A Hybrid Optimization Methods for Nonlinear Programming

Nonlinear programming models often arise in science and engineering. A nonlinear programming model consists of the optimization of a function subject to constraints, in which both the function and constraints may be nonlinear. This paper proposes the hybrid NM-PSO algorithm, which is based on Nelder-Mead (NM) simplex search method and particle swarm optimization (PSO), for solving nonlinear programming models. NM-PSO is easy to implement in practice as it does not require gradient computation and has been successfully applied in such unconstrained optimization problems as data clustering and image segmentation. Based on the results of solving six test functions taken from the literature, it is shown that the hybrid NM-PSO approach outperforms particle swarm optimization in terms of solution quality and convergence rate. The new algorithm proves to be extremely effective and efficient at locating optimal solutions.