  Many real-world problems have expensive-to-compute fitness functions and are
multi-objective in nature. Surrogate-assisted evolutionary algorithms are often
used to tackle such problems. Despite this, literature about analysing the
fitness landscapes induced by surrogate models is limited, and even
non-existent for multi-objective problems. This study addresses this critical
gap by comparing landscapes of the true fitness function with those of
surrogate models for multi-objective functions. Moreover, it does so temporally
by examining landscape features at different points in time during
optimisation, in the vicinity of the population at that point in time. We
consider the BBOB bi-objective benchmark functions in our experiments. The
results of the fitness landscape analysis reveals significant differences
between true and surrogate features at different time points during
optimisation. Despite these differences, the true and surrogate landscape
features still show high correlations between each other. Furthermore, this
study identifies which landscape features are related to search and
demonstrates that both surrogate and true landscape features are capable of
predicting algorithm performance. These findings indicate that temporal
analysis of the landscape features may help to facilitate the design of
surrogate switching approaches to improve performance in multi-objective
optimisation.
