Application of Fuzzy Sets for the Improvement of Routing Optimization Heuristic Algorithms

1. Applegate, D.L., Bixby, R.E., Chvátal, V. and Cook, W.J. (2007) The Traveling Salesman Problem: A Computational Study. Princeton (NJ): Princeton University Press.Search in Google Scholar

2. Bai, J., Yang, G.K., Chenb, Y.W., Hu, L.S. and Pan, C.C. (2012) A model induced max-min ant colony optimization for asymmetric travelling salesman problem. Applied Soft Computing, 13(3), 1365–1375. DOI: doi:10.1016/j.asoc.2012.04.008.10.1016/j.asoc.2012.04.008Search in Google Scholar

3. Bohács, G., Frikker, I. and Kovács, G. (2013) Intermodal logistics processes supported by electronic freight and warehouse exchanges. Transport and Telecommunication, 14(3), 206–213. DOI:10.2478/ttj-2013-0017.10.2478/ttj-2013-0017Search in Google Scholar

4. Botzoris, G. and Papadopoulos, B. (2015) Fuzzy Sets: Applications for the Design and Operation of Civil Engineering Projects (in Greek). Thessaloniki: Sofia Editions.Search in Google Scholar

5. Chernov, V., Dorokhov, O. and Malyaretz, L. (2012) Construction of estimates in the choice of alternative solutions by using the fuzzy utilities. Transport and Telecommunication, 13(1), 11–17. DOI: 10.2478/v10244-012-0002-z.10.2478/v10244-012-0002-zSearch in Google Scholar

6. Christofides, N. (1976) Worst-case Analysis of a New Heuristic for the Travelling Salesman Problem. Pittsburgh (PA): Carnegie Mellon University – Graduate School of Industrial Administration. (Technical Report 388, ADA025602).Search in Google Scholar

7. Dantzig, G., Fulkerson, R. and Johnson, S. (1954) Solution of a large-scale travelling-salesman problem. Operations Research, 2(4), 393–410. DOI: 10.1287/opre.2.4.393.10.1287/opre.2.4.393Search in Google Scholar

8. Garey, M.R. and Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. New York (NY): W.H. Freeman & Co.Search in Google Scholar

9. Genova, K. and Williamson, D.P. (2015) An experimental evaluation of the best-of-many Christofides algorithm for the traveling salesman problem. In: Algorithms - ESA 2015, (Eds.) N. Bansal, and I. Finocchi, Berlin, Heidelberg: Springer-Verlag, pp. 570-581.10.1007/978-3-662-48350-3_48Search in Google Scholar

10. Guh, Y.Y., Po, R.W. and Stanley Lee, E. (2008) The fuzzy weighted average within a generalized means function. Computers and Mathematics with Applications, 55(12), 2699–2706. DOI:10.1016/j.camwa.2007.09.009.10.1016/j.camwa.2007.09.009Search in Google Scholar

11. Gutin, G., Yeo, A. and Zverovich, A. (2002) Travelling salesman should not be greedy: Domination analysis of greedy-type heuristics for the TSP. Discrete Applied Mathematics, 117(1-3), 81–86. DOI:10.1016/S0166-218X(01)00195-0.10.1016/S0166-218X(01)00195-0Search in Google Scholar

12. Hansen, M. (2000) Use of substitute scalarizing functions to guide a local search based heuristics: The case of MOTSP. Journal of Heuristics, 6(3), 419–431. DOI: 10.1023/A:1009690717521.10.1023/A:1009690717521Search in Google Scholar

13. Hwang, C.P., Alidaee, B. and Johnson, J.D. (1999) A tour construction heuristic for the travelling salesman problem. The Journal of the Operational Research Society, 50(8), 797–809. DOI: 10.2307/3010339.10.2307/3010339Search in Google Scholar

