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GRASP

  • Paola Festa
  • Mauricio G. C. Resende
Reference work entry

Abstract

GRASP (greedy randomized adaptive search procedure) is a multistart metaheuristic for computing 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. Typically, the construction phase of GRASP is a randomized greedy algorithm, but other types of construction procedures have been also proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This chapter gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies.

Keywords

GRASP Combinatorial optimization Metaheuristics Local search Path-relinking Hybrid metaheuristics 

References

  1. 1.
    Abdinnour-Helm S, Hadley S (2000) Tabu search based heuristics for multi-floor facility layout. Int J Prod Res 38:365–383Google Scholar
  2. 2.
    Abello J, Pardalos P, Resende M (1999) 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. American Mathematical Society, Providence, pp 199–130Google Scholar
  3. 3.
    Ahuja R, Orlin J, Tiwari A (2000) A greedy genetic algorithm for the quadratic assignment problem. Comput Oper Res 27:917–934Google Scholar
  4. 4.
    Aiex R, Binato S, Resende M (2003) Parallel GRASP with path-relinking for job shop scheduling. Parallel Comput 29:393–430Google Scholar
  5. 5.
    Aiex R, Resende M, Pardalos P, Toraldo G (2005) GRASP with path relinking for three-index assignment. INFORMS J Comput 17(2):224–247Google Scholar
  6. 6.
    Alvarez-Valdes R, Parreño F, Tamarit J (2005) A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems. J Oper Res Soc 56(4):414–425Google Scholar
  7. 7.
    Alvarez-Valdes R, Parreño F, Tamarit J (2008) Reactive GRASP for the strip-packing problem. Comput Oper Res 35(4):1065–1083Google Scholar
  8. 8.
    Amaldi E, Capone A, Malucelli F (2003) Planning UMTS base station location: optimization models with power control and algorithms. IEEE Trans Wirel Commun 2(5):939–952Google Scholar
  9. 9.
    Andrade D, Resende M (2006) A GRASP for PBX telephone migration scheduling. In: Eighth INFORMS telecommunication conference, DallasGoogle Scholar
  10. 10.
    Andrade D, Resende M (2007) GRASP with path-relinking for network migration scheduling. In: Proceedings of the international network optimization conference (INOC 2007), SpaGoogle Scholar
  11. 11.
    Andres C, Miralles C, Pastor R (2008) Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. Eur J Oper Res 187(3):1212–1223Google Scholar
  12. 12.
    Areibi S (1999) GRASP: an effective constructive technique for VLSI circuit partitioning. In: Proceedings of the IEEE Canadian conference on electrical & computer engineering (CCECE’99), EdmontonGoogle Scholar
  13. 13.
    Areibi S, Vannelli A (1997) A GRASP clustering technique for circuit partitioning. In: Gu J, Pardalos P (eds) Satisfiability problems. DIMACS series on discrete mathematics and theoretical computer science, vol 35. American Mathematical Society, Providence, pp 711–724Google Scholar
  14. 14.
    Argüello M, Feo T, Goldschmidt O (1996) Randomized methods for the number partitioning problem. Comput Oper Res 23(2):103–111Google Scholar
  15. 15.
    Argüello M, Bard J, Yu G (1997) A GRASP for aircraft routing in response to groundings and delays. J Comb Optim 1:211–228Google Scholar
  16. 16.
    Armony M, Klincewicz J, Luss H, Rosenwein M (2000) Design of stacked self-healing rings using a genetic algorithm. J Heuristics 6:85–105Google Scholar
  17. 17.
    Arroyo J, Vieira P, Vianna D (2008) A GRASP algorithm for the multi-criteria minimum spanning tree problem. Ann Oper Res 159:125–133Google Scholar
  18. 18.
    Atkinson J (1998) A greedy randomised search heuristic for time-constrained vehicle scheduling and the incorporation of a learning strategy. J Oper Res Soc 49:700–708Google Scholar
  19. 19.
    Bäck T, Fogel D, Michalewicz Z (1997) Handbook of evolutionary computation. Oxford University Press, New YorkGoogle Scholar
  20. 20.
    Bard J (1997) An analysis of a rail car unloading area for a consumer products manufacturer. J Oper Res Soc 48:873–883Google Scholar
  21. 21.
