A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints

Friesz, Terry L.; Cho, Hsun Jung; Mehta, Nihal J.; Tobin, Roger L.; Anandalingam, G.

doi:10.1287/trsc.26.1.18

Cited by 235 publications

(147 citation statements)

References 16 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%

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

Wang

2017

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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%

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

Wang

2017

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“…SA was used to optimise a chemical process plant layout design problem formulated as a BLPP in [101] and a Network Design Problem formulated as an MPEC [43]. ACO techniques for BLPPs are found in [93].…”

Section: Solution Algorithms For the Blppmentioning

confidence: 99%

“…The continuous network design problem (CNDP) aims to determine the optimal capacity enhancements of existing facilities of a traffic network [43]. Care has to be taken when solving the CNDP because additional capacity can counter productively increase the total network travel time and this is a phenomenon is known as Braess's paradox [17].…”

Section: Continuous Network Design Problemmentioning

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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“…The optimal network design problem has been considered by many researchers (See e.g., Davis, 1994;Friesz et. al., 1992;Harker and Friesz, 1984;Suwansirikul et.…”

Section: The Problem Formulation and Previous Algorithmsmentioning

confidence: 99%

A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

Maher

Zhang

Vliet

2001

Transportation Research Part B: Methodological

116

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Article:Maher, M.J., Zhang, X. and van Vliet, D. (2001) Abstract ⎯ This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks.These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or, the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

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A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints

Cited by 235 publications

References 16 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

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

A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

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