幾何規劃的神經網路解法

A Neural Solution to Generalized Geometric Programming Problems

黃裕明(Yu-Ming Huang)

指導教授 ： 鍾 雲 恭

元智大學/工程學院/工業工程與管理學系/碩士(2000年)

摘要

本論文的主要目地在於探討如何利用神經網路(Neural Networks)解答幾何規劃(Geometric Programming(GP))問題。幾何規劃若依多項式的係數之正負號，可區分為正多項式(Posynomial)和正負多項式(Signomial)幾何規劃問題兩種。本文所採用的手法乃是利用神經網路的動態方程式，再根據Lagrange乘數法，將幾何規劃之限制式引入目標函數，使之變成無限制式問題，接著針對此無限制式問題定義其能量函數，並證明此函數為Lyapunov函數，這就說明了能量函數會隨著時間的遞增，而趨近一個穩定狀態。最後，只要利用能量函數和神經網路的動態方程式，即可得到一組差分方程組，再對差分方程組求解，就可得到幾何規劃問題內每個變數的最佳解。

關鍵字

幾何規劃 ； 神經網路 ； Lyapunov函數

並列摘要

The solution procedure to solve geometric programming (GP) problems in nonlinear programming using the neural network technique has been developed and investigated in this thesis. The both posynomial and signomial programs of GP were formulated with Lagrange multipliers to form neural energy functions without original GP-type constraints. The neural GP energy function has been proved to be a Lyapunov function, and its differential dynamic equations been derived as well. Also a lot of numerical GP examples were tested for the quality of the proposed neural GP solutions. Their optimal solutions were computed with those in published papers. The results of the comparison showed that neural GP solutions, in most cases, are the same as the standard GP solutions, and some examples converge to the better points. Further research directions are addressed.

並列關鍵字

geometric programming ； neural network ； Lyapunov function

參考文獻

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