An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

  • Guangmin Wang China University of Geosciences
  • Junwei Yu China University of Geosciences
  • Shubin Li Shandong Police College
Keywords: urban transportation network, continuous network design problem (CNDP), mathematical programs with complementarity constraints (MPCC), non-linear complementarity problem (NCP), user equilibrium (UE),

Abstract

Continuous network design problem (CNDP) is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE) to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC) by describing UE as a non-linear complementarity problem (NCP). To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fischer-Burmeister (FB) function, which can be smoothed by the introduction of the smoothing parameter. Therefore, the MPCC can be transformed into a well-behaved non-linear program (NLP) by replacing the complementarity constraints with a smooth equation. Consequently, the solver such as LINDOGLOBAL in GAMS can be used to solve the smooth approximate NLP to obtain the solution to MPCC for modelling CNDP. The numerical experiments on the example from the literature demonstrate that the proposed algorithm is feasible.

Author Biographies

Guangmin Wang, China University of Geosciences
Guangmin Wang is a professor in School of Economics and Management at China University of Geosciences. His interesting fields include transportation planning and management, theory and algorithms of optimization.
Junwei Yu, China University of Geosciences
Junwei Yu is a Master Degree Candidate in School of Economics and Management at China University of Geosciences. His interesting fields include transportation planning and management.
Shubin Li, Shandong Police College
Shubin Li is an associate professor in Department of Traffic Management Engineering at Shandong Police College. His interesting fields include transportation planning and management.

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Published
2017-12-21
How to Cite
1.
Wang G, Yu J, Li S. An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem. PROMET [Internet]. 2017Dec.21 [cited 2020Feb.17];29(6):569-80. Available from: http://traffic.fpz.hr/index.php/PROMTT/article/view/2250
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