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Solving the routing and wavelength assignment problem with a multilevel distributed memetic algorithm

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Abstract

The Routing and Wavelength Assignment problem is a graph optimization problem which deals with optical networks, where communication requests in a network have to be fulfilled. In this paper, we present a multilevel distributed memetic algorithm (ML-DMA) for the static RWA which finds provable optimal solutions for most benchmark instances with known lower bounds and is capable of handling large instances. Components of our ML-DMA include iterated local search, recombination, multilevel scaling, and a gossip-based distribution algorithm. Results demonstrated that our ML-DMA is among the most sophisticated heuristic RWA algorithms published so far.

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References

  1. Agrawal GP (2002) Fiber-optic communication systems, 3rd edn. Wiley, New York

    Google Scholar 

  2. Alkan A, Özcan E (2003) Memetic algorithms for timetabling. Congress on Evolutionary Computation (CEC’03)

  3. Atamtürk A, Rajan D (2008) Partition inequalities for capacitated survivable network design based on directed p-cycles. Discrete Optimization 5(2):415–433. Available at http://ieor.berkeley.edu/~atamturk/data/

    Google Scholar 

  4. Banerjee D, Mukherjee B (1996) A practical approach for routing and wavelength assignment in large wavelength-routed optical networks. IEEE J Select Areas Commun 14(5): 903–908

    Article  Google Scholar 

  5. Banerjee N, Mehta V, Pandey S (2004) A genetic algorithm approach for solving the routing and wavelength assignment problem in WDM networks. In: Proceedings of the international conference on networks (ICN’04)

  6. Banerjee N, Sharan S (2004) A evolutionary algorithm for solving the single objective static routing and wavelength assignment problem in WDM networks. In: Proceedings of international conference on intelligent sensing and information processing (ICISIP 2004), pp 13–18

  7. Banerjee S, Chen C (1996) Design of wavelength-routed optical networks for circuit switched traffic. In: Global telecommunications conference, GLOBECOM, vol 1, pp 306–310

  8. Baroni S, Bayvel P (1997) Wavelength requirements in arbitrarily connected wavelength-routed optical networks. J Lightwave Technol 15(2): 242–251

    Article  Google Scholar 

  9. Bauer K, Fischer T, Krumke SO, Gerhardt K, Westphal S, Merz P (2008) Improved construction heuristics and iterated local search for the routing and wavelength assignment problem. In: van Hemert J, Cotta C (eds) EvoCOP 2008—eighth european conference on evolutionary computation in combinatorial optimization. Lecture notes in computer science, vol 4972. Springer, Heidelberg, March, pp 158–169

  10. Bollobás B (2001) Random graphs. Cambridge Studies in advanced mathematics. Cambridge University Press, Cambridge

    Google Scholar 

  11. Chlamtac I, Faragó A, Zhang T (1996) Lightpath (wavelength) routing in large wdm networks. IEEE J Select Areas Commun 14(5)

  12. Chlamtac I, Ganz A, Karmi G (1992) Lightpath communications: an approach to high bandwidth optical WANs. IEEE Trans Commun 40(7): 1171–1182

    Article  Google Scholar 

  13. de Noronha TF, Resende MGC, Ribeiro CC (2007) A random-keys genetic algorithm for routing and wavelength assignment. In: Proceedings of the seventh metaheuristics international conference MIC (2007)

  14. Noronha TF, Ribeiro CC (2006) Routing and wavelength assignment by partition colouring. Eur J Oper Res 171(3): 797–810

    Article  MATH  MathSciNet  Google Scholar 

  15. Demers A, Greene D, Hauser C, Irish W, Larson J, Shenker S, Sturgis H, Swinehart D, Terry D (1987) Epidemic algorithms for replicated database maintenance. In: Schneider FB (ed) Proceedings of the 6th annual ACM symposium on principles of distributed computing. ACM Press, pp 1–12

  16. Erdős P, Rényi A (1959) On random graphs I. Publ Math Debrecen 6: 290–297

    MathSciNet  Google Scholar 

  17. Eugster PT, Guerraoui R, Kermarrec A-M, Massoulié L (2004) From epidemics to distributed computing. IEEE Comput

  18. Fischer T, Bauer K, Merz P (2008) A distributed memetic algorithm for the routing and wavelength assignment problem. In: Rudolph G, Jansen T, Lucas S, Poloni C, Beume N (eds) Parallel problem solving from nature—PPSN X—10th international conference. Lecture notes in computer science, vol 5199. Springer, Heidelberg, pp 879–888

