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Hybridizations of GRASP with Path-Relinking

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Hybrid Metaheuristics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 434))

Abstract

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. GRASP heuristics are multistart procedures which apply local search to a set of starting solutions generated with a randomized greedy algorithm or semi-greedy method. The best local optimum found over the iterations is returned as the heuristic solution. Path-relinking is a search intensification procedure that explores paths in the neighborhood solution space connecting two good-quality solutions. A local search procedure is applied to the best solution found in the path and the local optimum found is returned as the solution of path-relinking. The hybridization of path-relinking and GRASP adds memory mechanisms to GRASP. This chapter describes basic concepts of GRASP, path-relinking, and the hybridization of GRASP with path-relinking.

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References

  1. Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel GRASP with path-relinking for job shop scheduling. Parallel Computing 29, 393–430 (2003)

    Article  MathSciNet  Google Scholar 

  2. Aiex, R.M., Pardalos, P.M., Resende, M.G.C., Toraldo, G.: GRASP with path-relinking for three-index assignment. INFORMS J. on Computing 17, 224–247 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aiex, R.M., Resende, M.G.C.: Parallel strategies for GRASP with path-relinking. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as Real Problem Solvers, pp. 301–331. Springer (2005)

    Google Scholar 

  4. Aiex, R.M., Resende, M.G.C., Ribeiro, C.C.: TTTPLOTS: A perl program to create time-to-target plots. Optimization Letters 1, 355–366 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Alpay, S.: GRASP with path relinking for a multiple objective sequencing problem for a mixed-model assembly line. International J. of Production Research 47, 6001–6017 (2009)

    Article  MATH  Google Scholar 

  6. Andrade, D.V., Resende, M.G.C.: A GRASP for PBX telephone migration scheduling. In: Proceedings of The Eighth INFORMS Telecommunications Conference (2006)

    Google Scholar 

  7. Andrade, D.V., Resende, M.G.C.: GRASP with path-relinking for network migration scheduling. In: Proceedings of the International Network Optimization Conference (2007)

    Google Scholar 

  8. de Andrade, M.R.Q., de Andrade, P.M.F., Martins, S.L., Plastino, A.: GRASP with Path-Relinking for the Maximum Diversity Problem. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 558–569. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Bartkutė, V., Felinskas, G., Sakalauskas, L.: Optimality testing in stochastic and heuristic algorithms. Technological and Economic Development of Economy 12(1), 4–10 (2006)

    Google Scholar 

  10. Bastos, L.O., Ochi, L.S., Macambira, E.M.: GRASP with path-relinking for the SONET ring assignment problem. In: International Conference on Hybrid Intelligent Systems, pp. 239–244. IEEE Computer Society, Los Alamitos (2005)

    Google Scholar 

  11. Beasley, J.E.: A Lagrangian heuristic for set-covering problems. Naval Research Logistics 37, 151–164 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  12. Binato, S., Faria Jr., H., Resende, M.G.C.: Greedy randomized adaptive path relinking. In: Sousa, J.P. (ed.) Proceedings of the IV Metaheuristics International Conference, pp. 393–397 (2001)

    Google Scholar 

  13. Boender, C.G.E., Rinnooy Kan, A.H.G.: Bayesian stopping rules for multistart global optimization methods. Mathematical Programming 37, 59–80 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  14. Boudia, M., Louly, M.A.O., Prins, C.: A reactive GRASP and path relinking for a combined production-distribution problem. Computers and Operations Research 34, 3402–3419 (2007)

    Article  MATH  Google Scholar 

  15. Canuto, S.A., Resende, M.G.C., Ribeiro, C.C.: Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 38, 50–58 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Colomé, R., Serra, D.: Consumer choice in competitive location models: Formulations and heuristics. Papers in Regional Science 80, 439–464 (2001)

    Article  Google Scholar 

  17. Commander, C.W., Butenko, S.I., Pardalos, P.M., Oliveira, C.A.S.: Reactive GRASP with path relinking for the broadcast scheduling problem. In: Proceedings of the 40th Annual International Telemetry Conference, pp. 792–800 (2004)

