Assessment of problem modality by differential performance of lexicase selection in genetic programming

Many potential target problems for genetic programming are modal in the sense that qualitatively different modes of response are required for inputs from different regions of the problem's domain. This paper presents a new approach to solving modal problems with genetic programming, using a simple and novel parent selection method called lexicase selection. It then shows how the differential performance of genetic programming with and without lexicase selection can be used to provide a measure of problem modality, and it argues that defining such a measure in this way is not as methodologically problematic as it may initially appear. The modality measure is illustrated through the analysis of genetic programming runs on a simple modal symbolic regression problem. This is a preliminary report that is intended in part to stimulate discussion on the significance of modal problems, methods for solving them, and methods for measuring the modality of problems. Although the core concepts in this paper are presented in the context of genetic programming, they are also relevant to applications of other forms of evolutionary computation to modal problems.