改进NSGA-Ⅱ终止判断准则

A New Termination Criterion of NSGA-Ⅱ

在基于进化算法的多目标优化中,往往是通过设置最大进化代数来确定算法何时终止。但是,如果最大进化代数设置太大,会增加许多不必要的计算量,设置太小可能得不到理想的结果。为了解决上述问题,提出一种改进的终止判断准则,通过该终止判断准则,即使在最大进化代数设置得非常大的情况下,只要连续几次获得的相隔一定进化代数的Pareto优解集的种群距离均小于给定的阈值,算法即可终止,并得到理想的结果,算法不再继续计算直到进化到最大进化代数后才终止。从仿真结果可以看出,通过终止判断准则,不仅降低了进化代数,减少了计算量,证实了新终止判断准则可行。

The termination criterion in the multiobjective optimization problem based on genetic algorithm is that if the algorithm is executed to the maximal number of generations（ MAXGEN）, then algorithm stops. However, if the MAXGEN is set too great, the algorithm would increase too much unnecessary computational load, and if the MAXGEN is set too small, the algorithm would not get the ideal result. In order to solve this problem, the paper presents a new termination criterion of multiobjective evolutionary algorithm. With the help of the new termination criterion, even the MAXGEN is set very great, the algorithm would stop if all of the several continuous population distance of pareto optimal solutions at a distance of some generations are less than the given value, and the ideal result is got, then there is no need to continue till the MAXGEN. The simulation shows that the improved NSGA - II not only reduces the evolution generations and decreases the computing quantity, but also gets almost the true pareto optimal front. So the new termination criterion is feasible.