基于区间的不确定多目标优化方法研究  

UNCERTAIN MULTI-OBJECTIVE OPTIMIZATION METHOD BASED ON INTERVAL

作　　者：李方义[1] 李光耀[1] 郑刚[1] 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082

出　　处：《固体力学学报》2010年第1期86-93,共8页Chinese Journal of Solid Mechanics

基　　金：国家杰出青年科学基金(50625519);教育部长江学者和创新团队发展计划;汽车车身先进设计制造国家重点实验室自主研究课题(60870005);科技部国际合作项目(2008DFB50020)资助

摘　　要：基于非线性区间优化,提出了一种不确定多目标优化方法.基于区间序关系和区间可能度,把不确定多目标的目标函数和约束转化为确定性的目标函数和确定性的约束.对于复杂的工程优化问题,为了提高效率,采用拉丁方试验设计方法,构建响应面近似模型,并基于近似模型进行不确定多目标优化,从而形成了非线性区间优化方法与近似模型相结合的高效不确定多目标优化方法.数值算例表明了该方法的有效性和工程实用性.A new uncertain multi-objective optimization method is developed based on the nonlinear in- terval number programming（NINP）. Based on the order relation and possibility degree of interval number, the uncertain multi-objective optimization is transformed into a deterministic non-constraint multi-objective optimization problem in terms of a penalty function. To improve the optimization efficiency, the response surface approximation models are constructed for the uncertain objective functions based on the Latin Hy- percube Design（LHD）. The NINP method is combined with the approximation models to form an efficient uncertain multi-objective optimization method. Two numerical examples are presented to demonstrate the effectiveness and practicability of the present method.

关 键 词：不确定多目标优化 区间数 响应面 试验设计 

分 类 号：F281[经济管理—国民经济]