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7. The Robustness of Genetic Plans |
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We cannot distinguish between a realistic and an unrealistic adaptive hypothesis or algorithm without a good estimate of the underlying adaptive plan's robustnessits efficiency over the range of environments it may encounter. By determining the speed and flexibility of proposed adaptive mechanisms, in the intended domain(s) of action, we gain a critical index of their adequacy. The framework of concepts and theorems has expanded now to the point that we can tackle such questions rigorously. The robustness established here is a general property holding for particular plans of type  in any string-represented domain  ; furthermore, the basic theorem holds for any payoff function  . We can also address ourselves directly to related questions of the automatic determination, retention, and use of relevant history to increase efficiency. |
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1. Adaptive Plans of Type  |
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Genetic plans will be the main vehicle for this investigation, both as test cases and to illustrate formal approaches to questions of robustness. In particular, the investigation will use, as prototypes, plans of type  employing the three operators, simple crossover, simple inversion, and mutation. (To retain the one-operator format of the original specification of , the combined effect of the three operators could easily be reinterpreted as the effect of a single composite operator; for expository purposes it is easier to treat the operators individually.) The basic parameters are: |
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| Pc, | the constant probability of applying simple crossover to a selected individual, | | PI, | the constant probability of applying simple inversion to a selected individual, | | 1PM, | the initial probability of mutation of an allele (all alternatives for the allele being equilikely outcomes), |
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