Temporal True and Surrogate Fitness Landscape Analysis for Expensive Bi-Objective Optimisation

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.