A partitioning algorithm for the network loading problem

This paper proposes a Benders-like partitioning algorithm to solve the network loading 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 … Read more

An efficient method to compute traffic assignment problems with elastic demands

The traffic assignment problem with elastic demands can be formulated as an optimization problem, whose objective is 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 instances with different congestion functions (linear with … Read more

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 … Read more

Proximal-ACCPM: a versatile oracle based optimization method

Oracle Based Optimization (OBO) conveniently designates an approach to handle a class of convex optimization 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. We show, through three representative examples, how difficult problems can be … Read more

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 … Read more