Optimization Problems in Factorial and Response Adaptive Designs

实验设计是计划一项研究或研究为科学研究收集数据的有效方法的过程。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，迫切需要良好的设计来提高参数估计的效率和所产生的测试的统计能力。最优的实验设计以最小的成本提供了可解释的和准确的推理。优化设计中的问题包括选择适当的最优准则或几个准则的混合，以及实际设计的确定，无论是解析的还是数值的。优化设计中的挑战表现为方法学和计算问题，这为开发新的优化准则、优化设计理论、方法论和算法以寻找最优设计提供了机会。

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.