基于预算的随机多目标最优化：应用于具有量化不确定性的多道次拉丝
Stochastic Multi-objective Optimization on a Budget: Application to multi-pass wire drawing with quantified uncertainties
摘要：
具有多个竞争目标的工程系统的设计优化是一个非常繁琐的过程，特别是当目标函数对于评估具有参数不确定性的计算机代码来说是昂贵的时。最先进的技术的有效性大大降低，因为它们需要大量的客观评价，这使得它们对上述类型的问题不切实际。贝叶斯全局优化（BGO），已设法处理这些挑战，在解决单目标最优化问题，最近已扩展到多目标最优化（MOO）。BGO模型的目标，通过概率代理人，并使用认知的不确定性来定义一个信息采集功能（IAF），量化的优点，评估目标在新的设计。该迭代数据采集过程继续，直到满足停止标准。MOO最常用的IAF是对支配超体积（EIHV）的预期改进，其原始形式无法处理参数不确定性或测量噪声。在这项工作中，我们提供了一个系统的EIHV重新处理随机MOO问题。本文的主要贡献在于能够过滤掉噪声和重新制定的EIHV，而不必观察或估计的随机参数。我们的方法论的概率性质的一个补充是，它使我们能够描述我们对预测的帕累托前沿的信心。我们验证和验证所提出的方法，将其应用到合成测试问题与已知的解决方案。我们展示了我们的方法上的一个工业问题的模具孔型设计的钢丝拉拔过程。
英文摘要：
Design optimization of engineering systems with multiple competing objectives is a painstakingly tedious process especially when the objective functions are expensive-to-evaluate computer codes with parametric uncertainties. The effectiveness of the state-of-the-art techniques is greatly diminished because they require a large number of objective evaluations, which makes them impractical for problems of the above kind. Bayesian global optimization (BGO), has managed to deal with these challenges in solving single-objective optimization problems and has recently been extended to multi-objective optimization (MOO). BGO models the objectives via probabilistic surrogates and uses the epistemic uncertainty to define an information acquisition function (IAF) that quantifies the merit of evaluating the objective at new designs. This iterative data acquisition process continues until a stopping criterion is met. The most commonly used IAF for MOO is the expected improvement over the dominated hypervolume (EIHV) which in its original form is unable to deal with parametric uncertainties or measurement noise. In this work, we provide a systematic reformulation of EIHV to deal with stochastic MOO problems. The primary contribution of this paper lies in being able to filter out the noise and reformulate the EIHV without having to observe or estimate the stochastic parameters. An addendum of the probabilistic nature of our methodology is that it enables us to characterize our confidence about the predicted Pareto front. We verify and validate the proposed methodology by applying it to synthetic test problems with known solutions. We demonstrate our approach on an industrial problem of die pass design for a steel wire drawing process.
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