| 引用本文: | 李建平,王维平,李群,等.线性规划优化分析的元模型方法及其比较.[J].国防科技大学学报,2007,29(2):108-112 ,126.[点击复制] |
| LI Jianping,WANG Weiping,LI Qun,et al.A Comparative Study of Metamodels for Optimality Analysis of Linear Programming[J].Journal of National University of Defense Technology,2007,29(2):108-112 ,126[点击复制] |
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| 线性规划优化分析的元模型方法及其比较 |
| 李建平1, 王维平2, 李群2, 胡小荣1 |
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(1.国防科技大学 理学院，湖南 长沙 410073;2.国防科技大学 信息系统与管理学院，湖南 长沙 410073)
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| 摘要: |
| 线性规划优化分析在经济管理等领域有着广泛的应用。当线性规划约束条件的右端向量在一定范围内变化时，目标函数的最优值是右端向量的一个复杂的分片线性函数，但通常难以给出分析表达式。应用多项式回归、径向基函数、Kriging法及多项式回归+Kriging法这四种元模型方法，能快速预测最优值函数。通过仿真实验，对这四种形式的元模型作较全面的比较分析。数值实验的结果表明，用次数较少的实验设计，后三种方法都具有较高的拟合精度；特别地，多项式回归+Kriging法不仅拟合精度高，而且还能用一个二阶多项式给出最优值函数的一个简明的近似描述。结果表明，元模型方法是研究线性规划优化分析问题的有效途径。 |
| 关键词: 线性规划 优化分析 元模型 仿真 多项式回归 径向基函数 Kriging法 |
| DOI： |
| 投稿日期：2006-11-14 |
| 基金项目:国防科技大学博士生创新基金资助项目 |
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| A Comparative Study of Metamodels for Optimality Analysis of Linear Programming |
| LI Jianping1, WANG Weiping2, LI Qun2, HU Xiaorong1 |
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(1.College of Science, National Univ. of Defense Technology, Changsha 410073，China;2.College of Information System and Management, National Univ. of Defense Technology, Changsha 410073，China)
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| Abstract: |
| Optimality analysis of linear programming is used extensively in economy and management. The optimal objective value is a complicated piecewise linear function of the right-hand-side vector of the constraints, and its analytical expression is normally hard to obtain. Four metamodels, that is, polynomial regression, radial basis function, Kriging interpolation, and polynomial regression hybridized with Kriging interpolation, are used to rapidly predict the optimal objective function value. Comparative analysis through simulation experiments shows that the last three methods can provide higher accuracy fitting with fewer experimental designs. In particular, polynomial regression method hibridized with Kriging interpolation can not only have a good fitting accuracy but also give a simple approximate expression of the optimal objective function value using a second-order polynomial. The results show that the metamodel method is effective for optimality analysis of linear programming. |
| Keywords: linear programming optimality analysis metamodel simulation polynomial regression radial basis function kriging method |
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