040907 - Lecture Recall Talking about SGA as a Markov chain...

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Lecture ??: 04/09/2007 Recall: Talking about SGA as a Markov chain on population space (fitness-proportional selection.) Early examples (without mutation): had some absorbing states -these are the monomorphic populations (all indiciduals same,) all other states transient. Mutation: Introduce mutation => take non-generic Markov chain on population space and make it generic with very small є’s (ie, irreducible —whole state space is one big positively recurrent class.) The idea here is that it’s possible to move in one step from any population to any other—albeit often very hard (not really seen because it involves too many low-probability events.) Math-wise: there’s a unique stationary distribution π * p >0 for any population P; you’ll visit every P infinitely often if you run chain forever; etc. In “real life:” π p * larger for some P’s than others; when you run the algorithm, usually see this kind of thing: Population evolves toward a monomorphic one and stays “near” that for awhile Then shoots (via some mutations) to another monomorphic, stays there for awhile User choices (eg selection method, p m , p c , encoding) affect which monomorphics you see a lot, how long you linger around them, etc.
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  • Spring '07
  • Algorithms, Markov chain, highest fitness individual, population space

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