Advertisement

Greedy Randomized Adaptive Search Procedures: Advances, Hybridizations, and Applications

  • Mauricio G.C. Resende
  • Celso C. Ribeiro
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 146)

Abstract

GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, we first describe the basic components of GRASP. Successful implementation techniques are discussed and illustrated by numerical results obtained for different applications. Enhanced or alternative solution construction mechanisms and techniques to speed up the search are also described: alternative randomized greedy construction schemes, Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss implementation strategies of memory-based intensification and post-optimization techniques using path-relinking. Hybridizations with other metaheuristics, parallelization strategies, and applications are also reviewed.

Keywords

Local Search Tabu Search Construction Phase Iterate Local Search Bias Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abdinnour-Helm, S., Hadley, S.W.: Tabu search based heuristics for multi-floor facility layout. Int. J. Prod. Res. 38, 365–383 (2000)CrossRefGoogle Scholar
  2. 2.
    Abello, J., Pardalos, P.M., Resende, M.G.C.: On maximum clique problems in very large graphs. In: Abello, J., Vitter, J. (eds.) External Memory Algorithms and Visualization, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 50 pages 199–130. American Mathematical Society Boston, MA (1999)Google Scholar
  3. 3.
    Abello, J. Resende, M.G.C., Sudarsky, S.: Massive quasi-clique detection. In: Rajsbaum, S. (ed.) LATIN 2002: Theoretical Informatics, Lecture Notes in Computer Science, vol. 2286 pp. 598–612. Springer, Cancun (2002)CrossRefGoogle Scholar
  4. 4.
    Ahuja, R.K., Orlin, J.B., Sharma, D.: Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem. Math. Program. 91, 71–97 (2001)Google Scholar
  5. 5.
    Ahuja, R.K., Orlin, J.B., Tiwari, A.: A greedy genetic algorithm for the quadratic assignment problem. Comput. Op. Res. 27, 917–934 (2000)CrossRefGoogle Scholar
  6. 6.
    Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel GRASP with path-relinking for job shop scheduling. Parallel Comput. 29, 393–430 (2003)CrossRefGoogle Scholar
  7. 7.
    Aiex, R.M., Pardalos, P.M., Resende, M.G.C., Toraldo, G.: GRASP with path-relinking for three-index assignment. INFORMS J. Comput. 17, 224–247 (2005)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    álvarez-Valdés, R., Crespo, E., Tamarit, J.M., Villa, F.: GRASP and path relinking for project scheduling under partially renewable resources. Eur. J. Op. Res. 189, 1153–1170 (2008)CrossRefGoogle Scholar
  10. 10.
    álvarez-Valdés, R., Parreno, F., Tamarit, J.M.: A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems. J. Op. Res. Soc. 56, 414–425 (2005)CrossRefGoogle Scholar
  11. 11.
    Alvarez-Valdesa, R., Parreno, F., Tamarit, J.M.: Reactive GRASP for the strip-packing problem. Comput. Op. Res. 35, 1065–1083 (2008)CrossRefGoogle Scholar
  12. 12.
    Alvim, A.C.: Parallelization strategies for the metaheuristic GRASP. Master’s thesis, Department of Computer Science, Catholic University of Rio de Janeiro, Brazil [In Portuguese] (1998)Google Scholar
  13. 13.
    Alvim, A.C., Ribeiro, C.C.: Load balancing for the parallelization of the GRASP metaheuristic. In: Proceedings of the X Brazilian Symposium on Computer Architecture, pp. 279–282, Búzios [In Portuguese] (1998)Google Scholar
  14. 14.
    Amaldi, E., Capone, A., Malucelli, F.: Planning UMTS base station location: Optimization models With power control and algorithms. IEEE Trans. Wireless Commun. 2, 939–952 (2003)CrossRefGoogle Scholar
  15. 15.
    Amaldi, E., Capone, A., Malucelli, F., Signori, F.: Optimization models and algorithms for downlink UMTS radio planning. Proc. Wireless Commun. Networking, 2, 827–831 (2003)Google Scholar
  16. 16.
    Andrade, D.V., Resende, M.G.C.: A GRASP for PBX telephone migration scheduling. In: Proceedings of The 8th INFORMS Telecommunications Conference, Dallas, TX (2006)Google Scholar
  17. 17.
    Andrade, D.V., Resende, M.G.C.: GRASP with evolutionary path-relinking. Technical Report TD-6XPTS7, AT&T Labs Research, Florham Park (2007)Google Scholar
  18. 18.
    Andrade, D.V., Resende, M.G.C.: GRASP with path-relinking for network migration scheduling. In: Proceedings of the International Network Optimization Conference, Spa (2007)Google Scholar
  19. 19.
    Andreatta, A.A., Ribeiro, C.C.: Heuristics for the phylogeny problem. J. Heuristics 8, 429–447 (2002)CrossRefGoogle Scholar
  20. 20.
    Andrés, C., Miralles, C., Pastor, R.: Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. Eur. J. Op. Res. 187, 1212–1223 (2008)CrossRefGoogle Scholar
  21. 21.
