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

TL;DR

This paper introduces a double pivot degenerate-robust simplex algorithm for linear programming, implemented in MATLAB, demonstrating improved efficiency on large random problems but less so on benchmark problems.

Contribution

The paper proposes a novel double pivot algorithm that enhances degenerate tolerance and compares its performance with Dantzig's algorithm across various test sets.

Findings

More efficient than Dantzig's algorithm on large random LP problems.

Degenerate-tolerance feature confirmed in tests.

Less efficient on Netlib benchmark problems and small random problems.

Abstract

A double pivot algorithm that combines features of two recently published papers by these authors is proposed. The proposed algorithm is implemented in MATLAB. The MATLAB code is tested, along with a MATLAB implementation of Dantzig's algorithm, for several test sets, including a set of cycling LP problems, Klee-Minty's problems, randomly generated linear programming (LP) problems, and Netlib benchmark problems. The test result shows that the proposed algorithm is (a) degenerate-tolerance as we expected, and (b) more efficient than Dantzig's algorithm for large size randomly generated LP problems but less efficient for Netlib benchmark problems and small size randomly generated problems in terms of CPU time.