    Google Scholar 

  19. Fischer T, Bauer K, Merz P (2008) A multilevel approach for the routing and wavelength assignment problem. In: Köppen M, Raidl G (eds) Workshop on heuristic methods for the design, deployment, and reliability of networks and network applications (HEUNET 2008) at the international symposium on applications and the internet (SAINT 2008). IEEE Computer Society, Turku, pp 225–228

    Google Scholar 

  20. Fischer T, Merz P (2007) A memetic algorithm for the optimal communication spanning tree problem. In: Bartz-Beielstein T, Blesa Aguilera MJ, Blum C, Naujoks B, Roli A, Rudolph G, Sampels M (eds) Hybrid metaheuristics, 4th international workshop, HM. Proceedings, Lecture notes in computer science, vol 4771. Springer, Dortmund, pp 170–184 October 8–9

    Google Scholar 

  21. Fischer T, Merz P (2007) Embedding a chained Lin–Kernighan algorithm into a distributed algorithm. In: Doerner KF, Gendreau M, Greistorfer P, Gutjahr WJ, Hartl RF, Reimann M (eds) Metaheuristics—progress in complex systems optimization, vol 39. Operations Research/Computer Science Interfaces. Springer, Heidelberg, pp 277–295

    Google Scholar 

  22. Grote N, Venghaus H (2001) Fibre optic communication devices. Springer, Berlin

    Google Scholar 

  23. Hyytiä E (2004) Heuristic algorithms for the generalized routing and wavelength assignment problem. In: Seventeenth Nordic Teletraffic Seminar, NTS-17, Fornebu, Norway, pp. 373–386

  24. Hyytiä E, Virtamo J (1998) Wavelength assignment and routing in WDM networks. In: Fourteenth nordic teletraffic seminar, NTS-14, Lyngby, pp 31–40

  25. Jelasity M, Voulgaris S, Guerraoui R, Kermarrec A-M, van Steen M (2007) Gossip-based peer sampling. ACM Trans Comput Syst 25(3)

  26. Kleinberg J (1996) Approximation algorithms for disjoint paths problems. PhD thesis, Dept. of EECS, MIT, Cambridge

  27. Li G, Simha R (2000) The partition coloring problem and its application to wavelength routing and assignment. In: Prof. of Optical Networks Workshop

  28. Manohar P, Manjunath D, Shevgaonkar RK (2002) Routing and wavelength assignment in optical networks from edge disjoint path algorithms. IEEE Commun Lett 6(5): 211–213

    Article  Google Scholar 

  29. Margara L, Simon J (2000) Wavelength assignment problem on all-optical networks with k fibres per link. In: Automata, Languages and Programming, pp 768–779

  30. Mattern F (1987) Algorithms for distributed termination detection. Distribut Comput 2(3): 161–175

    Article  Google Scholar 

  31. Merz P (2000) Memetic algorithms for combinatorial optimization problems: fitness landscapes and effective search strategies. PhD thesis, Department of Electrical Engineering and Computer Science, University of Siegen, Germany

  32. Merz P, Freisleben B (2000) Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans Evol Comput 4(4): 337–352

    Article  Google Scholar 

  33. Merz P, Freisleben B (2001) Memetic algorithms for the traveling salesman problem. Complex Syst 13(4): 297–345

    MathSciNet  Google Scholar 

  34. Moscato P (1989) On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms. Technical Report Caltech Concurrent Computation Program, Report. 826, California Institute of Technology, Pasadena

  35. Moscato P (1999) Memetic algorithms: a short introduction. In: Corne D, Dorigo M, Glover F (eds) New ideas in optimization. McGraw-Hill, New York, pp 219–234

    Google Scholar 

  36. Mukherjee B (2006) Optical WDM networks. Optical Networks. Springer, Heidelberg

    Google Scholar 

  37. Nagatsu N, Hamazumi Y, Sato K-I (1995) Number of wavelengths required for constructing large-scale optical path networks. Electron Commun Jpn (Part I Commun) 78(9): 1–11

