Statistical Comparative Between Selection Rules for Adaptive Operator Selection in Vehicle Routing and Multi-knapsack Problems

  • Jorge A. Soria-AlcarazEmail author
  • Marco A. Sotelo-Figueroa
  • Andrés Espinal
Part of the Studies in Computational Intelligence book series (SCI, volume 749)


Autonomous Search is an important field of artificial intelligence which focuses on the analysis and design of auto-adaptive systems capable to improving their own search performance on a given problem at runtime. An autonomous search system must can modify or select its internal components, improving its performance at execution time. A case of such algorithms is the Adaptive Operator Selection (AOS) method. This method uses a record of the latest iterations to propose which operator use in later iterations. AOS has two phases: Credit assignment and Selection rule. The first phase penalizes or rewards a specific operator based on their observed performance. The second phase makes the selection of the operator to use in subsequent iterations. This article shows the performance-based statistical comparison between two selection rules: Probability Matching and Adaptive Pursuit when using two different domains; namely, Vehicle Routing Problem and Multi-knap-Sack. The comparison is done with statistical rigor when integrating contrast algorithms such as no adaptation rule and random adaptation rule. This paper can be seen as an introduction on how to make proper statistical comparisons between two AOS rules.


Autonomous search Adaptive operator selection Selection rule Vehicle routing problem Multi-knapsack problem 


  1. 1.
    Y. Hamadi, E. Monfroy, F. Saubion, AN Introduction to Autonomous Search. Autonomous Search (Springer, Berlin Heidelberg, 2012), pp. 1–11Google Scholar
  2. 2.
    A. Fialho, L. Costa, M. Schoenauer, M. Sebag. Dynamic multi-armed bandits and extreme value-based rewards for adaptive operator selection in evolutionary algorithms, in Learning and Intelligent Optimization, volume 5851 of Lecture Notes in Computer Science (Springer, Berlin Heidelberg, 2009), pp. 176–190Google Scholar
  3. 3.
    D.E. Goldberg, Probability matching, the magnitude of reinforcement, and classifier system bidding. Mach. Learn. 5(4), 407–425 (1990)Google Scholar
  4. 4.
    D. Walker, G. Ochoa, M. Gendreau, E.K. Burke, Vehicle routing and adaptive iterated local search within the HyFlex hyper-heuristic framework, in International Conference on Learning and Intelligent Optimization (LION 6), Lecture Notes in Computer Science (Springer, 2012), pp. 265–276Google Scholar
  5. 5.
  6. 6.
    N. Razali, Y.B. Wah, Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests (2011)Google Scholar
  7. 7.
    J.A. Soria-Alcaraz, G. Ochoa, M. Carpio, H. Puga, Evolvability metrics in adaptive operator selection, in Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation (GECCO’14) (ACM, New York, NY, USA, 2014), pp. 1327–1334Google Scholar
  8. 8.
    J.A. Soria-Alcaraz, G. Ochoa, J. Swan, M. Carpio, H. Puga, E.K. Burke, Effective learning hyper-heuristics for the course timetabling problem. Eur. J. Oper. Res. 238(1), 77–86 (2014). ISSN 0377-2217Google Scholar
  9. 9.
    S.S. Shapiro, M.B. Wilk, An analysis of variance test for normality (complete samples). Biometrika 52(3–4), 591–611 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    M.B. Wilk, R. Gnanadesikan, Probability plotting methods for the analysis of data. Biometrika Trust 55(1), 1–17 (1968)Google Scholar
  11. 11.
    R.A. Fisher, The correlation between relatives on the supposition of Mendelian inheritance. Philos. Trans. Roy. Soc. Edinb. 52, 399–433 (1918)Google Scholar
  12. 12.

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Jorge A. Soria-Alcaraz
    • 1
    Email author
  • Marco A. Sotelo-Figueroa
    • 1
  • Andrés Espinal
    • 1
  1. 1.Departamento de Estudios Organizacionales, División de Ciencias Económico-AdministrativasUniversidad de GuanajuatoGuanajuatoMexico

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