A new version of the Improved Primal Simplex for degenerate linear programs

Authors:
Vincent Raymond;François Soumis;Dominique Orban
Affiliations:
GERAD and ícole Polytechnique de Montréal, Montréal, Québec, Canada;GERAD and ícole Polytechnique de Montréal, Montréal, Québec, Canada;GERAD and ícole Polytechnique de Montréal, Montréal, Québec, Canada
Venue:
Computers and Operations Research
Year:
2010

Citing 5
Cited 1

On the solution of highly degenerate linear programs

Mathematical Programming: Series A and B
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization

SIAM Journal on Matrix Analysis and Applications
Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems

Transportation Science
Dynamic Aggregation of Set-Partitioning Constraints in Column Generation

Operations Research
Multi-phase dynamic constraint aggregation for set partitioning type problems

Mathematical Programming: Series A and B

An Improved Primal Simplex Algorithm for Degenerate Linear Programs

INFORMS Journal on Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

The Improved Primal Simplex (IPS) algorithm [Elhallaoui I, Metrane A, Desaulniers G, Soumis F. An Improved Primal Simplex algorithm for degenerate linear programs. SIAM Journal of Optimization, submitted for publication] is a dynamic constraint reduction method particularly effective on degenerate linear programs. It is able to achieve a reduction in CPU time of over a factor of three on some problems compared to the commercial implementation of the simplex method CPLEX. We present a number of further improvements and effective parameter choices for IPS. On certain types of degenerate problems, our improvements yield CPU times lower than those of CPLEX by a factor of 12.