基于动态混合约束框架的改进差分进化及其应用

针对动态随机选择多个体差分进化（DSS-MDE）在处理复杂约束问题时易陷入局部最优的缺陷，提出了基于动态混合约束框架的改进差分进化算法（DHCF-IDE）。首先，通过跟踪种群可行解比例，动态地执行可行解搜索和全局搜索，并分别使用动态随机排序和可行性规则作为两模型的约束处理方法。其次，分别采用多个体差分进化和基于幂律分布父代选择的改进差分进化作为两模型的算法实现。选取CEC2006中6个测试函数进行仿真实验，实验结果表明：与仅采用DSS-MDE或DyHF相比，DHCF-IDE能保持更快的收敛速度和较好的全局搜索能力。催化重整芳烃产率优化的工业案例也表明该改进算法在实际应用中具有可行性。

An Improved Differential Evolution Based on Dynamic Hybrid Constrained Framework and Its Application

Many problems in practical project optimization can be attributed to constrained optimization problems (COPs). The main difficulty in dealing with COPs is that there may not be a general algorithm to obtain the global optimal feasible solution when the feasible domain of the problem under consideration is small, discontinuous or multi-peaked. Therefore, it is quite necessary and important to investigate the promising infeasible solutions during the evolution process. Dynamic stochastic selection multi-member differential evolution (DSS-MDE) is effective in this aspect, but it is easily fallen into the local optimal when dealing with some complex constrained optimization problems. In order to deal with this shortcoming, this paper proposes an improved differential evolution algorithm based on dynamic hybrid constrained framework (DHCF-IDE). Firstly, by using the feature information of the current population feasible ratio, the feasible solution search model and the global search model are dynamically implemented. Moreover, the dynamic stochastic ranking and feasibility rule are taken as the constraint processing method for the two models, respectively. Secondly, the multimember differential evolution and the proposed improved differential evolution based on power-law distribution of parental selection are used for the two models, respectively. Finally, the simulation experiments are made via six complex benchmark functions chosen from CEC2006. Compared with DSS-MDE or dynamic hybrid framework (DyHF), the proposed DHCF-IDE can keep better convergence rate and global search ability. Furthermore, the feasibility of the improved algorithm in practical application is also demonstrated by the industrial case of maximizing aromatics yield in catalytic reforming.