    Google Scholar 

  18. de la Peña, M.G.B.: Heuristics and metaheuristics approaches used to solve the rural postman problem: A comparative case study. In: Proceedings of the Fourth International ICSC Symposium on Engineering of Intelligent Systems, EIS 2004 (2004), http://www.x-cd.com/eis04/22.pdf

  19. Delmaire, H., Díaz, J.A., Fernández, E., Ortega, M.: Reactive GRASP and tabu search based heuristics for the single source capacitated plant location problem. INFOR 37, 194–225 (1999)

    Google Scholar 

  20. Deng, Y., Bard, J.F.: A reactive GRASP with path relinking for capacitated clustering. J. of Heuristics 17, 119–152 (2011)

    Article  MATH  Google Scholar 

  21. Dorea, C.C.Y.: Stopping rules for a random optimization method. SIAM J. on Control and Optimization 28, 841 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  22. Duarte, A., Martí, R., Resende, M.G.C., Silva, R.M.A.: GRASP with path relinking heuristics for the antibandwidth problem. Networks 58, 171–189 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ribeiro, C.C., Vianna, D.S.: A GRASP/VND heuristic for the phylogeny problem using a new neighborhood structure. International Transactions in Operational Research 12, 325–338 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  24. Faria Jr., H., Binato, S., Resende, M.G.C., Falcão, D.J.: Transmission network design by a greedy randomized adaptive path relinking approach. IEEE Transactions on Power Systems 20, 43–49 (2005)

    Article  Google Scholar 

  25. Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters 8, 67–71 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  26. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. of Global Optimization 6, 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  27. Festa, P., Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: GRASP with path-relinking for the weighted MAXSAT problem. ACM J. of Experimental Algorithmics 11, 1–16 (2006)

    MathSciNet  Google Scholar 

  28. Festa, P., Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: GRASP with path relinking for the weighted MAXSAT problem. J. of Experimental Algorithmics 11(2.4) (2007)

    Google Scholar 

  29. Festa, P., Pardalos, P.M., Resende, M.G.C., Ribeiro, C.C.: Randomized heuristics for the MAX-CUT problem. Optimization Methods and Software 7, 1033–1058 (2002)

    Article  MathSciNet  Google Scholar 

  30. Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP, Part I: Algorithms. International Transactions in Operational Research 16, 1–24 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP, Part II: Applications. International Transactions in Operational Research 16, 131–172 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  32. Garey, M.R., Johnson, D.S.: Computers and intractability - A guide to the theory of NP-completeness. W.H. Freeman and Company (1979)

    Google Scholar 

  33. Gendreau, M., Potvin, J.-Y. (eds.): Handbook of Metaheuristics, 2nd edn. International Series in Operations Research & Management Science, vol. 146. Springer (2010)

    Google Scholar 

  34. Geng, Y., Li, Y., Lim, A.: A very large-scale neighborhood search approach to capacitated warehouse routing problem. In: 17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2005), pp. 58–65 (2005)

    Google Scholar 

  35. 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 Publishers (1996)

    Google Scholar 

  36. Glover, F., Kochenberger, G. (eds.): Handbook of Metaheuristics. Kluwer Academic Publishers (2003)

    Google Scholar 

  37. Gupta, S.R., Smith, J.S.: Algorithms for single machine total tardiness scheduling with sequence dependent setups. European J. of Operational Research 175, 722–739 (2006)

    Article  MATH  Google Scholar 

  38. Hart, J.P., Shogan, A.W.: Semi-greedy heuristics: An empirical study. Operations Research Letters 6, 107–114 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  39. Hart, W.E.: Sequential stopping rules for random optimization methods with applications to multistart local search. SIAM J. on Optimization, 270–290 (1998)

    Google Scholar 

  40. Laguna, M., González-Velarde, J.L.: A search heuristic for just-in-time scheduling in parallel machines. J. of Intelligent Manufacturing 2, 253–260 (1991)

