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Correlation of Fitness and Program Size

Figure 8 plots the correlation coefficient of program size and amount of food eaten by the ant it controls. (Correlation coefficients are equal to the covariance after it has been normalised to lie in the range . By considering food eaten we avoid the intermediate stage of converting program score to expected number of children required when applying Price's Theorem). Figure 8 shows that in all cases there is a positive correlation (typically ) between program performance and length of programs. Where selection is not used longer programs may be more fit simply because they are more likely to contain useful primitives (such as Move) than short programs. When selection is used the correlation may be because when crossover reduces the length of a program it is more likely to disrupt the operation of the program and so reduce its fitness.

Figure 8:   Correlation of program length and fitness, Normal runs, runs without selection and runs with selection removed halfway through. Means of 50 runs.

William B Langdon
Tue Jun 10 12:12:55 BST 1997