Effects of lexicase and tournament selection on diversity recovery and maintenance

In genetic programming systems, parent selection algorithms select the programs from which offspring will be produced by random variation and recombination. While most parent selection algorithms select programs on the basis of aggregate performance on multiple test cases, the lexicase selection algorithm considers each test case individually, in random order, for each parent selection event. Prior work has shown that lexicase selection can produce both more diverse populations and more solutions when applied to several hard problems. Here we examine the effects of lexicase selection, compared to those of the more traditional tournament selection algorithm, on population error diversity using two program synthesis problems. We conduct experiments in which the same initial population is used to start multiple runs, each using a different random number seed. The initial populations are extracted from genetic programming runs, and fall into three categories: high diversity populations, low diversity populations, and populations that occur after diversity crashes. The reported data shows that lexicase selection can maintain high error diversity and also that it can re-diversify less-diverse populations, while tournament selection consistently produces lower diversity.