Relaxations of Lexicase Parent Selection

In a genetic programming system, the parent selection algorithm determines which programs in the evolving population will be used as the material out of which new programs will be constructed. The lexicase parent selection algorithm chooses a parent by considering all test cases, individually, one at a time, in a random order, to reduce the pool of possible parent programs. Lexicase selection is ordinarily strict, in that a program can only be selected if it has the best error in the entire population on the first test case considered, and the best error relative to all other programs that remain in the pool each time it is reduced. This strictness may exclude high-quality candidates from consideration for parenthood, and hence from exploration by the evolutionary process. In this chapter we describe and present results of four variants of lexicase selection that relax these strict constraints: epsilon lexicase selection, random threshold lexicase selection, MADCAP epsilon lexicase selection, and truncated lexicase selection. We present the results of experiments with genetic programming systems using these and other parent selection algorithms on symbolic regression and software synthesis problems. We also briefly discuss the relations between lexicase selection and work on many-objective optimization, and the implications of these considerations for future work on parent selection in genetic programming.