  Explainable artificial intelligence (XAI) is an important and rapidly
expanding research topic. The goal of XAI is to gain trust in a machine
learning (ML) model through clear insights into how the model arrives at its
predictions. Genetic programming (GP) is often cited as being uniquely
well-suited to contribute to XAI because of its capacity to learn (small)
symbolic models that have the potential to be interpreted. Nevertheless, like
many ML algorithms, GP typically results in a single best model. However, in
practice, the best model in terms of training error may well not be the most
suitable one as judged by a domain expert for various reasons, including
overfitting, multiple different models existing that have similar accuracy, and
unwanted errors on particular data points due to typical accuracy measures like
mean squared error. Hence, to increase chances that domain experts deem a
resulting model plausible, it becomes important to be able to explicitly search
for multiple, diverse, high-quality models that trade-off different meanings of
accuracy. In this paper, we achieve exactly this with a novel multi-modal
multi-tree multi-objective GP approach that extends a modern model-based GP
algorithm known as GP-GOMEA that is already effective at searching for small
expressions.

Neural and Evolutionary Computing