Glass, CA and Shakhlevich, NV (2013) Minimising the number of gap-zeros in binary matrices. European Journal of Operational Research, 229 (1). 45 - 58. ISSN 0377-2217
Abstract
We study a problem of minimising the total number of zeros in the gaps between blocks of consecutive ones in the columns of a binary matrix by permuting its rows. The problem is referred to as the Consecutive Ones Matrix Augmentation Problem, and is known to be NP-hard. An analysis of the structure of an optimal solution allows us to focus on a restricted solution space, and to use an implicit representation for searching the space. We develop an exact solution algorithm, which is linear-time in the number of rows if the number of columns is constant, and two constructive heuristics to tackle instances with an arbitrary number of columns. The heuristics use a novel solution representation based upon row sequencing. In our computational study, all heuristic solutions are either optimal or close to an optimum. One of the heuristics is particularly effective, especially for problems with a large number of rows.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | (c) 2013, Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in the European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the European Journal of Operational Research, 229, 1, 2013, 10.1016/j.ejor.2013.01.028. |
Keywords: | Combinatorial optimisation; Binary matrices; Consecutive ones property; Scheduling; Heuristics |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Jun 2014 11:17 |
Last Modified: | 21 Jul 2014 03:33 |
Published Version: | http://dx.doi.org/10.1016/j.ejor.2013.01.028 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ejor.2013.01.028 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79240 |