Kocuk, Burak and Van Hoeve, Willem Jan
(2019)
*A computational comparison of optimization methods for the Golomb ruler problem.*
In: 16th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, CPAIOR 2019,
Thessaloniki, Greece

Official URL: https://dx.doi.org/10.1007/978-3-030-19212-9_27

## Abstract

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features.

Item Type: | Papers in Conference Proceedings |
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Uncontrolled Keywords: | Constraint programming; Golomb ruler; Integer programming |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Burak Kocuk |

Date Deposited: | 23 Jul 2023 14:24 |

Last Modified: | 23 Jul 2023 14:24 |

URI: | https://research.sabanciuniv.edu/id/eprint/46190 |