    Araújo, A.P.F.: Autonomic Parallelization of Metaheuristics in Grid Environments. PhD thesis, Department of Computer Science, Catholic University of Rio de Janeiro [In Portuguese] (2008)Google Scholar
  22. 22.
    Araújo, A.P.F., Boeres, C., Rebello, V.E.F., Ribeiro, C.C., Urrutia, S.: Exploring grid implementations of parallel cooperative metaheuristics: A case study for the mirrored traveling tournament problem. In: Doerner, K.F., Gendreau, M., Greistorfer, P., Gutjahr, W., Hartl, R.F., Reimann, M. (eds.) Metaheuristics: Progress in Complex Systems Optimization, pp. 297–322. Springer, New York, NY (2007)Google Scholar
  23. 23.
    Areibi, S., Vannelli, A.: A GRASP clustering technique for circuit partitioning. In: Gu J., Pardalos, P.M. (eds.) Satisfiability Problems, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 35 pp. 711–724. American Mathematical Society, Providence, Rhode Island, USA (1997)Google Scholar
  24. 24.
    Areibi, S.M.: >GRASP: An effective constructive technique for VLSI circuit partitioning. In: Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, Edmonton, AB (1999)Google Scholar
  25. 25.
    Argüello, M.F., Bard, J.F., Yu, G.: A GRASP for aircraft routing in response to groundings and delays. J. Comb. Op. 1, 211–228 (1997)CrossRefGoogle Scholar
  26. 26.
    Argüello, M.F., Feo, T.A., Goldschmidt, O. Randomized methods for the number partitioning problem. Comput. Op. Res. 23, 103–111 (1996)CrossRefGoogle Scholar
  27. 27.
    Armony, M., Klincewicz, J.C., Luss, H., Rosenwein, M.B. Design of stacked self-healing rings using a genetic algorithm. J. Heuristics 6, 85–105 (2000)CrossRefGoogle Scholar
  28. 28.
    Arroyo, J.E.C., Vieira, P.S., Vianna, D.S. A GRASP algorithm for the multi-criteria minimum spanning tree problem. Ann. Op. Res. 159, 125–133 (2008)CrossRefGoogle Scholar
  29. 29.
    Atkinson, J.B.: A greedy randomised search heuristic for time-constrained vehicle scheduling and the incorporation of a learning strategy. J. Op. Res. Soc. 49, 700–708 (1998)Google Scholar
  30. 30.
    Bard, J.F.: An analysis of a rail car unloading area for a consumer products manufacturer. J. Op. Res. Soc. 48, 873–883 (1997)Google Scholar
  31. 31.
    Bard, J.F., Feo, T.A.: Operations sequencing in discrete parts manufacturing. Manage. Sci. 35, 249–255 (1989)CrossRefGoogle Scholar
  32. 32.
    Bard, J.F., Feo, T.A.: An algorithm for the manufacturing equipment selection problem. IIE Trans. 23, 83–92 (1991)CrossRefGoogle Scholar
  33. 33.
    Bard, J.F., Feo, T.A., Holland, S.: A GRASP for scheduling printed wiring board assembly. IIE Trans. 28, 155–165 (1996)CrossRefGoogle Scholar
  34. 34.
    Bard, J.F., Huang, L., Jaillet, P., Dror, M.: A decomposition approach to the inventory routing problem with satellite facilities. Transp. Sci. 32, 189–203 (1998)CrossRefGoogle Scholar
  35. 35.
    Baum, E.B.: Iterated descent: A better algorithm for local search in combinatorial optimization problems. Technical report, California Institute of Technology (1986)Google Scholar
  36. 36.
    Baum, E.B. Towards practical ‘neural’ computation for combinatorial optimization problems. In: AIP Conference Proceedings 151 on Neural Networks for Computing, pp. 53–58, Woodbury, American Institute of Physics (1987)Google Scholar
  37. 37.
    Baxter, J.: Local optima avoidance in depot location. J. Op. Res. Soc. 32, 815–819 (1981)Google Scholar
  38. 38.
    Beasley, J.E.: OR-Library: Distributing test problems by electronic mail. J. Op. Res. Soc. 41, 1069–1072 (1990)Google Scholar
  39. 39.
    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 Kluwer, Porto, pp. 393–397 (2001)Google Scholar
  40. 40.
    Binato, S., Hery, W.J., Loewenstern, D., Resende, M.G.C. A GRASP for job shop scheduling. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 59–79. Kluwer, Norwell, MA (2002)Google Scholar
  41. 41.
    Binato, S., Oliveira, G.C.: A reactive GRASP for transmission network expansion planning. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 81–100. Kluwer, Norwell, MA (2002)Google Scholar
  42. 42.
    Binato, S., Oliveira, G.C., Araújo, J.L.: A greedy randomized adaptive search procedure for transmission expansion planning. IEEE Trans. Power Sys. 16, 247–253 (2001)CrossRefGoogle Scholar
  43. 43.
    Boudia, M., Louly, M.A.O., Prins, C.: A reactive GRASP and path relinking for a combined production-distribution problem. Comput. Op. Res. 34, 3402–3419 (2007)CrossRefGoogle Scholar
  44. 44.
