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Bi-Level Program of Transportation Network Design Problem Accounting for Equity and Exact Solution Methodology

Xiang Zhang, David Rey, and S. Travis Waller
School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia

Abstract—In the field of transportation planning, Network Design Problem (NDP) is a complex and challenging research area which aims to optimize a transportation network in order to maximize traffic and social benefits through capacity expansion and link addition. Recently, ‘equity’ has become highly valued in the decision process of NDP. The objective of this study is to propose novel approaches to integrate equity considerations into the NDP from the perspective of link travel time. First, equity is analysed and described mathematically in terms of travel time spent in traversing every unit-length on a link. The significance of accounting for the equity in the NDP is demonstrated through Braess Network. Then we formulate a bi-level program for NDP, where the upper level aims at optimizing system performance with respect to travel cost and equity, and the lower level is the traffic assignment problem under the user equilibrium condition. An exact solution methodology is developed based on programming techniques including interior point method, and branch and bound algorithm, which can be implemented in the general-purpose optimization software AMPL. The method can seek for the globally optimal solutions to the proposed bi-level equitable NDP model. Finally, the systematic evaluation of the developed model formulation and solution methodology is conducted on the Nguyen-Dupuis Network. The results highlight the importance of incorporating equity into transportation planning and demonstrate that the proposed approaches can generate desirable NDP decisions with respect to improving overall system performance.

Index Terms—equity, network design problem, bi-level program, exact solution methodology

Cite: Xiang Zhang, David Rey, and S. Travis Waller, "Bi-Level Program of Transportation Network Design Problem Accounting for Equity and Exact Solution Methodology," Journal of Traffic and Logistics Engineering, Vol. 3, No. 2, pp. 94-101, December 2015. doi: 10.12720/jtle.3.2.94-101

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