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Optimal nesting of species for exact cover of resources: two against many

Published: 07 July 2007 Publication History

Abstract

The application of resource-defined fitness sharing (RFS) to shape nesting problems reveals a remarkable ability to discover tilings [7, 8]. These tilings represent exact covers for a set of resources, and can be considered a maximally sized set of cooperating (non-competing) species. a recent paper by Horn [9] introduces the first formal analysis of this empirical phenomenon by examining a minimal case: two species a and b "cooperate" to exactly cover the resources, while a third species c "competes" with a and b by overlapping both in terms of covered resources. The analysis reveals that in cases in which a and b maximally compete with c for resources, species c will become extinct, while the optimal set of species, a and b, will survive. The current paper generalizes this three-species result by analyzing more complex situations with four or more species. Specifically, we consider two species cooperating against two species competing, and finally two species cooperating against an arbitrary number of competing species. In all cases, proofs are derived that show exactly when the two cooperating species are guaranteed to win out over all competitors. The results are clearly proven using algebra on the niching equilibrium equations for RFS; a purely static analysis.

References

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J. Horn. 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), pages 322--330. Omnipress, 2007.
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  • (2008)Optimal Nesting of Species for Exact CoverProceedings of the 10th International Conference on Parallel Problem Solving from Nature --- PPSN X - Volume 519910.5555/2951659.2951706(438-447)Online publication date: 13-Sep-2008
  • (2008)Optimal Nesting of Species for Exact Cover: Many against ManyParallel Problem Solving from Nature – PPSN X10.1007/978-3-540-87700-4_44(438-447)Online publication date: 2008

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    cover image ACM Conferences
    GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation
    July 2007
    2313 pages
    ISBN:9781595936974
    DOI:10.1145/1276958
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    Published: 07 July 2007

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    Author Tags

    1. coevolution
    2. evolutionary computation
    3. exact cover
    4. genetic algorithm
    5. niches
    6. niching
    7. shape nesting
    8. species
    9. tiling

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    • (2008)Optimal Nesting of Species for Exact CoverProceedings of the 10th International Conference on Parallel Problem Solving from Nature --- PPSN X - Volume 519910.5555/2951659.2951706(438-447)Online publication date: 13-Sep-2008
    • (2008)Optimal Nesting of Species for Exact Cover: Many against ManyParallel Problem Solving from Nature – PPSN X10.1007/978-3-540-87700-4_44(438-447)Online publication date: 2008

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