Evaluation of combinatorial optimisation algorithms for c-optimal experimental designs with correlated observations

Area of Science:

• Statistics
• Experimental Design
• Computational Science

Background:

• Identifying optimal experimental designs is crucial for efficient data collection.
• Correlations within and between experimental units complicate design optimization.
• Generalized linear mixed models (GLMMs) are frequently used for analyzing complex experimental data.

Purpose of the Study:

• To apply combinatorial optimization algorithms for identifying c-optimal experimental designs.
• To evaluate the performance of local search, greedy search, and reverse greedy search algorithms.
• To extend these algorithms for model-robust c-optimal designs.

Main Methods:

• Formulating the c-optimal design criterion as a monotone supermodular function.
• Applying minimization algorithms (local search, greedy search, reverse greedy search) to find optimal designs under GLMMs.
• Comparing algorithm performance against multiplicative weighting methods.

Main Results:

• Local search and reverse greedy search algorithms demonstrate comparable performance.
• Design outputs from these algorithms showed variance less than 10% greater than the best design across various covariance structures.
• The tested algorithms performed as well as or better than multiplicative methods.

Conclusions:

• Combinatorial optimization provides an effective framework for c-optimal experimental design with correlated data.
• Local and reverse greedy search algorithms are reliable and efficient for this task.
• The developed methods can be extended to find model-robust optimal designs.