    Bresina, J.L. Heuristic-biased stochastic sampling. In: Proceedings of the 13th National Conference on Artificial Intelligence, pp. 271–278, Portland (1996)Google Scholar
  45. 45.
    Campbell, A.M., Thomas, B.W.: Probabilistic traveling salesman problem with deadlines. Transp. Sci. 42, 1–21 (2008)CrossRefGoogle Scholar
  46. 46.
    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)CrossRefGoogle Scholar
  47. 47.
    Carreto, C., Baker, B. A GRASP interactive approach to the vehicle routing problem with backhauls. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 185–199. Kluwer, Norwell, MA (2002)Google Scholar
  48. 48.
    Charon, I., Hudry, O. The noising method: A new method for combinatorial optimization. Op. Res. Lett. 14, 133–137 (1993)CrossRefGoogle Scholar
  49. 49.
    Charon, I., Hudry, O.: The noising methods: A survey. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 245–261. Kluwer, Norwell, MA (2002)Google Scholar
  50. 50.
    Colomé, R., Serra, D.: Consumer choice in competitive location models: Formulations and heuristics. Pap. Reg. Sci. 80, 439–464 (2001)CrossRefGoogle Scholar
  51. 51.
    Commander, C., Oliveira, C.A.S., Pardalos, P.M., Resende, M.G.C.: A GRASP heuristic for the cooperative communication problem in ad hoc networks. In: Proceedings of the VI Metaheuristics International Conference, San Diego, CA pp. 225–330 (2005)Google Scholar
  52. 52.
    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. San Diego, California, USA (2004)Google Scholar
  53. 53.
    Corberán, A., Martí, R., Sanchís, J.M. A GRASP heuristic for the mixed Chinese postman problem. Eur. J. Op. Res. 142, 70–80 (2002)CrossRefGoogle Scholar
  54. 54.
    Cravo, G.L., Ribeiro, G.M., Nogueira Lorena, L.A.: A greedy randomized adaptive search procedure for the point-feature cartographic label placement. Comput. Geosci. 34, 373–386 (2008)CrossRefGoogle Scholar
  55. 55.
    Cung, V.-D., Martins, S.L., Ribeiro, C.C., Roucairol, C. Strategies for the parallel implementation of metaheuristics. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 263–308. Kluwer, Norwell, MA (2002)Google Scholar
  56. 56.
    De, P., Ghosj, J.B., Wells, C.E.: Solving a generalized model for con due date assignment and sequencing. Int. J. Prod. Econ. 34, 179–185 (1994)CrossRefGoogle Scholar
  57. 57.
    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
  58. 58.
    Deshpande, A.S., Triantaphyllou, E.: A greedy randomized adaptive search procedure (GRASP) for inferring logical clauses from examples in polynomial time and some extensions. Math. Comput. Model. 27, 75–99 (1998)CrossRefGoogle Scholar
  59. 59.
    Drexl, A., Salewski, F.: Distribution requirements and compactness constraints in school timetabling. Eur. J. Op. Res. 102, 193–214 (1997)CrossRefGoogle Scholar
  60. 60.
    Duarte, A., Ribeiro, C.C., Urrutia, S.: A hybrid ILS heuristic to the referee assignment problem with an embedded MIP strategy. Lect. Notes Comput. Sci. 4771, 82–95 (2007)CrossRefGoogle Scholar
  61. 61.
    Duarte, A.R., Ribeiro, C.C., Urrutia, S., Haeusler, E.H.: Referee assignment in sports leagues. Lect. Notes Comput. Sci. 3867, 158–173 (2007)CrossRefGoogle Scholar
  62. 62.
    Ribeiro, C.C., Vianna, D.S.: A GRASP/VND heuristic for the phylogeny problem using a new neighborhood structure. Int. Trans. Op. Res., 12, 325–338 (2005)CrossRefGoogle Scholar
  63. 63.
    Faria Jr., H., Binato, S., Resende, M.G.C., Falc ao, D.J.: Transmission network design by a greedy randomized adaptive path relinking approach. IEEE Trans. Power Syst. 20, 43–49 (2005)CrossRefGoogle Scholar
  64. 64.
    Feo, T.A., Bard, J.F.: Flight scheduling and maintenance base planning. Manag. Sci. 35, 1415–1432 (1989)CrossRefGoogle Scholar
  65. 65.
    Feo, T.A., Bard, J.F.: The cutting path and tool selection problem in computer-aided process planning. J. Manufact. Syst. 8, 17–26 (1989)CrossRefGoogle Scholar
  66. 66.
    Feo, T.A., Bard, J.F., Holland, S. Facility-wide planning and scheduling of printed wiring board assembly. Op. Res. 43, 219–230 (1995)CrossRefGoogle Scholar
  67. 67.
    Feo, T.A., González-Velarde, J.L.: The intermodal trailer assignment problem: Models, algorithms, and heuristics. Trans. Sci. 29, 330–341 (1995)CrossRefGoogle Scholar
  68. 68.
    Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Op. Res. Lett. 8, 67–71 (1989)CrossRefGoogle Scholar
  69. 69.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Global Optim. 6, 109–133 (1995)CrossRefGoogle Scholar
  70. 70.
