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Telecommunication Systems

, Volume 46, Issue 3, pp 253–271 | Cite as

GRASP: basic components and enhancements

  • P. Festa
  • M. G. C. Resende
Article

Abstract

GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. While, in general, the construction phase of GRASP is a randomized greedy algorithm, other types of construction procedures have been proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This paper gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies.

Keywords

GRASP Path-relinking Metaheuristics Hybrid metaheuristics 

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References

  1. 1.
    Abdinnour-Helm, S., & Hadley, S. W. (2000). Tabu search based heuristics for multi-floor facility layout. International Journal of Production Research, 38, 365–383. Google Scholar
  2. 2.
    Abello, J., Pardalos, P. M., & Resende, M. G. C. (1999). On maximum clique problems in very large graphs. In J. Abello & J. Vitter (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 50. External memory algorithms and visualization (pp. 199–130). Providence: American Mathematical Society. Google Scholar
  3. 3.
    Ahuja, R. K., Orlin, J. B., & Tiwari, A. (2000). A greedy genetic algorithm for the quadratic assignment problem. Computers and Operations Research, 27, 917–934. Google Scholar
  4. 4.
    Aiex, R. M., & Resende, M. G. C. (2005). Parallel strategies for GRASP with path-relinking. In T. Ibaraki, K. Nonobe, & M. Yagiura (Eds.), Metaheuristics: progress as real problem solvers (pp. 301–331). Berlin: Springer. Google Scholar
  5. 5.
    Aiex, R. M., Resende, M. G. C., & Ribeiro, C. C. (2002). Probability distribution of solution time in GRASP: an experimental investigation. Journal of Heuristics, 8, 343–373. Google Scholar
  6. 6.
    Aiex, R. M., Binato, S., & Resende, M. G. C. (2003). Parallel GRASP with path-relinking for job shop scheduling. Parallel Computing, 29, 393–430. Google Scholar
  7. 7.
    Aiex, R., Resende, M. G. C., Pardalos, P. M., & Toraldo, G. (2005). GRASP with path relinking for three-index assignment. INFORMS Journal on Computing, 17(2), 224–247. Google Scholar
  8. 8.
    Álvarez, A. M., González-Velarde, J. L., & De-Alba, K. (2005). Scatter search for network design problem. Annals of Operations Research, 138(1), 159–178. Google Scholar
  9. 9.
    Alvarez-Valdes, R., Parreño, F., & Tamarit, J. M. (2005). A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems. Journal of the Operational Research Society, 56(4), 414–425. Google Scholar
  10. 10.
    Alvarez-Valdes, R., Parreño, F., & Tamarit, J. M. (2008). Reactive GRASP for the strip-packing problem. Computers & Operations Research, 35(4), 1065–1083. Google Scholar
  11. 11.
    Alvim, A. C. F. (1998). Parallelization strategies for the metaheuristic GRASP. Master’s thesis, Department of Computer Science, Catholic University of Rio de Janeiro, Rio de Janeiro, RJ 22453-900 Brazil, April (in Portuguese). Google Scholar
  12. 12.
    Alvim, A. C. F., & Ribeiro, C. C. (1998). Load balancing in the parallelization of the metaheuristic GRASP. In Tenth Brazilian symposium of computer architecture (pp. 279–282). Porto Alegre: Brazilian Computer Society (in Portuguese). Google Scholar
  13. 13.
    Amaldi, E., Capone, A., & Malucelli, F. (2003). Planning umts base station location: Optimization models with power control and algorithms. IEEE Transactions on Wireless Communications, 2(5), 939–952. Google Scholar
  14. 14.
    Amaldi, E., Capone, A., Malucelli, F., & Signori, F. (2003). Optimization models and algorithms for downlink umts radio planning. In Proceedings of wireless communications and networking, (WCNC 2003) (Vol. 2, pp. 827–831). Google Scholar
  15. 15.
    Andrade, D. V., & Resende, M. G. C. (2006). A GRASP for PBX telephone migration scheduling. In Eighth INFORMS telecommunication conference, April. Google Scholar
  16. 16.
