A computational comparison of optimization methods for the Golomb ruler problem

Kocuk, Burak and Van Hoeve, Willem-Jan (2019) A computational comparison of optimization methods for the Golomb ruler problem. In: Rousseau, Louis-Martin and Stergiou, Kostas, (eds.) Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 16th International Conference, CPAIOR 2019, Thessaloniki, Greece, June 4–7, 2019, Proceedings. Lecture Notes in Computer Science, 11494. Springer International Publishing, Cham, Switzerland, pp. 409-425. ISBN 978-3-030-19211-2 (Print) 978-3-030-19212-9 (Online)

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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: Book Section / Chapter
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Industrial Engineering
Faculty of Engineering and Natural Sciences
Depositing User: Burak Kocuk
Date Deposited: 07 Aug 2019 11:40
Last Modified: 26 Apr 2022 08:37
URI: https://research.sabanciuniv.edu/id/eprint/37544

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