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

Authors:
Jeffrey Horn
Affiliations:
Northern Michigan University, Marquette, MI
Venue:
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Year:
2007

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Optimal Nesting of Species for Exact Cover: Many against Many

Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X

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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.