    Andrade, D. V., & Resende, M. G. C. (2007). GRASP with path-relinking for network migration scheduling. In Proceedings of the international network optimization conference (INOC 2007). Google Scholar
  17. 17.
    Andres, C., Miralles, C., & Pastor, R. (2008). Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. European Journal of Operational Research, 187(3), 1212–1223. Google Scholar
  18. 18.
    Areibi, S. M. (1999). GRASP: An effective constructive technique for VLSI circuit partitioning. In Proc. IEEE Canadian conference on electrical & computer engineering (CCECE’99), May. Google Scholar
  19. 19.
    Areibi, S., & Vannelli, A. (1997). A GRASP clustering technique for circuit partitioning. In J. Gu & P. M. Pardalos (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 35. Satisfiability problems (pp. 711–724). Providence: American Mathematical Society. Google Scholar
  20. 20.
    Argüello, M. F., Feo, T. A., & Goldschmidt, O. (1996). Randomized methods for the number partitioning problem. Computers & Operations Research, 23(2), 103–111. Google Scholar
  21. 21.
    Argüello, M. F., Bard, J. F., & Yu, G. (1997). A GRASP for aircraft routing in response to groundings and delays. Journal of Combinatorial Optimization, 1, 211–228. Google Scholar
  22. 22.
    Armony, M., Klincewicz, J. G., Luss, H., & Rosenwein, M. B. (2000). Design of stacked self-healing rings using a genetic algorithm. Journal of Heuristics, 6, 85–105. Google Scholar
  23. 23.
    Arroyo, J. E. C., Vieira, P. S., & Vianna, D. S. (2008). A GRASP algorithm for the multi-criteria minimum spanning tree problem. Annals of Operations Research, 159, 125–133. Google Scholar
  24. 24.
    Atkinson, J. B. (1998). A greedy randomised search heuristic for time-constrained vehicle scheduling and the incorporation of a learning strategy. Journal of the Operational Research Society, 49, 700–708. Google Scholar
  25. 25.
    Bard, J. F. (1997). An analysis of a rail car unloading area for a consumer products manufacturer. Journal of the Operational Research Society, 48, 873–883. Google Scholar
  26. 26.
    Bard, J. F., & Feo, T. A. (1989). Operations sequencing in discrete parts manufacturing. Management Science, 35, 249–255. Google Scholar
  27. 27.
    Bard, J. F., & Feo, T. A. (1991). An algorithm for the manufacturing equipment selection problem. IIE Transactions, 23, 83–92. Google Scholar
  28. 28.
    Bard, J. F., Huang, L., Jaillet, P., & Dror, M. (1998). A decomposition approach to the inventory routing problem with satellite facilities. Transportation Science, 32, 189–203. Google Scholar
  29. 29.
    Battiti, R., & Tecchiolli, G. (1992). Parallel biased search for combinatorial optimization: Genetic algorithms and tabu. Microprocessors and Microsystems, 16, 351–367. Google Scholar
  30. 30.
    Binato, S., & Oliveira, G. C. (2002). A reactive GRASP for transmission network expansion planning. In C. C. Ribeiro & P. Hansen (Eds.), Essays and surveys on metaheuristics (pp. 81–100). Dordrecht: Kluwer Academic. Google Scholar
  31. 31.
    Binato, S., Oliveira, G. C., & Araújo, J. L. (2001). A greedy randomized adaptive search procedure for transmission expansion planning. IEEE Transactions on Power Systems, 16, 247–253. Google Scholar
  32. 32.
    Binato, S., Hery, W. J., Loewenstern, D., & Resende, M. G. C. (2002). A greedy randomized adaptive search procedure for job shop scheduling. In C. C. Ribeiro & P. Hansen (Eds.), Essays and surveys on metaheuristics (pp. 58–79). Dordrecht: Kluwer Academic. Google Scholar
  33. 33.
    Boudia, M., Louly, M. A. O., & Prins, C. (2007). A reactive GRASP and path relinking for a combined production-distribution problem. Computers and Operations Research, 34, 3402–3419. Google Scholar
  34. 34.
    Bresina, J. L. (1996). Heuristic-biased stochastic sampling. In Proceedings of the thirteenth national conference on artificial intelligence (AAAI-96) (pp. 271–278). Google Scholar
  35. 35.
    Canuto, S. A., Resende, M. G. C., & Ribeiro, C. C. (2001). Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks, 38, 50–58. Google Scholar
  36. 36.
    Canuto, S. A., Resende, M. G. C., & Ribeiro, C. C. (2001). Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks, 38, 50–58. Google Scholar
  37. 37.
    Carreto, C., & Baker, B. (2002). A GRASP interactive approach to the vehicle routing problem with backhauls. In C. C. Ribeiro & P. Hansen (Eds.), Essays and surveys on metaheuristics (pp. 185–200). Dordrecht: Kluwer Academic. Google Scholar
  38. 38.
    Charon, I., & Hudry, O. (1993). The noising method: a new method for combinatorial optimization. Operations Research Letters, 14, 133–137. Google Scholar
  39. 39.
    Charon, I., & Hudry, O. (2002). The noising methods: A survey. In C. C. Ribeiro & P. Hansen (Eds.), Essays and surveys on metaheuristics (pp. 245–261). Dordrecht: Kluwer Academic. Google Scholar
  40. 40.
    Commander, C., Festa, P., Oliveira, C. A. S., Pardalos, P. M., Resende, M. G. C., & Tsitselis, M. (2006). A greedy randomized algorithm for the cooperative communication problem on ad hoc networks. In Eighth INFORMS telecommunications conference, April. Google Scholar
  41. 41.
    Contreras, I. A., & Díaz, J. A. (2008). Scatter search for the single source capacitated facility location problem. Annals of Operations Research, 157, 73–89. Google Scholar
  42. 42.
    Cravo, G. L., Ribeiro, G. M., & Nogueira Lorena, L. A. (2008). A greedy randomized adaptive search procedure for the point-feature cartographic label placement. Computers and Geosciences, 34(4), 373–386. Google Scholar
  43. 43.
    Delmaire, H., Díaz, J. A., Fernández, E., & Ortega, M. (1999). Reactive GRASP and tabu search based heuristics for the single source capacitated plant location problem. INFOR, 37, 194–225. Google Scholar
  44. 44.
    Deshpande, A. S., & Triantaphyllou, E. (1998). A greedy randomized adaptive search procedure (GRASP) for inferring logical clauses from examples in polynomial time and some extensions. Mathematical and Computer Modelling, 27, 75–99. Google Scholar
  45. 45.
    Dodd, N. (1990). Slow annealing versus multiple fast annealing runs: an empirical investigation. Parallel Computing, 16, 269–272. Google Scholar
  46. 46.
    Faria, H. Jr., Binato, M. G. C., Resende, S., & Falcão, D. J. (2005). Power transmission network design by a greedy randomized adaptive path relinking approach. IEEE Transactions on Power Systems, 20(1), 43–49. Google Scholar
  47. 47.
    Feo, T. A., & Bard, J. F. (1989). Flight scheduling and maintenance base planning. Management Science, 35, 1415–1432. Google Scholar
  48. 48.
    Feo, T. A., & González-Velarde, J. L. (1995). The intermodal trailer assignment problem: models, algorithms, and heuristics. Transportation Science, 29, 330–341. Google Scholar
  49. 49.
    Feo, T. A., & Resende, M. G. C. (1989). A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8, 67–71. Google Scholar
  50. 50.
    Feo, T. A., & Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133. Google Scholar
  51. 51.
    Feo, T. A., Venkatraman, K., & Bard, J. F. (1991). A GRASP for a difficult single machine scheduling problem. Computers & Operations Research, 18, 635–643. Google Scholar
  52. 52.
    Feo, T. A., Resende, M. G. C., & Smith, S. H. (1994). A greedy randomized adaptive search procedure for maximum independent set. Operations Research, 42, 860–878. Google Scholar
  53. 53.
