Abstract Information-based optimal experimental designs are effective offline quality improvement tools that provide insights into the information under complex engineering situations. In the literature, considerable attention has been focused on the regular design region-based experiments to generate design points for both qualitative and quantitative factors. However, there are several situations while some design points are infeasible due to the cost and resource-related restrictions. In such situations, an appropriate design should be selected to obtain feasible experimental design points. Therefore, this paper is three-fold. One, a D-optimal design is selected over other designs. Two, this paper is to develop models that interconnect experimental design as an information-gathering process in the early design phase with operations research in the optimization phase. To the best of our knowledge, there is not an optimization model for identifying optimum factor level settings by linking the D-optimal design concept to optimization. Thus, a 0–1 mixed-integer nonlinear programming model is proposed to obtain an optimal operating condition for both qualitative and quantitative factors. Relaxation and constraint enforcement concepts are also presented to solve the proposed optimization model. Besides, comparison studies of the proposed optimization model and counterparts are also conducted. Finally, the proposed methodology may have a potential impact to enhance complex engineering situations for both qualitative and quantitative factors in a linearly restricted experimental design region.

中文翻译：

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开发基于 D 最优设计的 0-1 混合整数非线性稳健参数设计优化模型，用于寻找最佳设计因子水平设置

摘要 基于信息的优化实验设计是有效的离线质量改进工具，可以深入了解复杂工程情况下的信息。在文献中，相当多的注意力集中在基于常规设计区域的实验上，以生成定性和定量因素的设计点。然而，由于成本和资源相关的限制，有些设计点是不可行的，有几种情况。在这种情况下，应选择合适的设计以获得可行的实验设计点。因此，这篇论文是三重的。一，选择 D 最优设计而不是其他设计。二，本文旨在开发将实验设计作为早期设计阶段的信息收集过程与优化阶段的运筹学研究相互关联的模型。据我们所知，不存在通过将 D 最优设计概念与优化联系起来来确定最优因子水平设置的优化模型。因此，提出了一个 0-1 混合整数非线性规划模型，以获得定性和定量因素的最佳操作条件。还提出了松弛和约束强制概念来解决所提出的优化模型。此外，还对所提出的优化模型和对应的优化模型进行了比较研究。最后，