Strength Through Diversity: Disaggregation and Multi-Objectivisation Approaches for Genetic Programming

An underlying problem in genetic programming (GP) is how to ensure sufficient useful diversity in the population during search. Having a wide range of diverse (sub)component structures available for recombination and/or mutation is important in preventing premature converge. We propose two new fitness disaggregation approaches that make explicit use of the information in the test cases (i.e., program semantics) to preserve diversity in the population. The first method preserves the best programs which pass each individual test case, the second preserves those which are non-dominated across test cases (multi-objectivisation). We use these in standard GP, and compare them to using standard fitness sharing, and using standard (aggregate) fitness in tournament selection. We also examine the effect of including a simple anti-bloat criterion in the selection mechanism. We find that the non-domination approach, employing anti-bloat, significantly speeds up convergence to the optimum on a range of standard Boolean test problems. Furthermore, its best performance occurs with a considerably smaller population size than typically employed in GP.