    Feo, T. A., Sarathy, K., & McGahan, J. (1996). A GRASP for single machine scheduling with sequence dependent setup costs and linear delay penalties. Computers & Operations Research, 23, 881–895. Google Scholar
  54. 54.
    Festa, P. (2007). On some optimization problems in molecular biology. Mathematical Bioscience, 207(2), 219–234. Google Scholar
  55. 55.
    Festa, P., & Resende, M. G. C. (2002). GRASP: An annotated bibliography. In C. C. Ribeiro & P. Hansen (Eds.), Essays and Surveys on Metaheuristics (pp. 325–367). Dordrecht: Kluwer Academic. Google Scholar
  56. 56.
    Festa, P., & Resende, M. G. C. (2009). An annotated bibliography of GRASP—part I: algorithms. International Transactions in Operational Research, 16(1), 1–24. Google Scholar
  57. 57.
    Festa, P., & Resende, M. G. C. (2009). An annotated bibliography of GRASP—part II: applications. International Transactions in Operational Research, 16(2), 131–172. Google Scholar
  58. 58.
    Festa, P., Pardalos, P. M., & Resende, M. G. C. (2001). Algorithm 815: FORTRAN subroutines for computing approximate solution to feedback set problems using GRASP. ACM Transactions on Mathematical Software, 27, 456–464. Google Scholar
  59. 59.
    Festa, P., Pardalos, P. M., Resende, M. G. C., & Ribeiro, C. C. (2002). Randomized heuristics for the MAX-CUT problem. Optimization Methods and Software, 7, 1033–1058. Google Scholar
  60. 60.
    Festa, P., Pardalos, P. M., Pitsoulis, L. S., & Resende, M. G. C. (2006). GRASP with path-relinking for the weighted MAXSAT problem. ACM Journal of Experimental Algorithmics, 11, 1–16. Google Scholar
  61. 61.
    Fleurent, C., & Glover, F. (1999). Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS Journal on Computing, 11, 198–204. Google Scholar
  62. 62.
    Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: W.H. Freeman. Google Scholar
  63. 63.
    Ghosh, J. B. (1996). Computational aspects of the maximum diversity problem. Operations Research Letters, 19, 175–181. Google Scholar
  64. 64.
    Glover, F. (1989). Tabu search—part I. ORSA Journal on Computing, 1, 190–206. Google Scholar
  65. 65.
    Glover, F. (1990). Tabu search—part II. ORSA Journal on Computing, 2, 4–32. Google Scholar
  66. 66.
    Glover, F. (1996). Tabu search and adaptive memory programing—advances, applications and challenges. In R. S. Barr, R. V. Helgason, & J. L. Kennington (Eds.), Interfaces in computer science and operations research (pp. 1–75). Dordrecht: Kluwer Academic. Google Scholar
  67. 67.
    Glover, F. (2000). Multi-start and strategic oscillation methods—principles to exploit adaptive memory. In M. Laguna & J. L. Gonzáles-Velarde (Eds.), Computing tools for modeling, optimization and simulation: interfaces in computer science and operations research (pp. 1–24). Dordrecht: Kluwer Academic. Google Scholar
  68. 68.
    Glover, F., & Laguna, M. (1997). Tabu search. Dordrecht: Kluwer Academic. Google Scholar
  69. 69.
    Glover, F., Laguna, M., & Martí, R. (2000). Fundamentals of scatter search and path relinking. Control and Cybernetics, 39, 653–684. Google Scholar
  70. 70.
    Goëffon, A., Richer, J.-M., & Hao, J.-K. (2008). Progressive tree neighborhood applied to the maximum parsimony problem. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 5(1), 136–145. Google Scholar
  71. 71.
    Goemans, M. X., Williamson, D. P. (1996). The primal dual method for approximation algorithms and its application to network design problems. In D. Hochbaum (Ed.), Approximation algorithms for NP-hard problems (pp. 144–191). Boston: PWS. Google Scholar
  72. 72.
    Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Reading: Addison-Wesley. Google Scholar
  73. 73.
    Hammer, P. L., & Rader, D. J. Jr. (2001). Maximally disjoint solutions of the set covering problem. Journal of Heuristics, 7, 131–144. Google Scholar
  74. 74.
    Hansen, P., & Mladenović, N. (1998). An introduction to variable neighborhood search. In S. Voss, S. Martello, I. H. Osman, & C. Roucairol (Eds.), Meta-heuristics, advances and trends in local search paradigms for optimization (pp. 433–458). Dordrecht: Kluwer Academic. Google Scholar
  75. 75.
    Hansen, P., & Mladenović, N. (2002). Developments of variable neighborhood search. In C. C. Ribeiro & P. Hansen (Eds.), Essays and surveys in metaheuristics (pp. 415–439). Dordrecht: Kluwer Academic. Google Scholar
  76. 76.
    Hart, J. P., & Shogan, A. W. (1987). Semi-greedy heuristics: an empirical study. Operations Research Letters, 6, 107–114. Google Scholar
  77. 77.
    Hirsch, M. J., Meneses, C. N., Pardalos, P. M., Ragle, M. A., & Resende, M. G. C. (2007). A continuous GRASP to determine the relationship between drugs and adverse reactions. In O. Seref, O. E. Kundakcioglu, & P. M. Pardalos (Eds.), AIP conference proceedings : Vol. 953. Data mining, systems analysis, and optimization in biomedicine (pp. 106–121). Berlin: Springer. Google Scholar
  78. 78.
    Johnson, D. S., Papadimitriou, C. H., & Yannakakis, M. (1988). How easy is local search? Journal of Computer and System Sciences, 17, 79–100. Google Scholar
  79. 79.
    Kernighan, B. W., & Lin, S. (1970). An efficient heuristic procedure for partitioning problems. Bell System Technical Journal, 49(2), 291–307. Google Scholar
  80. 80.
    Kirkpatrick, S. (1984). Optimization by simulated annealing: quantitative studies. Journal of Statistical Physics, 34, 975–986. Google Scholar
  81. 81.
    Klincewicz, J. G. (1992). Avoiding local optima in the p-hub location problem using tabu search and GRASP. Annals of Operations Research, 40, 283–302. Google Scholar
  82. 82.
    Klincewicz, J. G. (2002). Enumeration and search procedures for a hub location problem with economies of scale. Annals of Operations Research, 110, 107–122. Google Scholar
  83. 83.
    Klincewicz, J. G., & Rajan, A. (1994). Using GRASP to solve the component grouping problem. Naval Research Logistics, 41, 893–912. Google Scholar
  84. 84.
    Kontoravdis, G., & Bard, J. F. (1995). A GRASP for the vehicle routing problem with time windows. ORSA Journal on Computing, 7, 10–23. Google Scholar
  85. 85.
    Kumaran, K., Srinivasan, A., Wang, Q., Lanning, S., & Ramakrishnan, K. (2001). Efficient algorithms for location and sizing problems in network design. In IEEE global telecommunications conference (GLOBECOM ’01) (Vol. 4, pp. 2586----2590). Google Scholar
  86. 86.
    Laguna, M., & González-Velarde, J. L. (1991). A search heuristic for just-in-time scheduling in parallel machines. Journal of Intelligent Manufacturing, 2, 253–260. Google Scholar
  87. 87.
    Laguna, M., & Martí, R. (1999). GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS Journal on Computing, 11, 44–52. Google Scholar
  88. 88.
    Laguna, M., & Martí, R. (2001). A GRASP for coloring sparse graphs. Computational Optimization and Applications, 19, 165–178. Google Scholar
  89. 89.
    Laguna, M., Feo, T. A., & Elrod, H. C. (1994). A greedy randomized adaptive search procedure for the two-partition problem. Operations Research, 42, 677–687. Google Scholar
  90. 90.
