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No Free Lunch Theorem: A Review

In: Approximation and Optimization

Author

Listed:
  • Stavros P. Adam

    (University of Ioannina
    University of Patras)

  • Stamatios-Aggelos N. Alexandropoulos

    (University of Patras)

  • Panos M. Pardalos

    (University of Florida)

  • Michael N. Vrahatis

    (University of Patras)

Abstract

The “No Free Lunch” theorem states that, averaged over all optimization problems, without re-sampling, all optimization algorithms perform equally well. Optimization, search, and supervised learning are the areas that have benefited more from this important theoretical concept. Formulation of the initial No Free Lunch theorem, very soon, gave rise to a number of research works which resulted in a suite of theorems that define an entire research field with significant results in other scientific areas where successfully exploring a search space is an essential and critical task. The objective of this paper is to go through the main research efforts that contributed to this research field, reveal the main issues, and disclose those points that are helpful in understanding the hypotheses, the restrictions, or even the inability of applying No Free Lunch theorems.

Suggested Citation

  • Stavros P. Adam & Stamatios-Aggelos N. Alexandropoulos & Panos M. Pardalos & Michael N. Vrahatis, 2019. "No Free Lunch Theorem: A Review," Springer Optimization and Its Applications, in: Ioannis C. Demetriou & Panos M. Pardalos (ed.), Approximation and Optimization, pages 57-82, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-12767-1_5
    DOI: 10.1007/978-3-030-12767-1_5
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    Cited by:

    1. Marco-Antonio Moreno-Ibarra & Yenny Villuendas-Rey & Miltiadis D. Lytras & Cornelio Yáñez-Márquez & Julio-César Salgado-Ramírez, 2021. "Classification of Diseases Using Machine Learning Algorithms: A Comparative Study," Mathematics, MDPI, vol. 9(15), pages 1-21, July.
    2. Eliton Smith dos Santos & Marcus Vinícius Alves Nunes & Manoel Henrique Reis Nascimento & Jandecy Cabral Leite, 2022. "Rational Application of Electric Power Production Optimization through Metaheuristics Algorithm," Energies, MDPI, vol. 15(9), pages 1-31, April.
    3. Jorge M. Cruz-Duarte & José C. Ortiz-Bayliss & Iván Amaya & Yong Shi & Hugo Terashima-Marín & Nelishia Pillay, 2020. "Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    4. José-Luis Velázquez-Rodríguez & Yenny Villuendas-Rey & Oscar Camacho-Nieto & Cornelio Yáñez-Márquez, 2020. "A Novel and Simple Mathematical Transform Improves the Perfomance of Lernmatrix in Pattern Classification," Mathematics, MDPI, vol. 8(5), pages 1-46, May.
    5. Masoud Zahedi Vahid & Ziad M. Ali & Ebrahim Seifi Najmi & Abdollah Ahmadi & Foad H. Gandoman & Shady H. E. Abdel Aleem, 2021. "Optimal Allocation and Planning of Distributed Power Generation Resources in a Smart Distribution Network Using the Manta Ray Foraging Optimization Algorithm," Energies, MDPI, vol. 14(16), pages 1-25, August.
    6. Elena Niculina Dragoi & Vlad Dafinescu, 2021. "Review of Metaheuristics Inspired from the Animal Kingdom," Mathematics, MDPI, vol. 9(18), pages 1-52, September.
    7. Jilong Zhang & Yuan Diao, 2024. "Hierarchical Learning-Enhanced Chaotic Crayfish Optimization Algorithm: Improving Extreme Learning Machine Diagnostics in Breast Cancer," Mathematics, MDPI, vol. 12(17), pages 1-26, August.
    8. Hector Carreon-Ortiz & Fevrier Valdez & Oscar Castillo, 2023. "Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm," Mathematics, MDPI, vol. 11(11), pages 1-38, May.
    9. Xinghua Tao & Nan Mo & Jianbo Qin & Xiaozhe Yang & Linfei Yin & Likun Hu, 2023. "Parallel Multi-Layer Monte Carlo Optimization Algorithm for Doubly Fed Induction Generator Controller Parameters Optimization," Energies, MDPI, vol. 16(19), pages 1-20, October.
    10. Ahmed S. Menesy & Hamdy M. Sultan & Ibrahim O. Habiballah & Hasan Masrur & Kaisar R. Khan & Muhammad Khalid, 2023. "Optimal Configuration of a Hybrid Photovoltaic/Wind Turbine/Biomass/Hydro-Pumped Storage-Based Energy System Using a Heap-Based Optimization Algorithm," Energies, MDPI, vol. 16(9), pages 1-26, April.
    11. Mokhtar Said & Ali M. El-Rifaie & Mohamed A. Tolba & Essam H. Houssein & Sanchari Deb, 2021. "An Efficient Chameleon Swarm Algorithm for Economic Load Dispatch Problem," Mathematics, MDPI, vol. 9(21), pages 1-14, November.

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