A general MPCC model and its solution algorithm for continuous network design problem

Ban, Jeff; Liu, Henry; Ferris, Michael C.; Ran, Bin

doi:10.1016/j.mcm.2005.11.001

Cited by 58 publications

(46 citation statements)

References 19 publications

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“…The network has been extensively tested in the CNDP literatures such as Ref. [6,8,12,13,14,20,21]. As shown in Figure 1, the 16-link network consists of two OD pairs, six nodes and links.…”

Section: The 16-link Network Examplementioning

confidence: 99%

“…For the success of NLP solvers, Leyffer [40] relaxed equivalent condition to replace the usual complementarity condition. Through modelling CNDP as MPCC, Ban et al [14] relaxed the strict complementarity condition by a relaxation parameter. The relaxed NLP was solved by the existing NLP solvers when this parameter was progressively reduced.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the relaxation scheme proposed in Ref. [14] can guarantee to solve the original MPCC successfully under certain conditions [41,42]. In addition, Fletcher and Leyffer [43] considered solving MPCC as NLP using standard NLP solvers.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

2017

PROMET

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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

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“…The network has been extensively tested in the CNDP literatures such as Ref. [6,8,12,13,14,20,21]. As shown in Figure 1, the 16-link network consists of two OD pairs, six nodes and links.…”

Section: The 16-link Network Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Wang

2017

PROMET

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“…A large number of static network design studies focus on the economic dimension of sustainability (e.g., Ban et al 2006;Kim et al 2008;Lo and Szeto 2009). Zhou et al (2008), Yin and Lu (1999) and Huang et al (2010) solely considered environmental sustainability and used total traffic emissions as an indicator.…”

Section: Introductionmentioning

confidence: 99%

Analysis of interaction among land use, transportation network and air pollution using stochastic nonlinear programming

Shahraki

Türkay

2014

Int. J. Environ. Sci. Technol.

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This paper presents two novel models for land use and transportation to address the development of different functional zones in urban areas by considering the design of an efficient transportation network and reducing air pollution. Objective functions of the first model are maximizing utility function and maximizing reliability index. The utility is formulated as a function of travel cost and zonal attractiveness. Reliability index is defined as the probability that flow in each link of the network is less than the design capacity. Maximizing this probability is equivalent to minimizing congestion in the network. In addition, maximizing utility and minimizing carbon monoxide emission in the network are considered as objective functions in the second model. The formulated models are nonlinear and stochastic. We implement the e-constraint method for solving these bi-objective optimization problems. We analyze the models and solution characteristics of some examples. In addition, we evaluate the relation between computing time and complexity of the model. In this study, for the first time in the open literature, stochastic bi-objective optimization models are formulated to analyze interaction among land use, transportation network and air pollution. We also extract and summarize some useful insights on the relationship among land use, transportation network and environmental impact associated with them.

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“…Chiou exploited a gradient-based descent method to solve the CNDP with corresponding DUE flows following Wardrop's first principle (19). Ban et al proposed a general framework to describe the CNDP as a mathematical program with complementarity constraints, which was converted to a single-level problem and solved by a relaxation scheme (20). Josefsson and Patriksson made a sensitivity analysis of separable traffic equilibrium models and used a gradient projection algorithm to solve the CNDP with the DUE principle (21).…”

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confidence: 99%

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Wang²

2016

Transportation Research Record: Journal of the Transportation R

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To satisfy growing travel demand and reduce traffic congestion, the continuous network design problem (CNDP) is often proposed to optimize road network performance by the expansion of road capacity. In the determination of the equilibrium travel flow pattern, equilibrium principles such as deterministic user equilibrium (DUE) and stochastic user equilibrium (SUE) may be applied to describe travelers’ route choice behavior. Because of the different mathematical formulation structures for the CNDP with DUE and SUE principles, most of the existing solution algorithms have been developed to solve the CNDP for either DUE or SUE. In this study, a more general solution method is proposed by applying the generalized geometric programming (GGP) approach to obtain the global optimal solution of the CNDP with both DUE and SUE principles. Specifically, the original CNDP problem is reformulated into a GGP form, and then a successive monomial approximation method is employed to transform the GGP formulation into a standard geometric programming form, which can be cast into an equivalent nonlinear but convex optimization problem whose global optimal solution can be guaranteed and solved by many existing solution algorithms. Numerical experiments are presented to demonstrate the validity and efficiency of the solution method.

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A general MPCC model and its solution algorithm for continuous network design problem

Cited by 58 publications

References 19 publications

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

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

Analysis of interaction among land use, transportation network and air pollution using stochastic nonlinear programming

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

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