Multi-objective multi-fidelity optimization with ordinal transformation and optimal sampling

In simulation-optimization, the accurate evaluation of candidate solutions can be obtained by running a high-fidelity model, which is fully featured but time-consuming. Less expensive and lower fidelity models can be particularly useful in simulation-optimization settings. However, the procedure has to account for the inaccuracy of the low fidelity model. Xu et al. (2015) proposed the MO²TOS, a Multi-fidelity Optimization (MO) algorithm, which introduces the concept of ordinal transformation (OT) and uses optimal sampling (OS) to exploit models of multiple fidelities for efficient optimization. In this paper, we propose MO-MO²TOS for the multi-objective case using the concepts of non-dominated sorting and crowding distance to perform OT and OS in this setting. Numerical experiments show the satisfactory performance of the procedure while analyzing the behavior of MO-MO²TOS under different consistency scenarios of the low-fidelity model. This analysis provides insights on future studies in this area.