IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v199y2012i1p305-34110.1007-s10479-011-0994-0.html
   My bibliography  Save this article

An experimental analysis of evolutionary heuristics for the biobjective traveling purchaser problem

Author

Listed:
  • Carolina Almeida
  • Richard Gonçalves
  • Elizabeth Goldbarg
  • Marco Goldbarg
  • Myriam Delgado

Abstract

Given a set of markets and a set of products to be purchased on those markets, the Biobjective Traveling Purchaser Problem (2TPP) consists in determining a route through a subset of markets to collect all products, minimizing the travel distance and the purchasing cost simultaneously. As its single objective version, the 2TPP is an NP-hard Combinatorial Optimization problem. Only one exact algorithm exists that can solve instances up to 100 markets and 200 products and one heuristic approach that can solve instances up to 500 markets and 200 products. Since the Transgenetic Algorithms (TAs) approach has shown to be very effective for the single objective version of the investigated problem, this paper examines the application of these algorithms to the 2TPP. TAs are evolutionary algorithms based on the endosymbiotic evolution and other interactions of the intracellular flow interactions. This paper has three main purposes: the first is the investigation of the viability of Multiobjective TAs to deal with the 2TPP, the second is to determine which characteristics are important for the hybridization between TAs and multiobjective evolutionary frameworks and the last is to compare the ability of multiobjective algorithms based only on Pareto dominance with those based on both decomposition and Pareto dominance to deal with the 2TPP. Two novel Transgenetic Multiobjective Algorithms are proposed. One is derived from the NSGA-II framework, named NSTA, and the other is derived from the MOEA/D framework, named MOTA/D. To analyze the performance of the proposed algorithms, they are compared with their classical counterparts. It is also the first time that NSGA-II and MOEA/D are applied to solve the 2TPP. The methods are validated in 365 uncapacitated instances of the TPPLib benchmark. The results demonstrate the superiority of MOTA/D and encourage further researches in the hybridization of Transgenetic Algorithms and Multiobjective Evolutionary Algorithms specially the ones based on decomposition. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Carolina Almeida & Richard Gonçalves & Elizabeth Goldbarg & Marco Goldbarg & Myriam Delgado, 2012. "An experimental analysis of evolutionary heuristics for the biobjective traveling purchaser problem," Annals of Operations Research, Springer, vol. 199(1), pages 305-341, October.
    • Handle: RePEc:spr:annopr:v:199:y:2012:i:1:p:305-341:10.1007/s10479-011-0994-0
    DOI: 10.1007/s10479-011-0994-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0994-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0994-0?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Singh, Kashi N. & van Oudheusden, Dirk L., 1997. "A branch and bound algorithm for the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 97(3), pages 571-579, March.
    2. Goldbarg, M.C. & Bagi, L.B. & Goldbarg, E.F.G., 2009. "Transgenetic algorithm for the Traveling Purchaser Problem," European Journal of Operational Research, Elsevier, vol. 199(1), pages 36-45, November.
    3. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    4. José Arroyo & Pedro Vieira & Dalessandro Vianna, 2008. "A GRASP algorithm for the multi-criteria minimum spanning tree problem," Annals of Operations Research, Springer, vol. 159(1), pages 125-133, March.
    5. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    6. Riera-Ledesma, Jorge & Salazar-Gonzalez, Juan Jose, 2005. "A heuristic approach for the Travelling Purchaser Problem," European Journal of Operational Research, Elsevier, vol. 162(1), pages 142-152, April.
    7. Jorge Riera-Ledesma & Juan-José Salazar-González, 2006. "Solving the asymmetric traveling purchaser problem," Annals of Operations Research, Springer, vol. 144(1), pages 83-97, April.
    8. Matthias Ehrgott, 2006. "A discussion of scalarization techniques for multiple objective integer programming," Annals of Operations Research, Springer, vol. 147(1), pages 343-360, October.
    9. Riera-Ledesma, Jorge & Salazar-Gonzalez, Juan Jose, 2005. "The biobjective travelling purchaser problem," European Journal of Operational Research, Elsevier, vol. 160(3), pages 599-613, February.
    10. Molina, Julin & Santana, Luis V. & Hernandez-Daz, Alfredo G. & Coello Coello, Carlos A. & Caballero, Rafael, 2009. "g-dominance: Reference point based dominance for multiobjective metaheuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 685-692, September.
    11. Ulrich Junker, 2004. "Preference-Based Search and Multi-Criteria Optimization," Annals of Operations Research, Springer, vol. 130(1), pages 75-115, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Palomo-Martínez, Pamela J. & Salazar-Aguilar, M. Angélica, 2019. "The bi-objective traveling purchaser problem with deliveries," European Journal of Operational Research, Elsevier, vol. 273(2), pages 608-622.
    2. Manerba, Daniele & Mansini, Renata & Riera-Ledesma, Jorge, 2017. "The Traveling Purchaser Problem and its variants," European Journal of Operational Research, Elsevier, vol. 259(1), pages 1-18.

