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.

翻译：在追求高效优化高成本评估系统的过程中，本文研究了一种新颖的贝叶斯多目标与多保真度（MOMF）优化方法。传统优化方法虽有效，但在多维度优化一个或多个目标时往往面临难以承受的高昂成本。多保真度方法通过利用多个成本较低的信息源（如低分辨率模拟）提供了潜在的解决方案。然而，将这两种策略整合起来却是一项重大挑战。我们提出创新性地使用信任指标来支持多个目标和数据源的同步优化。该方法修改了多目标优化策略，将每次评估成本下的信任增益作为帕累托优化问题中的一个目标，从而实现成本更低的联合MOMF优化。我们提出并比较了两种MOMF优化方法：一种联合选择输入参数与信任参数的整体方法，以及一种用于基准测试的序贯方法。通过对合成测试函数的基准测试，本方法展现出显著的成本降低效果——相较于纯多目标优化，成本可降低一个数量级。此外，我们发现信任域与目标域的联合优化优于序贯处理方式。我们利用激光等离子体加速模拟优化案例验证了结果，展示了该方法在高成本黑箱函数帕累托优化中的潜力。将这些方法集成到现有贝叶斯框架中较为简便，且可轻松扩展至批处理优化。凭借处理各种连续或离散保真度维度的能力，我们的技术在等离子体物理与流体动力学等领域的仿真问题求解中具有广泛适用性。