Skip to main content

Scatter Search and Path Relinking: Advances and Applications

  • Chapter
Handbook of Metaheuristics

Abstract

Scatter search (SS) is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies for combining solution vectors that have proved effective in a variety of problem settings. Path relinking (PR) has been suggested as an approach to integrate intensification and diversification strategies in a search scheme. The approach may be viewed as an extreme (highly focused) instance of a strategy that seeks to incorporate attributes of high quality solutions, by creating inducements to favor these attributes in the moves selected. The goal of this paper is to examine SS and PR strategies that provide useful alternatives to more established search methods. We describe the features of SS and PR that set them apart from other evolutionary approaches, and that offer opportunities for creating increasingly more versatile and effective methods in the future. Specific applications are summarized to provide a clearer understanding of settings where the methods are being used.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Aiex, R.M., Resende, M.G.C., Pardalos, P.M. and Toraldo, G. (2000) GRASP with path relinking for the three-index assignment problem (submitted for publication).

    Google Scholar 

  • Aiex, R.M., Resende, M.G.C. and Ribeiro, C.C. (2002) Probability distribution of solution time in GRASP: An experimental investigation. Journal of Heuristics, 8, 343–373.

    Article  Google Scholar 

  • Alvarez, A., González, J.L. and De Alba, K. (2001a) Un algoritmo de búsqueda para un problema de red capacitada multiproducto. In: C. Zozaya, M. Mejía, P. Noriega, A. Sánchez (eds.), Proceedings of 3rd International Meeting of Computational Sciences, Aguascalientes Mexico, pp. 105–114.

    Google Scholar 

  • Alvarez, A., González, J.L. and De Alba, K. (2001 b) Scatter search for the multi-commodity capacitated network design problem. Proceedings of the 6th Annual International Conference on Industrial Engineering—Theory, Applications and Practice. San Francisco, CA, USA.

    Google Scholar 

  • Beausoleil, R.P. (2001) Multiple criteria scatter search. 4th Metaheuritics International Congress, Porto, Portugal, pp. 539–543.

    Google Scholar 

  • Bulut, G. (2001) Robust multi-scenario optimization of an air expeditionary force force structure applying scatter search to the combat forces assessment model. Masters Thesis, Department of Operational Sciences, Air Force Institute of Technology, AFIT/GOR/ENS/01M-05.

    Google Scholar 

  • Campos, V., Laguna, M. and Martí, R. (1999) Scatter search for the linear ordering problem. In: David Corne, Marco Dorigo and Fred Glover (eds.), New Ideas in Optimization, McGraw-Hill, pp. 331–340.

    Google Scholar 

  • Canuto, S. A. (2000) Local Search for the Prize-collecting Steiner Tree Problem (in Portuguese), M.Sc. Dissertation, Department of Computer Science, Catholic University of Rio de Janeiro.

    Google Scholar 

  • Canuto, S.A., Resende, M.G.C. and Ribeiro, C.C. (2001) Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks, 38, 50–58.

    Article  MathSciNet  Google Scholar 

  • Cavique, L., Rego, C. and Themido, I. (2001) A Scatter Search Algorithm for the Maximum Clique Problem. Essays and Surveys in Metaheuristics, Kluwer Academic Publishers.

    Google Scholar 

  • Chanas, S. and Kobylanski, P. (1996) A new heuristic algorithm solving the linear ordering problem. Computational Optimization and Applications, 6, 191–205.

    MathSciNet  Google Scholar 

  • Crowston, W.B., Thompson, G.L. and Trawick, J.D. (1963) Probabilistic learning combinations of local job shop scheduling rules. Chapters II and III, ONR Research Memorandum No. 117, GSIA, Carnegie Mellon University, Pittsburgh, PA.

    Google Scholar 

  • Cung, V.-D., Mautor, T., Michelon, P. and Tavares, A. (1997) A scatter search based approach for the quadratic assignment problem. In: T. Bäck, Z. Michalewicz and X. Yao (eds.), Proceedings of IEEE-ICEC-EPS’97, IEEE International Conference on Evolutionary Computation and Evolutionary Programming Conference. Indianapolis, pp. 165–170.

    Google Scholar 

  • Cung, V.D., Martins, S.L., Ribeiro, C.C. and Roucairol, C. (2001) Strategies for the parallel implementation of metaheuristics. In: C.C. Ribeiro and P. Hansen (eds.), Essays and Surveys in Metaheuristics. Kluwer, pp. 263–308.

