A Hybrid Simplex Search and Particle Swarm Optimization 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. Constraint handling is one of the major concerns when solving nonlinear programming problems by hybrid Nelder-Mead simplex search method and particle swarm optimization, denoted as NM-PSO. This paper proposes embedding constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, in NM-PSO as a special operator to deal with satisfying constraints. Experiments using 6 benchmark problems are presented and compared with the best known solutions reported in the literature. The comparison results with three different metaheuristics demonstrate that NM-PSO with the embedded constraint operator proves to be extremely effective and efficient at locating optimal solutions.