在求解號誌時制最佳化的相關研究中，雙層規劃模型已被證實為解決系統管理者與用路人之間互動關係的有效框架。該模型的上層以系統總旅行時間最小化為目標，下層則為用路人在給定號誌下的依時性均衡流量分佈。然而，求解此類雙層模型，需利用敏感度分析來計算梯度以尋找改善方向，但傳統敏感度分析的執行，卻常因均衡路徑流量解不唯一而遭遇理論上的困難，導致必須採用複雜的廣義反矩陣法。 為克服此一挑戰，本研究引入成對替選區段交通量指派演算法 (TAPAS) 作為雙層模型的下層求解演算法。由於TAPAS演算法能提供合理的唯一路徑解資訊，使得理論上更為直接、簡潔的路徑變數基礎的敏感度分析得以被應用，從而有機會簡化傳統的求解流程。因此，本論文嘗試將TAPAS演算法依循理論應用於最佳化問題，並分別根據唯一路徑流量解與路段流量解進行「路徑流量解」與「路段流量解」之兩種敏感度分析方法，並透過雙三角形小路網之數值範例驗證其在唯一解前提下兩者結果之一致性與正確性，最後提出整合TAPAS演算法、路徑基礎之敏感度分析與Frank-Wolfe演算法求解交通號誌時制最佳化雙層規劃問題。本研究證實TAPAS演算法於網路設計問題之應用潛力，文末並臚列具體結論與未來可行的研究建議。 ;In the research field of signal timing optimization, the bi-level programming model has been proven to be an effective framework for describing the interaction between system administrators and road users. The upper level of this model aims to minimize total system travel time, while the lower level simulates the time-dependent user equilibrium flow distribution under a given signal setting. However, solving such bilevel models requires sensitivity analysis to estimate the gradient for finding the improvement direction. The application of traditional sensitivity analysis is often hindered by the non-uniqueness of the equilibrium path flow solution, which necessitates the use of the more complex generalized inverse matrix approach. To overcome this challenge, this study introduces the Traffic Assignment by Paired Alternative Segments (TAPAS) algorithm as the lower-level solution algorithm for the bi-level model. Since the time-dependent TAPAS algorithm can provide a reasonable and unique path flow solution, the theoretically more direct and concise path-based sensitivity analysis can be rigorously applied, thus offering an opportunity to simplify the traditional solution procedure. Therefore, this study attempts to apply the TAPAS algorithm to the optimization problem according to theory. It implements and compares two sensitivity analysis methods based on the unique path flows and the corresponding link flows. The consistency and correctness of both approaches under the unique solution premise are verified through a numerical example on a double-triangle network. Finally, this study proposes an integrated framework that combines the TAPAS algorithm, path-based sensitivity analysis, and the Frank-Wolfe algorithm to solve the bi-level programming problem for traffic signal timing optimization. The results of this study confirm the application potential of the TAPAS algorithm for network design problems, and concludes with specific findings and suggestions for future research.
