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Approximating the Pareto front of a bi-objective problem in telecommunication networks using a co-evolutionary algorithm

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Abstract

This paper studies a telecommunication network design problem. In this network, users must be connected to capacitated hubs. Then, hubs that concentrate users must be connected to each other and possibly to other hubs with no users. The connections in the network must lead to a tree topology. Hence, connection between hubs can be considered as looking for forming a Steiner tree. This problem is modeled as a bi-objective mathematical programming problem. One objective function minimizes user’s latency with respect to the information packages flowing through the capacitated hubs, and the other objective function aims the minimization of the total network’s connection cost. To approximate the Pareto front of this bi-objective problem, a co-evolutionary algorithm is developed. In the proposed algorithm, two populations are considered. Each population is associated with one objective function. The co-evolutionary operator consists of an information exchange between both populations that occurs after the genetic operators have been applied. As a result of this co-evolutionary operator, the non-dominated solutions are identified. Computational experimentation shows that the approximated Pareto fronts are representative despite their non-convexity, and they contain a sufficient number of non-dominated solutions over the tested instances. Also, the kth distance among non-dominated solutions is relatively small, which indicates that the approximated Pareto fronts are dense. Furthermore, the required computational time is very small for a problem with the characteristics herein considered.

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References

  1. Van Hoesel, S. (2005). Optimization in telecommunication networks. Statistica Neerlandica, 59(2), 180–205.

    MathSciNet  MATH  Google Scholar 

  2. Corne, D., Oates, M. J., & Smith, G. D. (Eds.). (2000). Telecommunications optimization: Heuristics and adaptive techniques. New York: Wiley.

    Google Scholar 

  3. Vasant, P., Litvinchev, I., & Marmolejo-Saucedo, J. A. (Eds.). (2017). Modeling, simulation, and optimization. Berlin: Springer.

    Google Scholar 

  4. Minoux, M. (1989). Networks synthesis and optimum network design problems: Models, solution methods and applications. Networks, 19(3), 313–360.

    MathSciNet  MATH  Google Scholar 

  5. Winter, P. (1987). Steiner problem in networks: A survey. Networks, 17, 129–167.

    MathSciNet  MATH  Google Scholar 

  6. Du, D. Z., Lu, B., Ngo, H., & Pardalos, P. M. (2009). Steiner tree problems. In C. A. Floudas & P. M. Pardalos (Eds.), Encyclopedia of optimization (2nd ed.). Berlin: Springer.

    Google Scholar 

  7. Dror, M., & Haouari, M. (2000). Generalized Steiner problems and other variants. Journal of Combinatorial Optimization, 4, 415–436.

    MathSciNet  MATH  Google Scholar 

  8. Biniaz, A., Maheshwari, A., & Smid, M. (2015). On the hardness of full Steiner tree problems. Journal of Discrete Algorithms, 34, 118–127.

    MathSciNet  MATH  Google Scholar 

  9. Khuller, S., & Zhu, A. (2002). The general Steiner tree-star problem. Information Processing Letters, 84, 215–220.

    MathSciNet  MATH  Google Scholar 

  10. Marmolejo, J. A., Litvinchev, I., Aceves, R., & Ramirez, J. M. (2011). Multiperiod optimal planning of thermal generation using cross decomposition. Journal of Computer and Systems Sciences International, 50(5), 793–804.

    MathSciNet  MATH  Google Scholar 

  11. Voss, S. (1992). Steiner’s problem in graphs: Heuristic methods. Discrete Applied Mathematics, 40, 45–72.

    MathSciNet  MATH  Google Scholar 

  12. Plesník, J. (1992). Heuristics for the Steiner problem in graphs. Discrete Applied Mathematics, 37, 451–463.

    MathSciNet  MATH  Google Scholar 

  13. Martins, S. L., Ribeiro, C., & Souza, M. (1998). A parallel GRASP for the Steiner problem in graphs. In A. Ferreira, & J. Rolim, (Eds.), Proceedings of IRREGULAR98 5th international symposium on solving irregularly structured problems in parallel, vol. 1457 of lecture notes in computer science (pp. 285–297). Berlin: Springer.

  14. Consoli, S., Pérez, J. M., Darby-Dowman, K., & Mladenović, N. (2008). Discrete particle swarm optimization for the minimum labelling Steiner tree problem. In Nature inspired cooperative strategies for optimization (NICSO 2007) (pp. 313–322). Berlin: Springer.

  15. Ribeiro, C. C., & De Souza, M. C. (2000). Tabu search for the Steiner problem in graphs. Networks: An International Journal, 36(2), 138–146.

