Optimization Problems in Factorial and Response Adaptive Designs

实验设计是规划一项研究或调查收集科学探究数据的有效方法的过程。它是科学研究中常用的工具，应用于工业、农业、生物、制药和制造科学等领域。由于实验成本不断增加，迫切需要良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低的成本提供可解释且准确的推论。优化设计中的问题包括选择适当的优化标准或多个标准的混合以及通过分析或数值确定实际设计。优化设计中的挑战以方法论和计算问题为特征，这为开发新的优化标准、优化设计理论、方法论和搜索优化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.