, Volume 46, Issue 5, pp 1559–1589 | Cite as

Implications of link-based equity objectives on transportation network design problem

  • Xiang ZhangEmail author
  • S. Travis Waller


The objective of this study is to propose a novel definition of equity from the perspective of link performance with energy consumption and incorporate equity into the transportation network design problem (NDP). First, we introduce an aggregated equity measure and present the theoretical framework for the equity considering link travel time and energy consumption along with free flow traffic conditions. We demonstrate that a Braess paradox situation exists with regards to the proposed equity measure. Second, we formulate a bi-level modelling framework for the Link-based Equitable NDP (\(LE\)-NDP). The model is a multiobjective optimization program, where the upper level aims to minimize the total system travel time and optimize equity levels with respect to both travel time and energy consumption. The lower level then represents the flow response under user equilibrium conditions. To quantify the performance loss incurred relative to the equity criterion, we formulate the function of the price of fairness within the \(LE\)-NDP. Third, to solve the \(LE\)-NDP model, we develop a tailored heuristic solution method, which simulates the interaction between planners and travellers. The solution approach uses an \(\varepsilon\)-constraint method to identify Pareto-efficient solutions, and constraint optimization formulations are presented to solve the resulting single-objective program. Finally, the efficacy of the model and the solution algorithm is validated via case studies on three traffic networks. The results demonstrate that the proposed modelling device is capable of achieving more balanced solutions when the equity metrics are accounted for, and the developed solution method is efficient as a reference method in practice. The results also show the trade-offs between travel time and link-based equity, and indicate that equity metrics in terms of different travel costs, i.e. travel time and energy consumption, are shown to be conflicting design objectives for certain scenarios.


Link-based equity Network design problem Multiobjective optimization Energy consumption User equilibrium 



This study is supported by grant funding from the Australian Research Council (ARC) Linkage Projects.

Author’s contribution

(i) This study presents an approach for the multi-objective network design problem (NDP) considering link-based equity, which is an addition to literature and a modelling device ready for use by practitioners. (ii) The link-based equity metrics are defined in terms of both travel time and energy consumption along with free flow traffic conditions. Braess’ Paradox situation for the proposed equity is investigated. (iii) The multi-objective bi-level formulation of the equitable NDP is developed, where the price of fairness is estimated. (iv) The impacts of equity-oriented design options are evaluated in the NDP decision-making process. (v) A tailored heuristic algorithm is proposed and its performance is demonstrated via case analysis. This study provides insights into the proposed design projects, including the influencing factors of system-level travel cost, pursued equity level, the price of fairness, construction budget and road expansion strategy.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Centre for Integrated Transport Innovation, School of Civil and Environmental EngineeringUniversity of New South WalesSydneyAustralia

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