    Article  Google Scholar 

  41. Laguna, M., Martí, R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J. on Computing 11, 44–52 (1999)

    Article  MATH  Google Scholar 

  42. Liu, X., Pardalos, P.M., Rajasekaran, S., Resende, M.G.C.: A GRASP for frequency assignment in mobile radio networks. In: Badrinath, B.R., Hsu, F., Pardalos, P.M., Rajasejaran, S. (eds.) Mobile Networks and Computing. DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 52, pp. 195–201. American Mathematical Society (2000)

    Google Scholar 

  43. Marinakis, Y., Migdalas, A., Pardalos, P.M.: Multiple phase neighborhood search – GRASP based on Lagrangean relaxation, random backtracking Lin–Kernighan and path relinking for the TSP. J. of Combinatorial Optimization 17, 134–156 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  44. Martins, S.L., Pardalos, P.M., Resende, M.G.C., Ribeiro, C.C.: Greedy randomized adaptive search procedures for the Steiner problem in graphs. In: Pardalos, P.M., Rajasejaran, S., Rolim, J. (eds.) Randomization Methods in Algorithmic Design. DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 43, pp. 133–145. American Mathematical Society (1999)

    Google Scholar 

  45. Martins, S.L., Ribeiro, C.C., Rosseti, I.: Applications and Parallel Implementations of Metaheuristics in Network Design and Routing. In: Manandhar, S., Austin, J., Desai, U., Oyanagi, Y., Talukder, A.K. (eds.) AACC 2004. LNCS, vol. 3285, pp. 205–213. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  46. Mateus, G.R., Resende, M.G.C., Silva, R.M.A.: GRASP with path-relinking for the generalized quadratic assignment problem. J. of Heuristics 17, 527–565 (2011)

    Article  MATH  Google Scholar 

  47. Nascimento, M.C.V., Resende, M.G.C., Toledo, F.M.B.: GRASP with path-relinking for the multi-plant capacitated plot sizing problem. In: European J. of Operational Research (2008) (to appear)

    Google Scholar 

  48. Oliveira, C.A.S., Pardalos, P.M., Resende, M.G.C.: GRASP with Path-Relinking for the Quadratic Assignment Problem. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 356–368. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  49. Orsenigo, C., Vercellis, C.: Bayesian stopping rules for greedy randomized procedures. J. of Global Optimization 36(3), 365–377 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  50. Pacheco, J.A., Casado, S.: Solving two location models with few facilities by using a hybrid heuristic: A real health resources case. Computers and Operations Research 32, 3075–3091 (2005)

    Article  MATH  Google Scholar 

  51. Pessoa, L.S., Resende, M.G.C., Ribeiro, C.C.: A hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering. Technical report. AT&T Labs Research, Shannon Laboratory, Florham Park, NJ 07932 (2010)

    Google Scholar 

  52. Pessoa, L.S., Resende, M.G.C., Ribeiro, C.C.: Experiments with LAGRASP heuristic for set k-covering. Optimization Letters 5, 407–419 (2011)

    Article  MathSciNet  Google Scholar 

  53. Pinana, E., Plana, I., Campos, V., Martí, R.: GRASP and path relinking for the matrix bandwidth minimization. European J. of Operational Research 153, 200–210 (2004)

    Article  MATH  Google Scholar 

  54. Prais, M., Ribeiro, C.C.: Reactive GRASP: An application to a matrix decomposition problem in TDMA traffic assignment. INFORMS J. on Computing 12, 164–176 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  55. Reghioui, M., Prins, C., Labadi, N.: GRASP with Path Relinking for the Capacitated arc Routing Problem with Time Windows. In: Giacobini, M. (ed.) EvoWorkshops 2007. LNCS, vol. 4448, pp. 722–731. Springer, Heidelberg (2007)

    Google Scholar 

  56. Resende, M.G.C., Martí, R., Gallego, M., Duarte, A.: GRASP and path relinking for the max-min diversity problem. Computers and Operations Research 37, 498–508 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  57. Resende, M.G.C., Ribeiro, C.C.: A GRASP with path-relinking for private virtual circuit routing. Networks 41, 104–114 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  58. 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. Springer (2005)

