Exploring the Uncertainty of Approximated Fitness Landscapes via Gaussian Process Realisations

Gaussian processes (GPs) serve as powerful surrogate models in optimisation by providing a flexible data-driven framework for representing complex fitness landscapes. We provide an analysis of realisations drawn from GP models of fitness landscapes-which represent alternative coherent fits to the data-and use a network-based approach to investigate their induced landscape consistency. We consider the variation of constructed local optima networks (LONs: which provide a condensed representation of landscapes), analyse the fitness landscapes of GP realisations, and delve into the uncertainty associated with graph metrics of LONs. Our findings contribute to the understanding and practical application of GPs in optimisation and landscape analysis. Particularly that landscape consistency between GP realisations can vary considerably dependent on the model fit and underlying landscape complexity of the optimisation problem.