回應表面法的離散變數模糊最佳化與應用

Discrete Fuzzy Optimization Using Response Surface Approximation and Application

王正堯(Zheng-Yao Wang)

指導教授 ： 史建中

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00280

摘要

本文建構回應表面近似函數以替代目標函數及限制條件的最佳化，主要是為了發展適合求解離散變數且含有模糊允許值的結構設計問題。首先選取適當的起始值並以連續縮減空間的方法，建立回應表面近似函數，在最佳化設計的解題過程中，利用加入局部最佳解至實驗點中的方法，期使回應表面近似函數逐漸改變，使最終的回應表面能夠包含最佳解。在離散變數的最佳化設計問題中，以分支的概念與技術求得局部最佳解，再使局部最佳解逐漸逼近至靠近的離散值，再將此離散點的值加入實驗點群中，重新建構回應表面近似函數。如此重覆的調整局部最佳解至離散值來進行分支，使最後得到的連續解能夠逼近離散值，以最終的收斂值進而調控至最靠近的離散值當作最佳解。在含有模糊允許值的最佳化設計問題中，利用回應表面近似函數結合唯一解單切法與雙切法求解，可得到近似的模糊解。本文所發展的設計方法與程序已應用在結構設計問題，亦可應用在一般的機械與工程設計。

關鍵字

近似法 ； 離散變數 ； 回應表面近似法 ； 模糊允許值

並列摘要

This thesis study the fuzzy structural optimization problems under discrete design variables environment by using response surface approximation for objective and constraint functions. The fuzzy characteristic is lie in the fuzzy allowable limit of constraints. The difficulties of this problem primarily come from the handling of discrete variables and the solution search process. An effective increasing experimental points strategy gradually modifies the representative response surface so that the final response surface contains the optimum. It is delighted to see the success of the propose strategy. The propose method is stable, however is not very efficient. Because the branching concept can be further modified to improve the efficiency, as a future research. The extreme values of the objective function are sensitive to the final result. Therefore, a designer should be pay attention of selecting the suitable values. This paper presents a general and experimental approach as conclude as a stable and practical approach. The solution from the structural design, examples show that the reasonable optimum result can be obtained among the interrelated information of fuzzy, crisp, continuous and discrete variables.

並列關鍵字

approximation ； discrete design variables ； response surface approximation ； fuzzy allowable parameters

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