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GRASP: The basic heuristic

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Optimization by GRASP

Abstract

This chapter presents the basic structure of a greedy randomized adaptive search procedure (or, more simply, GRASP). We first introduce random and semi-greedy multistart procedures and show how solutions produced by both procedures differ. The hybridization of a semi-greedy procedure with a local search method constitutes a GRASP heuristic. The chapter concludes with some implementation details, including stopping criteria.

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References

  • C.H. Antunes, E. Oliveira, and P. Lima. A multi-objective GRASP procedure for reactive power compensation planning. Optimization and Engineering, 15: 199–215, 2014.

    Article  MATH  Google Scholar 

  • J.E.C. Arroyo, P.S. Vieira, and D.S. Vianna. A GRASP algorithm for the multi-criteria minimum spanning tree problem. Annals of Operations Research, 159:125–133, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  • V. Bartkutė and L. Sakalauskas. Statistical inferences for termination of Markov type random search algorithms. Journal of Optimization Theory and Applications, 141:475–493, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  • V. Bartkutė, G. Felinskas, and L. Sakalauskas. Optimality testing in stochastic and heuristic algorithms. Technical Report 12, Vilnius Gediminas Technical University, Vilnius, 2006.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • M. Chica, O. Cordón, S. Damas, and J. Bautista. A multiobjective GRASP for the 1/3 variant of the time and space assembly line balancing problem. In N. García-Pedrajas, F. Herrera, C. Fyfe, J. Benítez, and M. Ali, editors, Trends in applied intelligent systems, volume 6098 of Lecture Notes in Computer Science, pages 656–665. Springer, Berlin, 2010.

    Google Scholar 

  • W.B. Crowston, F. Glover, G.L. Thompson, and J.D. Trawick. Probabilistic and parametric learning combinations of local job shop scheduling rules. Technical Report 117, Carnegie-Mellon University, Pittsburgh, 1963.

    Google Scholar 

  • G. Dahl and B. Johannessen. The 2-path network design problem. Networks, 43:190–199, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  • H. Davoudpour and M. Ashrafi. Solving multi-objective SDST flexible flow shop using GRASP algorithm. The International Journal of Advanced Manufacturing Technology, 44:737–747, 2009.

    Article  Google Scholar 

  • X. Delorme, X. Gandibleux, and F. Degoutin. Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem. European Journal of Operational Research, 204:206–217, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  • C. Dorea. Stopping rules for a random optimization method. SIAM Journal on Control and Optimization, 28:841–850, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  • C. Duin and S. Voss. The Pilot method: A strategy for heuristic repetition with application to the Steiner problem in graphs. Networks, 34:181–191, 1999.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • T.A. Feo and M.G.C. Resende. Greedy randomized adaptive search procedures. Journal of Global Optimization, 6:109–133, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  • T.A. Feo, M.G.C. Resende, and S.H. Smith. A greedy randomized adaptive search procedure for maximum independent set. Technical report, AT&T Bell Laboratories, 1989.

    Google Scholar 

  • T.A. Feo, M.G.C. Resende, and S.H. Smith. A greedy randomized adaptive search procedure for maximum independent set. Operations Research, 42: 860–878, 1994.

    Article  MATH  Google Scholar 

  • P. Festa and M.G.C. Resende. GRASP: An annotated bibliography. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics, pages 325–367. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • W.E. Hart. Sequential stopping rules for random optimization methods with applications to multistart local search. SIAM Journal on Optimization, 9: 270–290, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Held and R.M. Karp. The traveling-salesman problem and minimum spanning trees. Operations Research, 18:1138–1162, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  • A.J. Higgins, S. Hajkowicz, and E. Bui. A multi-objective model for environmental investment decision making. Computers & Operations Research, 35:253–266, 2008.

    Article  MATH  Google Scholar 

  • C. Ishida, A. Pozo, E. Goldbarg, and M. Goldbarg. Multiobjective optimization and rule learning: Subselection algorithm or meta-heuristic algorithm? In N. Nedjah, L.M. Mourelle, and J. Kacprzyk, editors, Innovative applications in data mining, pages 47–70. Springer, Berlin, 2009.

    Google Scholar 

  • G.A. Kochenberger, B.A. McCarl, and F.P. Wyman. A heuristic for general integer programming. Decision Sciences, 5:36–41, 1974.

    Article  Google Scholar 

  • E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys, editors. The traveling salesman problem: A guided tour of combinatorial optimization. John Wiley & Sons, New York, 1985.

    MATH  Google Scholar 

  • H. Li and D. Landa-Silva. An elitist GRASP metaheuristic for the multi-objective quadratic assignment problem. In M. Ehrgott, C.M. Fonseca, X. Gandibleux, J.-K. Hao, and M. Sevaux, editors, Evolutionary multi-criterion optimization, volume 5467 of Lecture Notes in Computer Science, pages 481–494. Springer, Berlin, 2009.

    Google Scholar 

  • R. Martí, J.L. González-Velarde, and A. Duarte. Heuristics for the bi-objective path dissimilarity problem. Computers & Operations Research, 36:2905–2912, 2009.

    Article  MATH  Google Scholar 

  • R. Martí, M.G.C. Resende, and C.C. Ribeiro. Multi-start methods for combinatorial optimization. European Journal of Operational Research, 226:1–8, 2013a.

    Google Scholar 

  • R. Martí, V. Campos, M.G.C. Resende, and A. Duarte. Multiobjective GRASP with path relinking. European Journal of Operational Research, 240:54–71, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  • S.L. Martins, P.M. Pardalos, M.G.C. Resende, and C.C. Ribeiro. A parallel GRASP for the Steiner tree problem in graphs using a hybrid local search strategy. Journal of Global Optimization, 17:267–283, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  • J.F. Muth and G.L. Thompson. Industrial scheduling. Prentice-Hall, Boston, 1963.

    Google Scholar 

  • C. Orsenigo and C. Vercellis. Bayesian stopping rules for greedy randomized procedures. Journal of Global Optimization, 36:365–377, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  • L.S. Pitsoulis and M.G.C. Resende. Greedy randomized adaptive search procedures. In P.M. Pardalos and M.G.C. Resende, editors, Handbook of applied optimization, pages 168–183. Oxford University Press, New York, 2002.

    Google Scholar 

  • R.L. Rardin, R., and Uzsoy. Experimental evaluation of heuristic optimization algorithms: A tutorial. Journal of Heuristics, 7:261–304, 2001.

    Google Scholar 

  • M.G.C. Resende. Computing approximate solutions of the maximum covering problem using GRASP. Journal of Heuristics, 4:161–171, 1998.

    Article  MATH  Google Scholar 

  • M.G.C. Resende and T.A. Feo. A GRASP for satisfiability. In D.S. Johnson and M.A. Trick, editors, Cliques, coloring, and satisfiability: The second DIMACS implementation challenge, volume 26 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 499–520. American Mathematical Society, Providence, 1996.

    Google Scholar 

  • M.G.C. Resende and C.C. Ribeiro. Greedy randomized adaptive search procedures. In F. Glover and G. Kochenberger, editors, Handbook of metaheuristics, pages 219–249. Kluwer Academic Publishers, Boston, 2003b.

    Google Scholar 

  • M.G.C. Resende and C.C. Ribeiro. Greedy randomized adaptive search procedures: Advances and applications. In M. Gendreau and J.-Y. Potvin, editors, Handbook of metaheuristics, pages 293–319. Springer, New York, 2nd edition, 2010.

    Google Scholar 

  • M.G.C. Resende and C.C. Ribeiro. GRASP: Greedy randomized adaptive search procedures. In E.K. Burke and G. Kendall, editors, Search methodologies: Introductory tutorials in optimization and decision support systems, chapter 11, pages 287–312. Springer, New York, 2nd edition, 2014.

    Google Scholar 

  • M.G.C. Resende and R.M.A. Silva. GRASP: Greedy randomized adaptive search procedures. In J.J. Cochran, L.A. Cox, Jr., P. Keskinocak, J.P. Kharoufeh, and J.C. Smith, editors, Encyclopedia of operations research and management science, volume 3, pages 2118–2128. Wiley, New York, 2011.

    Google Scholar 

  • M.G.C. Resende, L.S. Pitsoulis, and P.M. Pardalos. Approximate solution of weighted MAX-SAT problems using GRASP. In J. Gu and P.M. Pardalos, editors, Satisfiability problems, volume 35 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 393–405. American Mathematical Society, Providence, 1997.

    Google Scholar 

  • A.P. Reynolds and B. de la Iglesia. A multi-objective GRASP for partial classification. Soft Computing, 13:227–243, 2009.

    Article  Google Scholar 

  • A.P. Reynolds, D.W. Corne, and B. de la Iglesia. A multiobjective GRASP for rule selection. In Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pages 643–650, Montreal, 2009. ACM.

    Google Scholar 

  • C.C. Ribeiro. GRASP: Une métaheuristique gloutonne et probabiliste. In J. Teghem and M. Pirlot, editors, Optimisation approchée en recherche opérationnelle, pages 153–176. Hermès, Paris, 2002.

    Google Scholar 

  • C.C. Ribeiro and I. Rosseti. A parallel GRASP heuristic for the 2-path network design problem. In B. Monien and R. Feldmann, editors, Euro-Par 2002 Parallel Processing, volume 2400 of Lecture Notes in Computer Science, pages 922–926. Springer, Berlin, 2002.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • C.C. Ribeiro, I. Rosseti, and R.C. Souza. Effective probabilistic stopping rules for randomized metaheuristics: GRASP implementations. In C.A.C. Coello, editor, Learning and intelligent optimization, volume 6683, pages 146–160. Springer, Berlin, 2011.

    Google Scholar 

  • C.C. Ribeiro, I. Rosseti, and R.C. Souza. Probabilistic stopping rules for GRASP heuristics and extensions. International Transactions in Operational Research, 20:301–323, 2013.

    Article  MATH  Google Scholar 

  • M.A. Salazar-Aguilar, R.Z. Ríos-Mercado, and J.L. González-Velarde. GRASP strategies for a bi-objective commercial territory design problem. Journal of Heuristics, 19:179–200, 2013.

    Article  Google Scholar 

  • S. Senju and Y. Toyoda. An approach to linear programming with 0-1 variables. Management Science, 15:196–207, 1968.

    Google Scholar 

  • F.S. Serifoglu and G. Ulusoy. Multiprocessor task scheduling in multistage hybrid flow-shops: A genetic algorithm approach. Journal of the Operational Research Society, 55:504–512, 2004.

    Article  MATH  Google Scholar 

  • D.S. Vianna and J.E.C. Arroyo. A GRASP algorithm for the multi-objective knapsack problem. In Proceedings of the 24th International Conference of the Chilean Computer Science Society, pages 69–75, Arica, 2004. IEEE.

    Google Scholar 

  • S. Voss, A. Fink, and C. Duin. Looking ahead with the Pilot method. Annals of Operations Research, 136:285–302, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  • F.P. Wyman. Binary programming: A occasion rule for selecting optimal vs. heuristic techniques. The Computer Journal, 16:135–140, 1973.

    Google Scholar 

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Authors and Affiliations

  1. Modeling and Optimization Group (MOP), Amazon.com, Inc., Seattle, WA, USA

    Mauricio G. C. Resende

  2. Instituto de Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro, Brazil

    Celso C. Ribeiro

Authors
  1. Mauricio G. C. Resende
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  2. Celso C. Ribeiro
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Resende, M.G.C., Ribeiro, C.C. (2016). GRASP: The basic heuristic. In: Optimization by GRASP. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6530-4_5

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