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Escaping Local Optima with Local Search: A Theory-Driven Discussion

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Parallel Problem Solving from Nature – PPSN XVII (PPSN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13399))

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Abstract

Local search is the most basic strategy in optimization settings when no specific problem knowledge is employed. While this strategy finds good solutions for certain optimization problems, it generally suffers from getting stuck in local optima. This stagnation can be avoided if local search is modified. Depending on the optimization landscape, different modifications vary in their success.

We discuss several features of optimization landscapes and give analyses as examples for how they affect the performance of modifications of local search. We consider modifying random local search by restarting it and by considering larger search radii. The landscape features we analyze include the number of local optima, the distance between different optima, as well as the local landscape around a local optimum. For each feature, we show which modifications of local search handle them well and which do not.

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Notes

  1. 1.

    The optimum of all test functions in this paper is given by the all-1 string, which leads to the observation that the optimum can be found in constant time by just conjecturing this string. Still theoretical research analyzes such functions, because (a) we can nonetheless observe the behavior of different algorithms on these functions, giving insights into the algorithms; and (b) these functions are representatives of much wider classes of functions with either isomorphic or at least similar properties, but for a theoretical analysis we restrict ourselves to the clean case where the rule “more 1 s means closer to the optimum” holds.

References

  1. Aarts, E., Aarts, E.H., Lenstra, J.K.: Local Search in Combinatorial Optimization. Princeton University Press, Princeton (2003)

    Book  Google Scholar 

  2. Antipov, D., Doerr, B.: Precise runtime analysis for plateau functions. ACM Trans. Evol. Learn. Optim. 1(4), 13:1–13:28 (2021). https://doi.org/10.1145/3469800

  3. Bambury, H., Bultel, A., Doerr, B.: Generalized jump functions. In: Proceedings of GECCO 2021, pp. 1124–1132. ACM (2021). https://doi.org/10.1145/3449639.3459367

  4. Bian, C., Qian, C., Tang, K., Yu, Y.: Running time analysis of the (1+1)-EA for robust linear optimization. Theor. Comput. Sci. 843, 57–72 (2020). https://doi.org/10.1016/j.tcs.2020.07.001

    Article  MathSciNet  MATH  Google Scholar 

  5. Doerr, B., Le, H.P., Makhmara, R., Nguyen, T.D.: Fast genetic algorithms. In: Proceedings of GECCO 2017, pp. 777–784. ACM Press (2017)

    Google Scholar 

  6. Doerr, B., Le, H.P., Makhmara, R., Nguyen, T.D.: Fast genetic algorithms. In: Bosman, P.A.N. (ed.) Proceedings of GECCO 2017, pp. 777–784. ACM (2017). https://doi.org/10.1145/3071178.3071301

  7. Doerr, B., Rajabi, A.: Stagnation detection meets fast mutation. In: Proceedings of EvoCOP 2022, pp. 191–207. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-04148-8_13

  8. Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theor. Comput. Sci. 276, 51–81 (2002)

    Article  MathSciNet  Google Scholar 

  9. Friedrich, T., Oliveto, P.S., Sudholt, D., Witt, C.: Analysis of diversity-preserving mechanisms for global exploration. Evol. Comput. 17(4), 455–476 (2009)

    Article  Google Scholar 

  10. Hansen, P., Mladenovic, N.: Variable neighborhood search. In: Martí, R., Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Heuristics, pp. 759–787. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-07124-4_19

  11. Horn, J., Goldberg, D.E.: Genetic algorithm difficulty and the modality of fitness landscapes. In: Proceedings of FOGA 1995, vol. 3, pp. 243–269. Elsevier (1995)

    Google Scholar 

  12. Jagerskupper, J., Storch, T.: When the plus strategy outperforms the comma strategy and when not. In: 2007 IEEE Symposium on Foundations of Computational Intelligence, pp. 25–32. IEEE (2007)

    Google Scholar 

  13. Jansen, T., Wegener, I.: A comparison of simulated annealing with a simple evolutionary algorithm on pseudo-Boolean functions of unitation. Theor. Comput. Sci. 386(1), 73–93 (2007). https://doi.org/10.1016/j.tcs.2007.06.003, https://www.sciencedirect.com/science/article/pii/S0304397507004811

