IDEAS home Printed from https://ideas.repec.org/p/jgu/wpaper/1609.html
   My bibliography  Save this paper

Communities of Local Optima as Funnels in Fitness Landscapes

Author

Listed:
  • Sebastian Herrmann

    (Johannes Gutenberg University Mainz)

  • Gabriela Ochoa

    (University of Stirling)

  • Franz Rothlauf

    (Johannes Gutenberg University Mainz)

Abstract

We conduct an analysis of local optima networks extracted from ?tness landscapes of the Kauffman NK model under iterated local search. Applying the Markov Cluster Algorithm for community detection to the local optima networks, we ?nd that the landscapes consist of multiple clusters. This result complements recent ?ndings in the literature that landscapes often decompose into multiple funnels, which increases their difficulty for iterated local search. Our results suggest that the number of clusters as well as the size of the cluster in which the global optimum is located are correlated to the search difficulty of landscapes. We conclude that clusters found by community detection in local optima networks offer a new way to characterize the multi-funnel structure of ?tness landscapes.

Suggested Citation

  • Sebastian Herrmann & Gabriela Ochoa & Franz Rothlauf, 2016. "Communities of Local Optima as Funnels in Fitness Landscapes," Working Papers 1609, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:1609
    as

    Download full text from publisher

    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1609.pdf
    File Function: First version, 2016
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David Applegate & William Cook & André Rohe, 2003. "Chained Lin-Kernighan for Large Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 82-92, February.
    2. D R Hains & L D Whitley & A E Howe, 2011. "Revisiting the big valley search space structure in the TSP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 305-312, February.
    3. Daolio, Fabio & Tomassini, Marco & Vérel, Sébastien & Ochoa, Gabriela, 2011. "Communities of minima in local optima networks of combinatorial spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1684-1694.
    4. 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.
    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. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.

    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. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.
    2. Taillard, Éric D., 2022. "A linearithmic heuristic for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 442-450.
    3. Andrzej Jaszkiewicz & Thibaut Lust, 2017. "Proper balance between search towards and along Pareto front: biobjective TSP case study," Annals of Operations Research, Springer, vol. 254(1), pages 111-130, July.
    4. Taillard, Éric D. & Helsgaun, Keld, 2019. "POPMUSIC for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 420-429.
    5. Gary R. Waissi & Pragya Kaushal, 2020. "A polynomial matrix processing heuristic algorithm for finding high quality feasible solutions for the TSP," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 73-87, March.
    6. César Rego & Fred Glover, 2010. "Ejection chain and filter-and-fan methods in combinatorial optimization," Annals of Operations Research, Springer, vol. 175(1), pages 77-105, March.
    7. Çavdar, Bahar & Sokol, Joel, 2015. "TSP Race: Minimizing completion time in time-sensitive applications," European Journal of Operational Research, Elsevier, vol. 244(1), pages 47-54.
    8. Elena Nechita & Gloria Cerasela Crişan & Laszlo Barna Iantovics & Yitong Huang, 2020. "On the Resilience of Ant Algorithms. Experiment with Adapted MMAS on TSP," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    9. Yuichi Nagata & Shigenobu Kobayashi, 2013. "A Powerful Genetic Algorithm Using Edge Assembly Crossover for the Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 346-363, May.
    10. repec:jss:jstsof:23:i02 is not listed on IDEAS
    11. William Cook & Paul Seymour, 2003. "Tour Merging via Branch-Decomposition," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 233-248, August.
    12. Sebastian Herrmann & Gabriela Ochoa & Franz Rothlauf, 2018. "PageRank centrality for performance prediction: the impact of the local optima network model," Journal of Heuristics, Springer, vol. 24(3), pages 243-264, June.
    13. Ahmed Kheiri & Alina G. Dragomir & David Mueller & Joaquim Gromicho & Caroline Jagtenberg & Jelke J. Hoorn, 2019. "Tackling a VRP challenge to redistribute scarce equipment within time windows using metaheuristic algorithms," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 561-595, December.
    14. Anurag Agarwal, 2009. "Theoretical insights into the augmented-neural-network approach for combinatorial optimization," Annals of Operations Research, Springer, vol. 168(1), pages 101-117, April.
    15. 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.
    16. Tomassini, Marco, 2021. "Complex networks analysis of the energy landscape of the low autocorrelation binary sequences problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    17. Aritra Pal & Hadi Charkhgard, 2019. "A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 115-133, February.
    18. 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.
    19. Stefan Poikonen & Bruce Golden, 2020. "The Mothership and Drone Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 249-262, April.
    20. Jung, Jung Woo & Lee, Young Hae, 2010. "Heuristic algorithms for production and transportation planning through synchronization of a serial supply chain," International Journal of Production Economics, Elsevier, vol. 124(2), pages 433-447, April.
    21. R Torres-Velázquez & V Estivill-Castro, 2004. "Local search for Hamiltonian Path with applications to clustering visitation paths," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(7), pages 737-748, July.

    More about this item

    Keywords

    Fitness landscape analysis; search difficulty; local optima networks; NK-landscapes.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:jgu:wpaper:1609. 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: Research Unit IPP (email available below). General contact details of provider: https://edirc.repec.org/data/vlmaide.html .

    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.