Abstract
GRASP is a multi-start metaheuristic for combinatorial 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 and parameter tuning strategies 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: Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss in detail implementation strategies of memory-based intensification and post-optimization techniques using path-relinking. Hybridizations with other metaheuristics, paral lelization strategies, and applications are also reviewed.
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S. Abdinnour-Helm and S.W. Hadley (2000) Tabu search based heuristics for multi-floor facility layout. International Journal of Production Research, 38, 365–383.
J. Abello, P.M. Pardalos and M.G.C. Resende (1999) On maximum clique problems in very large graphs. In: J. Abello and J. Vitter (eds.), External Memory Algorithms and Visualization, volume 50 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp. 199–130.
R.K. Ahuja, J.B. Orlin and A. Tiwari (2000) A greedy genetic algorithm for the quadratic assignment problem. Computers and Operations Research, 27, 917–934.
R.M. Aiex, M.G.C. Resende, P.M. Pardalos and G. Toraldo (2000) GRASP with path-relinking for the three-index assignment problem. Technical report, AT&T Labs—Research.
R,M. Aiex, M.G.C. Resende and C.C. Ribeiro (2002) Probability distribution of solution time in GRASP: an experimental investigation. Journal of Heuristics, 8, 343–373.
A.C. Alvim (1998) Parallelization strategies for the metaheuristic GRASP. Master’s thesis, Department of Computer Science, Catholic University of Rio de Janeiro, Brazil (in Portuguese).
A.C. Alvim and C.C. Ribeiro (1998) Load balancing for the parallelization of the GRASP metaheuristic. In: Proceedings of the X Brazilian Symposium on Computer Architecture, Búzios, pp. 279–282 (in Portuguese).
S. Areibi and A. Vannelli (1997) A GRASP clustering technique for circuit partitioning. In: J. Gu and P.M. Pardalos (eds.), Satisfiability Problems, Volume 35 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp. 711–724.
M.F. Argüello, J.F. Bard and G. Yu (1997) A GRASP for aircraft routing in response to groundings and delays. Journal of Combinatorial Optimization, 1, 211–228.
M.F. Argüello, T.A. Feo and O. Goldschmidt (1996) Randomized methods for the number partitioning problem. Computers and Operations Research, 23, 103–111.
M. Armony, J.C. Klincewicz, H. Luss and M.B. Rosenwein (2000) Design of stacked self-healing rings using a genetic algorithm. Journal of Heuristics, 6, 85–105.
J.B. Atkinson (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.
J.F. Bard and T.A. Feo (1989) Operations sequencing in discrete parts manufacturing. Management Science, 35, 249–255.
J.F. Bard and T.A. Feo (1991) An algorithm for the manufacturing equipment selection problem. IIE Transactions, 23, 83–92.
J.F. Bard, T.A. Feo and S. Holland (1996) A GRASP for scheduling printed wiring board assembly. IIE Transactions, 28, 155–165.
J.F. Bard, L. Huang, P. Jaillet and M. Dror (1998) A decomposition approach to the inventory routing problem with satellite facilities. Transportation Science, 32, 189–203.
R. Battiti and G. Tecchiolli (1992) Parallel biased search for combinatorial optimization: Genetic algorithms and tabu. Microprocessors and Microsystems, 16, 351–367.
J.E. Beasley (1990) OR-Library: Distributing test problems by electronic mail. Journal of the Operational Research Society, 41, 1069–1072.
S. Binato, W.J. Hery, D, Loewenstern and M.G.C. Resende (2002) A GRASP for job shop scheduling. In: C.C. Ribeiro and P. Hansen (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 59–79.
S. Binato and G.C. Oliveira (2002) A reactive GRASP for transmission network expansion planning. In: C.C. Ribeiro and P. Hansen (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 81–100.
J.L. Bresina (1996) Heuristic-biased stochastic sampling. In: Proceedings of the Thirteenth National Conference on Artificial Intelligence. Portland, pp. 271–278.
S.A. Canuto, M.G.C. Resende and C.C. Ribeiro (2001) Local search with perturbations for the prize-collecting Steinertree problem in graphs. Networks, 38, 50–58.
S.A. Canuto, C.C. Ribeiro and M.G.C. Resende (1999) Local search with perturbations for the prize-collecting Steiner tree problem. In: Extended Abstracts of the Third Metaheuristics International Conference. Angra dos Reis, pp. 115–119.
C. Carreto and B. Baker (2002) A GRASP interactive approach to the vehicle routing problem with backhauls. In: C.C. Ribeiro and P. Hansen (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 185–199.
I. Charon and O. Hudry (1993) The noising method: a new method for combinatorial optimization. Operations Research Letters, 14, 133–137.
I. Charon and O. Hudry (2002) The noising methods: a survey. In: C.C. Ribeiro and C.C. Ribeiro (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 245–261.
V.-D. Cung, S.L. Martins, C.C. Ribeiro and C. Roucairol (2002) Strategies for the parallel implementation of metaheuristics. In: C.C. Ribeiro and C.C. Ribeiro (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 263–308.
P. De, J.B. Ghosj and C.E. Wells (1994) Solving a generalized model for con due date assignment and sequencing. International Journal of Production Economics, 34, 179–185.
H. Delmaire, J.A. Díaz, E. Fernández and M. Ortega (1999) Reactive GRASP and Tabu Search based heuristics for the single source capacitated plant location problem. INFOR, 37, 194–225.
A.S. Deshpande and E. Triantaphyllou (1998) A greedy randomized adaptive search procedure (GRASP) for inferring logical clauses from examples in polynomial time and some extensions. Mathematical Computer Modelling, 27, 75–99.
N. Dodd (1990) Slow annealing versus multiple fast annealing runs: an empirical investigation. Parallel Computing, 16, 269–272.
A. Drexl and F. Salewski (1997) Distribution requirements and compactness constraints in school timetabling. European Journal of Operational Research, 102, 193–214.
H.T. Eikelder, M. Verhoeven, T. Vossen and E. Aarts (1996) A probabilistic analysis of local search. In: I. Osman and J. Kelly (eds.), Metaheuristics: Theory and Applications. Kluwer Academic Publishers, pp. 605–618.
T.A. Feo and J.F. Bard (1989) Flight scheduling and maintenance base planning. Management Science, 35, 1415–1432.
T.A. Feo and J.F. Bard (1989) The cutting path and tool selection problem in computer-aided process planning. Journal ofManufacturing Systems, 8, 17–26.
T.A. Feo, J.F. Bard and S. Holland (1995) Facility-wide planning and scheduling of printed wiring board assembly. Operations Research, 43, 219–230.
T.A. Feo and J.L. González-Velarde (1995) The intermodal trailer assignment problem: models, algorithms, and heuristics. Transportation Science, 29, 330–341.
T.A. Feo and M.G.C. Resende (1989) A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8, 67–71.
T.A. Feo and M.G.C. Resende (1995) Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133.
T.A. Feo, M.G.C. Resende and S.H. Smith (1994) A greedy randomized adaptive search procedure for maximum independent set. Operations Research, 42, 860–878.
T.A. Feo, K. Sarathy and J. McGahan (1996) A GRASP for single machine scheduling with sequence dependent setup costs and linear delay penalties. Computers and Operations Research, 23, 881–895.
T.A. Feo, K. Venkatraman and J.F. Bard (1991) A GRASP for a difficult single machine scheduling problem. Computers and Operations Research, 18, 635–643.
E. Fernández and R. Martí (1999) GRASP for seam drawing in mosaicking of aerial photographic maps. Journal of Heuristics, 5, 181–197.
P. Festa and M.G.C. Resende (2002) GRASP: an annotated bibliography. In: C.C. Ribeiro and P. Hansen (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 325–367.
P. Festa, M.G.C. Resende, P. Pardalos and C.C. Ribeiro (2001) GRASP and VNS for Max-Cut. In: Extended Abstracts of the Fourth Metaheuristics International Conference. Porto, pp. 371–376.
C. Fleurent and F. Glover (1999) Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS Journal on Computing, 11, 198–204.
J.B. Ghosh (1996) Computatinal aspects of the maximum diversity problem. Operations Research Letters, 19, 175–181.
F. Glover (1996) Tabu search and adaptive memory programming—advances, applications and challenges. In: R.S. Barr, R.V. Helgason and J.L. Kennington (eds.), Interfaces in Computer Science and Operations Research. Kluwer, pp. 1–75.
F. Glover (2000) Multi-start and strategic oscillation methods—principles to exploit adaptive memory. In: M. Laguna and J.L. Gonzáles-Velarde (eds.), Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research. Kluwer, pp. 1–24.
F. Glover and M. Laguna (1997) Tabu Search. Kluwer.
F. Glover, M. Laguna and R. Martí (2000) Fundamentals of scatter search and path relinking. Control and Cybernetics, 39, 653–684.
M.X. Goemans and D.P. Williamson (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. PWS Publishing Co., pp. 144–191.
P.L. Hammer and D.J. Rader, Jr. (2001) Maximally disjoint solutions of the set covering problem. Journal of Heuristics, 7, 131–144.
