Optimization Problems in Factorial and Response Adaptive Designs

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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.