    Li, Y., Pardalos, P. M., & Resende, M. G. C. (1994). A greedy randomized adaptive search procedure for the quadratic assignment problem. In P. M. Pardalos & H. Wolkowicz (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 16. Quadratic assignment and related problems (pp. 237–261). Providence: American Mathematical Society. Google Scholar
  91. 91.
    Li, B., Chen, F., & Yin, L. (2000). Server replication and its placement for reliable multicast. In Proceedings of the ninth IEEE international conference on computer communications and networks (ICCCN-00) (pp. 396–401). Google Scholar
  92. 92.
    Lin, S., & Kernighan, B. W. (1973). An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 21, 498–516. Google Scholar
  93. 93.
    Liu, X., Pardalos, P. M., Rajasekaran, S., & Resende, M. G. C. (2000). A GRASP for frequency assignment in mobile radio networks. In S. Rajasekaran, P. M. Pardalos, & F. Hsu (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 52. Mobile networks and computing (pp. 195–201). Providence: American Mathematical Society. Google Scholar
  94. 94.
    Martí, R., & Laguna, M. (2003). Heuristics and meta-heuristics for 2-layer straight line crossing minimization. Discrete Applied Mathematics, 127(3), 665–678. Google Scholar
  95. 95.
    Martins, S. L., Ribeiro, C. C., & Souza, M. C. (1998). A parallel GRASP for the Steiner problem in graphs. In A. Ferreira & J. Rolim (Eds.), Lecture notes in computer science : Vol. 1457. Proceedings of IRREGULAR’98—5th international symposium on solving irregularly structured problems in parallel (pp. 285–297). Berlin: Springer. Google Scholar
  96. 96.
    Martins, S. L., Pardalos, P. M., Resende, M. G. C., & Ribeiro, C. C. (1999). Greedy randomized adaptive search procedures for the Steiner problem in graphs. In P. M. Pardalos, S. Rajasekaran, & J. Rolim (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 43. Randomization methods in algorithmic design (pp. 133–145). Providence: American Mathematical Society. Google Scholar
  97. 97.
    Martins, S. L., Resende, M. G. C., Ribeiro, C. C., & Pardalos, P. (2000). A parallel GRASP for the Steiner tree problem in graphs using a hybrid local search strategy. Journal of Global Optimization, 17, 267–283. Google Scholar
  98. 98.
    Mavridou, T., Pardalos, P. M., Pitsoulis, L. S., & Resende, M. G. C. (1998). A GRASP for the biquadratic assignment problem. European Journal of Operational Research, 105, 613–621. Google Scholar
  99. 99.
    Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computers and Operations Research, 24, 1097–1100. Google Scholar
  100. 100.
    Mockus, J., Eddy, E., Mockus, A., Mockus, L., & Reklaitis, G. V. (1997). Bayesian discrete and global optimization. Dordrecht: Kluwer Academic. Google Scholar
  101. 101.
    Monkman, S. K., Morrice, D. J., & Bard, J. F. (2008). A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs. European Journal of Operational Research, 187(3), 1100–1114. Google Scholar
  102. 102.
    Myslek, A. (2001). Greedy randomised adaptive search procedures (GRASP) for topological design of MPLS networks. In Proceedings of the 8th Polish teletraffic symposium, 3–5 September. Google Scholar
  103. 103.
    Osborne, L., & Gillett, B. (1991). A comparison of two simulated annealing algorithms applied to the directed Steiner problem on networks. ORSA Journal on Computing, 3, 213–225. Google Scholar
  104. 104.
    Osman, I. H., Al-Ayoubi, B., & Barake, M. (2003). A greedy random adaptive search procedure for the weighted maximal planar graph problem. Computers and Industrial Engineering, 45(4), 635–651. Google Scholar
  105. 105.
    Pardalos, P. M., & Resende, M. G. C. (Eds.) (2002). Handbook of applied optimization. London: Oxford University Press. Google Scholar
  106. 106.
    Pardalos, P. M., Pitsoulis, L. S., & Resende, M. G. C. (1995). A parallel GRASP implementation for the quadratic assignment problem. In A. Ferreira & J. Rolim (Eds.), Parallel algorithms for irregularly structured problems—irregular’94 (pp. 115–130). Dordrecht: Kluwer Academic. Google Scholar
  107. 107.
