改进聚类算子的自适应多目标进化算法研究

Multi-Object Optimization Algorithm Based on Improved Adaptive Clustering Algorithm

对多个相互冲突的目标同时优化称作多目标优化问题,为解决多目标问题,多目标进化算法应运而生。在进化算法迭代过程中,算法使用恒定不变的交叉因子和变异因子,这显然不符合种群迭代进化特征,所以需要根据种群初始和种群后期解的收敛情况来定向调整种群进化方向。同时,在采用边界与交叉的聚合算法时,θ支配的聚类算法只参考了解到权重向量的垂直距离,权重向量的投影点到理想点的解的直线距离没有考虑,直接影响了解在Pareto前沿上的收敛结果。为此,利用改进后的自适应种群生成策略,动态改变交叉概率和变异概率,根据种群当前的迭代情况调整进化方向;通过增加投影点到理想点的距离和惩罚因子计算个体到聚类中心的距离,将个体放入聚类簇中随机选择,有效提高了算法的收敛性。在多目标问题测试集ZDT和DTLZ上进行实验,结果表明,NSGA-ACM在解集的收敛性和分布性上效果更好。

Simultaneous optimization of multiple conflicting goals is called a multi-objective optimization problem.Multi-objective evo⁃lutionary algorithms are developed to solve these multi-objective problems.In the iterative process of evolutionary algorithm,the algo⁃rithm uses constant crossover factor and mutation factor,which obviously does not meet the characteristics of the iterative evolution of the population,so it is necessary to adjust the evolution direction of the population according to the convergence of the initial and late population solutions.At the same time,when using the boundary and cross aggregation algorithm,the clustering algorithm dominated byθonly refers to the vertical distance of the weight vector,but the linear distance from the projection point of the weight vector to the ideal point is not considered,which directly affects the individual.The convergence problem on the Pareto frontier.Using the improved adaptive population generation strategy to dynamically change the crossover probability and mutation probability,and adjust the evolu⁃tion direction according to the current iteration of the population;by increasing the distance between the projection point and the ideal point and the penalty factor,calculate the individual to the center of aggregation The distance of the individual is randomly selected in the cluster,which effectively improves the convergence of the algorithm.By testing on the multi-objective problem test sets ZDT and DTLZ,NSGA-ACM has a better convergence and distribution effect on the solution set.