Instrumentos de evaluación

I hope that the reader, having followed the lines of discussion through this essay, may come away with the conclusion that the spectra of evolutionary sys­ tems provide a useful means to pose, and occasionally to solve, problems in evolutionary dynamics. I have used the spectral representation of the general­ ized mutation-selection system to address the question of when an evolution­ ary algorithm is useful for function optimization. I have described an analog to “rapidly mixing Markov chains” (Sinclair, 1992) that is appropriate for opti­ mization, “rapid first hitting time”. The conditions needed for an evolutionary algorithm to exhibit rapid first hitting time can be described in terms of the spectra of the linear systems that represent them.

I have also posed, questions on the dynamics of finite populations in terms of the spectra of the underlying operators. Tying together the spectra of infinite population models with the spectra of the finite population models into which they are embedded remains a major open question in the theory of evolutionary dynamics. Progress may result if flows over the low-dimensional boundaries of the simplex can be modeled.

Lastly, I have reviewed an important theorem by Karlin (1982) on the spec­ tral properties of genetic operator intensity. Extensions of this theorem would find immediate application.

Since these are spectral problems, there may indeed already be analytic tech­ niques that could be applied to their solution. It is hoped that this essay may bring attention to these problems and thus hasten their solution.

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SOLVING COMBINATORIAL OPTIMIZA­