An effective hybrid genetic algorithm with flexible allowance technique for constrained engineering design optimization

In this paper, a hybrid genetic algorithm with flexible allowance technique (GAFAT) is proposed for solving constrained engineering design optimization problems by fusing center based differential crossover (CBDX), Levenberg-Marquardt mutation (LMM) and non-uniform mutation (NUM). Inheriting the merits of mutation of differential evolution (DE), the proposed CBDX is a multi-parent recombination operator for generating offspring based on a parent vector and two parent center vectors. As an improvement of the gradient-based mutation, the proposed LMM is more numerically stable when enhancing the feasibility of the new individuals. To enrich the population diversity, NUM is incorporated into the hybrid algorithm. In addition, a flexible allowance technique (FAT) is designed and used in the hybrid algorithm to balance the selection of bad feasible solutions and good infeasible solutions. The proposed GAFAT is first tested based on the 13 widely used benchmark functions, which shows that GAFAT is of better or competitive performances when compared with six existing algorithms. The, GAFAT is applied to solve six well-known constrained engineering design problems, which also shows that GAFAT is of superior searching quality with fewer evaluation times than other algorithms. Finally, GAFAT is successfully applied to solve a real pipe frequency improvement problem.