A new proposal to hybridize the Nelder-Mead method to a differential evolution algorithm for constrained optimization

In this paper, we propose a new selection criterion for candidate solutions to a constrained optimization problem. Such a selection mechanism is incorporated into a differential evolution (DE) algorithm. This DE approach is then hybridized with an operator based on the Nelder-Mead method, whose aim is to speed up convergence towards good solutions. The proposed approach is called “Hybrid of Differential Evolution and the Simplex Method for Constrained Optimization Problems” (HDESMCO), and is validated using a well-know benchmark for constrained evolutionary optimization. The results indicate that our proposed approach produces solutions whose quality is competitive with respect to those generated by three evolutionary algorithms from the state-of-the-art (improved stochastic ranking, diversity-DE and Generalized Differential Evolution), but requiring a lower number of objective function evaluations.