Multi-fidelity simulation optimization with level set approximation using probabilistic branch and bound

Simulated systems are often described with a variety of models of different complexity. Making use of these models, algorithms can use low complexity, “low-fidelity” models or meta-models to guide sampling for purposes of optimization, improving the probability of generating good solutions with a small number of observations. We propose an optimization algorithm that guides the search for solutions on a high-fidelity model through the approximation of a level set from a low-fidelity model. Using the Probabilistic Branch and Bound algorithm to approximate a level set for the low-fidelity model, we are able to efficiently locate solutions inside of a target quantile and therefore reduce the number of high-fidelity evaluations needed in searches. The paper provides an algorithm and analysis showing the increased probability of sampling high-quality solutions within a low-fidelity level set. We include numerical examples that demonstrate the effectiveness of the multi-fidelity level set approximation method to locate solutions.