Seminar 2024-03-01

Graphical Methods for Order-of-Addition Experiments

Nicholas Rios

Assistant Professor

Department of Statistics

George Mason University

Date: Friday, March 01, 2024

Time: 11:00 A.M. – 12:00 P.M. Eastern Time

Location: Nguyen Engineering Building, Room 1109

In an order-of-addition (OofA) experiment, the order in which several components are added to a system influences a response. Although much research has been done on optimal OofA experiments, existing methodologies typically assume that all orders are possible. However, in many practical examples, there are directed constraints on the pairwise order of components, making some of the orders infeasible. These constraints can be represented by a directed acyclic graph (DAG). The goal of the OofA experiment is to find an optimal order, which is equivalent to finding an optimal topological sort of the DAG. A multiplicative algorithm is used to identify approximate optimal designs for an arbitrary DAG. Simulated annealing (SA) is proposed as a method to identify efficient exact designs. It is shown that the SA designs have high efficiency relative to the approximate optimal designs. A general procedure is proposed to search for the optimal order on a DAG given the results of an OofA experiment using two popular models. Applications to job scheduling are shown.

Nicholas Rios is an Assistant Professor in the department of Statistics at George Mason University. His research primarily focuses on experimental design in the presence of real-world constraints, and the use of metaheuristic algorithms to identify efficient designs. He is also interested in computational statistics, functional data analysis, and modeling of compositional data, with applications to chemical engineering and pharmaceutical industries. He earned his PhD in Statistics at Penn State University in 2022. His dissertation was focused on designing optimal mixture experiments, where multiple reagents, chemicals, or drugs were mixed to produce a response. 

David Kepplinger