Integrating Bayesian and Evolutionary Approaches for Multi-objective Optimisation

Both Multi-Objective Evolutionary Algorithms (MOEAs) and Multi-Objective Bayesian Optimisation (MOBO) are designed to address challenges posed by multi-objective optimisation problems. MOBO offers the distinct advantage of managing computationally or financially expensive evaluations by constructing Bayesian models based on the dataset. MOBO employs an acquisition function to strike a balance between convergence and diversity, facilitating the selection of an appropriate decision vector. MOEAs, similarly focused on achieving convergence and diversity, employ a selection criterion. This paper contributes to the field of multi-objective optimisation by constructing Bayesian models on the selection criterion of decomposition-based MOEAs within the framework of MOBO. The modelling process incorporates both mono and multi-surrogate approaches. The findings underscore the efficacy of MOEA selection criteria in the MOBO context, particularly when adopting the multi-surrogate approach. Evaluation results on both real-world and benchmark problems demonstrate the superiority of the multi-surrogate approach over its mono-surrogate counterpart for a given selection criterion. This study emphasises the significance of bridging the gap between these two optimisation fields and leveraging their respective strengths.