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Iterated Local Search: Framework and Applications

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Handbook of Metaheuristics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 272))

Abstract

The key idea underlying iterated local search is to focus the search not on the full space of all candidate solutions but on the solutions that are returned by some underlying algorithm, typically a local search heuristic. The resulting search behavior can be characterized as iteratively building a chain of solutions of this embedded algorithm. The result is also a conceptually simple metaheuristic that nevertheless has led to state-of-the-art algorithms for many computationally hard problems. In fact, very good performance is often already obtained by rather straightforward implementations of the metaheuristic. In addition, the modular architecture of iterated local search makes it very suitable for an algorithm engineering approach where, progressively, the algorithm’s performance can be further optimized. Our purpose here is to give an accessible description of the underlying principles of iterated local search and a discussion of the main aspects that need to be taken into account for a successful application of it. In addition, we review the most important applications of this method and discuss its relationship with other metaheuristics.

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Notes

  1. 1.

    The reader can check that very little of what we say really uses this property, and in practice, many successful implementations of iterated local search have non-deterministic local searches or include memory.

  2. 2.

    Note that the local search finds neighbors stochastically; generally there is no efficient way to ensure that one has tested all the neighbors of any given s ∗.

  3. 3.

    Recall that to simplify this section’s presentation, the local search is assumed to have no memory.

  4. 4.

    Note that the best possible greedy initial solution need not be the best choice when combined with a local search. For example, in [69], it is shown that the combination of the Clarke-Wright starting tour (one of the best performing TSP construction heuristics) with local search resulted in worse local optima than starting from random initial solutions when using 3-opt. Additionally, greedy algorithms which generate very high quality initial solutions can be quite time-consuming.

  5. 5.

    QAPLIB is accessible at http://www.seas.upenn.edu/qaplib.

  6. 6.

    TSPLIB is accessible at www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95.

  7. 7.

    This question is not specific to ILS; it arises for all multi-start-based metaheuristics.

  8. 8.

    In early TS publications, proposals similar to the use of perturbations were put forward under the name random shakeup [45]. These procedures where characterized as a “randomized series of moves that leads the heuristic (away) from its customary path” [45]. The relationship to perturbations in ILS is obvious.

  9. 9.

    Indeed, in [46], Glover uses “strategic oscillation” whereby one cycles over these procedures: the simplest moves are used till there is no more improvement, and then progressively more advanced moves are used.

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Acknowledgements

Helena Ramalhinho Lourenço acknowledges support from the Spanish Ministry of Economy and Competitiveness (TRA2013-48180-C3-P, TRA2015-71883-REDT), and Thomas Stützle acknowledges support from the F.R.S.-FNRS, of which he is a research director. This work received support from the COMEX project P7/36 within the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office.

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  1. Universitat Pompeu Fabra, Barcelona, Spain

    Helena Ramalhinho Lourenço

  2. INRA, Université Paris-Sud, Orsay, France

    Olivier C. Martin

  3. Université Libre de Bruxelles (ULB), Brussels, Belgium

    Thomas Stützle

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  1. Helena Ramalhinho Lourenço
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    Jean-Yves Potvin

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Lourenço, H.R., Martin, O.C., Stützle, T. (2019). Iterated Local Search: Framework and Applications. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-91086-4_5

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