    Bard J, Feo T (1989) Operations sequencing in discrete parts manufacturing. Manag Sci 35:249–255Google Scholar
  22. 22.
    Bard J, Feo T (1991) An algorithm for the manufacturing equipment selection problem. IIE Trans 23:83–92Google Scholar
  23. 23.
    Bard J, Huang L, Jaillet P, Dror M (1998) A decomposition approach to the inventory routing problem with satellite facilities. Transp Sci 32:189–203Google Scholar
  24. 24.
    Binato S, Oliveira G (2002) A reactive GRASP for transmission network expansion planning. In: Ribeiro C, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Boston, pp 81–100Google Scholar
  25. 25.
    Binato S, Oliveira G, Araújo J (2001) A greedy randomized adaptive search procedure for transmission expansion planning. IEEE Trans Power Syst 16:247–253Google Scholar
  26. 26.
    Binato S, Hery W, Loewenstern D, Resende M (2002) A greedy randomized adaptive search procedure for job shop scheduling. In: Ribeiro C, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Boston, pp 58–79Google Scholar
  27. 27.
    Boudia M, Louly M, Prins C (2007) A reactive GRASP and path relinking for a combined production-distribution problem. Comput Oper Res 34:3402–3419Google Scholar
  28. 28.
    Bresina J (1996) Heuristic-biased stochastic sampling. In: Proceedings of the thirteenth national conference on artificial intelligence (AAAI-96), Portland, pp 271–278Google Scholar
  29. 29.
    Canuto S, Resende M, Ribeiro C (2001) Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 38:50–58Google Scholar
  30. 30.
    Carreto C, Baker B (2002) A GRASP interactive approach to the vehicle routing problem with backhauls. In: Ribeiro C, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Boston, pp 185–200Google Scholar
  31. 31.
    Charon I, Hudry O (1993) The noising method: a new method for combinatorial optimization. Oper Res Lett 14:133–137Google Scholar
  32. 32.
    Charon I, Hudry O (2002) The noising methods: a survey. In: Ribeiro C, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Boston, pp 245–261Google Scholar
  33. 33.
    Commander C, Festa P, Oliveira C, Pardalos P, Resende M, Tsitselis M (2006) A greedy randomized algorithm for the cooperative communication problem on ad hoc networks. In: Eighth INFORMS telecommunications conference, DallasGoogle Scholar
  34. 34.
    Contreras I, Díaz J (2008) Scatter search for the single source capacitated facility location problem. Ann Oper Res 157:73–89Google Scholar
  35. 35.
    Cravo G, Ribeiro G, Lorena LN (2008) A greedy randomized adaptive search procedure for the point-feature cartographic label placement. Comput Geosci 34(4):373–386Google Scholar
  36. 36.
    Delmaire H, Díaz J, Fernández E, Ortega M (1999) Reactive GRASP and tabu search based heuristics for the single source capacitated plant location problem. INFOR 37:194–225Google Scholar
  37. 37.
    Deshpande A, Triantaphyllou E (1998) A greedy randomized adaptive search procedure (GRASP) for inferring logical clauses from examples in polynomial time and some extensions. Math Comput Model 27:75–99Google Scholar
  38. 38.
    Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, CambridgeGoogle Scholar
  39. 39.
    Faria H, Binato S, Resende M, Falcão D (2005) Power transmission network design by a greedy randomized adaptive path relinking approach. IEEE Trans Power Syst 20(1):43–49Google Scholar
  40. 40.
    Feo T, Bard J (1989) Flight scheduling and maintenance base planning. Manag Sci 35:1415–1432Google Scholar
  41. 41.
    Feo T, González-Velarde J (1995) The intermodal trailer assignment problem: models, algorithms, and heuristics. Transp Sci 29:330–341Google Scholar
  42. 42.
    Feo T, Resende M (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8:67–71Google Scholar
  43. 43.
    Feo T, Resende M (1995) Greedy randomized adaptive search procedures. J Glob Optim 6:109–133Google Scholar
  44. 44.
    Feo T, Venkatraman K, Bard J (1991) A GRASP for a difficult single machine scheduling problem. Comput Oper Res 18:635–643Google Scholar
  45. 45.
