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A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks

Author

Listed:
  • Julliany S. Brandão

    (Universidade Federal Fluminense (UFF))

  • Thiago F. Noronha

    (Universidade Federal de Minas Gerais (UFMG))

  • Celso C. Ribeiro

    (Universidade Federal Fluminense (UFF))

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 %.

Suggested Citation

  • Julliany S. Brandão & Thiago F. Noronha & Celso C. Ribeiro, 2016. "A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks," Journal of Global Optimization, Springer, vol. 65(4), pages 813-835, August.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0389-x
    DOI: 10.1007/s10898-015-0389-x
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    References listed on IDEAS

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    1. L. A. C. Roque & D. B. M. M. Fontes & F. A. C. C. Fontes, 2014. "A hybrid biased random key genetic algorithm approach for the unit commitment problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 140-166, July.
    2. Celso Ribeiro & Isabel Rosseti & Reinaldo Vallejos, 2012. "Exploiting run time distributions to compare sequential and parallel stochastic local search algorithms," Journal of Global Optimization, Springer, vol. 54(2), pages 405-429, October.
    3. Skorin-Kapov, Nina, 2007. "Routing and wavelength assignment in optical networks using bin packing based algorithms," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1167-1179, March.
    4. M. Ericsson & M.G.C. Resende & P.M. Pardalos, 2002. "A Genetic Algorithm for the Weight Setting Problem in OSPF Routing," Journal of Combinatorial Optimization, Springer, vol. 6(3), pages 299-333, September.
    5. Thiago Noronha & Mauricio Resende & Celso Ribeiro, 2011. "A biased random-key genetic algorithm for routing and wavelength assignment," Journal of Global Optimization, Springer, vol. 50(3), pages 503-518, July.
    6. Goncalves, Jose Fernando & de Magalhaes Mendes, Jorge Jose & Resende, Mauricio G. C., 2005. "A hybrid genetic algorithm for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 167(1), pages 77-95, November.
    7. James C. Bean, 1994. "Genetic Algorithms and Random Keys for Sequencing and Optimization," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 154-160, May.
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    1. Bruno Q. Pinto & Celso C. Ribeiro & Isabel Rosseti & Thiago F. Noronha, 2020. "A biased random-key genetic algorithm for routing and wavelength assignment under a sliding scheduled traffic model," Journal of Global Optimization, Springer, vol. 77(4), pages 949-973, August.

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