# American Institute of Mathematical Sciences

2015, 5(2): 135-149. doi: 10.3934/naco.2015.5.135

## A perturbation-based approach for continuous network design problem with emissions

 1 Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China, China, China 2 Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received  October 2014 Revised  April 2015 Published  June 2015

The objective of continuous network design problem (CNDP) is to determine the optimal capacity expansion policy under a limited budget. This transportation system is formulated as a bi-level program where the upper level aims to determine the link capacity expansion vector and emission while taking into account the lower level response. This problem can be solved using various optimization algorithms and software. In this study, the CNDP with environmental considerations is designed and solved using the perturbation based approach. The lower level representing the road users subjected to user equilibrium is solved using the Frank-Wolfe algorithm. The proposed model is tested using a small hypothetical network to show the efficacy of the method. As a contribution of this paper, first it suggests a perturbation based approach for planners to design the capacity expansion, which minimize the total system cost and emission. Second the proposed method solves the nonlinear mathematical program with complementarity constraints (NLMPCC) problem, which overcomes the lack of a suitable set of constraint qualifications, such as Mangasarian Fromovitz constraint qualifications (MFCQ). Although the proposed model illustrated using the CO only and small network, the approach is not limited to large-scale network design problems and other pollutants..
Citation: Robert Ebihart Msigwa, Yue Lu, Xiantao Xiao, Liwei Zhang. A perturbation-based approach for continuous network design problem with emissions. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 135-149. doi: 10.3934/naco.2015.5.135
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