  14. Jansen, T., Zarges, C.: Example landscapes to support analysis of multimodal optimisation. In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 792–802. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45823-6_74

    Chapter  Google Scholar 

  15. Johnson, D.S.: Local optimization and the Traveling Salesman Problem. In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 446–461. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0032050

    Chapter  Google Scholar 

  16. Neumann, F., Witt, C.: Bioinspired Computation in Combinatorial Optimization - Algorithms and Their Computational Complexity. Springer, Cham (2010). https://doi.org/10.1007/978-3-642-16544-3

  17. Nguyen, P.T.H., Sudholt, D.: Memetic algorithms outperform evolutionary algorithms in multimodal optimisation. Artif. Intell. 287, 103345 (2020). https://doi.org/10.1016/j.artint.2020.103345

  18. Pelikan, M., Goldberg, D.E.: Genetic algorithms, clustering, and the breaking of symmetry. In: Schoenauer, M., et al. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 385–394. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45356-3_38

    Chapter  Google Scholar 

  19. Prügel-Bennett, A.: When a genetic algorithm outperforms hill-climbing. Theoret. Comput. Sci. 320(1), 135–153 (2004)

    Article  MathSciNet  Google Scholar 

  20. Quick, R.J., Rayward-Smith, V.J., Smith, G.D.: Fitness distance correlation and Ridge functions. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 77–86. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0056851

    Chapter  Google Scholar 

  21. Rajabi, A., Witt, C.: Stagnation detection in highly multimodal fitness landscapes. In: Proceedings of GECCO 2021. ACM Press (2021)

    Google Scholar 

  22. Rajabi, A., Witt, C.: Stagnation detection with randomized local search. In: Zarges, C., Verel, S. (eds.) EvoCOP 2021. LNCS, vol. 12692, pp. 152–168. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72904-2_10

    Chapter  Google Scholar 

  23. Rajabi, A., Witt, C.: Self-adjusting evolutionary algorithms for multimodal optimization. Algorithmica 84, 1694–1723 (2022). https://doi.org/10.1007/s00453-022-00933-z. Preliminary version in GECCO 2020

  24. Simon, D.: Evolutionary Optimization Algorithms. Wiley, Hoboken (2013)

    Google Scholar 

  25. Stützle, T.: Applying iterated local search to the permutation flow shop problem. Technical report, Citeseer (1998)

    Google Scholar 

  26. Van Hoyweghen, C., Goldberg, D.E., Naudts, B.: From TwoMax to the Ising model: easy and hard symmetrical problems. Generations 11(01), 10 (2001)

    Google Scholar 

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Acknowledgments

This work was supported by a grant by the Independent Research Fund Denmark (DFF-FNU 8021-00260B), and by the Paris Île-de-France Region via the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 945298-ParisRegionFP.

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Authors and Affiliations

  1. Hasso Plattner Institute, University of Potsdam, Potsdam, Germany

    Tobias Friedrich & Timo Kötzing

  2. Sorbonne University, CNRS, LIP6, Paris, France

    Martin S. Krejca

  3. Technical University of Denmark, Kgs. Lyngby, Denmark

    Amirhossein Rajabi

Authors
  1. Tobias Friedrich
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  2. Timo Kötzing
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  3. Martin S. Krejca
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  4. Amirhossein Rajabi
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Corresponding author

Correspondence to Timo Kötzing .

Editor information

Editors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Günter Rudolph

  2. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  3. Shinshu University, Nagano, Japan

    Hernán Aguirre

  4. Technische Universität Dresden, Dresden, Germany

    Pascal Kerschke

  5. University of Stirling, Stirling, UK

    Gabriela Ochoa

  6. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

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Friedrich, T., Kötzing, T., Krejca, M.S., Rajabi, A. (2022). Escaping Local Optima with Local Search: A Theory-Driven Discussion. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13399. Springer, Cham. https://doi.org/10.1007/978-3-031-14721-0_31

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  • DOI: https://doi.org/10.1007/978-3-031-14721-0_31

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  • Online ISBN: 978-3-031-14721-0

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