The ideal free distribution: theory and engineering application.
We extend the theory of the "ideal free distribution" (IFD) from theoretical ecology by providing methods to analytically find the distribution for a relatively general class of "suitability" functions. We show that the resulting IFD is a Nash equilibrium and an evolutionarily stable strategy (ESS). Moreover, we show that for a certain cost function it is a global optimum point. We introduce the "replicator dynamics" for the IFD and show that we provide an allocation strategy that is guaranteed to achieve the IFD. Finally, we show how this allocation strategy can achieve an IFD for a multizone temperature control problem that corresponds to achieving the maximum uniform temperature on a grid under a multivariable saturation constraint.
Quijano
Nicanor
N
Department of Electrical and Computer Engineering, The Ohio State University, Columbus 43210, USA. quijano.2@osu.edu
Passino
Kevin M
KM
D000465:Algorithms; D000818:Animals; D001522:Behavior, Animal / Q000502:physiology*; D001698:Biomedical Engineering / Q000379:methods; D032701:Biomimetics / Q000379:methods*; D003198:Computer Simulation; D003710:Demography; D017753:Ecosystem; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics