Partial Functions in Fitness-Shared Genetic Programming

This paper investigates the use of partial functions and fitness sharing in genetic programming. Fitness sharing is applied to populations of either partial or total functions and the results compared. Applications to two classes of problem are investigated: learning multiplexer definitions, and learning (recursive) list membership functions. In both cases, fitness sharing approaches outperform the use of raw fitness, by generating more accurate solutions with the same population parameters. On the list membership problem, variants using fitness sharing on populations of partial functions outperform variants using total functions, whereas populations of total functions give better performance on some variants of multiplexer problems.