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**Harvard**

Patriksson, M. (2008) *Robust bilevel optimization models in transportation science*.

** BibTeX **

@article{

Patriksson2008,

author={Patriksson, Michael},

title={Robust bilevel optimization models in transportation science},

journal={Philosophical Transactions of the Royal Society, A},

volume={366},

issue={1872},

pages={1989-2004},

abstract={Mathematical programs with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place 'what-if' analyses in a proper
mathematical framework. We consider a class of stochastic MPEC traffic models which explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider 'here-and-now'
models where decisions must be made before observing the uncertain parameter values and the responses of the network users; the objective is to minimize the expectation of the upper-level objective function. Such a model could, for
example, be used to derive a fixed toll pricing scheme that provides the best revenue for a given network over a time period, where variations in traffic conditions and demand elasticities are described by distributions of
parameters in the travel time and demand functions.
We present new results on the stability of optimal solutions to perturbations in the probability distribution, establishing the robustness of the model. We also provide convergence results for algorithms based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution; the latter enables the utilization of standard MPEC algorithms.},

year={2008},

}

** RefWorks **

RT Journal Article

SR Print

ID 64366

A1 Patriksson, Michael

T1 Robust bilevel optimization models in transportation science

YR 2008

JF Philosophical Transactions of the Royal Society, A

VO 366

IS 1872

SP 1989

OP 2004

AB Mathematical programs with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place 'what-if' analyses in a proper
mathematical framework. We consider a class of stochastic MPEC traffic models which explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider 'here-and-now'
models where decisions must be made before observing the uncertain parameter values and the responses of the network users; the objective is to minimize the expectation of the upper-level objective function. Such a model could, for
example, be used to derive a fixed toll pricing scheme that provides the best revenue for a given network over a time period, where variations in traffic conditions and demand elasticities are described by distributions of
parameters in the travel time and demand functions.
We present new results on the stability of optimal solutions to perturbations in the probability distribution, establishing the robustness of the model. We also provide convergence results for algorithms based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution; the latter enables the utilization of standard MPEC algorithms.

LA eng

OL 30