Multi-objective optimization with Kriging surrogates using “moko”, an open source package

Abstract Many modern real-world designs rely on the optimization of multiple competing goals. For example, most components designed for the aerospace industry must meet some conflicting expectations. In such applications, low weight, low cost, high reliability, and easy manufacturability are desirable. In some cases, bounds for these requirements are not clear, and performing mono-objective optimizations might not provide a good landscape of the required optimal design choices. For these cases, finding a set of Pareto optimal designs might give the designer a comprehensive set of options from which to choose the best design. This article shows the main features and functionalities of an open source package, developed by the present authors, to solve constrained multi-objective problems. The package, named moko (acronym for Multi-Objective Kriging Optimization), was built under the open source programming language R. Popular Kriging based multi-objective optimization strategies, as the expected volume improvement and the weighted expected improvement, are available in the package. In addition, an approach proposed by the authors, based on the exploration using a predicted Pareto front is implemented. The latter approach showed to be more efficient than the two other techniques in some case studies performed by the authors with moko.

摘要 当前诸多现实工程设计均需针对多个相互冲突的目标开展优化工作。例如，航空航天领域的多数构件均需满足若干相互矛盾的性能要求。在这类应用场景中，轻量化、低成本、高可靠性以及易加工性均为理想的性能指标。部分场景下，这些性能要求的约束边界并不明确，仅开展单目标优化往往无法完整呈现所需最优设计方案的解集空间。针对这类场景，获取一组帕累托最优（Pareto optimal）设计方案，可为设计者提供一套全面的可选方案，便于其从中遴选最优设计。本文介绍了由本文作者团队开发的一款用于求解约束多目标优化问题的开源软件包的核心特性与功能。该软件包命名为moko（Multi-Objective Kriging Optimization的首字母缩写），基于开源编程语言R开发。软件包集成了主流的基于克里金（Kriging）的多目标优化策略，例如期望体积改进（expected volume improvement）与加权期望改进（weighted expected improvement）。此外，软件包还实现了本文作者团队提出的一种基于预测帕累托前沿（Pareto front）进行探索的优化方法。在本文作者使用moko开展的若干案例研究中，该方法展现出相较于前述两种技术更高的优化效率。