  In the pursuit of efficient optimization of expensive-to-evaluate systems,
this paper investigates a novel approach to Bayesian multi-objective and
multi-fidelity (MOMF) optimization. Traditional optimization methods, while
effective, often encounter prohibitively high costs in multi-dimensional
optimizations of one or more objectives. Multi-fidelity approaches offer
potential remedies by utilizing multiple, less costly information sources, such
as low-resolution simulations. However, integrating these two strategies
presents a significant challenge. We suggest the innovative use of a trust
metric to support simultaneous optimization of multiple objectives and data
sources. Our method modifies a multi-objective optimization policy to
incorporate the trust gain per evaluation cost as one objective in a Pareto
optimization problem, enabling simultaneous MOMF at lower costs. We present and
compare two MOMF optimization methods: a holistic approach selecting both the
input parameters and the trust parameter jointly, and a sequential approach for
benchmarking. Through benchmarks on synthetic test functions, our approach is
shown to yield significant cost reductions - up to an order of magnitude
compared to pure multi-objective optimization. Furthermore, we find that joint
optimization of the trust and objective domains outperforms addressing them in
sequential manner. We validate our results using the use case of optimizing
laser-plasma acceleration simulations, demonstrating our method's potential in
Pareto optimization of high-cost black-box functions. Implementing these
methods in existing Bayesian frameworks is simple, and they can be readily
extended to batch optimization. With their capability to handle various
continuous or discrete fidelity dimensions, our techniques offer broad
applicability in solving simulation problems in fields such as plasma physics
and fluid dynamics.