    Feo T, Resende M, Smith S (1994) A greedy randomized adaptive search procedure for maximum independent set. Oper Res 42:860–878Google Scholar
  46. 46.
    Feo T, Sarathy K, McGahan J (1996) A GRASP for single machine scheduling with sequence dependent setup costs and linear delay penalties. Comput Oper Res 23:881–895Google Scholar
  47. 47.
    Ferone D, Festa P, Resende M (2013) Hybrid metaheuristics for the far from most string problem. In: Proceedings of 8th international workshop on hybrid metaheuristics. Lecture notes in computer science, vol 7919. Springer, Berlin/New York, pp 174–188Google Scholar
  48. 48.
    Ferone D, Festa P, Resende M (2016) Hybridizations of GRASDP with path-relinking for the far from most string problem. Int Trans Oper Res 23(3):481–506Google Scholar
  49. 49.
    Festa P (2007) On some optimization problems in molecular biology. Math Biosci 207(2):219–234Google Scholar
  50. 50.
    Festa P, Resende M (2002) GRASP: an annotated bibliography. In: Ribeiro C, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Boston, pp 325–367Google Scholar
  51. 51.
    Festa P, Resende M (2013) Hybridizations of GRASP with path-relinking. In: Talbi EG (ed) Hybrid metaheuristics – studies in computational intelligence, vol 434. Springer, Berlin/New York, pp 135–155Google Scholar
  52. 52.
    Festa P, Resende MGC (2009) An annotated bibliography of grasp – part I: algorithms. Int Trans Oper Res 16(1):1–24Google Scholar
  53. 53.
    Festa P, Resende MGC (2009) An annotated bibliography of grasp – part II: applications. Int Trans Oper Res 16(2):131–172Google Scholar
  54. 54.
    Festa P, Pardalos P, Resende M (2001) Algorithm 815: FORTRAN subroutines for computing approximate solution to feedback set problems using GRASP. ACM Trans Math Softw 27:456–464Google Scholar
  55. 55.
    Festa P, Pardalos P, Resende M, Ribeiro C (2002) Randomized heuristics for the MAX-CUT problem. Optim Methods Softw 7:1033–1058Google Scholar
  56. 56.
    Festa P, Pardalos P, Pitsoulis L, Resende M (2006) GRASP with path-relinking for the weighted MAXSAT problem. ACM J Exp Algorithmics 11:1–16Google Scholar
  57. 57.
    Festa P, Gonçalves J, Resende M, Silva R (2010) Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm. In: Festa P (ed) Proceedings of 9th international symposium on experimental algorithms. Lecture notes in computer science, vol 6049. Springer, Berlin/New York, pp 338–349Google Scholar
  58. 58.
    Fleurent C, Glover F (1999) Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J Comput 11:198–204Google Scholar
  59. 59.
    Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. W.H. Freeman and Company, New YorkGoogle Scholar
  60. 60.
    Ghosh J (1996) Computational aspects of the maximum diversity problem. Oper Res Lett 19:175–181Google Scholar
  61. 61.
    Glover F (1989) Tabu search – part I. ORSA J Comput 1:190–206Google Scholar
  62. 62.
    Glover F (1990) Tabu search – part II. ORSA J on Comput 2:4–32Google Scholar
  63. 63.
    Glover F (1996) Tabu search and adaptive memory programing – advances, applications and challenges. In: Barr R, Helgason R, Kennington J (eds) Interfaces in computer science and operations research. Kluwer Academic Publishers, Boston, pp 1–75Google Scholar
  64. 64.
    Glover F (2000) Multi-start and strategic oscillation methods – principles to exploit adaptive memory. In: Laguna M, Gonzáles-Velarde J (eds) Computing tools for modeling, optimization and simulation: interfaces in computer science and operations research. Kluwer Academic Publishers, Boston, pp 1–24Google Scholar
  65. 65.
    Glover F, Laguna M (1997) Tabu search. Kluwer Academic Publishers, BostonGoogle Scholar
  66. 66.
    Glover F, Laguna M, Martí R (2000) Fundamentals of scatter search and path relinking. Control Cybern 39:653–684Google Scholar
  67. 67.