    Article  Google Scholar 

  38. Orlowski S, Pióro M, Tomaszewski A, Wessäly R (2007) SNDlib 1.0–Survivable Network Design Library. In: Proceedings of the 3rd international network optimization conference (INOC 2007), Spa, Belgium, April 2007. http://sndlib.zib.de

  39. Radcliffe NJ, Surry PD (1994) Fitness variance of formae and performance prediction. In: Whitley LD, Vose MD (eds) Proceedings of the third workshop on foundations of genetic algorithms. Morgan Kaufmann, San Francisco, pp 51–72

    Google Scholar 

  40. Ramaswami R, Sivarajan KN (1996) Design of logical topologies for wavelength-routed optical networks. IEEE J Select Areas Commun 14(5): 840–851

    Article  Google Scholar 

  41. Sharafat AR, Ma’rouzi OR (2004) The most congested cutset: deriving a tight lower bound for the chromatic number in the RWA problem. IEEE Commun Lett 8(7): 473–475

    Article  Google Scholar 

  42. Sinclair MC (1998) Minimum cost routing and wavelength allocation using a genetic-algorithm/heuristic hybrid approach. In: Proc. 6th IEE conf. telecommunications, March

  43. Skorin-Kapov N (2007) Routing and wavelength assignment in optical networks using bin packing based algorithms. Eur J Oper Res 177(2): 1167–1179

    Article  MATH  MathSciNet  Google Scholar 

  44. Stoer M (1992) Design of survivable networks Lecture notes in mathematics, vol 1531. Springer, Berlin

    Google Scholar 

  45. Tan LG, Sinclair MC (1995) Wavelength assignment between the central nodes of the COST 239 European optical network. In: 11th UK performance engineering workshop, pp 235– 247

  46. Tang M, Yao X (2007) A memetic algorithm for VLSI floorplanning. IEEE Trans Syst Man Cybernet (Part B Cybernet) 37(1): 62–69

    Article  Google Scholar 

  47. Varela GN, Sinclair MC (1999) Ant colony optimisation for virtual-wavelength-path routing and wavelength allocation. In: Proceedings of the congress on evolutionary computation, pp 1809–1816

  48. Walshaw C (2004) Multilevel refinement for combinatorial optimisation problems. Ann Oper Res 131: 325–372

    Article  MATH  MathSciNet  Google Scholar 

  49. Wang Y, Cheng TH, Lim MH (2005) A Tabu search algorithm for static routing and wavelength assignment problem. IEEE Commun Lett 9(9): 841–843

    Article  Google Scholar 

  50. Wauters N, Demeester P (1996) Design of the optical path layer in multiwavelength cross-connected networks. IEEE J Select Areas Commun 14(5): 881–892

    Article  Google Scholar 

  51. Xu S, Li L, Wang S (2000) Dynamic routing and assignment of wavelength algorithms in multifiber wavelength division multiplexing networks. IEEE J Select Areas Commun 18(10): 2130–2137

    Article  Google Scholar 

  52. Yoon WJ, Kim DH, Chung MY, Lee T-J, Choo H (2006) Routing with maximum EDPs and wavelength assignment with path conflict graphs. In: Gavrilova ML, Gervasi O, Kumar V, Tan CJK, Taniar D, Laganà A, Mun Y, Choo H (eds) ICCSA (2). Lecture notes in computer science, vol 3981. Springer, Heidelberg, pp 856–865

    Google Scholar 

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Authors and Affiliations

  1. Distributed Algorithms Group, Department of Computer Science, University of Kaiserslautern, Kaiserslautern, Germany

    Thomas Fischer, Kerstin Bauer & Peter Merz

  2. Embedded Systems Group, Department of Computer Science, University of Kaiserslautern, Kaiserslautern, Germany

    Kerstin Bauer

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  1. Thomas Fischer
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  2. Kerstin Bauer
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  3. Peter Merz
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  4. Kerstin Bauer
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Correspondence to Thomas Fischer.

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Fischer, T., Bauer, K., Merz, P. et al. Solving the routing and wavelength assignment problem with a multilevel distributed memetic algorithm. Memetic Comp. 1, 101–123 (2009). https://doi.org/10.1007/s12293-008-0006-3

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