Journal of Heuristics

, Volume 13, Issue 1, pp 35–47 | Cite as

Distance measures based on the edit distance for permutation-type representations

Article

Abstract

In this paper, we discuss distance measures for a number of different combinatorial optimization problems of which the solutions are best represented as permutations of items, sometimes composed of several permutation (sub)sets. The problems discussed include single-machine and multiple-machine scheduling problems, the traveling salesman problem, vehicle routing problems, and many others. Each of these problems requires a different distance measure that takes the specific properties of the representation into account. The distance measures discussed in this paper are based on a general distance measure for string comparison called the edit distance. We introduce several extensions to the simple edit distance, that can be used when a solution cannot be represented as a simple permutation, and develop algorithms to calculate them efficiently.

Keywords

Distance measures Edit distance Permutation-type representations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bierwirth, C. (1995). “A Generalized Permutation Approach to Job Shop Scheduling with Genetic Algorithms.” OR Spektrum 17, 87–92.MATHCrossRefGoogle Scholar
  2. Caprara, A. (1977). “Sorting by Reversal is Difficult.” In Proceedings of the the First Annual International Conference on Computational Molecular Biology (RECOMB'97), ACM Press, New York, pp. 75–83.Google Scholar
  3. Glover, F., M. Laguna, and R. Martí. (2000a). “Fundamentals of Scatter Search and Path Relinking.” Control and Cybernetics 39, 653–684.Google Scholar
  4. Glover, F., A. Løkketangen, and D.L. Woodruff. (2000b). “Scatter Search to Generate Diverse MIP Solutions.” In M. Laguna and J.L.G. Velarde (eds.), Computing Tools for Modeling Optimization and Simulation, Kluwer, Boston, pp. 299–320.Google Scholar
  5. Goldberg, D.E. and J. Richardson. (1987). “Genetic Algorithms with Sharing for Multimodal Function Optimization.” In Genetic Algorithms and their Applications: Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, Inc, Mahwah, NJ, pp. 41–49.Google Scholar
  6. P. Greistorfer and S. Voß. (2005). “Controlled Pool Maintenance for Metaheuristics.” In C. Rego and B. Alidaee (eds.), Metaheuristic Optimization Via Memory and Evolution, Kluwer, Boston, pp. 387–424.CrossRefGoogle Scholar
  7. Janssens, G.K. (2004). “A Proposition for a Distance Measure in Neighbourhood Search for Scheduling Problems.” Journal of the Chinese Institute of Industrial Engineers 21, 262–271.CrossRefGoogle Scholar
  8. Kendall, M. and J. Dickinson Gibbons. (1990). Rank Correlation Methods. Oxford University Press, New York.MATHGoogle Scholar
  9. Levenshtein, V.I. (1966). “Binary Codes Capable of Correcting Deletions, Insertions, and Reversals.” Soviet Physics-Doklady 10, 707–710.MathSciNetGoogle Scholar
  10. Maes, M. (1990). “On a Cyclic String-to-String Correction Problem.” Information Processing Letters 35, 73–78.MATHCrossRefMathSciNetGoogle Scholar
  11. Mahfoud, S.W. (1992). “Crowding and Preselection Revisited.” In R. Manner and B. Manderick (eds.), Parallel Problem Solving from Nature. Elsevier, Amsterdam, pp. 27–36.Google Scholar
  12. Martí, R., M. Laguna, and V. Campos. (2005). “Scatter Search vs. Genetic Algorithms: An Experimental Evaluation with Permutation Problems.” In C. Rego and B. Alidaee (eds.), Metaheuristic Optimization Via Adaptive Memory and Evolution: Tabu Search and Scatter Search, Kluwer Academic Publishers, Boston, pp. 263–282.CrossRefGoogle Scholar
  13. Mauldin, M. (1984). “Maintaining Diversity in Genetic Search.” In Proceedings of the National Conference on Artificial Intelligence, pp. 247–250.Google Scholar
  14. Ronald, S. (1998). “More Distance Functions for Order-Based Encodings.” In Proceedings of the IEEE Conference on Evolutionary Computation. IEEE Press, New York, pp. 558–563.Google Scholar
  15. Siegel, S. and N.J. Castellan. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, London.Google Scholar
  16. Sörensen, K. and M. Sevaux. (2006). “MA❘PM: Memetic Algorithms with Population Management.” Computers and Operations Research 33, 1214–1225.MATHCrossRefGoogle Scholar
  17. Ukkonen, E. (1985). “Finding Approximate Patterns in Strings.” Journal of Algorithms 6, 132–137.MATHCrossRefMathSciNetGoogle Scholar
  18. Wagner, R.A. and M.J. Fischer. (1974). “The String-to-String Correction Problem.” Journal of the Association for Computing Machinery 21, 168–173.MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.University of Antwerp, Faculty of Applied EconomicsAntwerpBelgium

Personalised recommendations