    Goëffon A, Richer JM, Hao JK (2008) Progressive tree neighborhood applied to the maximum parsimony problem. IEEE/ACM Trans Comput Biol Bioinform 5(1):136–145Google Scholar
  68. 68.
    Goemans M, Williamson D (1996) The primal dual method for approximation algorithms and its application to network design problems. In: Hochbaum D (ed) Approximation algorithms for NP-hard problems. PWS Publishing Co., Boston, pp 144–191Google Scholar
  69. 69.
    Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, ReadingGoogle Scholar
  70. 70.
    Gonçalves J, Resende M (2011) Biased random-key genetic algorithms for combinatorial optimization. J Heuristics 17(5):487–525Google Scholar
  71. 71.
    Hammer P, Rader D Jr (2001) Maximally disjoint solutions of the set covering problem. J Heuristics 7:131–144Google Scholar
  72. 72.
    Hansen P, Mladenović N (1998) An introduction to variable neighborhood search. In: Voss S, Martello S, Osman IH, Roucairol C (eds) Meta-heuristics, advances and trends in local search paradigms for optimization. Kluwer Academic Publishers, Boston, pp 433–458Google Scholar
  73. 73.
    Hansen P, Mladenović N (2002) Developments of variable neighborhood search. In: Ribeiro C, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer Academic Publishers, Boston, pp 415–439Google Scholar
  74. 74.
    Hart J, Shogan A (1987) Semi-greedy heuristics: an empirical study. Oper Res Lett 6:107–114Google Scholar
  75. 75.
    Hirsch M, Meneses C, Pardalos P, Ragle M, Resende M (2007) A continuous GRASP to determine the relationship between drugs and adverse reactions. In: Seref O, Kundakcioglu O, Pardalos P (eds) Data mining, systems analysis, and optimization in biomedicine. AIP conference proceedings, vol 953. Springer, Melville, pp 106–121Google Scholar
  76. 76.
    Hutter F, Hoos H, Leyton-Brown K, Stützle T (2009) ParamILS: an automatic algorithm configuration framework. J Artif Intell Res 36:267–306Google Scholar
  77. 77.
    Kernighan B, Lin S (1970) An efficient heuristic procedure for partitioning problems. Bell Syst Tech J 49(2):291–307Google Scholar
  78. 78.
    Kirkpatrick S (1984) Optimization by simulated annealing: quantitative studies. J Stat Phys 34:975–986Google Scholar
  79. 79.
    Klincewicz J (1992) Avoiding local optima in the p-hub location problem using tabu search and GRASP. Ann Oper Res 40:283–302Google Scholar
  80. 80.
    Klincewicz J, Rajan A (1994) Using GRASP to solve the component grouping problem. Nav Res Logist 41:893–912Google Scholar
  81. 81.
    Kontoravdis G, Bard J (1995) A GRASP for the vehicle routing problem with time windows. ORSA J Comput 7:10–23Google Scholar
  82. 82.
    Laguna M, González-Velarde J (1991) A search heuristic for just-in-time scheduling in parallel machines. J Intell Manuf 2:253–260Google Scholar
  83. 83.
    Laguna M, Martí R (1999) GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J Comput 11:44–52Google Scholar
  84. 84.
    Laguna M, Martí R (2001) A GRASP for coloring sparse graphs. Comput Optim Appl 19:165–178Google Scholar
  85. 85.
    Laguna M, Feo T, Elrod H (1994) A greedy randomized adaptive search procedure for the two-partition problem. Oper Res 42:677–687Google Scholar
  86. 86.
    Li Y, Pardalos P, Resende M (1994) A greedy randomized adaptive search procedure for the quadratic assignment problem. In: Pardalos P, Wolkowicz H (eds) Quadratic assignment and related problems. DIMACS series on discrete mathematics and theoretical computer science, vol 16. American Mathematical Society, Providence, pp 237–261Google Scholar
  87. 87.
    Liu X, Pardalos P, Rajasekaran S, Resende M (2000) A GRASP for frequency assignment in mobile radio networks. In: Rajasekaran S, Pardalos P, Hsu F (eds) Mobile networks and computing. DIMACS series on discrete mathematics and theoretical computer science, vol 52. American Mathematical Society, Providence, pp 195–201Google Scholar
  88. 88.
    Lourenço HR, Paixão J, Portugal R (2001) Multiobjective metaheuristics for the bus-driver scheduling problem. Transp Sci 35:331–343Google Scholar
  89. 89.
    Martí R, Laguna M (2003) Heuristics and meta-heuristics for 2-layer straight line crossing minimization. Discret Appl Math 127(3):665–678Google Scholar
  90. 90.
    Martins S, Ribeiro C, Souza M (1998) 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. Springer, Berlin/Heidelberg, pp 285–297Google Scholar
  91. 91.
    Martins S, Pardalos P, Resende M, Ribeiro C (1999) Greedy randomized adaptive search procedures for the Steiner problem in graphs. In: Pardalos P, Rajasekaran S, Rolim J (eds) Randomization methods in algorithmic design. DIMACS series on discrete mathematics and theoretical computer science, vol 43. American Mathematical Society, Providence, pp 133–145Google Scholar
  92. 92.
    Martins S, Resende M, Ribeiro C, Pardalos P (2000) A parallel GRASP for the Steiner tree problem in graphs using a hybrid local search strategy. J Glob Optim 17:267–283Google Scholar
  93. 93.
    Mavridou T, Pardalos P, Pitsoulis L, Resende M (1998) A GRASP for the biquadratic assignment problem. Eur J Oper Res 105:613–621Google Scholar
  94. 94.
    Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24: 1097–1100Google Scholar
  95. 95.
    Mockus J, Eddy E, Mockus A, Mockus L, Reklaitis G (1997) Bayesian discrete and global optimization. Kluwer Academic Publishers, Dordrecht/BostonGoogle Scholar
  96. 96.
    Monkman S, Morrice D, Bard J (2008) A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs. Eur J Oper Res 187(3): 1100–1114Google Scholar
  97. 97.
    Morán-Mirabal L, González-Velarde J, Resende M (2013) Automatic tuning of GRASP with evolutionary path-relinking. In: Proceedings of 8th international workshop on hybrid metaheuristics, Ischia. Lecture notes in computer science, vol 7919, pp 62–77Google Scholar
  98. 98.
    nez MLI, Dubois-Lacoste J, Stützle T, Birattari M (2011) The IRACE package, iterated race for automatic algorithm configuration. Technical report TR/IRIDIA/2011-004, IRIDIA, Université Libre de BruxellesGoogle Scholar
  99. 99.
    Osman I, Al-Ayoubi B, Barake M (2003) A greedy random adaptive search procedure for the weighted maximal planar graph problem. Comput Ind Eng 45(4):635–651Google Scholar
  100. 100.
    Pardalos P, Pitsoulis L, Resende M (1996) A parallel GRASP for MAX-SAT problems. Lect Notes Comput Sci 1184:575–585Google Scholar
  101. 101.
    Pardalos P, Pitsoulis L, Resende M (1997) Algorithm 769: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP. ACM Trans Math Softw 23:196–208Google Scholar
  102. 102.
    Pardalos P, Ramakrishnan K, Resende M, Li Y (1997) Implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem. SIAM J Optim 7:280–294Google Scholar
  103. 103.
    Pinãna E, Plana I, Campos V, R Martì (2004) GRASP and path relinking for the matrix bandwidth minimization. Eur J Oper Res 153(1):200–210Google Scholar
  104. 104.
    Prais M, Ribeiro C (1999) Parameter variation in GRASP implementations. In: Extended abstracts of the third metaheuristics international conference, Porto, pp 375–380Google Scholar
  105. 105.
    Prais M, Ribeiro C (2000) Parameter variation in GRASP procedures. Investigación Operativa 9:1–20Google Scholar
  106. 106.
    Prais M, Ribeiro C (2000) Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment. INFORMS J Comput 12:164–176Google Scholar
  107. 107.
    Pu G, Chong Z, Qiu Z, Lin Z, He J (2006) A hybrid heuristic algorithm for HW-SW partitioning within timed automata. In: Proceedings of knowledge-based intelligent information and engineering systems. Lecture notes in artificial intelligence, vol 4251. Springer, Berlin/Heidelberg, pp 459–466Google Scholar
  108. 108.
