基于NSGAⅡ的齿轮减速器多目标优化研究

为了解决工程设计中有离散变量、多约束的多目标优化问题,对改进的非占优排序遗传算法(NSGAⅡ)进行了研究,通过基于拥挤距离的非占优排序,提出了离散变量和多约束的处理方法,利用Matlab软件编写了NSGAⅡ的多目标优化程序,并以二级减速器多目标优化设计为例,建立了多目标优化数学模型,运用NSGAⅡ算法求解得到了帕累托最优解集,根据模糊集合理论的有关方法选取了最优解,与传统方法得到的结果相比,体积、失效概率和传动误差都有不同程度的降低。研究结果表明,修改后的NSGAⅡ能用于有效地求解有离散变量、多约束的多目标优化设计问题。

Multi-objective optimization of gear reducers based on NSGAII

Aiming at solving the multi-objective optimization problem with constraints and discrete variables in engineering design, non-dominated sorting in genetic algorithms II (NSGAII) was investigated. The methods were presented to handle the discrete variables and constraints by non-dominated sorting based on crowding distance, and Matlab was used as a tool to work out the multi-objective optimization program of NSGAII. The mathematical model of the multi-objective optimization design of two-stage gear reducer was established, the Pareto set was achieved by using the modified NSGAII and the optimal solution was selected according to the method of fuzzy set theory. The volume, the failure probability and the transmission error were decreased compared to traditional method. The results indicate that the modified NSGAII can effectively solve the multi-objective optimization problem with constraints and discrete variables. ABSTRACT FROM AUTHOR]