Dynamic GP fitness cases in static and dynamic optimisation problems

In Genetic Programming (GP), the fitness of individuals is normally computed by using a set of fitness cases (FCs). Research on the use of FCs in GP has primarily focused on how to reduce the size of these sets to, for instance, reduce the fitness evaluation time. However, often, only a small set of FCs is available and there is no need to reduce it. In this work, we are interested in using the whole FCs set, but rather than adopting the commonly used GP approach of presenting the entire set of FCs to the system from the beginning of the search, referred as static FCs, we allow the GP system to build it over time, named as dynamic FCs, to make the search more amenable. Moreover, to the best of our knowledge, there is no study on the use/impact of FCs in Dynamic Optimisation Problems (DOPs). To this end, we also propose the Kendall Tau Distance (KTD) approach, which quantifies pairwise dissimilarities among two lists of fitness values. KTD aims to capture the degree of a change in DOPs and we use this to promote diversity, which has constantly reported to be beneficial in a dynamic setting. Results on eight symbolic regression functions indicate that both approaches are highly beneficial in GP.