改进非劣分类遗传算法多目标优化效果评价及程序测试

Evaluation of Effect and Test of Programs of Multi-objective Optimize Based on Nondominated Sorting Genetic Algorithm Ⅱ

目的评价改进非劣分类遗传算法(NSGA-Ⅱ)进行多目标优化的效果,测试其程序的可靠性。方法应用两目标简单测试函数、两目标复杂测试函数、三目标复杂测试函数对NSGA-Ⅱ进行模拟测试,利用课题组成员英国Glasgow大学软件工程师陈益编写的Matlab 2009a外挂SGALAB工具箱beta5008完成遗传算法寻优。结果 NSGA-Ⅱ得到的两目标简单测试函数95%Pareto非劣解分布范围包含交叉点值1,前沿呈一条光滑的曲线分布;两目标复杂测试函数Pareto非劣解前沿在小于1的范围内呈下降的带状分布;三目标测试函数的Pareto非劣解前沿呈非线性、非对称的曲面分布。认为NSGA-Ⅱ可得到测试函数的Pareto非劣解集,供决策者合理选择。结论 NSGA-Ⅱ多目标优化可以给出合理的Pareto非劣解集,效果理想、程序可靠,可用于实际问题的分析。

Objective To evaluate the effect of Nondominated Sorting Genetic Algorithm Ⅱ,on multi-objective optimization,and test the reliability of its procedures.Methods Tesed NSGA-Ⅱ by simple two-objective optimization test function,complex two-objective optimization test function and three-objective optimization test function.Achieves NSGA-Ⅱ optimization using Matlab2009a plug SGALAB toolbox beta5008,which was written by Chen Yi in Glasgow University in the United Kingdom.Results The 95% confidence interval of Pareto optimal solution set of simple two-objective optimization test function using NSGA-Ⅱ contained the crossing point,Pareto optimal front showed a smooth curve of distribution;The Pareto optimal front of complex two-objective optimization test function was descending zonal distribution in the context of less than 1;The Pareto optimal front of three-objective optimization test functions was a Non-linear,non-symmetrical surface.Conclusion NSGAⅡ can give reasonable Pareto optimal solution set,the results are satisfactory,the program was reliable and it can also be used in actual analysis of the problem.