臺灣博碩士論文加值系統

本研究目的在於如何以類神經網路(artificial neural networks, ANNs)動態系統求解模糊多階層規劃問題(fuzzy multi-level programming problems, fuzzy MLPPs)。首先，討論類神經網路的概念與特性，並藉由Lagrangian乘數法(Lagrangian multiplier)與懲罰法函數法(penalty function)將最佳化問題(optimization problems)轉換成一個適切的能量函數(energy function)，並探究此類神經網路技術應用於最佳化問題的可行性。其次，探討如何以類神經網路解決明確(crisp)與具有模糊特質的多目標線性規劃問題，並期望整合於多階層規劃問題的模糊趨近法中，然後擴充至模糊多階層規劃問題上，再將所發展之演算法應用於路網設計(networks design)問題上。
在解決最佳化問題方面，自Hopefield and Tank (1985)提出類神經網路演算法後，此技術一直被視為一具有潛力之計算工具。其解法為利用能量函數將最佳化問題轉換為一非線性微分方程系統(a system of non-linear differential equations)，當此動態系統達到穩定狀態(steady state)時，能量函數將達到極小值，此即為其最佳解；雖然，現代數值方法已有效解決大型和複雜的最佳化問題。然而，類神經網路平行分散式(parallel-distributed)計算結構和非線性動力系統的演算機制，可以更快速且及時獲得解答，並藉由類神經網路計算的雛形(prototype)，實現於超大規模積體電路(very large scale integrated, VLSI)上，以求解及時多階層規劃問題。

This study aims to utilize the dynamic system of artificial neural networks (ANNs) to solve fuzzy multi-level programming problems (MLPPs). In this analysis, basic concepts of ANNs are discussed and an optimization problem is converted into an adequate energy function through Lagrangian multiplier and penalty function. Then, the proposed ANNs procedure is proven to be feasible for optimization. The procedure is extended to solve the multi-objective linear programming problem (MOLP) with crisp and fuzzy coefficients. After that, the procedure is adopted to deal with MLPPs with a top-down process. The issues relevant to both coefficients are also discussed. Furthermore, the procedure is verified through a network design example.
The algorithm of ANNs has been viewed as a computational technique since Hopefield and Tanks’ work (1985). It enables the transfer of the optimization problem into a system of non-linear differential equations based on an energy function. When the dynamic system reaches a steady state, the optimal solution can be obtained. The non-tradition algorithm is efficient for solving complex problems, and is especially useful for implementation on a very-large-scale-integrated (VLSI), in which the MLPPs can be solved on a real time basis.

中文摘要
英文摘要
誌謝
目錄 I
圖目錄 III
表目錄 IV
1. 緒論
1.1 研究動機與背景 1
1.2 研究目的 3
1.3 研究架構 3
2. 以類神經網路求解最佳化問題
2.1 類神經網路概觀 6
2.1.1 類神經網路架構 7
2.1.2 類神經網路類型 9
2.1.3 應用類神經網路可能遭遇之問題 10
2.2 文獻探討 11
2.2.1 Hopfield and Tank網路 13
2.2.2 Kennedy and Chua網路 14
2.2.3 Rodríguez-Vázquez網路 14
2.2.4 Lee’s連續型類神經網路模式 15
2.3 最佳化問題的求解方法 16
2.3.1 Lagrangian乘數法 16
2.3.2 懲罰函數法 18
2.4 類神經網路最佳化理論與穩定性 19
2.4.1 類神經網路最佳化理論 19
2.4.2 類神經網路的穩定性 20
2.5 類神經網路應用於最佳化問題 22
2.5.1 最陡降法 22
2.5.2 Runge-Kutta法 23
2.5.3 類神經網路架構對於標準形式的線性規劃問題 24
2.5.4 類神經網路架構對於具有不等限制式的線性規劃問題 28
2.5.5 類神經網路架構對於具有不等限制式的二次規劃問題 31
2.6 本章小結 36
3. 以類神經網路求解模糊多目標線性規劃問題
3.1 多目標決策問題 38
3.2 模糊理論 41
3.3 模糊多目標線性規劃 43
3.4 類神經網路方法 45
3.5 本章小結 49
4. 以類神經網路求解多階層規劃問題
4.1 文獻探討 50
4.2 多階層規劃問題之求解方法 51
4.3 混合整數法 53
4.4 可能性規劃 65
4.5 本章小結 70
5. 路網設計問題
5.1 文獻探討 71
5.1.1 均衡路網設計問題 72
5.1.2 均衡路網指派問題 73
5.1.3 連續型均衡路網設計問題之二階層規劃模式 74
5.2 均衡路網設計問題求解方法 75
5.3 簡單路網測試 75
5.4 本章小結 80
6. 結論與建議 83
6.1 結論 83
6.2 建議 84
參考文獻 85

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