改进的排序变异多目标差分进化算法

针对多目标差分进化算法在求解问题时收敛速度慢和均匀性欠佳的问题，提出了一种改进的排序变异多目标差分进化算法（MODE-IRM）。该算法将参与变异的三个父代个体中的最优个体作为基向量，提高了排序变异算子的求解速度；另外，算法采用反向参数控制方法在不同的优化阶段动态调整参数值，进一步提高了算法的收敛速度；最后，引入了改进的拥挤距离计算公式进行排序操作，提高了解的均匀性。采用标准多目标优化问题ZDTl~ZDT4，ZDT6和DTLZ6~DTLZ7进行仿真实验:MODE-IRM在总体性能上均优于MODE-RMO和PlatEMO平台上的MOEA/D-DE、RM-MEDA以及IM-MOEA；在世代距离（GD）、反向世代距离（IGD）和间隔指标（SP）性能度量指标方面，MODE-IRM在所有优化问题上的均值和方差均明显小于MODE-RMO。实验结果表明MODE-IRM在收敛性和均匀性指标上明显优于对比算法。

Multi-objective differential evolution algorithm with improved ranking-based mutation

Focusing on the slow convergence and the poor uniformity of multi-objective differential evolution algorithms when solving multi-objective optimization problems, a Multi-Objective Differential Evolution algorithm with Improved Ranking-based Mutation (MODE-IRM) was proposed. The optimal individual involved in the mutation was used as the base vector, which accelerated the resolving speed of the ranking-based mutation operator. In addition, a strategy of opposition-based parameter was adopted to dynamically adjust the values of parameters in different optimization stages, so the convergence rate was further accelerated. Finally, an improved crowding distance calculation formula was introduced in the sort operation, which improved the uniformity of solutions. Simulation experiments were conducted on the standard multi-objective optimization problems including ZDTl-ZDT4, ZDT6 and DTLZ6-DTLZ7. MODE-IRM's overall performance was much better than MODE-RMO and other three algorithms of the PlatEMO including MOEA/D-DE (Multiobjective Evolutionary Algorithm based on Decomposition with Differential Evolution), RM-MEDA (Regularity Model-based Multi-objective Estimation of Distribution Algorithm) and IM-MOEA (Inverse Modeling Multi-objective Evolutionary Algorithm). Moreover, in terms of the performance metrics including GD (Generational Distance), IGD (Inverted Generational Distance) and SP (Spacing), the mean and variance of MODE-IRM on all problems were significantly less than those of MODE-RMO. The simulation results show that MODE-IRM has better performance in convergence and uniformity.