An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem

Meng, Qiang; Yang, Hai; Bell, Michael G.H.

doi:10.1016/s0191-2615(00)00016-3

Cited by 213 publications

(120 citation statements)

References 31 publications

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“…More interestingly, DEBLP required less iterations than the deterministic method of [75]. The standard deviation is also very low which suggests that this heuristic is reasonably robust as well.…”

Section: Example 2: Sioux Falls Networkmentioning

confidence: 93%

“…Meng et al transformed the CNDP into a single level continuously differentiable problem using a marginal function and solved the resulting formulation with the Augmented Lagragian method [75]. Chiou investigated several variants of the descent based Karush-Khun-Tucker (KKT) approaches [24].…”

Section: Previous Work On Cndpmentioning

confidence: 99%

“…The network parameters and OD details are found in [75]. Only 10 links out of the 76 are subject to improvements.…”

Section: Example 2: Sioux Falls Networkmentioning

confidence: 99%

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A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader's decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal. We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity.

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Section: Example 2: Sioux Falls Networkmentioning

confidence: 93%

Section: Previous Work On Cndpmentioning

confidence: 99%

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A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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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%

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 CNDP deals with the expansion of the capacity of existing links, whereas the discrete NDP determines the optimal addition of new links, and the mixed NDP handles both of them simultaneously. A large body of literature exists on the NDP; some useful reviews can be found elsewhere (2)(3)(4)(5)(6).…”

mentioning

confidence: 99%

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

Wang²

2016

Transportation Research Record

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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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An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem

Cited by 213 publications

References 31 publications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

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

Solving Continuous Network Design Problem with Generalized Geometric Programming Approach

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