    Google Scholar 

  59. Resende, M.G.C., Ribeiro, C.C.: Greedy randomized adaptive search procedures: Advances and applications. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics, 2nd edn. International Series in Operations Research & Management Science, vol. 146, pp. 281–317. Springer (2010)

    Google Scholar 

  60. Resende, M.G.C., Ribeiro, C.C., Glover, F., Martí, R.: Scatter search and path-relinking: Fundamentals, advances, and applications. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics, 2nd edn. International Series in Operations Research & Management Science, vol. 146, pp. 87–107. Springer (2010)

    Google Scholar 

  61. Resende, M.G.C., Werneck, R.F.: A hybrid heuristic for the p-median problem. J. of Heuristics 10, 59–88 (2004)

    Article  MATH  Google Scholar 

  62. Resende, M.G.C., Werneck, R.F.: A hybrid multistart heuristic for the uncapacitated facility location problem. European J. of Operational Research 174, 54–68 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  63. Ribeiro, C.C., Resende, M.G.C.: Path-relinking intensification methods for stochastic local search algorithms. J. of Heuristics (2011) (to appear)

    Google Scholar 

  64. Ribeiro, C.C., Rosseti, I.: A Parallel GRASP Heuristic for the 2-Path Network Design Problem. In: Monien, B., Feldmann, R.L. (eds.) Euro-Par 2002. LNCS, vol. 2400, pp. 922–926. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  65. Ribeiro, C.C., Rosseti, I.: Efficient parallel cooperative implementations of GRASP heuristics. Parallel Computing 33, 21–35 (2007)

    Article  MathSciNet  Google Scholar 

  66. Ribeiro, C.C., Rosseti, I., Souza, R.C.: Effective Probabilistic Stopping Rules for Randomized Metaheuristics: GRASP Implementations. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 146–160. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  67. Ribeiro, C.C., Souza, M.C.: Variable neighborhood search for the degree constrained minimum spanning tree problem. Discrete Applied Mathematics 118, 43–54 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  69. Ribeiro, C.C., Urrutia, S.: Heuristics for the mirrored traveling tournament problem. European J. of Operational Research 179, 775–787 (2007)

    Article  MATH  Google Scholar 

  70. Ronconi, D.P., Henriques, L.R.S.: Some heuristic algorithms for total tardiness minimization in a flowshop with blocking. Omega 37, 272–281 (2009)

    Article  Google Scholar 

  71. Scaparra, M., Church, R.: A GRASP and path relinking heuristic for rural road network development. J. of Heuristics 11, 89–108 (2005)

    Article  MATH  Google Scholar 

  72. Schrijver, A.: Theory of linear and integer programming. John Wiley & Sons, Ltd., West Sussex (1996)

    Google Scholar 

  73. Souza, M.C., Duhamel, C., Ribeiro, C.C.: A GRASP heuristic for the capacitated minimum spanning tree problem using a memory-based local search strategy. In: Resende, M.G.C., de Sousa, J.P. (eds.) Metaheuristics: Computer Decision-Making, pp. 627–658. Kluwer Academic Publisher (2004)

    Google Scholar 

  74. Vazirani, V.V.: Approximation algorithms. Springer, Berlin (2001)

    Google Scholar 

  75. Williamson, D.P., Shmoys, D.B.: The design of approximation algorithms. Cambridge University Press, New York (2011)

    Book  MATH  Google Scholar 

  76. Wolsey, L.A., Nemhauser, G.L.: Integer and combinatorial optimization. John Wiley & Sons, Inc., New York (1999)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Applications, University of Napoli Federico II, 80126, Napoli, Italy

    Paola Festa

  2. Algorithms and Optimization Research Department, AT&T Labs Research, Florham Park, NJ, 07932, USA

    Mauricio G. C. Resende

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  1. Paola Festa
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  2. Mauricio G. C. Resende
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Correspondence to Paola Festa .

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  1. , Cite Scientifique, University of Lille 1, Bat.M3, Villeneuve d'Ascq, 59655, France

    El-Ghazali Talbi

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Festa, P., Resende, M.G.C. (2013). Hybridizations of GRASP with Path-Relinking. In: Talbi, EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_5

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