ABSTRACT

Model-based optimal designs for regression problems with multiple objectives are common in practice. The traditional approach is to construct an optimal design for the most important objective and hope that the design performs well for the other objectives. Analytical approaches are challenging because the objectives are often competitive and their relative importance has to be incorporated at the onset of the design construction. There are also no general and efficient algorithms for searching such designs for user-specified nonlinear models and criteria. We propose a new and effective approach for finding multiple-objective optimal designs via the CVX software and demonstrate it can efficiently find different types of multiple-objective optimal designs after the optimization problems are carefully formulated as convex optimization problems appropriate for CVX use. We provide three biomedical applications and show our MATLAB code producing the same few multiple-objective optimal designs reported in the statistical literature. MATLAB code files are available online in the supplementary materials of this article.

摘要

针对多目标回归问题的基于模型的优化设计在实践中很常见。传统的方法是针对最重要的目标构建最优设计，并希望该设计对于其他目标也能表现良好。分析方法具有挑战性，因为目标通常具有竞争性，并且必须在设计构建开始时就考虑到它们的相对重要性。也没有通用且有效的算法来搜索此类设计以获取用户指定的非线性模型和标准。我们提出了一种通过 CVX 软件寻找多目标最优设计的新有效方法，并证明在优化问题被仔细地表述为适合 CVX 使用的凸优化问题后，它可以有效地找到不同类型的多目标最优设计。我们提供了三个生物医学应用程序，并展示了我们的 MATLAB 代码，该代码可生成与统计文献中报告的相同的少数多目标优化设计。MATLAB 代码文件可在本文的补充材料中在线获取。