災區民眾疏散路網信賴度評估與重建模型之研究

A Study on Network Reliability Evaluation and Restoration Model for Victims Evacuation from Disaster Area

一般而言，天然災害的發生往往伴隨著運輸網路系統的大規模破壞，因此，對於災區運輸路網受破壞程度的評估與重建工作的進行，將影響災區民眾疏散的整體效率。在災區民眾疏散的工作上，首先必須考慮災後受破壞路網的容量是否能滿足災區民眾疏散的需求，是以災區路網的信賴度評估便是一項重要的工作；因應大規模天然災害所衍生災民疏散的問題，如何應用有限的修復資源，恢復災區路網的必要機能，將會影響災民的疏散效率。本研究將以兩階段進行討論，首先以最大流量問題對於災後路網進行信賴度評估，求出災後路網道路容量退化後災民可疏散的最大流量；第二階段，則是基於災後路網信賴度的基礎上，探討如何重建出最具民眾疏散信賴度與效率的災後路網。本研究屬網路設計問題之範疇，擬建立雙層規劃模型，上層為系統最佳化，以追求民眾疏散的系統總運輸成本最小為目標；下層問題則考量路段容量限制下，每一個災民均能在最短時間內由疏散起點至迄點的路徑選擇及區位選擇限制條件，分析災區路網受損後空間條件與地區吸引改變以及道路容量限制等因素的影響下，依災民在疏散過程中期待最短時間內脫離災區的疏散路徑及迄點規劃狀況，決定關鍵路段的修復及資源分配，滿足災區民眾疏散的運輸需求，建立具信賴度的緊急疏散路網。綜上所述，本研究旨在建立一套災後路網信賴度評估方法，以了解路網是否滿足災後疏散的運輸需求，並針對路段容量退化的關鍵路段進行修復，進而提供災害應變單位有效的決策支援。由於本研究問題解集合空間屬非凸性，在此將以敏感度分析方法配合廣義反矩陣及路徑型式之拉氏梯度投影法進行求解，並以台灣北部高、速公路所形成的測試路網進行範例說明，最後提出結論與未來可行之研究方向。

Natural disasters often lead to large-scale transportation network destruction. Besides an evaluation of the damages, an urgent issue would be how to restore the transportation network's basic capability in a timely manner after the occurrence of a natural disaster. This research aims to establish a network reliability evaluation process for solving the problem of whether the disaster area network capacity can satisfy the basic demands of evacuation, further for pointing out critical links where capacity may be degenerated by natural disaster. We can use the network reliability evaluation process to allocate resources on those critical links for restoring the emergency evacuation network. This research is discussed in two stages. First, Maximal Flow Problem is applied to evaluate the reliability of disastrous network for computing the maximal supply of the network. Second, an intention is given to restore the network for achieving the most efficient evacuation based on the reliability evaluation. This research belongs to the network design field and the subject can be formulated as a bi-level programming model. The upper level of the model is to minimize the system’s total travel cost under limited network restoration resources. The lower level is to analyze the destroyed network and allocate resources to those critical links for restoring the emergency evacuation network under link capacity constraints by considering victim evacuation route choice and O/D choice behaviors. After solving the problem, the variational inequality sensitivity analysis method, generalized inverse approach, and gradient projection method are adopted to provide the solution algorithms for the bi-level programming model. The numerical test results indicate that the Stackelberg equilibrium solution of the formulated bi-level programming model does exist. More significantly, the network reliability evaluation, optimal network restoration planning, disaster victim emergency evacuation route planning can be achieved.