IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/95-05-046.html
   My bibliography  Save this paper

What Makes an Optimization Problem Hard?

Author

Listed:
  • William G. Macready
  • David H. Wolpert

Abstract

We address the question "Are some classes of combinatorial optimization problems instrinsically harder than others, without regard to the algorithm one uses, or can difficulty only be assessed relative to particular algorithms?" We provide a measure of the hardness of a particular optimization problem for a particular optimization algorithm. We then present two algorithm-independent quantities that use this measure to provide answers to our question. In the first of these we average hardness over all possible algorithms for the optimization problem at hand. We show that according to this quantitiy, there is no distinction between optimization problems, and in this sense no problems are intrinsically harder than others. For the second quantitiy, rather than average over all algorithms we consider the level of hardness of a problem (or class of problems) for the algorithm that is optimal for that problem (or class of problems). Here there are classes of problems that are intrinsically harder than others.

Suggested Citation

  • William G. Macready & David H. Wolpert, 1995. "What Makes an Optimization Problem Hard?," Working Papers 95-05-046, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:95-05-046
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. David H. Wolpert & William G. Macready, 1995. "No Free Lunch Theorems for Search," Working Papers 95-02-010, Santa Fe Institute.
    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. Jui-Sheng Chou & Dinh-Nhat Truong & Chih-Fong Tsai, 2021. "Solving Regression Problems with Intelligent Machine Learner for Engineering Informatics," Mathematics, MDPI, vol. 9(6), pages 1-25, March.
    2. Sevvandi Kandanaarachchi & Mario A Munoz & Rob J Hyndman & Kate Smith-Miles, 2018. "On normalization and algorithm selection for unsupervised outlier detection," Monash Econometrics and Business Statistics Working Papers 16/18, Monash University, Department of Econometrics and Business Statistics.
    3. Aktaş, Dilay & Lokman, Banu & İnkaya, Tülin & Dejaegere, Gilles, 2024. "Cluster ensemble selection and consensus clustering: A multi-objective optimization approach," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1065-1077.
    4. Kamran Zolfi, 2023. "Gold rush optimizer: A new population-based metaheuristic algorithm," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(1), pages 113-150.
    5. Y.C. Ho & D.L. Pepyne, 2002. "Simple Explanation of the No-Free-Lunch Theorem and Its Implications," Journal of Optimization Theory and Applications, Springer, vol. 115(3), pages 549-570, December.
    6. Murtadha Al-Kaabi & Virgil Dumbrava & Mircea Eremia, 2022. "A Slime Mould Algorithm Programming for Solving Single and Multi-Objective Optimal Power Flow Problems with Pareto Front Approach: A Case Study of the Iraqi Super Grid High Voltage," Energies, MDPI, vol. 15(20), pages 1-33, October.
    7. Galioto, Francesco & Battilani, Adriano, 2021. "Agro-economic simulation for day by day irrigation scheduling optimisation," Agricultural Water Management, Elsevier, vol. 248(C).
    8. Abdel-Rahman Hedar & Emad Mabrouk & Masao Fukushima, 2011. "Tabu Programming: A New Problem Solver Through Adaptive Memory Programming Over Tree Data Structures," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 373-406.
    9. Murtadha Al-Kaabi & Virgil Dumbrava & Mircea Eremia, 2024. "Multi Criteria Frameworks Using New Meta-Heuristic Optimization Techniques for Solving Multi-Objective Optimal Power Flow Problems," Energies, MDPI, vol. 17(9), pages 1-39, May.
    10. Agarwal, Anurag & Colak, Selcuk & Eryarsoy, Enes, 2006. "Improvement heuristic for the flow-shop scheduling problem: An adaptive-learning approach," European Journal of Operational Research, Elsevier, vol. 169(3), pages 801-815, March.
    11. Murtadha Al-Kaabi & Virgil Dumbrava & Mircea Eremia, 2022. "Single and Multi-Objective Optimal Power Flow Based on Hunger Games Search with Pareto Concept Optimization," Energies, MDPI, vol. 15(22), pages 1-31, November.
    12. Muangkote, Nipotepat & Sunat, Khamron & Chiewchanwattana, Sirapat & Kaiwinit, Sirilak, 2019. "An advanced onlooker-ranking-based adaptive differential evolution to extract the parameters of solar cell models," Renewable Energy, Elsevier, vol. 134(C), pages 1129-1147.
    13. William G. Macready & David H. Wolpert, 1996. "On 2-Armed Gaussian Bandits and Optimization," Working Papers 96-03-009, Santa Fe Institute.
    14. Sharifian, Yeganeh & Abdi, Hamdi, 2023. "Solving multi-area economic dispatch problem using hybrid exchange market algorithm with grasshopper optimization algorithm," Energy, Elsevier, vol. 267(C).
    15. Díaz–Pachón, Daniel Andrés & Sáenz, Juan Pablo & Rao, J. Sunil, 2020. "Hypothesis testing with active information," Statistics & Probability Letters, Elsevier, vol. 161(C).
    16. Wang, Sinan & Zhao, Fuquan & Liu, Zongwei & Hao, Han, 2017. "Heuristic method for automakers' technological strategy making towards fuel economy regulations based on genetic algorithm: A China's case under corporate average fuel consumption regulation," Applied Energy, Elsevier, vol. 204(C), pages 544-559.
    17. Kimbrough, Steven Orla & Koehler, Gary J. & Lu, Ming & Wood, David Harlan, 2008. "On a Feasible-Infeasible Two-Population (FI-2Pop) genetic algorithm for constrained optimization: Distance tracing and no free lunch," European Journal of Operational Research, Elsevier, vol. 190(2), pages 310-327, October.
    18. Schirmer, Andreas & Riesenberg, Sven, 1998. "Class-based control schemes for parameterized project scheduling heuristics," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 471, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    19. Yi Peng & Gang Kou & Guoxun Wang & Honggang Wang & Franz I. S. Ko, 2009. "Empirical Evaluation Of Classifiers For Software Risk Management," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 749-767.
    20. Khalid Abdulaziz Alnowibet & Shalini Shekhawat & Akash Saxena & Karam M. Sallam & Ali Wagdy Mohamed, 2022. "Development and Applications of Augmented Whale Optimization Algorithm," Mathematics, MDPI, vol. 10(12), pages 1-33, June.

    More about this item

    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:wop:safiwp:95-05-046. 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: Thomas Krichel (email available below). General contact details of provider: https://edirc.repec.org/data/epstfus.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.