An Iterative Two-Stage Multifidelity Optimization Algorithm for Computationally Expensive Problems

Abstract

Engineering design optimization often involves use of numerical simulations to assess the performance of candidate designs. The simulations for computing high-fidelity (HF) performance estimates, such as finite element analysis or computational fluid dynamics, are typically computationally expensive. In some cases, it may also be possible to run an alternate or cheaper version of the simulation (through, e.g., use of a coarse mesh) to yield a low-fidelity (LF) performance estimate. Multi-fidelity optimization refers to the class of methods that aim to manage LF and HF evaluations efficiently to optimize computationally expensive problems within a limited computing budget. Among the prominent existing multi-fidelity approaches, some of them depend on a sufficiently dense a priori sampling; while others use unidirectional information exchange from LF to HF; both of which lead to a possibility of spending evaluation budget on unpromising search regions. This paper proposes an improved multi-fidelity approach using an iterative, two-stage scheme (MFITS). It uses the collective information from previously evaluated designs to determine a sampling neighbourhood for LF evaluations. These samples are in-turn used for building a co-kriging surrogate model that is then searched globally to identify a good candidate for HF evaluation. By restricting the LF sampling neighbourhood, the computational budget can be used more efficiently, as the search is focused on regions that have historically produced good quality solutions. Numerical experiments and benchmarking are conducted on two suites of test problems and two practical design optimization problems to demonstrate the efficacy of MFITS.