    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. Manerba, Daniele & Mansini, Renata & Riera-Ledesma, Jorge, 2017. "The Traveling Purchaser Problem and its variants," European Journal of Operational Research, Elsevier, vol. 259(1), pages 1-18.
    2. Palomo-Martínez, Pamela J. & Salazar-Aguilar, M. Angélica, 2019. "The bi-objective traveling purchaser problem with deliveries," European Journal of Operational Research, Elsevier, vol. 273(2), pages 608-622.
    3. Jaehn, Florian & Meissner, Finn, 2022. "The rebound effect in transportation," Omega, Elsevier, vol. 108(C).
    4. Goldbarg, M.C. & Bagi, L.B. & Goldbarg, E.F.G., 2009. "Transgenetic algorithm for the Traveling Purchaser Problem," European Journal of Operational Research, Elsevier, vol. 199(1), pages 36-45, November.
    5. Jorge Riera-Ledesma & Juan-José Salazar-González, 2006. "Solving the asymmetric traveling purchaser problem," Annals of Operations Research, Springer, vol. 144(1), pages 83-97, April.
    6. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    7. Mingyu Xiao & Jianan Zhang & Weibo Lin, 0. "Parameterized algorithms and complexity for the traveling purchaser problem and its variants," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    8. Po-Lung Yu & Yen-Chu Chen, 2012. "Dynamic multiple criteria decision making in changeable spaces: from habitual domains to innovation dynamics," Annals of Operations Research, Springer, vol. 197(1), pages 201-220, August.
    9. Mingyu Xiao & Jianan Zhang & Weibo Lin, 2022. "Parameterized algorithms and complexity for the traveling purchaser problem and its variants," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2269-2285, November.
    10. Zhang, Weihua & Reimann, Marc, 2014. "A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 15-24.
    11. Cacchiani, Valentina & D’Ambrosio, Claudia, 2017. "A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 920-933.
    12. Riera-Ledesma, Jorge & Salazar-Gonzalez, Juan Jose, 2005. "A heuristic approach for the Travelling Purchaser Problem," European Journal of Operational Research, Elsevier, vol. 162(1), pages 142-152, April.
    13. Caballero, William N. & Lunday, Brian J. & Meissner, Finn, 2024. "Regulating the rebound effect in the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 660-677.
    14. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    15. Derya Deliktaş, 2022. "Self-adaptive memetic algorithms for multi-objective single machine learning-effect scheduling problems with release times," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 748-784, September.
    16. Zi-bin Jiang & Qiong Yang, 2016. "A Discrete Fruit Fly Optimization Algorithm for the Traveling Salesman Problem," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-15, November.
    17. Stefan Poikonen & Bruce Golden, 2020. "The Mothership and Drone Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 249-262, April.
    18. Ibrahim Muter & Tevfik Aytekin, 2017. "Incorporating Aggregate Diversity in Recommender Systems Using Scalable Optimization Approaches," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 405-421, August.
    19. Luca Maria Gambardella & Marco Dorigo, 2000. "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 237-255, August.
    20. Rego, Cesar & Roucairol, Catherine, 1995. "Using Tabu search for solving a dynamic multi-terminal truck dispatching problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 411-429, June.

    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:spr:annopr:v:199:y:2012:i:1:p:305-341:10.1007/s10479-011-0994-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.