    Pardalos, P. M., Pitsoulis, L. S., & Resende, M. G. C. (1996). A parallel GRASP for MAX-SAT problems. In Lecture notes in computer science : Vol. 1184 (pp. 575–585). Berlin: Springer. Google Scholar
  108. 108.
    Pardalos, P. M., Pitsoulis, L. S., & Resende, M. G. C. (1997). Algorithm 769: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP. ACM Transactions on Mathematical Software, 23, 196–208. Google Scholar
  109. 109.
    Pardalos, P. M., Ramakrishnan, K. G., Resende, M. G. C., & Li, Y. (1997). Implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem. SIAM Journal on Optimization, 7, 280–294. Google Scholar
  110. 110.
    Pinãna, E., Plana, I., Campos, V., & Martì, R. (2004). GRASP and path relinking for the matrix bandwidth minimization. European Journal of Operational Research, 153(1), 200–210. Google Scholar
  111. 111.
    Poppe, F., Pickavet, M., Arijs, P., & Demeester, P. (1997). Design techniques for SDH mesh-restorable networks. In Proceedings of the European conference on networks and optical communications (NOC’97), Vol. 2: Core and ATM networks (pp. 94–101). Google Scholar
  112. 112.
    Prais, M., & Ribeiro, C. C. (1999). Parameter variation in GRASP implementations. In Extended abstracts of the third metaheuristics international conference (pp. 375–380). Google Scholar
  113. 113.
    Prais, M., & Ribeiro, C. C. (2000). Parameter variation in GRASP procedures. Investigación Operativa, 9, 1–20. Google Scholar
  114. 114.
    Prais, M., & Ribeiro, C. C. (2000). Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment. INFORMS Journal on Computing, 12, 164–176. Google Scholar
  115. 115.
    Pu, G. G., Chong, Z., Qiu, Z. Y., Lin, Z. Q., & He, J. F. (2006). A hybrid heuristic algorithm for HW-SW partitioning within timed automata. In Lecture notes in artificial intelligence : Vol. 4251. Proceedings of knowledge-based intelligent information and engineering systems (pp. 459–466). Berlin: Springer. Google Scholar
  116. 116.
    Ramalhinho Lourenço, H., Paixão, J. P., & Portugal, R. (2001). Multiobjective metaheuristics for the bus-driver scheduling problem. Transportation Science, 35, 331–343. Google Scholar
  117. 117.
    Resende, M. G. C., & Feo, T. A. (1996). A GRASP for satisfiability. In D. S. Johnson & M. A. Trick (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 26. Cliques, coloring, and satisfiability: the second DIMACS implementation challenge (pp. 499–520). Providence: American Mathematical Society. Google Scholar
  118. 118.
    Resende, M. G. C., & Ribeiro, C. C. (1997). A GRASP for graph planarization. Networks, 29, 173–189. Google Scholar
  119. 119.
    Resende, M. G. C., & Ribeiro, C. C. (2003). Greedy randomized adaptive search procedures. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 219–249). Dordrecht: Kluwer Academic. Google Scholar
  120. 120.
    Resende, M. G. C., & Ribeiro, C. C. (2003). Grasp with path-relinking for private virtual circuit routing. Networks, 41, 104–114. Google Scholar
  121. 121.
    Resende, M. G. C., & Ribeiro, C. C. (2005). GRASP with path-relinking: Recent advances and applications. In T. Ibaraki, K. Nonobe, & M. Yagiura (Eds.), Metaheuristics: progress as real problem solvers (pp. 29–63). Berlin: Springer. Google Scholar
  122. 122.
    Resende, M. G. C., & Ribeiro, C. C. (2005). Parallel greedy randomized adaptive search procedures. In E. Alba (Ed.), Parallel metaheuristics: a new class of algorithms (pp. 315–346). New York: Wiley. Google Scholar
  123. 123.
