In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing for nonlinear relationships in factor levels. We develop scalable algorithms suitable for cases where the number of candidate experiments grows exponentially with the factor dimension, focusing on both first- and second-order models under design constraints. Particularly, our approach integrates convex relaxation with pricing-based local search techniques, which can provide upper bounds and performance guarantees. Unlike traditional local search methods, such as the ``Fedorov exchange" and its variants, our method effectively accommodates arbitrary side constraints in the design space. Furthermore, it yields both a feasible solution and an upper bound on the optimal value derived from the convex relaxation. Numerical results highlight the efficiency and scalability of our algorithms, demonstrating superior performance compared to the state-of-the-art commercial software, JMP

翻译：在最优实验设计中，目标是根据因子水平选择一组有限的实验，以最大化关于未知模型参数的信息。本研究针对广义D-最优设计问题，允许因子水平之间存在非线性关系。我们开发了适用于候选实验数量随因子维度呈指数增长情况的可扩展算法，重点关注设计约束下的一阶和二阶模型。特别地，我们的方法将凸松弛与基于定价的局部搜索技术相结合，能够提供上界和性能保证。与传统的局部搜索方法（如“Fedorov交换”及其变体）不同，我们的方法能有效适应设计空间中的任意侧约束。此外，该方法既产生可行解，又提供源自凸松弛的最优值上界。数值结果突显了我们算法的高效性和可扩展性，其性能优于当前最先进的商业软件JMP。