Title: A double-pivot degenerate-robust simplex algorithm for linear programming

Authors: Yaguang Yang; Fabio Vitor

Addresses: US Department of Commerce, Rockville, MD, USA ' Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, USA

Abstract: A double pivot simplex algorithm that combines features of two recently published papers by these authors is proposed. The proposed algorithm is implemented in MATLAB. The MATLAB implementation is tested, along with a MATLAB implemention of Dantzig's algorithm, for several test sets, including a set of cycling linear programming problems, Klee-Minty's problems, randomly generated linear programs, and Netlib benchmark problems. The test results show that the proposed algorithm, with a careful implementation is: 1) degenerate-robust as expected; 2) more efficient than Dantzig's algorithm for large size randomly generated linear programming problems, but less efficient for Netlib benchmark problems and small size randomly generated problems in terms of CPU time.

Keywords: double pivots; degenerate-robust; simplex method; linear programming; Klee-Minty cube.

DOI: 10.1504/IJOR.2025.144321

International Journal of Operational Research, 2025 Vol.52 No.2, pp.192 - 210

Received: 12 Jan 2022
Accepted: 28 Jun 2022
Published online: 07 Feb 2025 *

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