Simplex and Interior Point Specialized Algorithms for Solving Nonoriented Multicommodity Flow Problems

Solving Difficult Multicommodity Problems with a Specialized Interior-Point Algorithm

Due to recent advances in the development of linear programming solvers, some of the formerly considered difficult multicommodity problems can today be solved in few minutes, even faster than with specialized methods. However, for other kind of multicommodity instances, general linear solvers can still be quite inefficient. In this paper we will give an overview of the current state-of-the-art ...

Interior Point Methods for Linear Multicommodity Flow Problems

This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primal-dual interior-point method is designed to solve the problem. In the interior-point method, at each iteration, the corresponding linear problem, expressed as an augmented indefinite system, is solved by using the AINV algorithm c...

Solving Quadratic Multicommodity Problems through an Interior-Point Algorithm

Standard interior-point algorithms usually show a poor performance when applied to multicommodity network flows problems. A recent specialized interior-point algorithm for linear multicommodity network flows overcame this drawback, and was able to efficiently solve large and difficult instances. In this work we perform a computational evaluation of an extension of that specialized algorithm for...

A Specialized Interior-Point Algorithm for Multicommodity Network Flows

Despite the efficiency shown by interior-point methods in large-scale linear programming, they usually perform poorly when applied to multicommodity flow problems. The new specialized interior-point algorithm presented here overcomes this drawback. This specialization uses both a preconditioned conjugate gradient solver and a sparse Cholesky factorization to solve a linear system of equations a...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems