The Practical Handbook of Genetic Algorithms: Applications, by Lance D. Chambers

By Lance D. Chambers

The connection of the stucture of genetic set of rules and its convergencrs

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5 Interpretation of the Parameters The assays are all from different locations. 87 of the intercept parameter “a” for Model 2 can be interpreted as our best estimate of the correlation that would be found between two assays made of samples taken from identical locations. However, each of these two assays can be considered as the combination of the “true” assay plus some orthogonal noise. Assuming the noise components of the two assays to be not correlated with each other, the accuracy of a single estimate, or the correlation between a single estimate and the “true” assay is given by √a.

The correlation between assays at two separated points is now ρ(ra , rb , rc ), a function of (ra , rb , rc ), the distance between the points along the directions of the three orthogonal major axes. exp[-sqrt(ka2 ra2 + kb2 rb2 + kc2 rc2 )] (16) In Model 3, the correlation coefficient still falls off exponentially in any direction, but the rate of fall-off depends upon the direction. Along the first major axis, the correlation falls off by a ratio 1/e for an increase of 1/ka in the separation. Along © 2001 by Chapman & Hall/CRC the second and third axes, the correlation falls off by 1/e when the separation increases by 1/kb and 1/kc, respectively.

The curved thin line represents a negative exponential fitted by eye. It is clear that the scatter in the observed data does not vary greatly with the radial distance. There is also no particular evidence of any cyclic pattern to the assay values. The data provide empirical support for the exponential decay model that we had derived theoretically. 4 The Appropriate Misfit Function The cross product of two items selected from a pair of correlated standardized normal distributions has an expected value equal to the correlation between the two distributions.

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