基于径向基函数响应面优化方法研究

发布时间：2018-01-03 09:03

本文关键词：基于径向基函数响应面优化方法研究　出处：《华中科技大学》2012年硕士论文　论文类型：学位论文

【摘要】：在仿真模型多变量优化设计中，采用传统仿真优化方法效率低下，可行性不高，在高维情况下劣势尤为明显。基于试验设计的响应面方法可以有效的减少优化过程中源模型的仿真次数，提高复杂模型设计优化效率，，因而得到广泛关注。本文从径向基函数(Radial Basis Function)插值方法出发，对RBF响应面方法和基于RBF响应面的全局优化算法进行研究。 RBF响应面方法以径向函数作为基函数，以样本数据作为插值节点，可通过样本点方便的构造出响应面，插值函数唯一确定，构造算法简单、易于计算机实现，且在高维非线性系统中表现卓越。目前，全局优化方法主要包括确定性方法、元启发式（进化）方法、启发式直接搜索方式、以及基于“黑箱”的响应面优化方法等四类。本文将着重研究基于试验设计的响应面全局优化方法，通过较少的试验构造足够精确的响应面，利用响应面技术减少计算成本，结合响应面快速重构方法和改进的寻优方法最终得到最优解。目前各种基于响应面的全局优化方法主要区别也在于试验设计、响应面构造和寻优方法这三个方面。在面对较难优化的复杂函数以及最优解在边界条件上等问题时，现存的一些基于响应面的全局优化算法表现不理想，估值次数较多，为此本文引入增量LHD采样方法和一种算法重启策略。同时，提出一种RBF响应面增量重构方法，在保证原来精度的前提下，有效的降低了响应面更新消耗的时间，并与一种CORS寻优方法相结合，构成一种改进的全局优化算法。最后，使用不同算法对多个测试函数进行优化比较，分析新方法的优势与不足，并将改进后的全局优化方法应用于工程优化实例。
[Abstract]:In the multivariable optimization design of simulation model, the traditional simulation optimization method is inefficient and feasible. The response surface method based on experimental design can effectively reduce the number of simulation of the source model in the optimization process and improve the efficiency of complex model design optimization. This paper is based on Radial Basis function (RBF) interpolation method. RBF response surface method and global optimization algorithm based on RBF response surface are studied. The RBF response surface method takes radial function as basis function and sample data as interpolation node. The response surface can be easily constructed by sample points. The interpolation function is uniquely determined and the construction algorithm is simple. At present, global optimization methods mainly include deterministic method, meta-heuristic (evolution) method and heuristic direct search method. And four kinds of response surface optimization methods based on "black box". This paper focuses on the global optimization method of response surface based on experimental design, and constructs a sufficiently accurate response surface through fewer experiments. The response surface technique is used to reduce the computation cost, and the response surface reconstruction method and the improved optimization method are combined to obtain the optimal solution. At present, the main difference of the global optimization methods based on response surface is also the experimental design. Response surface construction and optimization methods. In the face of complex functions which are difficult to be optimized and the boundary conditions of the optimal solutions, some existing global optimization algorithms based on response surface are not satisfactory, and the estimation times are many. In this paper, an incremental LHD sampling method and an algorithm restart strategy are introduced. At the same time, an incremental reconstruction method of RBF response surface is proposed to ensure the original accuracy. Effectively reduce the response surface update time, and combined with a CORS optimization method, constitute an improved global optimization algorithm. Finally, using different algorithms to optimize the comparison of multiple test functions. The advantages and disadvantages of the new method are analyzed, and the improved global optimization method is applied to the engineering optimization example.
【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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