一种基于正交设计的快速差分演化算法及其应用研究

为了进一步加快差分演化算法的速度和增强算法的鲁棒性,提出了一种基于正交设计的快速差分演化算法,并把它应用于函数优化问题的求解中.新算法在保持传统差分演化算法的简单、有效等特性的同时,具有以下特征：1）采用基于正交设计的杂交算子,并结合直观统计法产生最优子个体;2）采用决策变量分块策略,以减少正交实验次数,加快算法收敛速度;3）提出一种基于非凸理论的多父体混合自适应杂交变异算子,以增强算法的非凸搜索能力和自适应能力;4）简化基本差分演化算法的缩放因子,尽量减少算法的控制参数,方便工程人员的使用.通过对12个标准测试函数进行实验,并与其他演化算法的结果相比较,其结果表明,新算法在解的精度、稳定性和收敛性上表现出很好的性能.

Research on a Fast Differential Evolution Based on Orthogonal Design and its Application

To make the differential evolution(DE) faster and more robust,a fast DE based on the orthogonal design(ODE) is proposed,and then it is used to solve the function optimization problems.The ODE combines the conventional DE(CDE),which is simple and efficient,with the orthogonal design,which can exploit the optimum offspring.The ODE has some features.1) It uses a robust crossover based on orthogonal design(OCX) and an optimal offspring is generated with the statistical optimal method.2) To decrease the number of the orthogonal design and make the algorithm converge faster,decision variable fraction strategy is applied here.3) A multi-parent hybrid crossover-mutation operator based on the non-convex theory is proposed,which can enhance the non-convex search ability.4) The ODE simplifies the scaling factor F of the CDE,which can reduce the parameters of the algorithm and make it easy to use for engineers.We execute the proposed algorithm to solve 12 benchmark functions with low or high dimensions and very large numbers of local minima.Through comparison with some state-of-theart evolutionary algorithms,the experimental results demonstrate that the performance of the ODE outperforms other evolutionary algorithms in terms of the quality of the final solution and the stability;and its computational cost(measured by the average number of fitness function evaluations) is lower than the cost required by the other techniques compared.