New Symmetry-less ILP Formulation for the Classical One Dimensional Bin-Packing Problem

• Published in: Computing and Combinatorics Vol. 12273; pp. 423 - 434
• Main Authors: Hadj Salem, Khadija, Kieffer, Yann
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2020; Springer International Publishing; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Bin packing; Computer Science; Cutting plane; Integer linear programming; Operations Research; Bin packing; Integer linear programming; Cutting plane
• ISBN: 9783030581497; 3030581497
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-58150-3_34

In this article, we address the classical One-Dimensional Bin Packing Problem (1D-BPP), an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {NP}$$\end{document}-hard combinatorial optimization problem. We propose a new formulation of integer linear programming for the problem, which reduces the search space compared to those described in the literature, as well as two families of cutting planes. Computational experiments are conducted on the data-set found in BPPLib and the results show that it is possible to solve more instances and to decrease the computation time by using our new formulation.