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Classification of Permutation Distance Metrics for Fitness Landscape Analysis

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Bio-inspired Information and Communication Technologies (BICT 2019)

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Abstract

Commonly used computational and analytical tools for fitness landscape analysis of optimization problems require identifying a distance metric that characterizes the similarity of different solutions to the problem. For example, fitness distance correlation is Pearson correlation between solution fitness and distance to the nearest optimal solution. In this paper, we survey the available distance metrics for permutations, and use principal component analysis to classify the metrics. The result is aligned with existing classifications of permutation problem types produced through less formal means, including the A-permutation, R-permutation, and P-permutation types, and has also identified subtypes. The classification can assist in identifying appropriate metrics based on optimization problem feature for use in fitness landscape analysis. Implementations of all of the permutation metrics, and the code for our analysis, are available as open source.

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References

  1. Campos, V., Laguna, M., Martí, R.: Context-independent Scatter and Tabu search for permutation problems. INFORMS Comput. 17(1), 111–122 (2005)

    Article  MathSciNet  Google Scholar 

  2. Caprara, A.: Sorting by reversals is difficult. In: Proceedings of the First International Conference on Computational Molecular Biology, pp. 75–83. ACM (1997)

    Google Scholar 

  3. Cicirello, V.A.: On the effects of window-limits on the distance profiles of permutation neighborhood operators. In: Proceedings of the International Conference on Bioinspired Information and Communications Technologies, pp. 28–35, December 2014. https://doi.org/10.4108/icst.bict.2014.257872

  4. Cicirello, V.A.: The permutation in a haystack problem and the calculus of search landscapes. IEEE Trans. Evol. Comput. 20(3), 434–446 (2016). https://doi.org/10.1109/TEVC.2015.2477284

    Article  Google Scholar 

  5. Cicirello, V.A.: JavaPermutationTools: a Java library of permutation distance metrics. J. Open Source Softw. 3(31), 950 (2018). https://doi.org/10.21105/joss.00950

    Article  Google Scholar 

  6. Cicirello, V.A., Cernera, R.: Profiling the distance characteristics of mutation operators for permutation-based genetic algorithms. In: Proceedings of the 26th International Conference of the Florida Artificial Intelligence Research Society, pp. 46–51. AAAI Press, May 2013

    Google Scholar 

  7. Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. SIAM J. Discret. Math. 17(1), 134–160 (2003)

    Article  MathSciNet  Google Scholar 

  8. Hernando, L., Mendiburu, A., Lozano, J.A.: A tunable generator of instances of permutation-based combinatorial optimization problems. IEEE Trans. Evol. Comput. 20(2), 165–179 (2016)

    Article  Google Scholar 

  9. Hunt, J.W., Szymanski, T.G.: A fast algorithm for computing longest common subsequences. Commun. ACM 20(5), 350–353 (1977)

    Article  MathSciNet  Google Scholar 

  10. Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann (1995)

    Google Scholar 

  11. Kendall, M.G.: A new measure of rank correlation. Biometrika 30(1/2), 81–93 (1938)

    Article  Google Scholar 

  12. Lee, C.: Some properties of nonbinary error-correcting codes. IRE Trans. Inf. Theory 4(2), 77–82 (1958)

    Article  MathSciNet  Google Scholar 

  13. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions and reversals. Sov. Phys. Dokl. 10(8), 707–710 (1966)

    MathSciNet  Google Scholar 

  14. Meilă, M., Bao, L.: An exponential model for infinite rankings. J. Mach. Learn. Res. 11, 3481–3518 (2010)

    MathSciNet  MATH  Google Scholar 

  15. Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1998)

    MATH  Google Scholar 

  16. Ronald, S.: Finding multiple solutions with an evolutionary algorithm. In: IEEE Congress on Evolutionary Computation, pp. 641–646. IEEE Press (1995)

    Google Scholar 

  17. Ronald, S.: Distance functions for order-based encodings. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 49–54. IEEE Press (1997)

    Google Scholar 

  18. Ronald, S.: More distance functions for order-based encodings. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 558–563. IEEE Press (1998)

    Google Scholar 

  19. Schiavinotto, T., Stützle, T.: A review of metrics on permutations for search landscape analysis. Comput. Oper. Res. 34(10), 3143–3153 (2007)

    Article  Google Scholar 

  20. Sevaux, M., Sörensen, K.: Permutation distance measures for memetic algorithms with population management. In: Proceedings of the Metaheuristics International Conference (MIC 2005), pp. 832–838, August 2005

    Google Scholar 

  21. Sörensen, K.: Distance measures based on the edit distance for permutation-type representations. J. Heuristics 13(1), 35–47 (2007)

    Article  Google Scholar 

  22. Tayarani-N, M.H., Prugel-Bennett, A.: On the landscape of combinatorial optimization problems. IEEE Trans. Evol. Comput. 18(3), 420–434 (2014). https://doi.org/10.1109/TEVC.2013.2281502

    Article  Google Scholar 

  23. Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. J. ACM 21(1), 168–173 (1974)

    Article  MathSciNet  Google Scholar 

  24. Wright, S.: Evolution in Mendelian populations. Genetics 16(2), 97–159 (1931)

    Google Scholar 

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Authors and Affiliations

  1. Stockton University, Galloway, NJ, 08205, USA

    Vincent A. Cicirello

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  1. Vincent A. Cicirello
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Correspondence to Vincent A. Cicirello .

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Editors and Affiliations

  1. Stefens Institute of Technology USA, Hoboken, NJ, USA

    Adriana Compagnoni

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    William Casey

  3. Cylab, Carnegie Mellon University, Pittsburgh, PA, USA

    Yang Cai

  4. New York University, New York, NY, USA

    Bud Mishra

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© 2019 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Cicirello, V.A. (2019). Classification of Permutation Distance Metrics for Fitness Landscape Analysis. In: Compagnoni, A., Casey, W., Cai, Y., Mishra, B. (eds) Bio-inspired Information and Communication Technologies. BICT 2019. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 289. Springer, Cham. https://doi.org/10.1007/978-3-030-24202-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-24202-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24201-5

  • Online ISBN: 978-3-030-24202-2

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