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Optimal Nesting of Species for Exact Cover: Many against Many

  • Jeffrey Horn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

Experiments with resource-defined fitness sharing (RFS) applied to shape nesting problems indicate a remarkable ability to discover exact covers of resources [1, 2]. These exact covers are represented by a maximally sized set of cooperating (non-competing) species. Recent papers by Horn [3, 4] introduce the first formal analyses of this empirical phenomenon. In [3], a minimal case of two species, a and b, against a third, c, is considered: the two-against-one scenario. It is shown that if the team of a and b form an exact cover, then c will be extinct at niching equilibrium. In [4], this result is generalized to the case of two-against-many: if a and b form an exact cover against an arbitrary number of competing species, under very general assumptions, a and b will be the only survivors at niching equilibirum. In the current paper, we extend these results to the most general scenario: many-against-many. We prove that, under certain very general assumptions, any size team of species forming an exact cover will dominate a population with any number of competing species: at niching equilibirum, all such competitors will be extinct. The results are more general than shape-nesting problems, applying as well to the NP-complete problem exact cover by k-sets.

Keywords

Size Team Empirical Phenomenon Proportionate Selection Minimal Case Exact Cover 
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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References

  1. 1.
    Horn, J.: Resource-based fitness sharing. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN VII 2002. LNCS, vol. 2439, pp. 381–390. Springer, Heidelberg (2002)Google Scholar
  2. 2.
    Horn, J.: Coevolving species for shape nesting. In: Schaffer, J.D. (ed.) The 2005 IEEE Congress on Evolutionary Computation (IEEE CEC 2005), Piscataway, NJ, pp. 1800–1807. IEEE Computer Society Press, Los Alamitos (2005)CrossRefGoogle Scholar
  3. 3.
    Horn, J.: Optimal nesting of species for exact cover of resources: Two against one. In: Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), pp. 322–330. Omnipress (2007)Google Scholar
  4. 4.
    Horn, J.: Optimal nesting of species for exact cover of resources: Two against many. In: Proceedings of the 2007 Genetic And Evolutionary Computation Conference (GECCO 2007), pp. 448–455. The Association For Computing Machinery (2007)Google Scholar
  5. 5.
    Kendall, G.: Applying Meta-Heuristic Algorithms to the Nesting Problem Utilising the No Fit Polygon. PhD thesis, University of Nottingham (2000)Google Scholar
  6. 6.
    Dighe, R., Jakiela, M.J.: Solving pattern nesting problems with genetic algorithms: employing task decomposition and contact detection between adjacent pieces. Evolutionary Computation 3(3), 239–266 (1996)CrossRefGoogle Scholar
  7. 7.
    Maynard-Smith, J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)CrossRefGoogle Scholar
  8. 8.
    Friedman, D.: Evolutionary games in economics. Econometrica 59(3), 637–666 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jeffrey Horn
    • 1
  1. 1.Northern Michigan UniversityMarquette MIUSA

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