A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks

Research Report UPC-DEIO DR 2018-01. November 2018The computation of the Newton direction is the most time consuming step of interior-point methods. This direction was efficiently computed by a combination of Cholesky factorizations and conjugate gradients in a specialized interior-point method for block-angular structured problems. In this work we apply this algorithmic approach to solve very large instances of minimum cost flows problems in bipartite networks, for convex objective functions with diagonal Hessians (i.e., either linear, quadratic or separable nonlinear objectives). After analyzing the theoretical properties of the interior-point method for this kind of problems, we provide extensive computational experiments with linear and quadratic instances of up to one billion arcs and 200 and five million nodes in each subset of the node partition. For linear and quadratic instances our approach is compared with the barriers algorithms of CPLEX (both standard path-following and homogeneous-self-dual); for linear instances it is also compared with the different algorithms of the state-of-the-art network flow solver LEMON (namely: network simplex, capacity scaling, cost scaling and cycle canceling). The specialized interior-point approach significantly outperformed the other approaches in most of the linear and quadratic transportation instances tested. In particular, it always provided a solution within the time limit and it never exhausted the 192 Gigabytes of memory of the server used for the runs. For assignment problems the network algorithms in LEMON were the most efficient option.Peer ReviewedPreprin

A Faster Primal Network Simplex Algorithm

We present a faster implementation of the polynomial time primal simplex algorithm due to Orlin [23]. His algorithm requires O(nm min{log(nC), m log n}) pivots and O(n2 m ??n{log nC, m log n}) time. The bottleneck operations in his algorithm are performing the relabeling operations on nodes, selecting entering arcs for pivots, and performing the pivots. We show how to speed up these operations so as to yield an algorithm whose running time is O(nm. log n) per scaling phase. We show how to extend the dynamic-tree data-structure in order to implement these algorithms. The extension may possibly have other applications as well

A polynomial time primal network simplex algorithm for minimum cost flows

Cover title.Includes bibliographical references (p. 25-27).Supported by ONR. N00014-94-1-0099 Supported in part by a grant from the UPS foundation.by James B. Orlin

Short-term generation scheduling in a hydrothermal power system.

SIGLEAvailable from British Library Document Supply Centre- DSC:D173872 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A faster strongly polynomial minimum cost flow algorithm

Includes bibliographical references.Supported in part by the Presidential Young Investigator Grant of the National Science Foundation. 8451517-ECS Supported in part by the Air Force Office of Scientific Research. AFOSR-88-0088 Supported in part by grants from Analog Devices, Apple Computers, Inc. and Prime Computer.James B. Orlin

The auction algorithm : a distributed relaxation method for the assignment problem

Bibliography: p. 15-19.Work supported by grant NSF-ECS-8217668by Dimitri P. Bertsekas