Gaussian adaptation

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Gaussian adaptation is designed for the maximization of manufacturing yield due to statistical deviation of component values of signal processing systems. The process uses the theorem of Gaussian adaptation stating that: if the centre of gravity of a high-dimensional Gaussian distribution coincides with the centre of gravity of the part of the distribution belonging to some region of acceptability in a state of selective equilibrium, then the hitting probability on the region is maximal. The theorem is valid for all regions of acceptability and all Gaussian distributions. It may be used by cyclic repetition of random variation and selection (like the natural evolution). In every cycle a sufficiently large number of Gaussian distributed points are sampled and tested for membership in the region of acceptability. The centre of gravity of the Gaussian is then moved to the centre of gravity of the approved points. Thus, the process converges to a state of equilibrium fulfilling the theorem. A solution is always approximate because the centre of gravity is always determined for a limited number of points.

It was used for the first time in 1969 as a pure optimization algorithm making the regions of acceptability smaller and smaller. Since 1970 it has been used for both ordinary optimization and manufacturing yield maximization.


Gaussian adaptation as a model of evolution

It has also been compared to the natural evolution of populations of living organisms. In this case the region of acceptability is replaced by a probability function, s(x), where x is an array of phenotypes determining the organism. This is possible because the theorem of Gaussian adaptation is valid for any region of acceptability. Then it is fairly easily proved that the process is maximizing the mean fitness of a large population with respect to Gaussian distributed quantitative characters.

As long as the ontogenetic program my be seen as a stepwise modified recapitulation of the evolution of a particular individual organism, the central limit theorem states that the sum of contributions from many random steps tend to become Gaussian distributed. A necessary condition for the natural evolution to be able to fulfill the theorem of Gaussian adaptation is that it may push the centre of gravity of the Gaussian to the centre of gravity of the surviving individuals. The Hardy-Weinberg law may accomplish this.

In this case the rules of genetic variation such as crossover, inversion, transposition etcetera may be seen as random number generators for the phenotypes. So, in this sense GA may be seen as a genetic algorithm. --Gregor 05:08, 13 February 2008 (EST)

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--Gregor 05:08, 13 February 2008 (EST)

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