發(fā)布時間：2018-01-03 09:03

  本文關(guān)鍵詞：基于徑向基函數(shù)響應(yīng)面優(yōu)化方法研究　出處：《華中科技大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 試驗設(shè)計 響應(yīng)面方法 RBF 增量法 全局優(yōu)化方法 仿真優(yōu)化

【摘要】：在仿真模型多變量優(yōu)化設(shè)計中，采用傳統(tǒng)仿真優(yōu)化方法效率低下，可行性不高，在高維情況下劣勢尤為明顯�；�于試驗設(shè)計的響應(yīng)面方法可以有效的減少優(yōu)化過程中源模型的仿真次數(shù)，提高復(fù)雜模型設(shè)計優(yōu)化效率，，因而得到廣泛關(guān)注。本文從徑向基函數(shù)(Radial Basis Function)插值方法出發(fā)，對RBF響應(yīng)面方法和基于RBF響應(yīng)面的全局優(yōu)化算法進行研究。 RBF響應(yīng)面方法以徑向函數(shù)作為基函數(shù)，以樣本數(shù)據(jù)作為插值節(jié)點，可通過樣本點方便的構(gòu)造出響應(yīng)面，插值函數(shù)唯一確定，構(gòu)造算法簡單、易于計算機實現(xiàn)，且在高維非線性系統(tǒng)中表現(xiàn)卓越。目前，全局優(yōu)化方法主要包括確定性方法、元啟發(fā)式（進化）方法、啟發(fā)式直接搜索方式、以及基于“黑箱”的響應(yīng)面優(yōu)化方法等四類。本文將著重研究基于試驗設(shè)計的響應(yīng)面全局優(yōu)化方法，通過較少的試驗構(gòu)造足夠精確的響應(yīng)面，利用響應(yīng)面技術(shù)減少計算成本，結(jié)合響應(yīng)面快速重構(gòu)方法和改進的尋優(yōu)方法最終得到最優(yōu)解。目前各種基于響應(yīng)面的全局優(yōu)化方法主要區(qū)別也在于試驗設(shè)計、響應(yīng)面構(gòu)造和尋優(yōu)方法這三個方面。 在面對較難優(yōu)化的復(fù)雜函數(shù)以及最優(yōu)解在邊界條件上等問題時，現(xiàn)存的一些基于響應(yīng)面的全局優(yōu)化算法表現(xiàn)不理想，估值次數(shù)較多，為此本文引入增量LHD采樣方法和一種算法重啟策略。同時，提出一種RBF響應(yīng)面增量重構(gòu)方法，在保證原來精度的前提下，有效的降低了響應(yīng)面更新消耗的時間，并與一種CORS尋優(yōu)方法相結(jié)合，構(gòu)成一種改進的全局優(yōu)化算法。最后，使用不同算法對多個測試函數(shù)進行優(yōu)化比較，分析新方法的優(yōu)勢與不足，并將改進后的全局優(yōu)化方法應(yīng)用于工程優(yōu)化實例。
[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.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH122

【參考文獻】

相關(guān)期刊論文 前1條

1 吳宗敏;函數(shù)的徑向基表示[J];數(shù)學(xué)進展;1998年03期

本文編號：1373259