method (FPEea) is proposed. To develop the FPEea, an expanded Aitken rapid model is firstly constructed; Then, three polynomials which are derived from the expanded Aitken rapid model are used as the reproduction operator of the FPEea to produce offsprings. The performance of the FPEea is investigated on CEC2019, CEC2020 benchmark function sets as well as four engineering design problems. Experimental results show that the FPEea is a effective and competitive algorithm compared with several classical evolution algorithms and state-of-the-art algorithms.