Abstract
The problem of routing and wavelength assignment in wavelength division multiplexing optical networks consists in routing a set of lightpaths and assigning a wavelength to each of them, such that lightpaths whose routes share a common fiber are assigned different wavelengths. This problem was shown to be NP-hard when the objective is to minimize the total number of wavelengths used. We propose a genetic algorithm with random keys for routing and wavelength assignment with the goal of minimizing the number of different wavelengths used in the assignment. This algorithm extends the best heuristic in the literature by embedding it into an evolutionary framework. Computational results show that the new heuristic improves the state-of-the-art algorithms in the literature.
Similar content being viewed by others
References
Aiex R.M., Resende M.G.C., Ribeiro C.C.: Probability distribution of solution time in GRASP: an experimental investigation. J. Heuristics 8, 343–373 (2002)
Aiex R.M., Resende M.G.C., Ribeiro C.C.: TTTPLOTS: a Perl program to create time-to-target plots. Optim. Lett. 1, 355–366 (2007)
Bannerjee D., Mukherjee B.: Practical approach for routing and wavelength assignment in large wavelength routed optical networks. IEEE J. Sel. Areas Commun. 14, 903–908 (1995)
Bean J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 2, 154–160 (1994)
Buriol L.S., Resende M.G.C., Ribeiro C.C., Thorup M.: A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing. Networks 46, 36–56 (2005)
Buriol L.S., Resende M.G.C., Thorup M.: Survivable IP network design with OSPF routing. Networks 49, 51–64 (2007)
Choi, J.S., Golmie, N., Lapeyrere, F., Mouveaux, F., Su, D.: A functional classification of routing and wavelength assignment schemes in DWDM networks: static case. In: Proceedings of the 7th International Conference on Optical Communication and Networks, pp. 1109–1115. Paris (2000)
Ericsson M., Resende M.G.C., Pardalos P.M.: A genetic algorithm for the weight setting problem in OSPF routing. J. Comb. Optim. 6, 299–333 (2002)
Erlebach T., Jansen K.: The complexity of path coloring and call scheduling. Theor. Comput. Sci. 255, 33–50 (2001)
Frota Y., Maculan N., Noronha T.F., Ribeiro C.C.: A branch-and-cut algorithm for partition coloring. Networks 55, 194–204 (2010)
Gonçalves J.F., Mendes J.J.M., Resende M.G.C.: A hybrid genetic algorithm for the job shop scheduling problem. Eur. J. Oper. Res. 167, 77–95 (2005)
Gonçalves J.F., Mendes J.J.M., Resende M.G.C.: A genetic algorithm for the resource constrained multi-project scheduling problem. Eur. J. Oper. Res. 189, 1171–1190 (2008)
Gonçalves J.F., Mendes J.J.M., Resende M.G.C.: A random key based genetic algorithm for the resource constrained project scheduling problems. Comput. Oper. Res. 36, 92–109 (2009)
Gonçalves J.F., Resende M.G.C.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47, 247–273 (2004)
Gonçalves, J.F., Resende, M.G.C.: Biased random-key genetic algorithms for combinatorial optimization. Technical report, AT& T Labs Research. Florham Park, NJ, To appear in J. of Heuristics (2009)
Hertz A., de Werra D.: Using tabu search techniques for graph coloring. Computing 39, 345–351 (1987)
Hyytia, E., Virtamo, J.: Wavelength assignment and routing in WDM networks. In: Fourteenth Nordic Teletraffic Seminar, pp. 31–40. Copenhagen (1998)
Jaumard, B.: Network and traffic data sets for optical network optimization. Online publication in http://users.encs.concordia.ca/~bjaumard/CRC_Chair/Research/Optical_Networks/Optical_Networks_Data.htm, last visited on April 1st (2010)
Jaumard, B., Meyer, C., Thiongane, B.: ILP formulations for the RWA problem for symmetrical systems. In: Handbook for Optimization in Telecommunications, pp. 637–677. Springer Science + Business Media (2006)
Jaumard B., Meyer C., Thiongane B.: On column generation formulations for the RWA problem. Discrete Appl. Math. 157, 1291–1308 (2009)
Kleinberg, J.M.: Approximation algorithms for disjoint paths problems. PhD thesis, MIT, Cambridge (1996)
Li, G., Simha, R.: The partition coloring problem and its application to wavelength routing and assignment. In: Proceedings of the First Workshop on Optical Networks. Dallas (2000)
Manohar P., Manjunath D., Shevgaonkar R.K.: Routing and wavelength assignment in optical networks from edge disjoint path algorithms. IEEE Commun. Lett. 5, 211–213 (2002)
Noronha, T.F., Resende, M.G.C., Ribeiro, C.C.: Efficient implementation of heuristics for routing and wavelength assignment. In: McGeoch, C.C. (ed.) Proceedings of the 7th International Workshop on Experimental Algorithms, volume 5038 of Lecture Notes in Computer Science, pp. 169–180. Springer, Provincetown, Mass (2008)
Noronha T.F., Ribeiro C.C.: Routing and wavelength assignment by partition coloring. Eur. J. Oper. Res. 171, 797–810 (2006)
Schrage L.: A more portable Fortran random number generator. ACM Trans. Math. Softw. 5, 132–138 (1979)
Skorin-Kapov N.: Routing and wavelength assignment in optical networks using bin packing based algorithms. Eur. J. Oper. Res. 177, 1167–1179 (2007)
Spears, W., de Jong, K.: On the virtues of parameterized uniform crossover. In: Belew, R., Booker, L. (eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 230–236. San Mateo, Morgan Kaufman (1991)
Zang H., Jue J.P., Mukherjee B.: A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks. Opt. Netw. Mag. 1, 47–60 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Noronha, T.F., Resende, M.G.C. & Ribeiro, C.C. A biased random-key genetic algorithm for routing and wavelength assignment. J Glob Optim 50, 503–518 (2011). https://doi.org/10.1007/s10898-010-9608-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-010-9608-7