Title: A perturbation-based approach for continuous network design problem with link capacity expansion
Authors: Robert Ebihart Msigwa; Yue Lu; Li-Wei Zhang
Addresses: Department of Mathematics, Humanities and Social Sciences, National Institute of Transport, Dar es Salaam, Tanzania ' Department of Mathematics, Tianjin Normal University, Tianjin, China ' Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China
Abstract: This paper formulates a continuous network design problem (CNDP) as a nonlinear mathematical program with complementarity constraints (NLMPCC) and then a perturbation-based approach is proposed to overcome the NLMPCC problem and the lack of constraint qualifications. This formulation permits a more general route cost structure and every stationary point of it corresponds to a global optimal solution of the perturbed problem. The contribution of this paper from the mathematical perspective is that, instead of using the conventional nonlinear programming methodology, variational analysis is taken as a tool to analyse the convergence of the perturbation-based method. From the practical point of view, a convergent algorithm is proposed for the CNDP and employs the sequential quadratic program (SQP) solver to obtain the solution of the perturbed problem. Numerical experiments are carried out in both 16 and 76-link road networks to illustrate the capability of the perturbation-based approach to the CNDP with elastic demand. Results showed that the proposed model will solve a wider class of transportation equilibrium problems than the existing ones.
Keywords: continuous network design problem; CNDP; bilevel programming; nonlinear mathematical program with complementarity constraints; MPCC; variational analysis; perturbation-based approach.
International Journal of Operational Research, 2020 Vol.37 No.1, pp.105 - 134
Received: 12 Aug 2016
Accepted: 09 Feb 2017
Published online: 18 Dec 2019 *