| Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
|---|---|---|
| Page(s) | 3171 - 3188 | |
| DOI | https://doi.org/10.1051/ro/2024121 | |
| Published online | 08 August 2024 | |
Partial reformulation-linearization based optimization models for the Golomb ruler problem
Sorbonne Université, CNRS, 4 Place Jussieu, Paris 75252, France
* Corresponding author: hacene.ouzia@sorbonne-universite.fr
Received:
26
February
2024
Accepted:
31
May
2024
In this paper, we provide a straightforward proof of a conjecture proposed in [P. Duxbury, C. Lavor and L.L. de Salles-Neto, RAIRO:RO 55 (2021) 2241–2246.] regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in [B. Kocuk and W.-J. van Hoeve, A Computational Comparison of Optimization Methods for the Golomb Ruler Problem. (2019) 409–425.], utilizing the reformulation-linearization technique. Finally, we provide the correct outputs of the greedy heuristic proposed in [P. Duxbury, C. Lavor and L.L. de Salles-Neto, RAIRO:RO 55 (2021) 2241–2246.] and correct false conclusions stated or implied therein.
Mathematics Subject Classification: 90C10 / 90C11 / 90C20 / 90C26 / 90C27 / 90C30
Key words: Golomb ruler problem / reformulation-linearization techniques / mixed integer linear programming / integer nonlinear programming / quadratic programming
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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