Distance measures based on the edit distance for permutation-type representations
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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.
KeywordsDistance measures Edit distance Permutation-type representations
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- 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
- Glover, F., M. Laguna, and R. Martí. (2000a). “Fundamentals of Scatter Search and Path Relinking.” Control and Cybernetics 39, 653–684.Google Scholar
- 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
- 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
- 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
- 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
- Mauldin, M. (1984). “Maintaining Diversity in Genetic Search.” In Proceedings of the National Conference on Artificial Intelligence, pp. 247–250.Google Scholar
- 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
- Siegel, S. and N.J. Castellan. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, London.Google Scholar