    Resende M, Feo T (1996) A GRASP for satisfiability. In: Johnson D, Trick M (eds) Cliques, coloring, and satisfiability: the second DIMACS implementation challenge. DIMACS series on discrete mathematics and theoretical computer science, vol 26. American Mathematical Society, Providence, pp 499–520Google Scholar
  109. 109.
    Resende M, Ribeiro C (1997) A GRASP for graph planarization. Networks 29:173–189Google Scholar
  110. 110.
    Resende M, Ribeiro C (2003) Greedy randomized adaptive search procedures. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. Kluwer Academic Publishers, Boston, pp 219–249Google Scholar
  111. 111.
    Resende M, Ribeiro C (2005) GRASP with path-relinking: recent advances and applications. In: Ibaraki T, Nonobe K, Yagiura M (eds) Metaheuristics: progress as real problem solvers. Springer, New York, pp 29–63Google Scholar
  112. 112.
    Resende M, Pardalos P, Li Y (1996) Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP. ACM Trans Math Softw 22:104–118Google Scholar
  113. 113.
    Resende M, Pitsoulis L, Pardalos P (1997) Approximate solution of weighted MAX-SAT problems using GRASP. In: Gu J, Pardalos P (eds) Satisfiability problems. DIMACS series on discrete mathematics and theoretical computer science, vol 35. American Mathematical Society, Providence, pp 393–405Google Scholar
  114. 114.
    Resende M, Pitsoulis L, Pardalos P (2000) Fortran subroutines for computing approximate solutions of MAX-SAT problems using GRASP. Discret Appl Math 100:95–113Google Scholar
  115. 115.
    Ribeiro C, Resende M (1999) Fortran subroutines for approximate solution of graph planarization problems using GRASP. ACM Trans Math Softw 25:341–352Google Scholar
  116. 116.
    Ribeiro C, Souza M (2002) Variable neighborhood search for the degree constrained minimum spanning tree problem. Discret Appl Math 118:43–54Google Scholar
  117. 117.
    Ribeiro C, Urrutia S (2007) Heuristics for the mirrored traveling tournament problem. Eur J Oper Res 179:775–787Google Scholar
  118. 118.
    Ribeiro C, Uchoa E, Werneck R (2002) A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J Comput 14:228–246Google Scholar
  119. 119.
    Ríos-Mercado R, Bard J (1998) Heuristics for the flow line problem with setup costs. Eur J Oper Res 110(1):76–98Google Scholar
  120. 120.
    Ríos-Mercado R, Bard J (1999) An enhanced TSP-based heuristic for makespan minimization in a flow shop with setup costs. J Heuristics 5:57–74Google Scholar
  121. 121.
    Rivera L (1998) Evaluation of parallel implementations of heuristics for the course scheduling problem. Master’s thesis, Instituto Tecnologico y de Estudios Superiores de Monterrey, MonterreyGoogle Scholar
  122. 122.
    Robertson A (2001) A set of greedy randomized adaptive local search procedure (GRASP) implementations for the multidimensional assignment problem. Comput Optim Appl 19: 145–164MathSciNetCrossRefGoogle Scholar
  123. 123.
    Sosnowska D (2000) Optimization of a simplified fleet assignment problem with metaheuristics: simulated annealing and GRASP. In: Pardalos P (ed) Approximation and complexity in numerical optimization. Kluwer Academic Publishers, BostonzbMATHGoogle Scholar
  124. 124.
    Srinivasan A, Ramakrishnan K, Kumaram K, Aravamudam M, Naqvi S (2000) Optimal design of signaling networks for Internet telephony. In: IEEE INFOCOM 2000, Tel-Aviv, vol 2, pp 707–716Google Scholar
  125. 125.
    Takahashi H, Matsuyama A (1980) An approximate solution for the Steiner problem in graphs. Math Jpn 24:573–577MathSciNetzbMATHGoogle Scholar
  126. 126.
    Urban T (1998) Solution procedures for the dynamic facility layout problem. Ann Oper Res 76:323–342CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Applications “Renato Caccioppoli”University of Napoli FEDERICO IINapoliItaly
  2. 2.Amazon.com, Inc. and University of WashingtonSeattleUSA

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