P. Hansen and N. Mladenović (2002) Developments of variable neighborhood search. In: C.C. Ribeiro and P. Hansen (eds.), Essays and Surveys in Metaheuristics. Kluwer Academic Publishers, pp. 415–439.
J.P. Hart and A.W. Shogan (1987) Semi-greedy heuristics: an empirical study. Operations Research Letters, 6, 107–114.
H. Hoos and T. Stützle (1999) Towards a characterisation of the behaviour of stochastic local search algorithms for SAT. Artificial Intelligence, 112, 213–232.
J.G. Klincewicz (1992) Avoiding local optima in the p-hub location problem using tabu search and GRASP. Annals of Operations Research, 40, 283–302.
J.G. Klincewicz and A. Rajan (1994) Using GRASP to solve the component grouping problem. Naval Research Logistics, 41, 893–912.
G. Kontoravdis and J.F. Bard (1995) A GRASP for the vehicle routing problem with time windows. ORSA Journal on Computing, 7, 10–23.
M. Laguna, T.A. Feo and H.C. Elrod (1994) A greedy randomized adaptive search procedure for the two-partition problem. Operations Research, 42, 677–687.
M. Laguna and J.L. González-Velarde (1991) A search heuristic for just-in-time scheduling in parallel machines. Journal of Intelligent Manufacturing, 2, 253–260.
M. Laguna and R. Martí (1999) GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS Journal on Computing, 11, 44–52.
Y. Li, P.M. Pardalos and M.G.C. Resende (1994) A greedy randomized adaptive search procedure for the quadratic assignment problem. In: P.M. Pardalos and H. Wolkowicz (eds.), Quadratic Assignment and Related Problems, volume 16 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp. 237–261.
X. Liu, P.M. Pardalos, S. Rajasekaran and M.G.C. Resende (2000) A GRASP for frequency assignment in mobile radio networks. In: B.R. Badrinath, F. Hsu, P.M. Pardalos and S. Rajasekaran (eds.), Mobile Networks and Computing, volume 52 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp. 195–201.
S.L. Martins, P.M. Pardalos, M.G.C. Resende and C.C. Ribeiro (1999) Greedy randomized adaptive search procedures for the steiner problem in graphs. In: P.M. Pardalos, S. Rajasekaran and J. Rolim (eds.), Randomization Methods in Algorithmic Design, volume 43 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp. 133–145.
S.L. Martins, M.G.C. Resende, C.C. Ribeiro and P. Pardalos (2000) A parallel GRASP for the Steiner tree problem in graphs using a hybrid local search strategy. Journal of Global Optimization, 17, 267–283.
S.L. Martins, C.C. Ribeiro and M.C. Souza (1998) A parallel GRASP for the Steiner problem in graphs. In: A. Ferreira and J. Rolim (eds.), Proceedings of IRREGULAR’98—5th International Symposium on Solving Irregularly Structured Problems in Parallel, volume 1457 of Lecture Notes in Computer Science. Springer-Verlag, pp. 285–297.
T. Mavridou, P.M. Pardalos, L.S. Pitsoulis and M.G.C. Resende (1998) A GRASP for the biquadratic assignment problem. European Journal of Operational Research, 105, 613–621.
N. Mladenović and P. Hansen (1997) Variable neighborhood search. Computers and Operations Research, 24, 1097–1100.
R. A. Murphey, P.M. Pardalos and L.S. Pitsoulis (1998) A parallel GRASP for the data association multidimensional assignment problem. In: P.M. Pardalos (ed.), Parallel Processing of Discrete Problems, volume 106 of The IMA Volumes in Mathematics and Its Applications, Springer-Verlag, pp. 159–180.
L. Osborne and B. Gillett (1991) A comparison of two simulated annealing algorithms applied to the directed Steiner problem on networks. ORSA Journal on Computing, 3, 213–225.
P.M. Pardalos, T. Qian and M.G.C. Resende (1999) A greedy randomized adaptive search procedure for the feedback vertex set problem. Journal of Combinatorial Optimization, 2, 399–412.
P.M. Pardalos, L.S. Pitsoulis and M.G.C. Resende (1995) A parallel GRASP implementation for the quadratic assignment problem. In: A. Ferreira and J. Rolim (eds.), Parallel Algorithms for Irregularly Structured Problems—Irregular’94.Kluwer Academic Publishers, pp. 115–133.
P.M. Pardalos, L.S. Pitsoulis and M.G.C. Resende (1996) A parallel GRASP for MAX-SAT problems. Lecture Notes in Computer Science, 1184, 575–585.
L.S. Pitsoulis, P.M. Pardalos and D.W. Hearn (2001) Approximate solutions to the turbine balancing problem. European Journal of Operational Research, 130, 147–155.
