Efficient multi-fidelity simulation optimization

Simulation models of different fidelity levels are often available for a complex system. High-fidelity simulations are accurate but time-consuming. Therefore, they can only be applied to a small number of solutions. Low-fidelity simulations are faster and can evaluate a large number of solutions. But their results may contain significant bias and variability. We propose an Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling (MO²TOS) framework to exploit the benefits of high- and low-fidelity simulations to efficiently identify a (near) optimal solution. MO2TOS uses low-fidelity simulations for all solutions and then assigns a fixed budget of high-fidelity simulations to solutions based on low-fidelity simulation results. We show the benefits of MO²TOS via theoretical analysis and numerical experiments with deterministic simulations and stochastic simulations where noise is negligible with sufficient replications. We compare MO²TOS to Equal Allocation (EA) and Optimal Computing Budget Allocation (OCBA). MO²TOS consistently outperforms both EA and OCBA.