A hybrid model-classifier framework for managing prediction uncertainty in expensive optimisation problems

Many real-world optimisation problems rely on computationally expensive simulations to evaluate candidate solutions. Often, such problems will contain candidate solutions for which the simulation fails, for example, due to limitations of the simulation. Such candidate solutions can hinder the effectiveness of the optimisation since they may consume a large portion of the optimisation budget without providing new information to the optimiser, leading to search stagnation and a poor final result. Existing approaches to handle such designs either discard them altogether, or assign them a penalised fitness. However, this results in loss of beneficial information, or in a model with a severely deformed landscape. To address these issues, this study proposes a hybrid classifier-model framework. The role of the classifier is to predict which candidate solutions are likely to crash the simulation, and this prediction is then used to bias the search towards valid solutions. Furthermore, the proposed framework employs a trust-region approach, and several other procedures, to manage the model and classifier, and to ensure the progress of the optimisation. Performance analysis using an engineering application of airfoil shape optimisation shows the efficacy of the proposed framework, and the possibility to use the knowledge accumulated in the classifier to gain new insights into the problem being solved.