    Google Scholar 

  • Delgado, C., Laguna, M. and Pacheco, J. (2002) Minimizing Labor Requirements in a Periodic Vehicle Loading Problem. University of Burgos, Spain.

    Google Scholar 

  • Dorne, R. and Hao, J.-K. (1998) Tabu search for graph coloring, T-colorings and set T-colorings. In: S. Voss, S. Martello, I.H. Osman and C. Roucairol (eds.), Meta-heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer, pp. 77–92.

    Google Scholar 

  • Eades, P. and Kelly, D. (1986) Heuristics for drawing 2-layered networks. Ars Combinatoria, 21, 89–98.

    MathSciNet  Google Scholar 

  • Festa, P. and Resendee, M.G.C. (2001) GRASP: an annotated bibliography. In: P. Hansen and C. Riberio (eds.), Essays and Surveys on Meta-Heuristics, Kluwer Academic Publishers, Boston, USA.

    Google Scholar 

  • Fleurent, C. and Glover, F. (1999) Improved constructive multi-start strategies for the quadratic assignment problem using adaptive memory. INFORMS Journal on Computing, 11, 198–204.

    MathSciNet  Google Scholar 

  • Funabiki, N. and Higashino, T. (2000) A minimal-state processing search algorithm for graph colorings problems. IEICE Transactions on Fundamentals, E83-A(7), 1420–1430.

    Google Scholar 

  • Galinier, P. and Hao, J.-K. (1999) Hybrid evolutionary algorithms for graph coloring. Journal of Combinatorial Optimization, 3(4), 379–397.

    Article  MathSciNet  Google Scholar 

  • García, F., Melián, B., Moreno, J.A. and Moreno, J.M. (2001) Hybrid metaheuristics based on the scatter search. Proceeding of EUNITE 2001. pp. 479–485. ISBN: 3-89653-916-7. (European Symposium on Intelligent Technologies, Hybriis Systems and their implementation on Smart Adaptive Systems. December 13–14. Puerto de la Cruz, Tenerife, Spain.)

    Google Scholar 

  • Garey, M. and Johnson, D. (1979) Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York.

    Google Scholar 

  • Ghamlouche, I., Crainic, T.G. and Gendreau, M. (2002) Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Publication CRT-2002-01, Centre de recherche sur les transports, Université de Montréal.

    Google Scholar 

  • Ghamlouche, I., Crainic, T.G. and Gendreau, M. (2001) Cycle-based neighbourhoods for fixed-charge capacitated multicommodity network design. Publication CRT-2001-01, Centre de recherche sur les transports, Université de Montréal.

    Google Scholar 

  • Glover, F. (1963) Parametric combinations of local job shop scheduling rules. Chapter IV, ONR Research Memorandum No. 117, GSIA, Carnegie Mellon University, Pittsburgh, PA.

    Google Scholar 

  • Glover, F. (1965) A multiphase dual algorithm for the zero-one integer programming problem. Operations Research, 13(6), 879–919.

    MATH  MathSciNet  Google Scholar 

  • Glover, F. (1968) Surrogate constraints. Operations Research, 16(4), 741–749.

    MATH  MathSciNet  Google Scholar 

  • Glover, F. (1977) Heuristics for integer programming using surrogate constraints. Decision Sciences, 8(1), 156–166.

    Google Scholar 

  • Glover, F. (1994) Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). Discrete Applied Mathematics, 49, 231–255.

    Article  MATH  MathSciNet  Google Scholar 

  • Glover, F. (1995) Scatter search and star paths: beyond the genetic metaphor. OR Spektrum, 17, 125–137.

    Article  MATH  Google Scholar 

  • Glover, F. (1997) Tabu search and adaptive memory programming—advances, applications and challenges. In. R. Barr, Helgason and Kennington (Co-eds.), Advances in Meta-heuristics, Optimization and Stochastic Modeling Techniques. Kluwer Academic Publishers, Boston, USA, pp. 1–175.

    Google Scholar 

  • Glover, F. (1998) A template for scatter search and path relinking. In: J.-K. Hao, E. Lutton, E. Ronald, M. Schoenauer and D. Snyers (eds.), Artificial Evolution, Lecture Notes in Computer Science 1363. Springer, pp. 3–51.

    Google Scholar 

  • Glover, F. and Laguna, M. (1997) Tabu Search. Kluwer Academic Publishers, Boston.

    Google Scholar 

  • Glover, F., Løkketangen, A. and Woodruff, D.L. (2000) Scatter search to generate diverse MIP solutions. In: M. Laguna and J.L. González-Velarde (eds.), OR Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, pp. 299–317.

