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.

翻译：许多现实世界问题具有计算昂贵的适应度函数且本质上是多目标的。代理模型辅助的进化算法常被用来解决此类问题。然而，关于代理模型所诱导的适应度景观分析文献有限，针对多目标问题的研究更是空白。本研究通过比较多目标函数真实适应度景观与代理模型景观，填补了这一关键空白。此外，研究采用时序视角，在优化过程中不同时间点、于该时刻种群邻域内考察景观特征。实验采用BBOB双目标基准函数。适应度景观分析结果显示，优化过程中不同时间点的真实与代理特征存在显著差异。尽管存在这些差异，真实与代理景观特征之间仍表现出高度相关性。进一步，本研究识别出与搜索相关的景观特征，并证明代理与真实景观特征均能预测算法性能。这些发现表明，景观特征的时序分析可能有助于设计代理切换策略以提升多目标优化性能。