An efficiency and convergence analysis of multi-fidelity optimization with ordinal transformation and optimal sampling

Simulation and analytical tools are useful modeling methods to solve complex optimization problems. In this paper, we propose a simulation optimization framework called "Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling" (MO2TOS) when multi-fidelity models are available, and prove its efficiency by analyzing its convergence mechanism. The MO2TOS is a two-stage method combining the information of both low- and high-fidelity models. In the Ordinal Transformation (OT) stage, the low-fidelity model is estimated to rank candidates and to partition the solution set into groups, while in the Optimal Sampling (OS) stage, the Optimal Computing Budget Allocation (OCBA) rule guides the sampling budget allocated to each group. We derive the convergence pattern of the expected gap between true and observed optimums using MO2TOS, and compare its performance with other methods. Related numerical experiments validate the efficiency of MO2TOS and the derived convergence pattern.