Information theoretic indicators of fitness, relevant diversity & pairing potential in genetic programming

Commonly used fitness measures, such as mean squared error, often fail to reward individuals whose presence in the population is necessary to explain substantial portions of the data variance. Diversity indicators are often arbitrary, may reflect diversity irrelevant to solving the problem, and are incommensurate with fitness measures. By contrast, information theoretic functional are computable general indicators of fitness and diversity without these typical failings. We propose normalized mutual information, redundancy and synergy measures for genetic programming. We also propose selection for recombination and survival by "pairing potential" and "pair potential" estimation, and offer numerical examples as empirical support for theoretical claims.