Advertisement

Run-Time Analysis of Classical Path-Planning Algorithms

  • Pablo Muñoz
  • David F. Barrero
  • María D. R-Moreno
Conference paper

Abstract

Run-time analysis is a type of empirical tool that studies the time consumed by running an algorithm. This type of analysis has been successfully used in some Artificial Intelligence (AI) fields, in paticular in Metaheuristics. This paper is an attempt to bring this tool to the path-planning community. In particular, we analyse the statistical properties of the run-time of the A*, Theta* and S-Theta* algorithms with a variety of problems of different degrees of complexity. Traditionally, the path-planning literature has compared run-times just comparing their mean values. This practice, which unfortunately is quite common in the literature, raises serious concerns from a methodological and statistical point of view. Simple mean comparison provides poorly supported conclusions, and, in general, it can be said that this practice should be avoided.

After our analysis, we conclude that the time required by these three algorithms follows a lognormal distribution. In low complexity problems, the lognormal distribution looses some accuracy to describe the algorithm run-times. The lognormality of the run-times opens the use of powerful parametric statistics to compare execution times, which could lead to stronger empirical methods.

Keywords

Mobile Robot Lognormal Distribution Path Planning Problem Hardness Timetabling Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Ayorkor, A. Stentz, and M. B. Dias. Continuous-field path planning with constrained pathdependent state variables. In ICRA 2008 Workshop on Path Planning on Costmaps, May 2008.Google Scholar
  2. 2.
    R. Barr and B. Hickman. Reporting Computational Experiments with Parallel Algorithms: Issues, Measures, and Experts’ Opinions. ORSA Journal on Computing, 5:2–2, 1993.zbMATHCrossRefGoogle Scholar
  3. 3.
    D. F. Barrero, B. Casta˜no, M. D. R-Moreno, and D. Camacho. Statistical Distribution of Generation-to-Success in GP: Application to Model Accumulated Success Probability. In Proceedings of the 14th European Conference on Genetic Programming, (EuroGP 2011), volume 6621 of LNCS, pages 155–166, Turin, Italy, 27-29 Apr. 2011. Springer Verlag.Google Scholar
  4. 4.
    A. Botea, M. Muller, and J. Schaeffer. Near optimal hierarchical path-finding. Journal of Game Development, 1:1–22, 2004.Google Scholar
  5. 5.
    M. Chiarandini and T. St‥utzle. Experimental Evaluation of Course Timetabling Algorithms. Technical Report AIDA-02-05, Intellectics Group, Computer Science Department, Darmstadt University of Technology, Darmstadt, Germany, April 2002.Google Scholar
  6. 6.
    K. Daniel, A. Nash, S. Koenig, and A. Felner. Theta*: Any-angle path planning on grids. Journal of Artificial Intelligence Research, 39:533–579, 2010.MathSciNetzbMATHGoogle Scholar
  7. 7.
    S. Epstein and X. Yun. From Unsolvable to Solvable: An Exploration of Simple Changes. In Workshops at the Twenty-Fourth AAAI Conference on Artificial Intelligence, 2010.Google Scholar
  8. 8.
    M. Erdmann and T. Lozano-Perez. On multiple moving objects. Algorithmica, 2:477–521, 1987.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    D. Ferguson and A. Stentz. Field D*: An interpolation-based path planner and replanner. In Proceedings of the International Symposium on Robotics Research (ISRR), October 2005.Google Scholar
  10. 10.
    D. Frost, I. Rish, and L. Vila. Summarizing CSP Hardness with Continuous Probability Distributions. In Proceedings of the Fourteenth National Conference on Artificial Intelligence and Ninth Conference on Innovative Applications of Artificial Intelligence (AAAI97/IAAI97), pages 327–333. AAAI Press, 1997.Google Scholar
  11. 11.
    O. Hachour. Path planning of autonomous mobile robot. International Journal of Systems, Applications, Engineering & Development, 2(4):178–190, 2008.Google Scholar
  12. 12.
    P. Hart, N. Nilsson, and B. Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics., 4:100–107, 1968.CrossRefGoogle Scholar
  13. 13.
    H. Hoos and T. St‥utzle. Characterizing the Run-Time Behavior of Stochastic Local Search. In Proceedings AAAI99, 1998.Google Scholar
  14. 14.
    H. Hoos and T. St‥utzle. Towards a Characterisation of the Behaviour of Stochastic Local Search Algorithms for SAT. Artificial Intelligence, 112(1-2):213–232, 1999.Google Scholar
  15. 15.
    H. Hoos and T. St‥utzle. Local Search Algorithms for SAT: An Empirical Evaluation. Journal of Automated Reasoning, 24(4):421–481, 2000.Google Scholar
  16. 16.
    H. H. Hoos and T. St‥utzle. Evaluating Las Vegas Algorithms – Pitfalls and Remedies. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), pages 238–245. Morgan Kaufmann Publishers, 1998.Google Scholar
  17. 17.
    I. Millington and J. Funge. Artificial Intelligence for Games. Morgan Kaufmann Publishers, 2 edition, 2009.Google Scholar
  18. 18.
    P. Mu˜noz and M. D. R-Moreno. S-Theta*: low steering path-planning algorithm. In Thirtysecond SGAI International Conference on Artificial Intelligence (AI-2012), Cambridge, UK, 2012.Google Scholar
  19. 19.
    A. Nash, K. Daniel, S. Koenig, and A. Felner. Theta*: Any-angle path planning on grids. In In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), pages 1177–1183, 2007.Google Scholar
  20. 20.
    N. Nilsson. Principles of Artificial Intelligence. Tioga Publishing Company, Palo Alto, CA. ISBN 0-935382-01-1, 1980.Google Scholar
  21. 21.
    K. Sugihara and J. Smith. A genetic algorithm for 3-d path planning of a mobile robot. Technical report, Tech. Rep. No. 96-09-01. Software Engineering Research Laboratory,University of Hawaii at Manoa, 1996.Google Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Pablo Muñoz
    • 1
  • David F. Barrero
    • 1
  • María D. R-Moreno
    • 1
  1. 1.Departamento de AutomáticaUniversidad de AlcaláMadridSpain

Personalised recommendations