Adaptive memory in multistart heuristics for multicommodity network design | Journal of Heuristics Skip to main content
Springer Nature Link
Log in

Adaptive memory in multistart heuristics for multicommodity network design

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

This paper focuses on the use of different memory strategies to improve multistart methods. A network design problem in which the costs are given by discrete stepwise increasing cost functions of the capacities installed in the edges is used to illustrate the contributions of adaptive memory and vocabulary building strategies. Heuristics based on shortest path and maximum flow algorithms are combined with adaptive memory in order to obtain an approximate solution to the problem in the framework of a multistart algorithm. Furthermore, a vocabulary building intensification mechanism supported by the resolution of a linear program is also explored. Numerical experiments have shown that the proposed algorithm obtained the best known solutions for some instances in the literature. These results show the contribution of each memory component and the effectiveness of their combination.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Ahuja, R., Ergun, O., Orlin, J., Punnen, A.: A survey of very large-scale neighborhood search techniques. Discrete Appl. Math. 123, 75–102 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Aiex, R.M., Resende, M.G.C., Ribeiro, C.C.: TTTPLOTS: a Perl program to create time-to-target plots. Opt. Lett. 1, 355–366 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • An, L.T.H., Tao, P.D.: D.C. programming approach for multicommodity network optimization problems with step increasing cost functions. J. Glob. Optim. 22, 205–232 (2002)

    Article  MATH  Google Scholar 

  • Bazlamaçci, C.F., Say, F.: Minimum concave cost multicommodity network design. Telecommun. Syst. 36, 181–203 (2007)

    Article  Google Scholar 

  • Berger, D., Gendron, B., Potvin, J.-Y., Raghavan, S., Soriano, P.: Tabu search for a network loading problem with multiple facilities. J. Heuristics 6, 253–267 (2000)

    Article  MATH  Google Scholar 

  • Cherkassky, B., Goldberg, A.: On implementing Push-Relabel method for the maximum flow problem. Algorithmica 19, 390–410 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Chopra, S., Gilboa, I., Sastry, S.: Algorithms and extended formulations for one and two facility network design. In: Lecture Notes in Computer Science, vol. 1084, pp. 44–57. Springer, Berlin (1996)

    Google Scholar 

  • Fleurent, C., Glover, F.: Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J. Comput. 11, 198–204 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Fratta, L., Gerla, M., Kleinrock, L.: The flow-deviation method: an approach to store-and-forward communication network design. Networks 3, 97–133 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • Gabrel, V., Knippel, A., Minoux, M.: Exact solution of multicommodity network optimization problems with general step cost functions. Oper. Res. Lett. 25, 15–23 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Gabrel, V., Knippel, A., Minoux, M.: A comparison of heuristics for the discrete cost multicommodity network optimization problem. J. Heuristics 9, 429–445 (2003)

    Article  Google Scholar 

  • Gabrel, V., Minoux, M.: LP relaxations better than convexification for multicommodity networks optimization problems with step increasing cost functions. Acta Math. Vietnam. 22, 123–145 (1997)

    MathSciNet  MATH  Google Scholar 

  • Geoffrion, G., Graves, G.: Multicommodity distribution system design by Benders decomposition. Manag. Sci. 5, 822–844 (1974)

    Article  MathSciNet  Google Scholar 

  • Ghamlouche, I., Crainic, T., Gendreau, M.: Path-relinking, cycle-based neighborhoods and capacitated multicommodity network design. Ann. Oper. Res. 131, 109–133 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Glover, F.: Ejection chains, reference structures and alternating path methods for traveling salesman problem. Discrete Appl. Math. 49, 231–255 (1992)

    Article  MathSciNet  Google Scholar 

  • Glover, F.: Tabu search and adaptive memory programming—advances, applications and challenges. In: Barr, R.S., Helgason, R.V., Kennington, J.L. (eds.) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer Academic, Norwell (1996)

    Google Scholar 

  • Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Norwell (1997)

    MATH  Google Scholar 

  • Goldberg, A.: An efficient implementation of a scaling minimum-cost flow algorithm. J. Algorithms 22, 1–29 (1997)

    Article  MathSciNet  Google Scholar 

  • Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)

    Article  MATH  Google Scholar 

  • Jain, R.: The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling. Wiley, New York (1991)

    MATH  Google Scholar 

  • Kennington, J.: A survey of linear cost multicommodity network flows. Oper. Res. 26, 209–236 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • Knippel, A.: Modèles et algorithmes de multiflots à cout discontinu pour l’optimisation de réseau de télécommunications. PhD thesis, Université Paris VI (2001)

  • Laguna, M., Martí, R., Campos, V.: Intensification and diversification with elite tabu search solutions for the linear ordering problem. Comput. Oper. Res. 26, 1217–1230 (1999)

    Article  MATH  Google Scholar 

  • Magnanti, T., Wong, R.: Network design and transportation planning-models and algorithms. Transp. Sci. 18, 1–55 (1984)

    Article  Google Scholar 

  • Mahey, P., Ouorou, A., LeBlanc, L., Chifflet, J.: A new proximal decomposition algorithm for routing in telecommunication networks. Networks 31, 227–238 (1998)

    Article  MATH  Google Scholar 

  • Melián, B., Laguna, M., Moreno-Pérez, J.A.: Capacity expansion of fiber optic networks with WDM systems: problem formulation and comparative analysis. Comput. Oper. Res. 31, 461–472 (2004)

    Article  MATH  Google Scholar 

  • Minoux, M.: Network synthesis and optimum network design problems: models, solution methods and applications. Networks 19, 313–360 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • Minoux, M.: Discrete cost multicommodity network optimization problems and exact solution methods. Ann. Oper. Res. 106, 19–46 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Mrad, M., Haouari, M.: Optimal solution of the discrete cost multicommodity network design problem. Appl. Math. Comput. 204, 745–753 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Resende, M.G.C., Ribeiro, C.C.: GRASP with path-relinking: recent advances and applications. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as Real Problem Solvers, pp. 29–63. Kluwer Academic, Norwell (2005)

    Chapter  Google Scholar 

  • Ribeiro, C.C.: Approximate algorithms for the automatic planning of power transmission systems (in Portuguese). Master’s thesis, COPPE, Universidade Federal do Rio de Janeiro (1978)

  • Ribeiro, C.C., Uchoa, E., Werneck, R.F.: A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J. Comput. 14, 228–246 (2002)

    Article  MathSciNet  Google Scholar 

  • Rochat, Y., Taillard, É.: Probabilistic diversification and intensification in local search for vehicle routing. J. Heuristics 1, 147–167 (1995)

    Article  MATH  Google Scholar 

  • Rolland, E., Patterson, R.A., Pirkul, H.: Memory adaptive reasoning and greedy assignment techniques for the CSMT. In: Voss, S., Martello, S., Osman, I., Roucairol, C. (eds.) Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pp. 487–498. Kluwer Academic, Norwell (1999)

    Google Scholar 

  • Schrage, L.: A more portable FORTRAN random number generator. ACM Trans. Math. Softw. 5, 132–138 (1979)

    Article  MATH  Google Scholar 

  • Stoer, M., Dahl, G.: A polyhedral approach to multicommodity survivable network design. Numer. Math. 68, 149–167 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Stoer, M., Dahl, G.: A cutting-plane algorithm for multicommodity survivable network design problem. INFORMS J. Comput. 10, 1–11 (1998)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Production Engineering, Universidade Federal do Rio Grande do Norte, Natal, RN, 59072-970, Brazil

    Daniel Aloise

  2. Department of Computer Science, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, RJ, 24210-240, Brazil

    Celso C. Ribeiro

Authors
  1. Daniel Aloise
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Celso C. Ribeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Aloise.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aloise, D., Ribeiro, C.C. Adaptive memory in multistart heuristics for multicommodity network design. J Heuristics 17, 153–179 (2011). https://doi.org/10.1007/s10732-010-9130-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-010-9130-6

Keywords

Search

Navigation