Design and performance analysis of a new optimization algorithm based on Finite Element Analysis

Abstract

Aiming at the problem that many algorithms could not effectively balance the global search ability and local search ability, a new optimization algorithm is proposed. Inspired by Finite Element Analysis (FEA) approach, a relationship of mapping between Finite Element Analysis approach and a population-based optimization algorithm is constructed through comparing the similarities and differences of FEA node and ideal particle. In algorithm framework, the stiffness coefficient corresponds to a user-defined function of the value of an objective function to be optimized, and the node forces among individuals are defined and an attraction-repulsion rule is established among them. The FEA approach that can simulate multi- states of matter is adopted to balance the global search ability and local search ability in the novel optimization algorithm. A theoretical analysis is made for algorithm parallelism. The conditions for convergence are deduced through analyzing the algorithm based on discrete-time linear system theory. In addition, the performance of the algorithm is compared with PSO for five states which include free state, diffusion state, solid state, entirely solid state, synthesis state. The simulation results of six benchmark functions show that the algorithm is effective. The algorithm supplies a new method to solve optimization problem.