    MathSciNet  MATH  Google Scholar 

  16. Gendreau, M., Larochelle, J. F., & Sanso, B. (1999). A tabu search heuristic for the Steiner tree problem. Networks: An International Journal, 34(2), 162–172.

    MathSciNet  MATH  Google Scholar 

  17. Bastos, M. P., & Ribeiro, C. C. (2002). Reactive tabu search with path-relinking for the Steiner problem in graphs. In C. C. Ribeiro, & P. Hansen (Eds.), Essays and surveys in metaheuristics. Operations research/computer science interfaces series (Vol. 15, pp. 39–58). Boston, MA: Springer.

    Google Scholar 

  18. Consoli, S., Darby-Dowman, K., Mladenović, N., & Moreno-Pérez, J. A. (2009). Variable neighbourhood search for the minimum labelling Steiner tree problem. Annals of Operations Research, 172(1), 71–96.

    MathSciNet  MATH  Google Scholar 

  19. Camacho-Vallejo, J.-F., Mar-Ortiz, J., López-Ramos, F., & Rodríguez, R. P. (2015). A genetic algorithm for the bi-level topological design of local area networks. PLoS ONE, 10(6), 1–21.

    Google Scholar 

  20. Dehouche, N. (2018). Devolutionary genetic algorithms with application to the minimum labeling Steiner tree problem. Evolving Systems, 9, 157–168.

    Google Scholar 

  21. Liu, L., Song, Y., Zhang, H., Ma, H., & Vasilakos, A. V. (2015). Physarum optimization: A biology-inspired algorithm for the Steiner tree problem in networks. IEEE Transactions on Computers, 64(3), 818–831.

    MathSciNet  MATH  Google Scholar 

  22. Gouveia, L., Leitner, M., & Ljubić, I. (2014). Hop constrained Steiner trees with multiple root nodes. European Journal of Operational Research, 236, 100–112.

    MathSciNet  MATH  Google Scholar 

  23. Fu, Z.-H., & Hao, J.-K. (2014). Breakout local search for the Steiner tree problem with revenue, budget and hop constraints. European Journal of Operational Research, 232, 209–220.

    MathSciNet  MATH  Google Scholar 

  24. Leggieri, V., Haouari, M., & Triki, Ch. (2014). The Steiner tree problem with delays: A compact formulation and reduction procedures. Discrete Applied Mathematics, 164, 178–190.

    MathSciNet  MATH  Google Scholar 

  25. DiPuglia, L., Gaudioso, M., Guerriero, F., & Miglionico, G. (2018). A Lagrangean-based decomposition approach for the link constrained Steiner tree problem. Optimization Methods and Software, 33(3), 650–670.

    MathSciNet  MATH  Google Scholar 

  26. Xu, J., Chiu, S. Y., & Glover, F. (1996). Using tabu search to solve the Steiner tree-star problem in telecommunications network design. Telecommunication Systems, 6, 117–125.

    Google Scholar 

  27. Lee, Y., Lu, L., & Qiu, Y. (1994). Strong formulations and cutting planes for designing digital data service networks. Telecommunication Systems, 2, 261–274.

    Google Scholar 

  28. Clarke, L. W., & Anandalingam, G. (1996). An integrated system for designing minimum cost survivable telecommunications networks. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 26(6), 856–862.

    Google Scholar 

  29. Ersoy, C., & Panwar, S. S. (1993). Topological design of interconnected LAN/MAN networks. IEEE Journal on Selected Areas in Communications, 2(8), 1172–1182.

    Google Scholar 

  30. Girard, A. (1993). Revenue optimization of telecommunication networks. IEEE Transactions on Communications, 41(4), 583–591.

    MATH  Google Scholar 

  31. Chen, D., Du, D. Z., Hu, X. D., Lin, G. H., Wang, L., & Xue, G. (2000). Approximations for Steiner trees with minimum number of Steiner points. Journal of Global Optimization, 18(1), 17–33.

    MathSciNet  MATH  Google Scholar 

  32. Orlowski, S., & Wessaly, R. (2006). The effect of hop limits on optimal cost in survivable network design. In S. Raghavan, & G. Anandalingam (Eds.) Telecommunications planning: Innovations in pricing, network design and management. Operations research/computer science interfaces series (Vol. 33, pp. 151–166). Boston, MA: Springer.

    Google Scholar 

  33. Sitters, R. (2002). The minimum latency problem is NP-hard for weighted trees. In International conference on integer programming and combinatorial optimization (pp. 230–239), Berlin: Springer.

  34. Martins, S. L., & Ferreira, N. G. (2011). A bi-criteria approach for Steiner’s tree problems in communication networks. In U. Krieger, & P. Van Mieghem (Eds.), Proceedings of international workshop on modeling, analysis and control of complex networks, ITCP (International Teletraffic Congress, San Francisco) (pp. 37–44).

  35. Marathe, M. V., Ravi, R., Sundaram, R., Ravi, S. S., Rosenkrantz, D. J., & Hunt, H. B, I. I. I. (1998). Bicriteria network design problems. Journal of Algorithms, 28(1), 142–171.

    MathSciNet  MATH  Google Scholar 

  36. Potter, M. A. (1997). The design and analysis of a computational model of cooperative co-evolution, Ph.D. Thesis, George Mason University.

  37. Venter, G., & Haftka, R. T. (1996). A two species genetic algorithm for designing composite laminates subjected to uncertainty. In Proceedings of 37th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference (pp. 1848–1857).

  38. Sun, Y., Zhang, L., & Gu, X. (2012). A hybrid co-evolutionary cultural algorithm based on particle swarm optimization for solving global optimization problems. Neurocomputing, 98, 76–89.

    Google Scholar 

  39. Goh, C. K., Tan, K. C., Liu, D. S., & Chiam, S. C. (2010). A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design. European Journal of Operational Research, 202(1), 42–54.

    MATH  Google Scholar 

  40. Gen, M., Kumar, A., & Kim, J. R. (2005). Recent network design techniques using evolutionary algorithms. International Journal of Production Economics, 98(2), 251–261.

    Google Scholar 

  41. Wang, X., Wang, S., & Ma, J. J. (2007). An improved co-evolutionary particle swarm optimization for wireless sensor networks with dynamic deployment. Sensors, 7(3), 354–370.

    Google Scholar 

  42. Casas-Ramírez, M. S., & Camacho-Vallejo, J. F. (2017). Solving the p-median bilevel problem with order through a hybrid heuristic. Applied Soft Computing, 60, 73–86.

    Google Scholar 

  43. Kim, J. R., Lee, J. U., & Jo, J. B. (2009). Hierarchical spanning tree network design with Nash genetic algorithm. Computers & Industrial Engineering, 56(3), 1040–1052.

    Google Scholar 

  44. Sipper, M., Fu, W., Ahuja, K., & Moore, J. H. (2018). Investigating the parameter space of evolutionary algorithms. BioData Mining, 11(2), 2–14.

    Google Scholar 

  45. Martí, R., González-Velarde, J. L., & Duarte, A. (2009). Heuristics for the bi-objective path dissimilarity problem. Computers & Operations Research, 36(11), 2905–2912.

    MATH  Google Scholar 

  46. Bard, J. F. (1998). Practical bilevel optimization: Algorithms and applications. Dordrecht: Kluwer.

    MATH  Google Scholar 

  47. Kalashnikov, V. V., Dempe, S., Pérez-Valdés, G. A., Kalashnykova, N. I., & Camacho-Vallejo, J.-F. (2015). Bilevel programming and applications. Mathematical Problems in Engineering. https://doi.org/10.1155/2015/310301

    Article  MathSciNet  MATH  Google Scholar 

  48. Sinha, A., Malo, P., & Deb, K. (2018). A review on bilevel optimization: From classical to evolutionary approaches and applications. IEEE Transactions on Evolutionary Computation, 22(2), 276–295.

    Google Scholar 

  49. Cruz-Mejia, O., Marmolejo, J. A., & Vasant, P. (2018). Lead time performance in a internet product delivery supply chain with automatic consolidation. Journal of Ambient Intelligence and Humanized Computing, 9(3), 867–874.

    Google Scholar 

  50. Ibarra-Rojas, O. J., Delgado, F., Giesen, R., & Muñoz, J. C. (2015). Planning, operation, and control of bus transport systems: A literature review. Transportation Research Part B: Methodological, 77, 38–75.

    Google Scholar 

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Acknowledgements

The research of the first author has been partially supported by the program of professional development of professors with the Grant PRODEP/511-6/17/7425 for research stays during his sabbatical year.

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Authors and Affiliations

  1. Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, San Nicolás, Mexico

    José-Fernando Camacho-Vallejo

  2. Centro de Investigación en Matemáticas A.C., Guanajuato, Mexico

    Cristóbal Garcia-Reyes

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  1. José-Fernando Camacho-Vallejo
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  2. Cristóbal Garcia-Reyes
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Correspondence to José-Fernando Camacho-Vallejo.

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Camacho-Vallejo, JF., Garcia-Reyes, C. Approximating the Pareto front of a bi-objective problem in telecommunication networks using a co-evolutionary algorithm. Wireless Netw 26, 4881–4893 (2020). https://doi.org/10.1007/s11276-018-01921-4

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