14. Johnson, D.S., Gutin, G., McGeoch, L.A., Yeo, A., Zhang, W. and Zverovitch, A. (2002) Experimental analysis of heuristics for the ATSP. In: The Travelling Salesman Problem and its Variations, (Eds.) G. Gutin and A.P. Punnen, Dordrecht: Kluwer Academic Publishers, pp. 485-488.Search in Google Scholar

15. Junjie, P. and Dingwei, W. (2006) An ant colony optimization algorithm for multiple travelling salesman problem. In: Proceedings of the 1^st International Conference on Innovative Computing, Information and Control, Beijing, August 2006, pp. 210-213.10.1109/ICICIC.2006.40Search in Google Scholar

16. Khuller, S. and Vishkin, U. (1994) Biconnectivity approximations and graph carvings. Journal of the Association for Computing Machinery, 41(2), 214–235. DOI:10.1145/174652.174654.10.1145/174652.174654Search in Google Scholar

17. Laporte, G. (1992) The travelling salesman problem: An overview of exact and approximate algorithms. European Journal of Operational Research, 59(2), 231–247. DOI:10.1016/0377-2217(92)90138-Y.10.1016/0377-2217(92)90138-YSearch in Google Scholar

18. Lin, S. (1965) Computer solutions of the travelling salesman problem. The Bell System Technical Journal, 44(10), 2245–2269. DOI:10.1002/j.1538-7305.1965.tb04146.x.10.1002/j.1538-7305.1965.tb04146.xSearch in Google Scholar

19. Liu, W., Li, S., Zhao, F. and Zheng, A. (2009) An ant colony optimization algorithm for the multiple traveling salesmen problem. In: Proceeding of the 4^th IEEE Conference on Industrial Electronics and Applications, Xi'an, May 2009, pp. 1533-1537.Search in Google Scholar

20. Mattas, K., Botzoris, G. and Papadopoulos, B. (2015) Improvement of route optimization algorithmic methods with application of fuzzy sets. In: Proceeding of the 7^th International Congress on Transportation Research, Athens, November 2015.Search in Google Scholar

21. Padberg, M. and Rinaldi, G. (1991) A branch-and-cut algorithm for the resolution of large-scale symmetric travelling salesman problems. Society for Industrial and Applied Mathematics, 33(1), 60–100. DOI:10.1137/1033004.10.1137/1033004Search in Google Scholar

22. Papadimitriou, C.H. (1977) The Euclidean travelling salesman problem is np-complete. Theoretical Computer Science, 4(3), 237–244. DOI:10.1016/0304-3975(77)90012-3.10.1016/0304-3975(77)90012-3Search in Google Scholar

23. Reinelt, G. (1991) TSPLIB – A travelling salesman problem library. ORSA Journal on Computing, 3(4), 376–384. DOI: 10.1287/ijoc.3.4.376.10.1287/ijoc.3.4.376Search in Google Scholar

24. Reinelt, G. (1994) The Traveling Salesman: Computational Solutions for TSP Applications. Berlin, Heidelberg: Springer-Verlag.Search in Google Scholar

25. Schonlau, M., Welch, W.J. and Jones, D.R. (1998) Global versus local search in constrained optimization of computer models. Institute of Mathematical Statistics: Lecture Notes-Monograph Series, 34, 11–25. doi:10.1214/lnms/1215456182.10.1214/lnms/1215456182Search in Google Scholar

26. Stattenberger, G., Dankesreiter, M., Baumgartner, F. and Schneider, J. (2007) On the neighbourhood structure of the travelling salesman problem generated by local search moves. Journal of Statistical Physics, 129(4), 623–648. DOI: 10.1007/s10955-007-9382-1.10.1007/s10955-007-9382-1Search in Google Scholar

27. Xu, Z., Xu, L., and Rodrigues, B. (2011) An analysis of the extended Christofides heuristic for the kdepot TSP. Operations Research Letters, 39(3), 218–223. DOI:10.1016/j.orl.2011.03.002.10.1016/j.orl.2011.03.002Search in Google Scholar