    Feo, T.A., Resende, M.G.C., Smith, S.H.: A greedy randomized adaptive search procedure for maximum independent set. Op. Res. 42, 860–878 (1994)CrossRefGoogle Scholar
  71. 71.
    Feo, T.A., Sarathy, K., McGahan, J.: A GRASP for single machine scheduling with sequence dependent setup costs and linear delay penalties. Comput. Op. Res. 23, 881–895 (1996)CrossRefGoogle Scholar
  72. 72.
    Feo, T.A., Venkatraman, K., Bard, J.F.: A GRASP for a difficult single machine scheduling problem. Comput. Op. Res. 18, 635–643 (1991)CrossRefGoogle Scholar
  73. 73.
    Fernández, E., Martí, R.: GRASP for seam drawing in mosaicking of aerial photographic maps. J. Heuristics 5, 181–197 (1999)CrossRefGoogle Scholar
  74. 74.
    Festa, P.: On some optimization problems in molecular biology. Math. Biosci. 207, 219–234 (2007)CrossRefGoogle Scholar
  75. 75.
    Festa, P., Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: GRASP with path-relinking for the weighted MAXSAT problem. ACM J. Exp. Algorithmics 11, 1–16 (2006)Google Scholar
  76. 76.
    Festa, P., Pardalos, P.M., Resende, M.G.C.: Algorithm 815: FORTRAN subroutines for computing approximate solution to feedback set problems using GRASP. ACM Trans. Math. Softw 27, 456–464 (2001)CrossRefGoogle Scholar
  77. 77.
    Festa, P., Pardalos, P.M., Resende, M.G.C., Ribeiro, C.C.: Randomized heuristics for the MAX-CUT problem. Optim. Methods Softw. 7, 1033–1058 (2002)CrossRefGoogle Scholar
  78. 78.
    Festa, P., Resende, M.G.C.: GRASP: An annotated bibliography. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 325–367. Kluwer Norwell, MA (2002)Google Scholar
  79. 79.
    Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP, Part I: Algorithms. Int. Trans. Op. Res. 16, 1–24 (2009)CrossRefGoogle Scholar
  80. 80.
    Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP, Part II: Applications. Int. Trans. Op. Res., 16, 131–172 (2009)CrossRefGoogle Scholar
  81. 81.
    Festa, P., Resende, M.G.C., Pardalos, P., Ribeiro, C.C.: GRASP and VNS for Max-Cut. In: Extended Abstracts of the Fourth Metaheuristics International Conference, Porto pp. 371–376, Porto, July 2001Google Scholar
  82. 82.
    Fleurent, C., Glover, F.: Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J. Comput. 11, 198–204 (1999)CrossRefGoogle Scholar
  83. 83.
    Foster, I., Kesselman, C. (eds.): The GRID: Blueprint for a New Computing Infrastructure, Morgan Kaufmann San Francisco, CA (2004)Google Scholar
  84. 84.
    Foster, I., Kesselman, C., Tuecke, S. The anatomy of the grid: Enabling scalable virtual organizations. Int. J. Supercomput. Appl. 15, 200–222 (2001)CrossRefGoogle Scholar
  85. 85.
    Ghosh, J.B., Computational aspects of the maximum diversity problem. Op. Res. Lett. 19, 175–181 (1996)CrossRefGoogle Scholar
  86. 86.
    Glover, F.: New ejection chain and alternating path methods for traveling salesman problems. In: Balci, O., Sharda, R., Zenios, S. (eds.) Computer Science and Operations Research: New Developments in Their Interfaces, pp. 449–509. Elsevier, Oxford, UK (1992)Google Scholar
  87. 87.
    Glover, F.: Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Appl. Math. 65, 223–254 (1996)CrossRefGoogle Scholar
  88. 88.
    Glover, F.: Tabu search and adaptive memory programing – 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, Boston, MA, USA (1996)Google Scholar
  89. 89.
    Glover, F.: Multi-start and strategic oscillation methods – Principles to exploit adaptive memory. In: Laguna, M., Gonzáles-Velarde, J.L. (eds.) Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, pp. 1–24. Kluwer, Boston, MA, USA (2000)CrossRefGoogle Scholar
  90. 90.
    Glover, F., Laguna, M. Tabu Search. Kluwer, Boston, MA, USA (1997)CrossRefGoogle Scholar
  91. 91.
    Glover, F., Laguna, M., Martí, R.: Fundamentals of scatter search and path relinking. Control Cybern. 39, 653–684 (2000)Google Scholar
  92. 92.
    Goemans, M.X., Williamson, D.P.: The primal dual method for approximation algorithms and its application to network design problems. In: Hochbaum, D. (ed.) Approximation algorithms for NP-hard problems, pp. 144–191. PWS Publishing, Boston, MA, USA (1996)Google Scholar
  93. 93.
    Gomes, F.C., Oliveira, C.S., Pardalos, P.M., Resende, M.G.C. Reactive GRASP with path relinking for channel assignment in mobile phone networks. In: Proceedings of the 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 60–67. ACM Press, Rome, Italy (2001)Google Scholar
  94. 94.
