Nature-inspired computational intelligence integration with Nelder–Mead method to solve nonlinear benchmark models

Abstract

In the present study, nature-inspired computing technique has been designed for the solution of nonlinear systems by exploiting the strength of particle swarm optimization (PSO) hybrid with Nelder–Mead method (NMM). Fitness function based on least square approximation theory is developed for the systems, while optimization of the design variables is performed with PSO, an efficient global search method, refined with NMM for rapid local convergence. Sixteen variants of the proposed hybrid scheme PSO-NMM have been evaluated on five benchmark nonlinear systems, namely interval arithmetic benchmark model, kinematic application model, neurophysiology problem, combustion model and chemical equilibrium system. Reliability and effectiveness of the proposed solver have been validated after comparison with the results of statistical analysis based on massive data generated for sufficiently large number of independent executions.