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Local Search-based Hybrid Algorithms for Finding Golomb Rulers

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Abstract

The Golomb ruler problem is a very hard combinatorial optimization problem that has been tackled with many different approaches, such as constraint programming (CP), local search (LS), and evolutionary algorithms (EAs), among other techniques. This paper describes several local search-based hybrid algorithms to find optimal or near-optimal Golomb rulers. These algorithms are based on both stochastic methods and systematic techniques. More specifically, the algorithms combine ideas from greedy randomized adaptive search procedures (GRASP), scatter search (SS), tabu search (TS), clustering techniques, and constraint programming (CP). Each new algorithm is, in essence, born from the conclusions extracted after the observation of the previous one. With these algorithms we are capable of solving large rulers with a reasonable efficiency. In particular, we can now find optimal Golomb rulers for up to 16 marks. In addition, the paper also provides an empirical study of the fitness landscape of the problem with the aim of shedding some light about the question of what makes the Golomb ruler problem hard for certain classes of algorithm.

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Authors and Affiliations

  1. Dept. Lenguajes y Ciencias de la Computación, E.T.S.I. Informática, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Carlos Cotta & Antonio J. Fernández

  2. Dept. Ingeniería Informática, Universidad Autónoma de Madrid, Madrid, Spain

    Iván Dotú

  3. Brown University, Box 1910, Providence, RI, 02912, USA

    Pascal Van Hentenryck

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  1. Carlos Cotta
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  2. Iván Dotú
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  4. Pascal Van Hentenryck
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Correspondence to Carlos Cotta.

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Cotta, C., Dotú, I., Fernández, A.J. et al. Local Search-based Hybrid Algorithms for Finding Golomb Rulers. Constraints 12, 263–291 (2007). https://doi.org/10.1007/s10601-007-9020-1

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