M. Prais and C.C. Ribeiro (1999) Parameter variation in GRASP implementations. In: Extended Abstracts of the Third Metaheuristics International Conference. Angra dos Reis, pp. 375–380.
M. Prais and C.C. Ribeiro (2000) Parameter variation in GRASP procedures. InvestigaciónOperativa, 9, 1–20.
M. Prais and C.C. Ribeiro (2000) Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment. INFORMS Journal on Computing, 12, 164–176.
M.G.C. Resende (1998) Computing approximate solutions of the maximum covering problem using GRASP. Journal of Heuristics, 4, 161–171.
M.G.C. Resende and T.A. Feo (1996) A GRASP for satisfiability. In: D.S. Johnson and M.A. Trick (eds.), Cliques, Coloring, and Satisfiability: The Second DIMACS Implementation Challenge, volume 26 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, pp. 499–520.
M.G.C. Resende, T.A. Feo and S.H. Smith (1998) Algorithm 787: Fortran subroutines for approximate solution of maximum independent set problems using GRASP. ACM Transactions on Mathematical Software, 24, 386–394.
M.G.C. Resende, P.M. Pardalos and Y. Li (1996) Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP. ACM Transactions on Mathematical Software, 22, 104–118.
M.G.C. Resende, L.S. Pitsoulis and P.M. Pardalos (1997) Approximate solution of weighted MAX-SAT problems using GRASP. In: J. Gu and P.M. Pardalos (eds.), Satisfiability Problems, volume 35 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, pp. 393–405.
M.G.C. Resende, L.S. Pitsoulis and P.M. Pardalos (2000) Fortran subroutines for computing approximate solutions of MAX-SAT problems using GRASP. Discrete Applied Mathematics, 100, 95–113.
M.G.C. Resende and C.C. Ribeiro (1997) A GRASP for graph planarization. Networks, 29, 173–189.
M.G.C. Resende and C.C. Ribeiro (2001) A GRASP with path-relinking for private virtual circuit routing. Technical report, AT&T Labs Research.
C.C. Ribeiro and M.G.C. Resende (1999) Algorithm 797: Fortran subroutines for approximate solution of graph planarization problems using GRASP. ACM Transactions on Mathematical Software, 25, 342–352.
C.C. Ribeiro, C.D. Ribeiro and R.S. Lanzelotte (1997) Query optimization in distributed relational databases. Journal of Heuristics, 3, 5–23.
C.C. Ribeiro and M.C. Souza (2002) Variable neighborhood search forthe degree constrained minimum spanning tree problem. Discrete Applied Mathematics, 118, 43–54.
C.C. Ribeiro, E. Uchoa and R.F. Werneck (2002) A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing, 14, 228–246.
R.Z. Ríos-Mercado and J.F. Bard (1998) Heuristics for the flow line problem with setup costs. European Journal of Operational Research, 76–98.
R.Z. Ríos-Mercado and J.F. Bard (1999) An enhanced TSP-based heuristic for makespan minimization in a flow shop with setup costs. Journal of Heuristics, 5, 57–74.
B. Selman, H. Kautz and B. Cohen (1994) Noise strategies for improving local search. In: Proceedings of the Twelfth National Conference on Artificial Intelligence. Seattle, MIT Press, pp. 337–343.
E. Taillard (1991) Robust taboo search forthe quadratic assignment problem. Parallel Computing, 7, 443–455.
H. Takahashi and A. Matsuyama (1980) An approximate solution for the Steiner problem in graphs. Mathematica Japonica, 24, 573–577.
T.L. Urban (1998) Solution procedures for the dynamic facility layout problem. Annals of Operations Research, 323–342.
T.L. Urban, W.-C. Chiang and R.A. Russel (2000) The integrated machine allocation and layout problem. International Journal of Production Research, 2913–2930.
M.G.A. Verhoeven and E.H.L. Aarts (1995) Parallel local search. Journal of Heuristics, 1, 43–65.
S. Voss, A. Martin and T. Koch (2001) Steinlib testdata library. Online document at http://elib.zib.de/steinlib/steinlib.html, last visited on May 1.
D.L. Woodruff and E. Zemel (1993) Hashing vectors for tabu search. Annals of Operations Research, 41, 123–137.
J. Yen, M. Carlsson, M. Chang, J.M. Garcia and H. Nguyen (2000) Constraint solving for inkjet print mask design. Journal of Imaging Science and Technology, 44, 391–397.
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Resende, M.G.C., Ribeiro, C.C. (2003). Greedy Randomized Adaptive Search Procedures. In: Glover, F., Kochenberger, G.A. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 57. Springer, Boston, MA. https://doi.org/10.1007/0-306-48056-5_8
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