Original scientific paper
https://doi.org/10.7307/ptt.v29i6.2250
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
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.
Keywords
urban transportation network; continuous network design problem (CNDP); mathematical programs with complementarity constraints (MPCC); non-linear complementarity problem (NCP); user equilibrium (UE)
Hrčak ID:
192584
URI
Publication date:
21.12.2017.
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