Abstract
The Covering Tour Problem (CTP) is a generalization of the Traveling Salesman Problem (TSP) which has several practical applications in the area of distribution network design. Given an undirected graph, the problem asks to identify a minimum cost cycle passing through a subset of vertices such that every vertex not in the cycle lies within a given distance from at least one node in the cycle. Being a generalization of the TSP, CTP is NP-hard. This paper presents three original Scatter Search heuristic algorithms for the CTP. Computational results are reported.
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References
Arkin, E.M., M.M. Halldorsson and R. Hassin (1993) "Approximating the Tree and Tour Covers of a Graph," Information Processing Letters, 47:275–282.
Arkin, E.M. and R. Hassin (1994) "Approximation Algorithms for the Geometric Covering Salesman Problem," Discrete Appl. Math., 55:197–218.
Balas, E. (1989) "The Prize Collecting Traveling Salesman Problem," Networks, 19:621–636.
Balas, E. and A. Ho (1980) "Set Covering Algorithms Using Cutting Planes, Heuristic, and Subgradient Optimisation: A Computational Study," Mathematical Programming Study, 12:37–60.
Baldacci, R. (1999) "Algorithms for Location and Routing Problems in Distribution Systems," Ph.D. Thesis, Management Science Dept., Imperial College, London.
Baldacci, R., A. Mingozzi and E. Hadjiconstantinou (1999) "An Exact Algorithm for the Capacitated Vehicle Routing Problem based on a Two-Commodity Network Flow Formulation," Working Paper, Department of Mathematics, University of Bologna.
CPLEX Optimization Inc. (1996) Using the Cplex Callable Library and Cplex Mixed Integer Library. 930 Tahoe Blvd 802-297, Incline Viallge, NV89451, U.S.A.
Current, J.R. and D.A. Schilling (1989) "The Covering Salesman Problem," Transp. Sci., 23:208–213.
Current, J.R. and D.A Schilling (1994) "The Median Tour and Maximal Covering Problems," European Journal of Operational Research, 73:114–126.
Finke, G., A. Claus and E. Gunn (1984) "A Two-Commodity Network Flow Approach to the Traveling Salesman Problem," Congress. Numerantium, 41:167–178.
Fischetti, M., J.J. Salazar and P. Toth (1997) "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, 45:378–394.
Fischetti, M. and P. Toth (1988) An Additive Approach for the Optimal Solution of the Prize Collecting Traveling Salesman Problem. In Vehicle Routing: Methods and Studies, B.L. Golden and A.A. Assad (eds.), North-Holland, Amsterdam, 319–343.
Gendreau, M., A. Hertz and G. Laporte (1992) "New Intersection and Postoptimization Procedures for the Traveling Salesman Problem," Operations Research, 40:1086–1094.
Gendreau, M., G. Laporte and F. Semet (1995) "The Covering Tour Problem," Operations Research, 45:568–576.
Glover, F. (1977) "Heuristics for Integer Programming using Surrogate Constraints," Decision Sciences, 8:156–166.
Glover, F. (1995) "Scatter Search and Star Paths: Beyond the Genetic Metaphor," OR Spektrum, 17:125–137.
Glover, F. (1997) A Template for Scattersearch and Path Relinking. Lecture Notes in Computer Science, J.K. Hao, E. Lutton, E. Ronald, M. Schoenauer, D. Snyers (Eds.).
Glover, F. and M. Laguna (1997) Tabu Search, Kluwer Academic Publishers.
Kourtz, P. (1987) The Need for Improved Forest Fire Detection, The Forestry Chronicle, 272–277.
Labbe, M. and G. Laporte (1986) "Maximizing User Convenience and Postal Service Efficiency in Post Box Location," Belgian J. Opns. res. Statist. and Computer Sci., 26:21–35.
Langevin, A., M. Desrochers, J. Desrosiers, S. Gelinas and F. Soumis (1993) "A Two-Commodity Flow Formulation for the Traveling Salesman and the Makespan Problems with Time Windows," Networks, 23:631–640.
Laporte, G. and S. Martello (1990) "The Selective Traveling Salesman Problem," Discrete Appl. Math., 26:193–207.
Lucena, A. (1986) "Exact Solution Approaches for the Vehicle Routing Problem," Ph.D. Thesis, Management Science Dept., Imperial College, London.
Ntafos, S. (1992) "Watchman Routes under Limited Visibility," Computational Geometry, 1:149–209.
Oppong, J.R. and M.J. Hodgson (1994) "Spatial Accessibility to Health Care Facilities in Suhum District, Ghana," Professional Geographer, 46:199–209.
Reinelt, G. (1991) "Tsplib-a Traveling Salesman Problem Library," ORSA Journal on Computing, 3:376–384.
ReVelle, C.S. and G. Laporte (1993) "New Directions in Plant Location," Studies in Locational Analysis, 5:31–58.
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Baldacci, R., Boschetti, M.A., Maniezzo, V., Zamboni, M. (2005). Scatter Search Methods for the Covering Tour Problem. In: Sharda, R., Voß, S., Rego, C., Alidaee, B. (eds) Metaheuristic Optimization via Memory and Evolution. Operations Research/Computer Science Interfaces Series, vol 30. Springer, Boston, MA. https://doi.org/10.1007/0-387-23667-8_3
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DOI: https://doi.org/10.1007/0-387-23667-8_3
Publisher Name: Springer, Boston, MA
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