    Hammer, P.L., Rader Jr, D.J. Maximally disjoint solutions of the set covering problem. J. Heuristics 7, 131–144 (2001)CrossRefGoogle Scholar
  95. 95.
    Han, B.T., Raja, V.T. A GRASP heuristic for solving an extended capacitated concentrator location problem. Int. J. Inf. Technol. Deci. Mak. 2, 597–617 (2003)CrossRefGoogle Scholar
  96. 96.
    Hansen, P., Mladenović, N. Developments of variable neighborhood search. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 415–439. Kluwer Norwoll, MA (2002)Google Scholar
  97. 97.
    Hart, J.P., Shogan, A.W.: Semi-greedy heuristics: An empirical study. Op. Res. Lett. 6, 107–114 (1987)CrossRefGoogle Scholar
  98. 98.
    Holmqvist, K., Migdalas, A., Pardalos, P.M.: Greedy randomized adaptive search for a location problem with economies of scale. In: Bomze, I.M. et al. (eds.) Developments in Global Optimization, pp. 301–313. Kluwer, Boston, MA, USA (1997)Google Scholar
  99. 99.
    Holmqvist, K., Migdalas, A., Pardalos, P.M.: A GRASP algorithm for the single source uncapacitated minimum concave-cost network flow problem. In: Pardalos, P.M., Du, D.-Z. (eds.) Network design: Connectivity and Facilities Location, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 40 pp. 131–142. American Mathematical Society, Providence, Rhode Island, USA (1998)Google Scholar
  100. 100.
    Johnson, D.S.: Local optimization and the traveling salesman problem. In: Proceedings of the 17th Colloquium on Automata, LNCS, vol. 443 pp. 446–461. Springer, London, UK (1990)Google Scholar
  101. 101.
    Klincewicz, J.G.: Avoiding local optima in the p-hub location problem using tabu search and GRASP. Ann. Op. Res. 40, 283–302 (1992)CrossRefGoogle Scholar
  102. 102.
    Klincewicz, J.G., Rajan, A.: Using GRASP to solve the component grouping problem. Nav. Res. Logist. 41:893–912 (1994)CrossRefGoogle Scholar
  103. 103.
    Kontoravdis, G., Bard, J.F.: A GRASP for the vehicle routing problem with time windows. ORSA J. Comput. 7, 10–23 (1995)Google Scholar
  104. 104.
    Laguna, M., Feo, T.A., Elrod, H.C.: A greedy randomized adaptive search procedure for the two-partition problem. Op. Res. 42, 677–687 (1994)CrossRefGoogle Scholar
  105. 105.
    Laguna, M., González-Velarde, J.L.: A search heuristic for just-in-time scheduling in parallel machines. J. Intell. Manufact. 2, 253–260 (1991)CrossRefGoogle Scholar
  106. 106.
    Laguna, M., Martí, R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J. Comput. 11, 44–52 (1999)CrossRefGoogle Scholar
  107. 107.
    Laguna, M., Martí, R.: A GRASP for coloring sparse graphs. Computt. Op. Appl. 19, 165–178 (2001)CrossRefGoogle Scholar
  108. 108.
    Li, Y., Pardalos, P.M., Resende, M.G.C.: A greedy randomized adaptive search procedure for the quadratic assignment problem. In: Pardalos, P.M., Wolkowicz, H. (eds.) Quadratic Assignment and Related Problems, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 16 pp. 237–261. American Mathematical Society, Providence, Rhode Island, USA (1994)Google Scholar
  109. 109.
    Lim, A., Rodrigues, B., Wang, C.: Two-machine flow shop problems with a single server. J. Scheduling 9, 515–543 (2006)CrossRefGoogle Scholar
  110. 110.
    Lim, A., Wang, F.: A smoothed dynamic tabu search embedded GRASP for m-VRPTW. In: Proceedings of ICTAI 2004, pp. 704–708, Boca Raton, Florida, USA (2004)Google Scholar
  111. 111.
    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, Providence, Rhode Island, USA (2000)Google Scholar
  112. 112.
    Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 321–353. Kluwer, Boston, MA, USA (2003)Google Scholar
  113. 113.
    Lourenço, H.R., Serra, D.: Adaptive approach heuristics for the generalized assignment problem. Mathware Soft Comput. 9, 209–234 (2002)Google Scholar
  114. 114.
    Lucena, A.P., Ribeiro, C.C., Santos, A.C.: A hybrid heuristic for the diameter constrained minimum spanning tree problem. J. Global Optim. 46, 363–381 (2010)CrossRefGoogle Scholar
  115. 115.
    Martí, R.: Arc crossing minimization in graphs with GRASP. IEE Trans. 33, 913–919 (2001)Google Scholar
  116. 116.
    Martí, R.: Arc crossing minimization in graphs with GRASP. IEEE Trans. 33, 913–919 (2002)Google Scholar
  117. 117.
    Martí, R., Estruch, V.: Incremental bipartite drawing problem. Comput. Op. Res. 28, 1287–1298 (2001)CrossRefGoogle Scholar
  118. 118.
