Optimization Problems in Factorial and Response Adaptive Designs

实验设计是为科学探究收集数据的有效方法进行计划研究或调查的过程。它是科学研究中常用的工具，在工业、农业、生物、制药和制造科学等领域都有应用。由于实验成本的增加，迫切需要好的设计来提高参数估计的效率和结果测试的统计能力。最佳的实验设计以最小的成本提供可解释和准确的推断。优化设计中的问题包括选择适当的最优性准则或几种准则的混合，以及确定实际设计，无论是解析还是数值。优化设计中的挑战以方法和计算问题为特征，这为开发新的优化标准、优化设计理论、方法和搜索最佳设计的算法提供了机会。

Experimental design is a process of planning a study or investigating efficient methods for collecting data for scientific inquiry. It is a commonly used tool in scientific investigations with applications in industrial, agricultural, biological, pharmaceutical, and manufacturing sciences, etc. Due to the increasing cost of experiments, there is an urgent need for good designs that increase the efficiency of parameter estimation and the statistical power of the resulting tests. An optimal experimental design provides interpretable and accurate inference at minimal cost. Problems in optimal design include the selection of an appropriate optimality criterion or a mixture of several criteria and the determination of actual design, either analytically or numerically. The challenges in optimal design are characterized by methodological and computational issues, which provide opportunities for developing new optimality criteria, optimal design theory, methodology, and algorithms for searching for optimal designs.