Frédéric Babonneau

Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM

In this paper, we propose to solve the linear multicommodity flow problem using a partial Lagrangian relaxation. The relaxation is restricted to the set of arcs that are likely to be saturated at the optimum. This set is itself approximated by an active set strategy. The partial Lagrangian dual is solved with Proximal-ACCPM, a variant of the analytic center cutting-plane method. The new approach makes it possible to solve huge problems when few arcs are saturated at the optimum, as appears to be the case in many practical problems.

Proximal-ACCPM: A Versatile Oracle Based Optimisation Method

Oracle Based Optimisation (OBO) conveniently designates an approach to handle a class of convex optimisation problems in which the information pertaining to the function to be minimized and/or to the feasible set takes the form of a linear outer approximation revealed by an oracle. Three representative examples are introduced to show how one can cast difficult problems in this format, and solve them. An efficient method, Proximal-ACCPM, is presented to trigger the OBO approach. Numerical results for these examples are provided to illustrate the behavior of the method. This paper summarizes several contributions with the OBO approach and aims to give, in a single report, enough information on the method and its implementation to facilitate new applications

ACCPM with a nonlinear constraint and an active set strategy to solve nonlinear multicommodity flow problems

This paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity flow problems. The new approach exploits the property that the objective of the Lagrangian dual problem has a smooth component with second order derivatives readily available in closed form. The cutting planes issued from the nonsmooth component and the epigraph set of the smooth component form a localization set that is endowed with a self-concordant augmented barrier. Our implementation uses an approximate analytic center associated with that barrier to query the oracle of the nonsmooth component. The paper also proposes an approximation scheme for the original objective. An active set strategy can be applied to the transformed problem: it reduces the dimension of the dual space and accelerates computations. The new approach solves huge instances with high accuracy. The method is compared to alternative approaches proposed in the literature.

An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands

The traffic assignment problem (TAP) with elastic demands can be formulated as an optimization problem, the objective of which is the sum of a congestion function and a disutility function. We propose to use a variant of the analytic center cutting plane method to solve this problem. We test the method on TAP instances with the Bureau of Public Roads congestion function and different demand functions (constant elasticity and linear). The results of the numerical experiments show that it is possible to solve large instances with high accuracy.

A partitioning algorithm for the network loading problem

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities. Rather, it selects an integer solution that is closest to the best known integer solution. Contrary to previous approaches, the method does not exploit the original mixed integer programming formulation of the problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds.

ACCPM with a nonlinear constraint and an active set strategy to solve nonlinear multicommodity flow problems: a corrigendum

This paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity flow problems. The new approach exploits the property that the objective of the Lagrangian dual problem has a smooth component with second order derivatives readily available in closed form. The cutting planes issued from the nonsmooth component and the epigraph set of the smooth component form a localization set that is endowed with a self-concordant augmented barrier. Our implementation uses an approximate analytic center associated with that barrier to query the oracle of the nonsmooth component. The paper also proposes an approximation scheme for the original objective. An active set strategy can be applied to the transfomed problem: it reduces the dimension of the dual space and accelerates computations. The new approach solves huge instances with high accuracy. The method is compared to alternative approaches proposed in the literature.

Meta-Modeling to Assess the Possible Future of Paris Agreement

In the meta-modeling approach, one builds a numerically tractable dynamic optimization or game model in which the parameters are identified through statistical emulation of a detailed large scale numerical simulation model. In this paper, we show how this approach can be used to assess the economic impacts of possible climate policies compatible with the Paris Agreement. One indicates why it is appropriate to assume that an international carbon market, with emission rights given to different groups of countries will exist. One discusses the approach to evaluate correctly abatement costs and welfare losses incurred by different groups of countries when implementing climate policies. Finally, using a recently proposed meta-model of game with a coupled constraint on a cumulative CO2 emissions budget, we assess several new scenarios for possible fair burden sharing in climate policies compatible with the Paris Agreement.

Energy technology environment model with smart grid and robust nodal electricity prices

This paper deals with the modeling of power flow in a transmission grid within the multi-sectoral multi-energy long-term regional energy model ETEM-SG. This extension of the model allows a better representation of demand response for flexible loads triggered by nodal marginal cost pricing. To keep the global model in the realm of linear programming one uses a linearized DC power flow model that represents the transmission grid with the main constraints on the power flowing through the different arcs of the electricity transmission network. Robust optimization is used to take into account the uncertainty on the capacity limits resulting from inter-regional transit. A numerical illustration is carried out for a data set corresponding roughly to the Leman Arc region.

Test Instances for the Multicommodity Flow Problem: An Erratum

This note is an erratum to Babonneau et al. (2006) in which some data were incorrectly described. In Babonneau et al. (2006), the ACCPM method is used to solve the linear multicommodity flow problem on four sets of instances, i.e., the planar and the grid instances, some telecommunication problems, and some transportation problems, from Bar-Gera (2007), http://www.bgu.ac.il/~bargera/tntp/ (Sioux Falls, Winnipeg, Barcelona, Chicago region, and Philadelphia). The mistakes concern the last category of instances. The new data and the associated results can now be found in the electronic companion at http://or.journal.informs.org/. This site also provides the full information on test instances in the multicommodity flow problem (MCF) and the traffic assignment problem to facilitate benchmarking. It gives the data and the results using three specific objective functions used in the literature, e.g., Bureau of Public Roads (BPR), Kleinrock, or linear. For more details on the optimization problem, we refer the reader to Babonneau et al. (2006) and Babonneau and Vial (2007).