    Google Scholar 

  • Grabowski, J. and Wodecki, M. (2001) A new very fast tabu search algorithm for the job shop problem. Preprint 21/2001, Instytut Cybernetyki Techncznej Politechniki Wroclawskiej, Wroclaw.

    Google Scholar 

  • Greistorfer, P. (1995) Computational experiments with heuristics for a capacitated arc routing problem. In: U. Derigs, A. Bachem and A. Drexl (eds.), Operations Research Proceedings 1994. Springer-Verlag, Berlin, pp. 185–190.

    Google Scholar 

  • Greistorfer, P. (2001a) A tabu scatter search metaheuristic for the arc routing problem. Computers & Industrial Engineering (forthcoming).

    Google Scholar 

  • Greistorfer, P. (2001b) Testing population designs. 4th Metaheuristics International Conference (MIC’2001). Porto, pp. 713–717 (17 pages submitted as “Experimental pool design”).

    Google Scholar 

  • Hamiez, J.P. and Hao, J.K. (2001) Scatter search for graph coloring. To appear in the LNCS series (Springer).

    Google Scholar 

  • Herrmann J.W., Ioannou, G., Minis, I. and Proth, J.M. (1996) A dual ascent approach to the fixed-charge capacitated network design problem. European Journal of Operational Research, 95, 476–490.

    Article  Google Scholar 

  • Hill, R.R. and McIntyre, G. (2000) A methodology for robust, multi-scenario optimization. Phalanx, 33(3).

    Google Scholar 

  • Johnson, D.S. and Trick, M.A. (eds.) (1996) Cliques, Coloring, and Satisfiability: 2nd DIMACS Implementation Challenge, 1993, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26, American Mathematical Society.

    Google Scholar 

  • Knuth, D.E. (1993) The Stanford GraphBase: A Platform for Combinatorial Computing. Addison Wesley, New York.

    Google Scholar 

  • Laguna, M. (1999) Scatter search. In: P.M. Pardalos and M.G.C. Resende (eds.), Handbook of Applied Optimization. Oxford Academic Press (to appear).

    Google Scholar 

  • Laguna, M. and Martí, R. (1999) GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS Journal on Computing, 11(1), 44–52.

    Google Scholar 

  • Laguna, M. and Martí, R. (2002) The OptQuest callable library. In: S. Voss and D.L. Woodruff (eds.), Optimization Software Class Libraries, Kluwer, Boston.

    Google Scholar 

  • Laguna, M., Martí, R. and Campos, V. (1999) Intensification and diversification with Elite Tabu search solutions for the linear ordering problem. Computers and Operations Research, 26, 1217–1230

    Article  Google Scholar 

  • Løkketangen, A. and Woodruff (2000) Integrating pivot based search with branch and bound for binary MIP’s. Control and Cybernetics, Special Issue on Tabu Search, 29(3), 741–760.

    Google Scholar 

  • Løkketangen, A. and Glover, F. (1998) Solving zero-one mixed integer programming problems using tabu search. European Journal of Operational Research, 106, 624–658.

    Google Scholar 

  • Løkketangen, A. and Glover, F. (1995) Tabu search for zero/one mixed integer programming with advanced level strategies and learning. International Journal of Operations and Quantitative Management, 1(2), 89–109.

    Google Scholar 

  • Løkketangen, A. and Glover, F. (1996) Probabilistic move selection in Tabu search for 0/1 mixed integer programming problems. In: Metaheuristics: Theory and Applications, by Kluwer, March 96. An earlier version is in the conference proceedings from MIC’95.

    Google Scholar 

  • Løkketangen, A. and Glover, F. (1999) Candidate list and exploration strategies for solving 0/1 MIP problems using a Pivot neighborhood. In: S. Voß, S. Martello, I.H. Osman and C. Roucairol (eds.), Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers, pp. 141–155.

    Google Scholar 

  • Magnanti, T. and Wong, R. (1984) Network design and transportation planning: models and algorithms. Transportation Science, 18, 1–55.

    Google Scholar 

  • Martí, R. (1998) A Tabu search algorithm for the Bipartite drawing problem. European Journal of Operational Research, 106, 558–569.

    Article  MATH  Google Scholar 

  • Martí, R. and Laguna, M. (1997) Heuristics and metaheuristics for 2-layer straight line crossing minimization. Discrete and Applied Mathematics (to appear).

    Google Scholar 

  • Martí, R., Lourenço, L. and Laguna, M. (2000) Assigning proctors to exams with scatter search. In: M. Laguna and J.L. González Velarde (eds.), Computing Tools for Modeling, Optimization and Simulation, Kluwer Academic Publishers, pp.215–228.

    Google Scholar 

  • Martí, R., Lourenço, L. and Laguna, M. (2001) Assigning proctors to exams with scatter search (second part), Economic Working Papers Series, Department of Economics and Business, Universitat Pompeu Fabra, no. 534.

    Google Scholar 

  • Morgenstern, C. A. (1996) Distributed coloration neighborhood search. In Johnson and Trick (1996), pp. 335–357.

    Google Scholar 

  • Nowicki, E. and Smutnicki, C. (1996) A fast tabu search algorithm for the job-shop problem. Management Science, 42(6), 797–813.

    Google Scholar 

  • Nowicki, E., and Smutnicki, C. (2001a) New ideas in TS for job-shop scheduling. Technical Report 50/2001. In: C. Rego and B. Alidaee (eds.), Adaptive Memory and Evolution: Tabu Search and Scatter Search. Kluwer Academic Publishers.

    Google Scholar 

  • Nowicki, E. and Smutnicki, C. (2001b) New tools to solve the job-shop problem. Technical Report 51.

    Google Scholar 

  • Osman, I.H. (2000) Meta-heuristics: A general framework. In: Proceedings of the Workshop on “algorithm engineering as a new paradigm: a challenge to hard computation problems” October 30–November 2, Research Institute for Mathematical Science, Kyoto University, Japan, pp. 117–118.

    Google Scholar 

  • Osman, I.H. and Samad Ahmadi (2001) Guided Construction search Meta-Heuristics for the Capacitated Clustering Problem. Working Paper, School of Business, American University of Beirut.

    Google Scholar 

  • Osman, I.H. (1994) Capacitated clustering problems by hybrid simulated annealing and tabu search. International Transactions in Operational Research, I, 317–336.

    Google Scholar 

  • Rego, Cesar and Pedro Leão (2000) A Scatter Search Tutorial for Graph-Based Permutation Problems. Hearin Center for Enterprise Science, U of Mississippi, Report Number: HCES-10-00.

    Google Scholar 

  • Reinelt, G. (1985) The Linear Ordering Problem: Algorithms and Applications, Research and Exposition in Mathematics, Vol. 8, H.H. Hofmann and R. Wille (eds.), Heldermann Verlag Berlin.

    Google Scholar 

  • Resende, M.G.C. and Ribeiro, C.C. (2001) A GRASP with path relinking for permanent virtual circuit routing. Research Report (submitted for publication).

    Google Scholar 

  • Resende, M.G.C. and C.C. Ribeiro (2002) “GRASP”, In: F. Glover and G. Kochenberger (eds.), State-of-the-Art Handbook of Metaheuristics. Kluwer (to appear).

    Google Scholar 

  • Ribeiro, C.C, ∼Uchoa, E. and Werneck, R.F. (2002) A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing (to appear)

    Google Scholar 

  • Rusell, R.A. and Igo, W. (1979) An assignment routing problem. Networks, 9, 1–17.

    Google Scholar 

  • Souza, M.C., Duhamel, C. and Ribeiro, C.C. (2002) A GRASP heuristic using a path-based local search for the capacitated minimum spanning tree problem. Research Report (submitted for publication).

    Google Scholar 

  • Valls, V., Quintanilla, S. and Ballestín, F. (2001) A Population Based Approach to the Resource ConstrainedProject Scheduling. TR06-2001, Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universitat de Valencia (Spain).

    Google Scholar 

  • Verhoeven, M.G.A. and Aarts, E.H.L. (1995) Parallel local search. Journal of Heuristics, 1, 43–65.

    Google Scholar 

  • Voss, S., Martin, A. and Koch, T. (2001) SteinLib testdata library. online document at http://elib.zib.de/steinlib/steinlib.html.

  • Woodruff, D.L. (1998) Proposals for chunking and Tabu search. European Journal of Operation Research, 106, 585–598.

    MATH  Google Scholar 

  • Woodruff, D.L. (2001) General purpose metrics for solution variety. Technical Report, Graduate School of Management, UC Davis, Davis CA 95616.

    Google Scholar 

  • Woodruff, D.L. (1996) Chunking applied to reactive Tabu search. In: I.H. Osman and J.P. Kelly (eds.), Metaheuristics: Theory and Applications. pp. 555–570.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Glover, F., Laguna, M., Marti, R. (2003). Scatter Search and Path Relinking: Advances and Applications. 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_1

Download citation

  • DOI: https://doi.org/10.1007/0-306-48056-5_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-7263-5

  • Online ISBN: 978-0-306-48056-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics