Skip to main content

Network-Based Problem Difficulty Prediction Measures

  • Chapter
  • First Online:
Evolutionary Computation and Complex Networks

Abstract

The most important purpose of problem difficulty analysis is to design measures that can easily evaluate the difficulty of different types of problems for EAs. In this chapter, existing predictive problem difficulty measures are introduced; first, nonnetwork-based measures are introduced briefly, and then the network-based measures are introduced in detail, with thorough experiments to illustrate their performance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Altenberg, L., et al.: Fitness distance correlation analysis: an instructive counterexample. In: ICGA, pp. 57–64 (1997)

    Google Scholar 

  2. Barabási, A.L., Albert, R.: Emergence of scaling in random networks (1999)

    Google Scholar 

  3. Borenstein, Y.: Problem hardness for randomized search heuristics with comparison-based selection: a focus on evolutionary algorithms. Ph.D. thesis, University of Essex, UK (2008)

    Google Scholar 

  4. Borenstein, Y., Poli, R.: Information landscapes. In: Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, pp. 1515–1522. ACM (2005)

    Google Scholar 

  5. Borenstein, Y., Poli, R.: Information landscapes and problem hardness. In: Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, pp. 1425–1431. ACM (2005)

    Google Scholar 

  6. Davidor, Y.: Epistasis Variance: A Viewpoint on GA-Hardness, pp. 23–35 (1991)

    MATH  Google Scholar 

  7. Forrest, S., Mitchell, M.: Relative building block fitness and the building block hypothesis. In: D. Whitley (ed.) Proceedings of Foundations of Genetic Algorithms, pp. 109–126. Morgan Kaufmann, San Mateo, CA (1993)

    Google Scholar 

  8. Ghoneim, A., Abbass, H., Barlow, M.: Characterizing game dynamics in two-player strategy games using network motifs. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 38(3), 682–690 (2008)

    Article  Google Scholar 

  9. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    Google Scholar 

  10. He, J., Reeves, C., Witt, C., Yao, X.: A note on problem difficulty measures in black-box optimization: classification, realizations and predictability. Evol. Comput. 15(4), 435–443 (2007)

    Article  Google Scholar 

  11. Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Eshelman, L.J. (ed.) 6th International Conference Genetic Algorithms, pp. 184–192. Morgan Kaufmann, San Mateo, CA (1995)

    Google Scholar 

  12. Kallel, L., Naudts, B., Reeves, C.R.: Properties of fitness functions and search landscapes. In: Theoretical Aspects of Evolutionary Computing, pp. 175–206. Springer (2001)

    Google Scholar 

  13. Liu, J., Abbass, H.A., Green, D.G., Zhong, W.: Motif difficulty (md): a predictive measure of problem difficulty for evolutionary algorithms using network motifs. Evol. Comput. 20(3), 321–347 (2012)

    Article  Google Scholar 

  14. Lu, G., Li, J., Yao, X.: Fitness-probability cloud and a measure of problem hardness for evolutionary algorithms. In: European Conference on Evolutionary Computation in Combinatorial Optimization, pp. 108–117. Springer (2011)

    Google Scholar 

  15. Malan, K.M., Engelbrecht, A.P.: Fitness landscape analysis for metaheuristic performance prediction. In: Recent Advances in the Theory and Application of Fitness Landscapes, pp. 103–132. Springer (2014)

    Google Scholar 

  16. Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans. Evol. Comput. 4(4), 337–352 (2000)

    Article  Google Scholar 

  17. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)

    Article  Google Scholar 

  18. Mitchell, M., Forrest, S., Holland, J.H.: The royal road for genetic algorithms: fitness landscapes and GA performance. In: Proceedings of the First European Conference on Artificial Life, pp. 245–254 (1992)

    Google Scholar 

  19. Naudts, B.: Measuring GA-hardness. Ph.D. thesis, University of Antwerp, Belgium (1998)

    Google Scholar 

  20. Naudts, B., Kallel, L.: A comparison of predictive measures of problem difficulty in evolutionary algorithms. IEEE Trans. Evol. Comput. 4(1), 1–15 (2000)

    Article  Google Scholar 

  21. Tavares, J., Pereira, F.B., Costa, E.: Multidimensional knapsack problem: a fitness landscape analysis. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 38(3), 604–616 (2008)

    Article  Google Scholar 

  22. Vose, G.E.L.M.D.: Deceptiveness and genetic algorithm dynamics. In: Foundations of Genetic Algorithms 1991 (FOGA 1), vol. 1, p. 36 (2014)

    Google Scholar 

  23. Yossi, B., Poli, R.: Information landscapes and the analysis of search algorithms. In: Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, pp. 1287–1294. ACM (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jing Liu .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Liu, J., Abbass, H.A., Tan, K.C. (2019). Network-Based Problem Difficulty Prediction Measures. In: Evolutionary Computation and Complex Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-60000-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60000-0_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59998-4

  • Online ISBN: 978-3-319-60000-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics