Long path problems

  • Jeffrey Horn
  • David E. Goldberg
  • Kalyanmoy Deb
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 866)


We demonstrate the interesting, counter-intuitive result that simple paths to the global optimum can be so long that climbing the path is intractable. This means that a unimodal search space, which consists of a single hill and in which each point in the space is on a simple path to the global optimum, can be difficult for a hillclimber to optimize. Various types of hillclimbing algorithms will make constant progress toward the global optimum on such long path problems. They will continuously improve their best found solutions, and be guaranteed to reach the global optimum. Yet we cannot wait for them to arrive. Early experimental results indicate that a genetic algorithm (GA) with crossover alone outperforms hillclimbers on one such long path problem. This suggests that GAs can climb hills faster than hillclimbers by exploiting building blocks when they are present. Although these problems are artificial, they introduce a new dimension of problem difficulty for evolutionary computation. Path length can be added to the ranks of multimodality, deception/misleadingness, noise, variance, etc., as a measure of fitness landscapes and their amenability to evolutionary optimization.


Genetic Algorithm Search Space Global Optimum Fitness Evaluation Fitness Landscape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Forrest, S., Mitchell, M.: Relative building-block fitness and the building-block hypothesis. In: L.D. Whitley (ed.): Foundations of Genetic Algorithms, 2. San Mateo, CA: Morgan Kaufmann (1993) 109–126Google Scholar
  2. 2.
    Goldberg, D. E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley (1989)Google Scholar
  3. 3.
    Goldberg, D. E.: Making genetic algorithms fly: a lesson from the Wright brothers. Advanced Technology for Developers. 2 February (1993) 1–8Google Scholar
  4. 4.
    Jones, T., Rawlins, G. J. E.: Reverse hillclimbing, genetic algorithms and the busy beaver problem. In: S. Forrest (ed.): Proceedings of the Fifth International Conference on Genetic Algorithms. San Mateo, CA: Morgan Kaufmann (1993) 70–75Google Scholar
  5. 5.
    Holland, J. H.: Adaptation in natural and artificial systems. Ann Arbor, MI: University of Michigan Press (1975)Google Scholar
  6. 6.
    Hoffmeister, F., Bäck, T.: Genetic algorithms and evolutionary strategies: similarities and differences. Technical Report “Grüne Reihe” No. 365. Department of Computer Science, University of Dortmund. November (1990)Google Scholar
  7. 7.
    MacWilliams, F. J., Sloane, N. J. A.: The Theory of Error Correcting Codes. Amsterdam, New York: North-Holland (1977)Google Scholar
  8. 8.
    Mitchell, M., Holland, J. H.: When will a genetic algorithm outperform hill climbing? In: S. Forrest (ed.): Proceedings of the Fifth International Conference on Genetic Algorithms. San Mateo, CA: Morgan Kaufmann (1993) 647Google Scholar
  9. 9.
    Mitchell, M., Holland, J. H., Forrest, S.: When will a genetic algorithm outperform hill climbing? Advances in Neural Information Processing Systems 6. San Mateo, CA: Morgan Kaufmann (to appear)Google Scholar
  10. 10.
    Mühlenbein, H.: How genetic algorithms really work, I. fundamentals. In: R. Männer, B. Manderick (eds.): Parallel Problem Solving From Nature, 2. Amsterdam: North-Holland (1992) 15–26Google Scholar
  11. 11.
    Preparata, F. P., Niervergelt, J.: Difference-preserving codes. IEEE Transactions on Information Theory. IT-20:5 (1974) 643–649CrossRefGoogle Scholar
  12. 12.
    Wilson, S. W.: GA-easy does not imply steepest-ascent optimizable. In: R.K. Belew, L.B. Booker (eds.): Proceedings of the Fourth International Conference on Genetic Algorithms. San Mateo, CA: Morgan Kaufmann (1991) 85–89Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jeffrey Horn
    • 1
  • David E. Goldberg
    • 1
  • Kalyanmoy Deb
    • 2
  1. 1.Illinois Genetic Algorithms LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKanpur, UPIndia

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