IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v327y2025i3p717-734.html

Greedy Randomized Adaptive Search Procedures with Path Relinking. An analytical review of designs and implementations

Author

Listed:
  • Laguna, Manuel
  • Martí, Rafael
  • Martínez-Gavara, Anna
  • Pérez-Peló, Sergio
  • Resende, Mauricio G.C.

Abstract

This is a comprehensive review of the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic and its hybridization with Path Relinking (PR). GRASP with PR has become a widely adopted approach for solving hard optimization problems since its proposal in 1999. The paper covers the historical development of GRASP with PR and its theoretical foundations, as well as recent advances in its implementation and application. The review includes a careful analysis of PR variants, paying special attention to memory-based and randomized designs, with a total of ten different implementations. It identifies the design questions that are still open in the scientific literature. The experimental section applies advanced PR implementations on two well-known combinatorial optimization problems, linear ordering and max-cut, in an effort to answer these open questions. The paper also explores the hybridization of PR and other metaheuristics, such as tabu search, scatter search, and random-keys genetic algorithms. Overall, this review provides valuable insights for researchers and practitioners seeking to implement GRASP with PR for solving optimization problems.

Suggested Citation

  • Laguna, Manuel & Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Resende, Mauricio G.C., 2025. "Greedy Randomized Adaptive Search Procedures with Path Relinking. An analytical review of designs and implementations," European Journal of Operational Research, Elsevier, vol. 327(3), pages 717-734.
    • Handle: RePEc:eee:ejores:v:327:y:2025:i:3:p:717-734
    DOI: 10.1016/j.ejor.2025.02.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725001456
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.02.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Fadi K Dib & Peter Rodgers, 2018. "Graph drawing using tabu search coupled with path relinking," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-36, May.
    2. Andrade, Carlos E. & Toso, Rodrigo F. & Gonçalves, José F. & Resende, Mauricio G.C., 2021. "The Multi-Parent Biased Random-Key Genetic Algorithm with Implicit Path-Relinking and its real-world applications," European Journal of Operational Research, Elsevier, vol. 289(1), pages 17-30.
    3. Mauricio G. C. Resende & Celso C. Ribeiro, 2019. "Greedy Randomized Adaptive Search Procedures: Advances and Extensions," International Series in Operations Research & Management Science, in: Michel Gendreau & Jean-Yves Potvin (ed.), Handbook of Metaheuristics, edition 3, chapter 0, pages 169-220, Springer.
    4. Duarte, Abraham & Martí, Rafael & Álvarez, Ada & Ángel-Bello, Francisco, 2012. "Metaheuristics for the linear ordering problem with cumulative costs," European Journal of Operational Research, Elsevier, vol. 216(2), pages 270-277.
    5. F. Rodriguez & C. Blum & C. García-Martínez & M. Lozano, 2012. "GRASP with path-relinking for the non-identical parallel machine scheduling problem with minimising total weighted completion times," Annals of Operations Research, Springer, vol. 201(1), pages 383-401, December.
    6. Manuel Laguna & Rafael Marti, 1999. "GRASP and Path Relinking for 2-Layer Straight Line Crossing Minimization," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 44-52, February.
    7. Fred Glover, 2014. "Exterior Path Relinking for Zero-One Optimization," International Journal of Applied Metaheuristic Computing (IJAMC), IGI Global Scientific Publishing, vol. 5(3), pages 1-8, July.
    8. W. Art Chaovalitwongse & Carlos A. S. Oliveira & Bruno Chiarini & Panos M. Pardalos & Mauricio G. C. Resende, 2011. "Revised GRASP with path-relinking for the linear ordering problem," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 572-593, November.
    9. Rafael Martí & Gerhard Reinelt & Abraham Duarte, 2012. "A benchmark library and a comparison of heuristic methods for the linear ordering problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1297-1317, April.
    10. Celso C. Ribeiro & Eduardo Uchoa & Renato F. Werneck, 2002. "A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 228-246, August.
    11. Thiago Noronha & Mauricio Resende & Celso Ribeiro, 2011. "A biased random-key genetic algorithm for routing and wavelength assignment," Journal of Global Optimization, Springer, vol. 50(3), pages 503-518, July.
    12. Rafael Martí & Abraham Duarte & Manuel Laguna, 2009. "Advanced Scatter Search for the Max-Cut Problem," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 26-38, February.
    13. Francisco Barahona & Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1988. "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, INFORMS, vol. 36(3), pages 493-513, June.
    14. Jesús Sánchez-Oro & Ana D. López-Sánchez & Anna Martínez-Gavara & Alfredo G. Hernández-Díaz & Abraham Duarte, 2021. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k -Balanced Center Location Problem," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    15. A. D. López-Sánchez & J. Sánchez-Oro & M. Laguna, 2021. "A New Scatter Search Design for Multiobjective Combinatorial Optimization with an Application to Facility Location," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 629-642, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fernando Stefanello & Vaneet Aggarwal & Luciana S. Buriol & Mauricio G. C. Resende, 2019. "Hybrid algorithms for placement of virtual machines across geo-separated data centers," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 748-793, October.
    2. Martí, Rafael & Sevaux, Marc & Sörensen, Kenneth, 2025. "Fifty years of metaheuristics," European Journal of Operational Research, Elsevier, vol. 321(2), pages 345-362.
    3. Fuda Ma & Jin-Kao Hao, 2017. "A multiple search operator heuristic for the max-k-cut problem," Annals of Operations Research, Springer, vol. 248(1), pages 365-403, January.
    4. García-Martínez, C. & Rodriguez, F.J. & Lozano, M., 2014. "Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 454-463.
    5. Cleder M. Schenekemberg & Antonio A. Chaves & Thiago A. Guimarães & Leandro C. Coelho, 2025. "Hybrid metaheuristic for the dial-a-ride problem with private fleet and common carrier integrated with public transportation," Annals of Operations Research, Springer, vol. 351(1), pages 809-847, August.
    6. Iain Dunning & Swati Gupta & John Silberholz, 2018. "What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 608-624, August.
    7. F. Rodriguez & C. Blum & C. García-Martínez & M. Lozano, 2012. "GRASP with path-relinking for the non-identical parallel machine scheduling problem with minimising total weighted completion times," Annals of Operations Research, Springer, vol. 201(1), pages 383-401, December.
    8. Qinghua Wu & Yang Wang & Fred Glover, 2020. "Advanced Tabu Search Algorithms for Bipartite Boolean Quadratic Programs Guided by Strategic Oscillation and Path Relinking," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 74-89, January.
    9. Wenxing Zhu & Geng Lin & M. M. Ali, 2013. "Max- k -Cut by the Discrete Dynamic Convexized Method," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 27-40, February.
    10. R. B. Damm & A. A. Chaves & J. A. Riveaux & D. P. Ronconi, 2025. "Scheduling technicians and tasks through an adaptive multi-objective biased random-key genetic algorithm," Annals of Operations Research, Springer, vol. 346(2), pages 945-980, March.
    11. Daniele Ferone & Paola Festa & Tommaso Pastore, 2025. "GRASP: an application to efficiently plan the low carbon emission distributed additive manufacturing," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 199-228, July.
    12. Rafael A. Melo & Celso C. Ribeiro & Jose A. Riveaux, 2025. "A biased random-key genetic algorithm for the minimum quasi-clique partitioning problem," Annals of Operations Research, Springer, vol. 351(1), pages 575-607, August.
    13. Yong-Hyuk Kim & Zong Woo Geem & Yourim Yoon, 2025. "Population-Based Redundancy Control in Genetic Algorithms: Enhancing Max-Cut Optimization," Mathematics, MDPI, vol. 13(9), pages 1-21, April.
    14. Londe, Mariana A. & Andrade, Carlos E. & Pessoa, Luciana S., 2025. "A multi-stage approach for Root Sequence Index allocation," European Journal of Operational Research, Elsevier, vol. 327(1), pages 95-114.
    15. Londe, Mariana A. & Pessoa, Luciana S. & Andrade, Carlos E. & Resende, Mauricio G.C., 2025. "Biased random-key genetic algorithms: A review," European Journal of Operational Research, Elsevier, vol. 321(1), pages 1-22.
    16. Ceberio, Josu & Mendiburu, Alexander & Lozano, Jose A., 2015. "The linear ordering problem revisited," European Journal of Operational Research, Elsevier, vol. 241(3), pages 686-696.
    17. Dell'Amico, Mauro & Trubian, Marco, 1998. "Solution of large weighted equicut problems," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 500-521, April.
    18. Goldengorin, Boris, 2009. "Maximization of submodular functions: Theory and enumeration algorithms," European Journal of Operational Research, Elsevier, vol. 198(1), pages 102-112, October.
    19. Fatma-Zohra Baatout & Mhand Hifi, 2023. "A two-phase hybrid evolutionary algorithm for solving the bi-objective scheduling multiprocessor tasks on two dedicated processors," Journal of Heuristics, Springer, vol. 29(2), pages 229-267, June.
    20. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:327:y:2025:i:3:p:717-734. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.