Abstract
Given a set of lightpath requests, the problem of routing and wavelength (RWA) assignment in wavelength division multiplexing (WDM) optical networks consists in routing a subset of these requests and assigning a wavelength to each of them, such that two lightpaths that share a common link are assigned to different wavelengths. There are many variants of this problem in the literature. We focus in the variant in which the objective is to maximize the number of requests that may be accepted, given a limited set of available wavelengths. This problem is called max-RWA and it is of practical and theoretical interest, because algorithms for this variant can be extended for other RWA problems that arise from the design of WDM optical networks. A number of exact algorithms based on integer programming formulations have been proposed in the literature to solve max-RWA, as well as algorithms to provide upper bounds to the optimal solution value. However, the algorithms based on the state-of-the-art formulations in the literature cannot solve the largest instances to optimality. For these instances, only upper bounds to the value of the optimal solutions are known. The literature on heuristics for max-RWA is short and focus mainly on solving small size instances with up to 27 nodes. In this paper, we propose new greedy constructive heuristics and a biased random-key genetic algorithm, based on the best of the proposed greedy heuristics. Computational experiments showed that the new heuristic outperforms the best ones in literature. Furthermore, for the largest instances in the literature where only upper bounds to the value of the optimal solutions are known, the average optimality gap of the best of the proposed heuristics is smaller than 4 %.
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Aiex, R., Resende, M., 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)
Banerjee, D., Mukherjee, B.: A practical approach for routing and wavelength assignment in large wavelength-routed optical networks. IEEE J. Sel. Areas Commun. 14, 903–908 (1996)
Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 2, 154–160 (1994)
Belgacem, L., Puech, N.: Solving large size instances of the RWA problem using graph partitioning. In: International Conference on Optical Network Design and Modeling, IEEE, Barcelona (2008)
Brandão, J.S., Noronha, T.F., Resende, M.G.C., Ribeiro, C.C.: A biased random-key genetic algorithm for single-round divisible load scheduling. Int. Trans. Oper. Res. 22, 823–839 (2015)
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)
Buriol, L.S., Hirsch, M.J., Pardalos, P.M., Querido, T., Resende, M.G.C., Ritt, M.: A biased random-key genetic algorithm for road congestion minimization. Optim. Lett. 4, 619–633 (2010)
Chen, C., Banerjee, S.: A new model for optimal routing and wavelength assignment in wavelength division multiplexed optical networks. In: Proceedings of the Fifteenth Annual Joint Conference of the IEEE Computer Societies. Networking the Next Generation, vol. 1, pp. 64–171. San Francisco (1996)
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)
Dzongang, C., Galinier, P., Pierre, S.: A tabu search heuristic for the routing and wavelength assignment problem in optical networks. IEEE Commun. Lett. 9, 426–428 (2005)
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)
Gonçalves, J.F., de Magalhães Mendes, J.J., 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.: A hybrid genetic algorithm for assembly line balancing. J. Heuristics 8, 629–642 (2002)
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. J. Heuristics 17, 487–525 (2011)
Goulart, N., de Souza, S.R., Dias, L.G.S., Noronha, T.F.: Biased random-key genetic algorithm for fiber installation in optical network optimization. In: Proceedings of the 2011 IEEE Congress on Evolutionary Computation, pp. 2267–2271. New Orleans (2011)
Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)
Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics, vol. 2. Springer, Berlin (1993)
Hoos, H., Stützle, T.: Evaluation of Las Vegas algorithms - Pitfalls and remedies. In: Cooper, G., Moral, S. (eds.) Proceedings of the 14th Conference on Uncertainty in Artificial Intelligence, pp. 238–245. Madison (1998)
Hou, E.S., Ansari, N., Ren, H.: A genetic algorithm for multiprocessor scheduling. IEEE Trans. Parallel Distrib. Syst. 5(2), 113–120 (1994)
Hyytiä, E., Virtamo, J.: Wavelength assignment and routing in WDM networks. In: Fourteenth Nordic Teletraffic Seminar, pp. 31–40. Copenhagen (1998)
Hyytiä, E., Virtamo, J.: Wavelength assignment in multifibre in WDM-networks. Technical report COST257TD(99)04, Helsinki University of Technology (1999)
Jaumard, B., Meyer, C., Thiongane, B., Yu, X.: ILP formulations and optimal solutions for the RWA problem. In: Proceedings of the IEEE Global Telecommunications Conference, vol. 3, pp. 1918–1924. Dallas (2004)
Jaumard, B., Meyer, C., Thiongane, B.: ILP formulations for the routing and wavelength assignment problem: symmetric systems. In: Handbook of Optimization in Telecommunications, pp. 637–677. Springer, Berlin (2006)
Jaumard, B., Meyer, C., Yu, X.: How much wavelength conversion allows a reduction in the blocking rate? J. Opt. Netw. 5, 81–900 (2006)
Jaumard, B., Meyer, C., Thiongane, B.: Comparison of ILP formulations for the RWA problem. Opt. Switch. Netw. 4, 157–172 (2007)
Jaumard, B., Meyer, C., Thiongane, B.: On column generation formulations for the RWA problem. Discrete Appl. Math. 157, 1291–1308 (2009)
Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3, 299–325 (1974)
Kleinberg, J.: Approximation algorithms for disjoint paths problems. Ph.D. thesis, MIT, Cambridge (1996)
Krishnaswamy, R., Sivarajan, K.: Algorithms for routing and wavelength assignment based on solutions of LP-relaxation. IEEE Commun. Lett. 5, 435–437 (2001)
Lee, T., Lee, K., Park, S.: Optimal routing and wavelength assignment in WDM ring networks. IEEE J. Sel. Areas Commun. 18, 2146–2154 (2000)
Lei, D.: Fuzzy job shop scheduling problem with availability constraints. Comput. Ind. Eng. 58, 610–617 (2010)
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, pp. 1–19. Dallas (2000)
Malve, S., Uzsoy, R.: A genetic algorithm for minimizing maximum lateness on parallel identical batch processing machines with dynamic job arrivals and incompatible job families. Comput. Oper. Res. 34, 3016–3028 (2007)
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)
Marković, G., Aćimović-Raspopović, V.: Solving the RWA problem in WDM optical networks using the BCO meta-heuristic. Telfor J. 2, 43–48 (2010)
Martins, A.X., Duhamel, C., De Souza, M.C., Saldanha, R.R., Mahey, P.: A VND-ILS heuristic to solve the RWA problem. In: Pahl, J., Reiners, T., Vo, S. (eds.) Network Optimization, pp. 577–582. Springer, Berlin (2011)
Martins, A.X., Duhamel, C., Mahey, P., de Souza, M.C., Saldanha, R.R.: Geração de colunas para o problema de roteamento e atribuição de comprimentos de onda. In: Anais do XLIV Simp. Bras. Pesq. Operacional, pp. 1–12. Rio de Janeiro (2012)
Martins, A.X.: Metaheurísticas e formulações para a resolução do problema de roteamento e alocação de comprimentos de onda em redes ópticas. Ph.D. thesis, Universidade Federal de Minas Gerais (2011)
Martins, A.X., Duhamel, C., Mahey, P., Saldanha, R.R., de Souza, M.C.: Variable neighborhood descent with iterated local search for routing and wavelength assignment. Comput. Oper. Res. 39, 2133–2141 (2012)
Noronha, T.F., Resende, M.G.C., Ribeiro, C.C.: Efficient implementation of heuristics for routing and wavelength assigment. Lect. Notes Comput. Sci. 5038, 169–180 (2008)
Noronha, T.F., Resende, M.G.C., Ribeiro, C.C.: A biased random-key genetic algorithm for routing and wavelength assignment. J. Global Optim. 50, 503–518 (2011)
Noronha, T.F., Ribeiro, C.C.: Routing and wavelength assignment by partition coloring. Eur. J. Oper. Res. 171, 797–810 (2006)
Qin, H., Liu, Z., Zhang, S., Wen, A.: Routing and wavelength assignment based on genetic algorithm. Commun. Lett. 6(10), 455–457 (2002)
Ramaswami, R., Sivarajan, K.: Optimal routing and wavelength assignment in all-optical networks. In: Proceedings of IEEE INFOCOM Conference on Computer Communications, pp. 970–979. Toronto (1994)
Reis, R., Ritt, M., Buriol, L.S., Resende, M.G.C.: A biased random-key genetic algorithm for OSPF and DEFT routing to minimize network congestion. Int. Trans. Oper. Res. 18, 401–423 (2011)
Ribeiro, C.C., Rosseti, I.: tttplots-compare: a perl program to compare time-to-target plots or general runtime distributions of randomized algorithms. Optim. Lett. 9, 601–614 (2015)
Ribeiro, C.C., Rosseti, I., Vallejos, R.: Exploiting run time distributions to compare sequential and parallel stochastic local search algorithms. J. Global Optim. 54, 405–429 (2012)
Roque, L., Fontes, D., Fontes, F.: A hybrid biased random key genetic algorithm approach for the unit commitment problem. J. Comb. Optim. 28(1), 140–166 (2014)
Schrage, L.: A more portable Fortran random number generator. ACM Trans. Math. Softw. 5, 132–138 (1979)
Skorin-Kapov, N.: Routing and wavelength assigment in optical networks using bin packing based algorithms. Eur. J. Oper. Res. 177, 1167–1179 (2007)
Spears, W., deJong, 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. Morgan Kaufman, San Mateo (1991)
Wang, C.S., Uzsoy, R.: A genetic algorithm to minimize maximum lateness on a batch processing machine. Comput. Oper. Res. 29, 1621–1640 (2002)
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)
Zheng, J.N., Chien, C.F., Gen, M.: Multi-objective multi-population biased random-key genetic algorithm for the 3-D container loading problem. Comput. Ind. Eng. 89, 80–87 (2015)
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This work was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq), the Foundation for Support of Research of the State of Minas Gerais (FAPEMIG), the Foundation for Support of Research of the State of Rio de Janeiro (FAPERJ), and the Coordination for the Improvement of Higher Education Personnel, Brazil (CAPES).
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Brandão, J.S., Noronha, T.F. & Ribeiro, C.C. A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks. J Glob Optim 65, 813–835 (2016). https://doi.org/10.1007/s10898-015-0389-x
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DOI: https://doi.org/10.1007/s10898-015-0389-x