Creating Advanced Bases For Large Scale Linear Programs Exploiting Embedded Network Structure

Authors:
Nalâv Gülpinar;Gautam Mitra;István Maros
Affiliations:
Department of Computing, Imperial College of Science, Technology and Medicine, University of London, 180 Queen's Gate, London SW7 2BZ, UK;Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex, London UB8 3PH, UK;Department of Computing, Imperial College of Science, Technology and Medicine, University of London, 180 Queen's Gate, London SW7 2BZ, UK
Venue:
Computational Optimization and Applications
Year:
2002

Citing 15
Cited 0

A multiplier adjustment method for the generalized assignment problem

Management Science
Finding embedded network rows in linear programs. I. Extraction heuristics

Management Science
A surrogate and Lagrangian approach to constrained network problems

Annals of Operations Research
New crash procedures for large systems of linear constraints

Mathematical Programming: Series A and B
Parametric programming and Lagrangian relaxation: the case of the network problem with a single side-constraint

Computers and Operations Research
Network flows: theory, algorithms, and applications

Network flows: theory, algorithms, and applications
A parametric programming methodology to solve the Lagrangian dual for network problems with multiple side-constraints

Computers and Operations Research
Lagrangian relaxation

Modern heuristic techniques for combinatorial problems
Dynamic factorization in large-scale optimization

Mathematical Programming: Series A and B
Simplex algorithms

Advances in linear and integer programming
A hybrid algorithm for solving network flow problems with side constraints

Computers and Operations Research
Detecting Embedded Networks in LP Using GUB Structures and IndependentSet Algorithms

Computational Optimization and Applications
Advances in Solving the Multicommodity-Flow Problem

Interfaces
Strategies for Creating Advanced Bases for Large-Scale Linear Programming Problems

INFORMS Journal on Computing
A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem

Management Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we investigate how an embedded pure network structure arising in many linear programming (LP) problems can be exploited to create improved sparse simplex solution algorithms. The original coefficient matrix is partitioned into network and non-network parts. For this partitioning, a decomposition technique can be applied. The embedded network flow problem can be solved to optimality using a fast network flow algorithm. We investigate two alternative decompositions namely, Lagrangean and Benders. In the Lagrangean approach, the optimal solution of a network flow problem and in Benders the combined solution of the master and the subproblem are used to compute good (near optimal and near feasible) solutions for a given LP problem. In both cases, we terminate the decomposition algorithms after a preset number of passes and active variables identified by this procedure are then used to create an advanced basis for the original LP problem. We present comparisons with unit basis and a well established crash procedure. We find that the computational results of applying these techniques to a selection of Netlib models are promising enough to encourage further research in this area.