    Martí, R., Laguna, M.: Heuristics and meta-heuristics for 2-layer straight line crossing minimization. Discrete App. Math. 127, 665–678 (2003)CrossRefGoogle Scholar
  119. 119.
    Martin, O., Otto, S.W.: Combining simulated annealing with local search heuristics. Ann. Op. Res. 63, 57–75 (1996)CrossRefGoogle Scholar
  120. 120.
    Martin, O., Otto, S.W., Felten, E.W.: Large-step Markov chains for the traveling salesman problem. Comp. Syst. 5, 299–326 (1991)Google Scholar
  121. 121.
    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, Providence, Rhode Island, USA (1999)Google Scholar
  122. 122.
    Martins, S.L., Resende, M.G.C., Ribeiro, C.C., Pardalos, P.: A parallel GRASP for the Steiner tree problem in graphs using a hybrid local search strategy. J. Global Optim. 17, 267–283 (2000)CrossRefGoogle Scholar
  123. 123.
    Martins, S.L., Ribeiro, C.C., Souza, M.C.: A parallel GRASP for the Steiner problem in graphs. In: Ferreira, A., Rolim, J. (eds.) Proceedings of IRREGULAR’98 – 5th International Symposium on Solving Irregularly Structured Problems in Parallel, Lecture Notes in Computer Science, vol. 1457 pp. 285–297. Springer, Berkeley, California, USA (1998)Google Scholar
  124. 124.
    Mavridou, T., Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: A GRASP for the biquadratic assignment problem. Eur. J. Op. Res. 105, 613–621 (1998)CrossRefGoogle Scholar
  125. 125.
    Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Op. Res. 24, 1097–1100 (1997)CrossRefGoogle Scholar
  126. 126.
    Monkman, S.K., Morrice, D.J., Bard, J.F.: A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs. Eur. J. Op. Res. 187, 1100–1114 (2008)CrossRefGoogle Scholar
  127. 127.
    Murphey, R.A., Pardalos, P.M., Pitsoulis, L.S.: A greedy randomized adaptive search procedure for the multitarget multisensor tracking problem. In: Pardalos, P.M., Du, D.-Z. (eds.) Network Design: Connectivity and Facilities Location, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 40 pp. 277–301. American Mathematical Society, Providence, Rhode Island, USA (1998)Google Scholar
  128. 128.
    Murphey, R.A., Pardalos, P.M., Pitsoulis, L.S.: A parallel GRASP for the data association multidimensional assignment problem. In: Pardalos, P.M. (ed.) Parallel Processing of Discrete Problems, The IMA Volumes in Mathematics and Its Applications, vol. 106 pp. 159–180. Springer, New York, NY, USA (1998)Google Scholar
  129. 129.
    Nascimento, M.C.V., Resende, M.G.C., Toledo, F.M.B.: GRASP with path-relinking for the multi-plant capacitated plot sizing problem. Euro. J. Oper. Res., 200(3), 747–754 (2010)CrossRefGoogle Scholar
  130. 130.
    Oliveira, C.A., Pardalos, P.M., Resende, M.G.C.: GRASP with path-relinking for the quadratic assignment problem. In: Ribeiro, C.C., Martins, S.L. (eds.) Proceedings of III Workshop on Efficient and Experimental Algorithms, LNCS, vol. 3059, pp. 356–368. Springer, Angra dos Reis, Brazil, (2004)CrossRefGoogle Scholar
  131. 131.
    Osman, I.H., Al-Ayoubi, B., Barake, M.: A greedy random adaptive search procedure for the weighted maximal planar graph problem. Comput. Ind. Eng. 45, 635–651 (2003)CrossRefGoogle Scholar
  132. 132.
    Pacheco, J.A., Casado, S.: Solving two location models with few facilities by using a hybrid heuristic: A real health resources case. Comput. Op. Res. 32, 3075–3091 (2005)CrossRefGoogle Scholar
  133. 133.
    Pardalos, P.M., Qian, T., Resende, M.G.C.: A greedy randomized adaptive search procedure for the feedback vertex set problem. J. Comb. Optim. 2, 399–412 (1999)CrossRefGoogle Scholar
  134. 134.
    Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: A parallel GRASP implementation for the quadratic assignment problem. In: Ferreira, A., Rolim, J. (eds.) Parallel Algorithms for Irregularly Structured Problems – Irregular’94, pp. 115–133. Kluwer, Dordrecht, The Netherlands (1995)Google Scholar
  135. 135.
    Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: A parallel GRASP for MAX-SAT problems. Lect. Notes Comput. Sci. 1184, 575–585 (1996)Google Scholar
  136. 136.
    Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C.: Algorithm 769: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP. ACM Trans. Math. Softw. 23, 196–208 (1997)CrossRefGoogle Scholar
  137. 137.
    Patterson, R.A., Pirkul, H., Rolland, E.: A memory adaptive reasoning technique for solving the capacitated minimum spanning tree problem. J. Heuristics 5, 159–180 (1999)CrossRefGoogle Scholar
  138. 138.
    Pinana, E., Plana, I., Campos, V., Martí, R.: GRASP and path relinking for the matrix bandwidth minimization. Eur. J. Op. Res. 153, 200–210 (2004)CrossRefGoogle Scholar
  139. 139.
