Statistical Algorithms for Optimal Experimental Design with Correlated Observations

Abstract

The first part of my dissertation demonstrates that a modified simulated annealing algorithm can successfully determine highly efficient D-optimal designs for second order polynomial regression for a variety of correlated error structures. In the second part, I solved weak universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. In the third part, we propose an improved Particle Swarm Optimization (PSO) algorithm with time varying parameters. Then combining the theorem of decision making and PSO, we innovated nested PSO algorithms with all of these three criteria and make comparison among the quality of solutions found from the three criteria