    Resende, M. G. C., Pardalos, P. M., & Li, Y. (1996). Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP. ACM Transactions on Mathematical Software, 22, 104–118. Google Scholar
  124. 124.
    Resende, M. G. C., Pitsoulis, L. S., & Pardalos, P. M. (1997). Approximate solution of weighted MAX-SAT problems using GRASP. In J. Gu & P. M. Pardalos (Eds.), DIMACS series on discrete mathematics and theoretical computer science : Vol. 35. Satisfiability problems (pp. 393–405). Providence: American Mathematical Society. Google Scholar
  125. 125.
    Resende, M. G. C., Pitsoulis, L. S., & Pardalos, P. M. (2000). Fortran subroutines for computing approximate solutions of MAX-SAT problems using GRASP. Discrete Applied Mathematics, 100, 95–113. Google Scholar
  126. 126.
    Ribeiro, C. C., & Resende, M. G. C. (1999). Fortran subroutines for approximate solution of graph planarization problems using GRASP. ACM Transactions on Mathematical Software, 25, 341–352. Google Scholar
  127. 127.
    Ribeiro, C. C., & Rosseti, I. (2002). A parallel GRASP for the 2-path network design problem. In Lecture notes in computer science : Vol. 2400. Proceedings of Euro-Par 2002 (pp. 922–926). Berlin: Springer. Google Scholar
  128. 128.
    Ribeiro, C. C., & Souza, M. C. (2002). Variable neighborhood search for the degree constrained minimum spanning tree problem. Discrete Applied Mathematics, 118, 43–54. Google Scholar
  129. 129.
    Ribeiro, C. C., & Urrutia, S. (2007). Heuristics for the mirrored traveling tournament problem. European Journal of Operational Research, 179, 775–787. Google Scholar
  130. 130.
    Ribeiro, C. C., Uchoa, E., & Werneck, R. F. (2002). A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing, 14, 228–246. Google Scholar
  131. 131.
    Ribeiro, C. C., Uchoa, E., & Werneck, R. F. (2002). A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing, 14, 228–246. Google Scholar
  132. 132.
    Ríos-Mercado, R. Z., & Bard, J. F. (1998). Heuristics for the flow line problem with setup costs. European Journal of Operational Research, 76–98. Google Scholar
  133. 133.
    Ríos-Mercado, R. Z., & Bard, J. F. (1999). An enhanced TSP-based heuristic for makespan minimization in a flow shop with setup costs. Journal of Heuristics, 5, 57–74. Google Scholar
  134. 134.
    Rivera, L. I. D. (1998). Evaluation of parallel implementations of heuristics for the course scheduling problem. Master’s thesis, Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Mexico. Google Scholar
  135. 135.
    Robertson, A. J. (2001). A set of greedy randomized adaptive local search procedure (GRASP) implementations for the multidimensional assignment problem. Computational Optimization and Applications, 19, 145–164. Google Scholar
  136. 136.
    Sosnowska, D. (2000). Optimization of a simplified fleet assignment problem with metaheuristics: simulated annealing and GRASP. In P. M. Pardalos (Ed.), Approximation and complexity in numerical optimization. Dordrecht: Kluwer Academic. Google Scholar
  137. 137.
    Srinivasan, A., Ramakrishnan, K. G., Kumaram, K., Aravamudam, M., & Naqvi, S. (2000). Optimal design of signaling networks for Internet telephony. In IEEE INFOCOM 2000, March (Vol. 2, pp. 707–716). Google Scholar
  138. 138.
    Taillard, E. (1991). Robust taboo search for the quadratic assignment problem. Parallel Computing, 7, 443–455. Google Scholar
  139. 139.
    Takahashi, H., & Matsuyama, A. (1980). An approximate solution for the Steiner problem in graphs. Mathematica Japonica, 24, 573–577. Google Scholar
  140. 140.
    Urban, T. L. (1998). Solution procedures for the dynamic facility layout problem. Annals of Operations Research, 323–342. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.DMAUniversity of Napoli Federico IINapoliItaly
  2. 2.AT&T Labs ResearchFlorham ParkUSA

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