Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems

Constrained optimization problems are very important in that they frequently appear in the real world. A constrained optimization problem 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 constrained optimization 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 three benchmark function and three engineering design problems are presented and compared with the best known solutions reported in the literature. The comparison results with other evolutionary optimization methods demonstrate that NM–PSO with the embedded constraint operator proves to be extremely effective and efficient at locating optimal solutions.