A Differential Evolution and Nelder-Mead hybrid algorithm for constrained Engineering Design problems

Resumo

Engineering design optimization problems frequently involve complex, nonlinear, and computationally expensive objective functions subject to various constraints. Differential Evolution (DE) is a population-based evolutionary algorithm well-suited for global optimization, whereas the Nelder-Mead (NM) simplex method offers efficient local search capabilities without requiring gradient information. This paper investigates a hybrid optimization strategy that integrates DE with the NM method to exploit their complementary strengths. The DE algorithm is initially employed to explore the global search space and identify promising regions by iteratively evolving a population of candidate solutions based on a predefined stopping criterion. Once a suitable region is identified, the NM algorithm is applied to perform local refinement, enhancing convergence toward the optimal solution. To handle constrained problems, the NM method is extended using the penalty function method proposed by Deb, wherein constraint violations are incorporated into the objective function. The proposed hybrid algorithm taking into account Deb's penalization approach is evaluated on a suite of constrained engineering design benchmarks using MATLAB. The results demonstrate superior performance compared to the standalone DE algorithm, yielding improved solution accuracy and a reduced number of objective function evaluations.