    Pitsoulis, L.S., Pardalos, P.M., Hearn, D.W.: Approximate solutions to the turbine balancing problem. Eur. J. Op. Res. 130, 147–155 (2001)CrossRefGoogle Scholar
  140. 140.
    Poppe, F., Pickavet, M., Arijs, P., Demeester, P.: Design techniques for SDH mesh-restorable networks. In: Proceedings of the European Conference on Networks and Optical Communications, Volume 2: Core and ATM Networks, pp. 94–101. Antwerp, Belgium (1997)Google Scholar
  141. 141.
    Prais, M., Ribeiro, C.C.: Parameter variation in GRASP implementations. In: Extended Abstracts of the Third Metaheuristics International Conference, pp. 375–380, Angra dos Reis, Brazil (1999)Google Scholar
  142. 142.
    Prais, M., Ribeiro, C.C.: Parameter variation in GRASP procedures. Investigación Operativa. 9, 1–20 (2000)Google Scholar
  143. 143.
    Prais, M., Ribeiro, C.C.: Reactive GRASP: An application to a matrix decomposition problem in TDMA traffic assignment. INFORMS J. Comput. 12, 164–176 (2000)CrossRefGoogle Scholar
  144. 144.
    Rangel, M.C., Abreu, N.M.M., Boaventura Netto, P.O.: GRASP in the QAP: An acceptance bound for initial solutions. Pesqui. Operacional 20, 45–58 (2000)Google Scholar
  145. 145.
    Ravetti, M.G., Nakamura, F.G., Meneses, C.N., Resende, M.G.C., Mateus, G.R., Pardalos, P.M.: Hybrid heuristics for the permutation flow shop problem. Technical report, AT&T Labs Research Technical Report, Florham Park, New Jersey, USA (2006)Google Scholar
  146. 146.
    Reghioui, M., Prins, C., Nacima, L.: GRASP with path relinking for the capacitated arc routing problem with time windows. In: Giacobini, M. et al., (ed.) Applications of Evolutionary Computing, Lecture Notes in Computer Science, vol. 4448, pp. 722–731. Springer, Valencia, Spain (2007)Google Scholar
  147. 147.
    Resende, L.I.P., Resende, M.G.C.: A GRASP for frame relay permanent virtual circuit routing. In: Ribeiro, C.C., Hansen, P. (eds.) Extended Abstracts of the III Metaheuristics International Conference, pp. 397–401, Angra dos Reis, Brazil (1999)Google Scholar
  148. 148.
    Resende, M.G.C.: Computing approximate solutions of the maximum covering problem using GRASP. J. Heuristics 4, 161–171 (1998)CrossRefGoogle Scholar
  149. 149.
    Resende, M.G.C., Feo, T.A.: A GRASP for satisfiability. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, Coloring, and Satisfiability: The Second DIMACS Implementation Challenge, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 26 pp. 499–520. American Mathematical Society (1996)Google Scholar
  150. 150.
    Resende, M.G.C., Feo, T.A., Smith, S.H.: Algorithm 787: Fortran subroutines for approximate solution of maximum independent set problems using GRASP. ACM Trans. Math. Softw. 24, 386–394 (1998)CrossRefGoogle Scholar
  151. 151.
    Resende, M.G.C., Martí, R., Gallego, M., Duarte, A.: GRASP and path relinking for the max-min diversity problem. Computers and Operations Research, vol. 37, pp. 498–508 (2010)CrossRefGoogle Scholar
  152. 152.
    Resende, M.G.C., Pardalos, P.M., Li, Y.: Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP. ACM Trans. Math. Softw. 22, 104–118 (1996)CrossRefGoogle Scholar
  153. 153.
    Resende, M.G.C., Pitsoulis, L.S., Pardalos, P.M.: Approximate solution of weighted MAX-SAT problems using GRASP. In: Gu, J., Pardalos, P.M., (eds.) Satisfiability Problems, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 35 pp. 393–405. American Mathematical Society, Providence, Rhode Island, USA (1997)Google Scholar
  154. 154.
    Resende, M.G.C., Pitsoulis, L.S., Pardalos, P.M.: Fortran subroutines for computing approximate solutions of MAX-SAT problems using GRASP. Discrete Appl. Math. 100, 95–113 (2000)CrossRefGoogle Scholar
  155. 155.
    Resende, M.G.C., Ribeiro, C.C.: A GRASP for graph planarization. Networks 29, 173–189 (1997)CrossRefGoogle Scholar
  156. 156.
    Resende, M.G.C., Ribeiro, C.C.: A GRASP with path-relinking for private virtual circuit routing. Networks 41, 104–114 (2003)CrossRefGoogle Scholar
  157. 157.
    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, Boston, MA, USA (2005)CrossRefGoogle Scholar
  158. 158.
    Resende, M.G.C., Werneck, R.F.: A hybrid heuristic for the p-median problem. J. Heuristics 10, 59–88 (2004)CrossRefGoogle Scholar
  159. 159.
