多响应稳健性优化的贝耶斯分析  

Robust Optimization for Multi-Response Using Bayesian Analysis

作　　者：张旭涛[1,2] 何桢[1] 

机构地区：[1]天津大学管理与经济学部,天津300072 [2]军事交通学院装备保障系,天津300161

出　　处：《系统工程》2015年第9期127-132,共6页Systems Engineering

基　　金：国家自然科学基金重点资助项目(70931004);国家自然科学基金委杰出青年基金资助项目(71225006)

摘　　要：针对产品质量改进中的多响应稳健性优化问题,提出了一种基于贝耶斯分析的递阶优化方法。首先基于满意度函数方法求出初始优化解,然后通过贝耶斯分析评价解的稳健性,以初始优化解为起始搜索点进行稳健性寻优;针对现有稳健最优解可靠性较差的情况,给出了两种改进策略下仿真数据的产生方法,利用贝耶斯预后验分析来对未来改进措施的效果进行定量评价。该方法可以实现最优解和稳健解的权衡,降低算法的复杂度并提高寻优效率,且适用于响应曲面模型回归项不一致的情况。算例表明,对多响应优化问题进行贝耶斯分析能有效找到稳健最优解,并可以为后续实验改进提供依据。A hierarchical optimization approach based on Bayesian analysis is proposed for multi-response optimization problems in product quality improvement.First,initial optimal solutions are found using desirability functions method.Second,the robustness of the solution is taken into consideration based on Bayesian inference.For the case that current robust optimal solution has a poor reliability,simulation data are generated through two different ways.The effects of future remedial measures are accessed quantitatively by the pre-posterior analysis.The proposed method allows a quality engineer to make balance between optimality and robustness.The hierarchical strategy can reduce the complexity of the algorithm and improve the efficiency of optimization procedures.What is more,it is more flexible for the situation where each response model has different regressors.The illustrated example shows that using Bayesian analysis can obtain the robust optimal solutions efficiently.In addition,it can provide some guidance for subsequent experiments for improvement.

关 键 词：多响应优化 稳健性 贝耶斯方法 满意度函数 递阶优化 预后验分析 响应曲面法 

分 类 号：F406[经济管理—产业经济]