類神經網路序列近似法於工程設計最佳化之應用

A Sequential Approximation Method Using Neural Network For Engineering Design Optimization

王樹根(Shu-Gen Wang)

指導教授 ： 徐 業 良

元智大學/工程學院/機械工程學系/博士(2004年)

摘要

工程最佳化問題有三個特性：(1)設計變數常為離散式變數，(2)限制條件常為不能以設計變數解析形式表示之內隱式設計變數，(3)在許多工程應用上，限制條件常包括「通過－不通過」的二元限制條件。本研究提出一「類神經網路序列近似法」，應用在此類工程最佳化設計問題中。
在此方法中，離散式變數初始以直交表具有代表性之少數資料訓練類神經網路，模擬真實複雜具有隱性限制條件問題的近似可行區間。接著搜尋演算法於類神經網路模擬的可行區域中尋找出一最佳設計點。利用此一最佳設計點代入原始最佳化設計模型進行可行性的檢驗後，將此新增設計點加入訓練資料中重新訓練，重新產生一更接近原始最佳化設計模型的近似可行區域，然後在這個更新的近似的可行區域中再次尋找最佳設計點。利用這個過程以迭代模式反覆執行，直到連續得到同一最佳設計點，近似可行區域無法再被更新為止。
本研究中同時提出restart和zooming兩項策略，以確保類神經網路序列近似法有更佳機會搜尋到全域最佳解，並能過致離散變數之解析度。論文中以多個研究文獻中常用的例子，來說明類神經網路序列近似法之程序，並驗證所得到解之品質。本論文並將此法應用在多個工程最佳化設計實例上，以展示本研究所發展出的適用性。

關鍵字

類神經網路 ； 序列近似法最佳化 ； 非線性離散變數最佳化 ； 內隱式限制條件

並列摘要

There are three characteristics in engineering design optimization problems: (1) the design variables are often discrete physical quantities; (2) the constraint functions often cannot be expressed analytically in terms of design variables; (3) in many engineering design applications, critical constraints are often “pass-fail”, “0-1” type binary constraints. This paper presents a sequential neural network approximation method (SNA method) specifically for engineering optimization problems with the three characteristics.
In this method a back-propagation neural network is trained to simulate a rough map of the feasible domain formed by the constraints using a few representative training data. A training data consists of a discrete design point and whether this design point is feasible or infeasible. Function values of the constraints are not required. A search algorithm then searches for the “optimal point” in the feasible domain simulated by the neural network. This new design point is checked against the true constraints to see whether it is feasible, and is then added to the training set. The neural network is trained again with this added information, in the hope that the network will better simulate the boundary of the feasible domain of the true optimization problem. Then we search for the “optimal point” in this new approximated feasible domain again.
This process continues in an iterative manner until the approximate model insists the same “optimal point” in consecutive iterations. A restart strategy is also employed so that the method may have a better chance to reach a global optimum. A zooming strategy is employed so that that SNA method could have a better resolution to meet the requirement on discrete optimal solution. Design examples commonly seen in literatures are solved to verify the quality of the results by SNA method. Several real engineering design examples are also solved to demonstrate the practicality of SNA method.

並列關鍵字

Neural network ； sequential approximation method ； nonlinear discrete-variable optimization ； implicit constraint

參考文獻

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