公車路線設計與時刻表訂定之最佳化架構

Abstract

本研究建立混合整數線性規劃模式的大眾運輸路線設計以及時刻表訂定最佳化架構，該架構具有高度規劃彈性以及相容性，可用於「公車路網設計最佳化」、「公車時刻表訂定最佳化」、與「公車路網設計以及時刻表訂定最佳化」等三大類問題並考慮大多數文獻中相關研究所考慮的目標式與限制式。本研究整理相關文獻，發現本研究所提出之最佳化架構相容於公車路網設計相關文獻中所有的線性限制式與目標式以及大多數的非線性限制式與目標式，本研究進一步發現文獻中的線性目標式可被歸類為六大類。接著，文獻回顧也發現時刻表訂定之相關研究所採用的目標式可分為以乘客為基礎以及以公車班次為基礎，本研究認為大眾運輸設計之精神在於服務乘客，因此採用前者建構模式，經過回顧與比較，本研究之最佳化架構可幾乎完全相容於相關研究中以乘客為基礎之目標式與限制式，本研究也發現以乘客為基礎之目標式可歸類為兩大類。最後在案例測試中分析比較不同公車路網最佳化目標式與不同時刻表訂定最佳化目標式下的規劃方案，其結果顯示本最佳化架構可有效考量不同的營運者或使用者成本以及營運限制式，再者，由於本架構同時包含路網設計與時刻表訂定，經常可產生優於單獨路網設計模式或時刻表訂定模式更好的結果，因此，本研究所提出最佳化架構可提供決策者於不同目標與限制下規劃大眾運輸路網的參考依據，以建立更有效率之大眾運輸系統。

In this study, we propose a mixed integer linear programming (MILP) model as an optimization framework for transit network design and timetabling. The framework has high flexibility and compatibility because it can be used to solve three major categories of transit network problems, bus network design problems, bus timetabling problems, and bus network and timetabling problems, considering most of the constraints and objectives adopted in the related studies. For bus network design problems, the optimization framework is compatible with all the linear and a great majority of nonlinear constraints and objective functions appeared in the past studies. Moreover, we found that the linear objective functions of bus network design problems in the literature can be classified into six major types. For bus timetabling problems, there are two major types of objectives and constraints in the related studies: passenger-based and bus-based. Since the major purpose of transit systems is to serve passengers, the former is chosen in the framework. As a result, the framework is almost fully compatable with the passenger-based objectives and constraints. It is also found that the passenger-based objectives in the literature can be categorized into two major types. In the case study, all categories of objective functions above are tested using the same numerical example. The results show that various types of operator or user costs and constraints in bus network design and timetabling are effectively considered. Furthermore, because the optimization framework integrates network design and timetabling, it often provides better overall results than the individual network design models and timetabling models. Therefore, the proposed framework is a useful tool for decision-makers under different objectives and constraints and has potential for improving the efficiency of urban transit systems.