中文摘要：

为了克服传统差分演化（DE）算法在求解约束优化问题时出现的收敛性慢和容易陷入早熟等缺陷,提出一种新的基于单形正交实验设计的差分演化（SO-DE）算法。该算法设计了一种结合单形交叉和正交实验设计的混合交叉算子来提高差分演化算法的搜索能力;同时采用了一种改进的个体优劣比较准则对种群个体进行比较和选择。这种新的混合交叉算子利用多个父代个体进行单形交叉产生多个子代个体,从两者中选择优秀个体进行正交实验设计得到下一代种群个体。改进的个体优劣比较准则对不同状态下的种群采用不同的处理方案,其目的在于能够有效地权衡目标函数值和约束违反量之间的关系,从而选择优秀个体进入下一代种群。通过对13个标准测试函数和2个工程设计问题进行仿真实验,实验结果表明SO-DE算法求解的精度和标准方差都要优于HEAA算法和COEA/OED算法。SO-DE算法具有更高的精度以及更好的稳定性。

英文摘要：

Focusing on the defects, such as slow convergence and premature phenomenon, in solving constrained optimization problems by the traditional Differential Evolution（ DE） algorithm, a novel DE based on Simplex-Orthogonal experimental design（ SO-DE） algorithm was proposed. The algorithm designed a new hybrid crossover operator that combined simplex crossover and orthogonal experimental design to improve the search ability of DE algorithm, and the improved comparison criteria was used to compare and select the individuals of population. Several parent individuals were used to produce multiple offspring individuals by simplex crossover in the new hybrid crossover operator, then the multiple excellent individuals, which were selected from two set by orthogonal experimental design, were copied in the next generation. Different treatment schemes were used for different stages of population in the improved comparison criterion, which aimed to effectively weigh the relationship between the value of the objective function and the degree of constraint violation, thus better individuals were chosen into the next generation. Simulation experiments were conducted on 13 standard test functions and 2 engineering design problems. The SO-DE algorithm is much better than HEAA（ Hybrid Evolutionary Algorithm and Adaptive constrainthandling technique） and COEA / ODE（ a novel Constrained Optimization Evolutionary Algorithm based on Orthogonal Experimental Design） in terms of the accuracy and standard variance of final solution. The experimental results demonstrate that the SO-DE algorithm has better accuracy and stability.