Statistics PhD Defense with Stephen Walsh (Dept. of Mathematical Sciences, MSU)

03/10/2021  1:00-2:00pm  WebEx Meeting

Abstract:  Particle swarm optimization (PSO) is a wildly popular metaheuristic. Its strengths lie in its simplicity and few assumptions regarding characteristics of the optimization objective. PSOs widespread application and success notwithstanding, it has surprisingly been applied in very few statistical applications. In this talk I will present my Ph.D. research and efforts to adapt PSO to the exact optimal design of experiments problem. I will first discuss the computational issues of extending PSO to optimizing functions which take matrix inputs and illustrate the validation of my implementation of PSO in the Julia language. Then I will present new results regarding fast and efficient generation of G-optimal designs and a detailed comparison to recent literature. Next, I will illustrate how we exploited PSO to produce the first known optimal design generation algorithm which allows the user to specify some number of pure replicates to be maintained during the optimization search. Last, I will show the construction and use of a novel PSO algorithm based on the Aitchison geometry which optimizes functions over the Cartesian product of standard K-simplices (i.e. generating optimal designs for mixture experiments via PSO).  A general conclusion of my research is that PSO will prove to be superior to the current domain standard algorithm, the coordinate exchange, for generating exact optimal designs.