基于支持向量回归的全局仿真优化算法

发布时间：2018-01-22 04:35

本文关键词： 试验设计全局仿真优化响应面支持向量回归增量法　出处：《华中科技大学》2012年硕士论文　论文类型：学位论文

【摘要】：囿于传统全局优化方法及其它基于替代模型的全局仿真优化方法存在估值次数多、无法应对高维优化问题等缺点，近些年开始流行基于“黑箱”的元模型（响应面）方法，，主要包括基于SVR、基于RSM、基于Kriging、基于RBF等元模型的全局优化方法。该方法是以试验设计与数理统计为基础的函数逼近类全局优化方法，可通过较少的试验在设计变量和设计目标之间获得一个足够准确的函数关系，利用响应面替代模型有效降低了优化问题的计算成本。支撑向量回归（SVR，Support Vector Regression）基于SVM理论，通过获得训练样本的最大间隔建立分类超平面，以构造源模型的替代模型响应面。目前存在的基于SVR的全局仿真优化方法无法保证样本数较少时，遴选出具有代表性的样本，使之覆盖整个设计区间；重构SVR模型时间较长；最优点搜索速度较慢；不能有效应对约束条件下的全局寻优。本文提出一种基于增量SVR模型的全局优化算法DISVR：采用一种新的最小距离最大化增量LHD采样方法，以确保样本集分布均匀；利用支持向量机理论中支持向量集与训练样本集之间存在等价关系的自身特点，构建一种增量SVR算法重构响应面，以快速优化大批量采样点；采用加约束的DIRECT算法作为搜索策略对结构模型进行求解，以有效解决带约束优化问题。本文对于DISVR算法各重要环节均有相关章节铺述，标准函数及工程实例的测试结果表明，本文提出的DISVR算法可高效稳定地得到优化结果，具有良好的应用前景。
[Abstract]:Due to the disadvantages of traditional global optimization methods and other global simulation optimization methods based on alternative models, there are many disadvantages such as the number of estimates and the inability to cope with high-dimensional optimization problems. In recent years, the meta-model (response surface) method based on "black box" has become popular, including SVR-based, RSM-based and Kriging based. The global optimization method based on RBF iso-element model, which is based on experimental design and mathematical statistics, is a functional approximation class global optimization method. A sufficiently accurate functional relationship between design variables and design objectives can be obtained by fewer experiments, and the computational cost of the optimization problem can be effectively reduced by using the response surface substitution model. Support Vector regression support Vector Regression is based on the SVM theory and establishes the classification hyperplane by obtaining the maximum interval of training samples. The existing global simulation optimization method based on SVR can not guarantee that the representative samples can be selected to cover the whole design interval when the number of samples is small. The reconstruction time of SVR model is longer; The best search speed is slow; It can not effectively deal with the global optimization under constraint conditions. A global optimization algorithm based on incremental SVR model is presented in this paper. A new minimum distance maximization incremental LHD sampling method is adopted to ensure the uniform distribution of the sample set. Taking advantage of the equivalent relationship between the support vector set and the training sample set in the support vector machine theory, an incremental SVR algorithm is constructed to reconstruct the response surface in order to quickly optimize the mass sampling points. The constrained DIRECT algorithm is used as a search strategy to solve the structural model effectively. The test results of standard function and engineering examples show that the proposed DISVR algorithm can get the optimization results efficiently and stably. It has good application prospect.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122

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