    Resende, M.G.C., Werneck, R.F.: A hybrid multistart heuristic for the uncapacitated facility location problem. Eur. J. Op. Res. 174, 54–68 (2006)CrossRefGoogle Scholar
  160. 160.
    Ribeiro, C.C.: GRASP: Une métaheuristique gloutone et probabiliste. In: Teghem, J., Pirlot, M. (eds.) Optimisation approchée en recherche opérationnelle, pp. 153–176. Hermès, Paris, France (2002)Google Scholar
  161. 161.
    Ribeiro, C.C., Resende, M.G.C.: Algorithm 797: Fortran subroutines for approximate solution of graph planarization problems using GRASP. ACM Trans. Math. Softw. 25, 342–352 (1999)CrossRefGoogle Scholar
  162. 162.
    Ribeiro, C.C., Ribeiro, C.D., Lanzelotte, R.S.: Query optimization in distributed relational databases. J. Heuristics 3, 5–23 (1997)CrossRefGoogle Scholar
  163. 163.
    Ribeiro, C.C., Rosseti, I.: Efficient parallel cooperative implementations of GRASP heuristics. Parall. Comput. 33, 21–35 (2007)CrossRefGoogle Scholar
  164. 164.
    Ribeiro, C.C., Souza, M.C.: Variable neighborhood search for the degree constrained minimum spanning tree problem. Discrete Appl. Math. 118, 43–54 (2002)CrossRefGoogle Scholar
  165. 165.
    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)CrossRefGoogle Scholar
  166. 166.
    Ribeiro, C.C., Urrutia, S.: Heuristics for the mirrored traveling tournament problem. Eur. J. Op. Res. 179, 775–787 (2007)CrossRefGoogle Scholar
  167. 167.
    Ríos-Mercado, R.Z., Bard, J.F.: Heuristics for the flow line problem with setup costs. Eur. J. Op. Res. 110, 76–98 (1998)CrossRefGoogle Scholar
  168. 168.
    Ríos-Mercado, R.Z., Bard, J.F.: An enhanced TSP-based heuristic for makespan minimization in a flow shop with setup costs. J. Heuristics 5, 57–74 (1999)CrossRefGoogle Scholar
  169. 169.
    Robertson, A.J.: A set of greedy randomized adaptive local search procedure (GRASP) implementations for the multidimensional assignment problem. Comput. Optim. Appl. 19, 145–164 (2001)CrossRefGoogle Scholar
  170. 170.
    Rocha, P.L., Ravetti, M.G., Mateus, G.R.: The metaheuristic GRASP as an upper bound for a branch and bound algorithm in a scheduling problem with non-related parallel machines and sequence-dependent setup times. In Proceedings of the 4th EU/ME Workshop: Design and Evaluation of Advanced Hybrid Meta-Heuristics, vol. 1, pp. 62–67, Nottingham, UK (2004)Google Scholar
  171. 171.
    Scaparra, M., Church, R.: A GRASP and path relinking heuristic for rural road network development. J. Heuristics 11, 89–108 (2005)CrossRefGoogle Scholar
  172. 172.
    Sosnowska, D.: Optimization of a simplified fleet assignment problem with metaheuristics: Simulated annealing and GRASP. In: Pardalos, P.M. (ed.) Approximation and complexity in numerical optimization. Kluwer, Boston, MA, USA (2000)Google Scholar
  173. 173.
    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., Souza, J. (eds.) Metaheuristics: Computer Decision-Making, pp. 627–658. Kluwer, Boston, MA, USA (2004)Google Scholar
  174. 174.
    Srinivasan, A., Ramakrishnan, K.G., Kumaram, K., Aravamudam, M., Naqvi, S.: Optimal design of signaling networks for Internet telephony. In IEEE INFOCOM 2000, vol. 2, pp. 707–716, Tel-Aviv, Israel (2000)Google Scholar
  175. 175.
    Takahashi, H., Matsuyama, A.: An approximate solution for the Steiner problem in graphs. Math. J. 24, 573–577 (1980)Google Scholar
  176. 176.
    Urban, T.L.: Solution procedures for the dynamic facility layout problem. Ann. Op. Res. 76, 323–342 (1998)CrossRefGoogle Scholar
  177. 177.
    Urban, T.L., Chiang, W.-C., Russel, R.A.: The integrated machine allocation and layout problem. Int. J. Prod. Res. 38, 2913–2930 (2000)CrossRefGoogle Scholar
  178. 178.
    Woodruff, D.L., Zemel, E.: Hashing vectors for tabu search. Ann. Op. Res. 41, 123–137 (1993)CrossRefGoogle Scholar
  179. 179.
    Xu, J.Y., Chiu, S.Y.: Effective heuristic procedure for a field technician scheduling problem. J. Heuristics 7, 495–509 (2001)CrossRefGoogle Scholar
  180. 180.
    Yen, J., Carlsson, M., Chang, M., Garcia, J.M., Nguyen, H.: Constraint solving for inkjet print mask design. J. Imaging Sci. Technol. 44, 391–397 (2000)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.AT&T Labs ResearchFlorham ParkUS
  2. 2.Universidade Federal FluminenseNiteróiBrazil

Personalised recommendations