A Note on the Output of a Coordinate-Exchange Algorithm for Optimal Experimental Design

TL;DR

This paper investigates the order of design points generated by the coordinate-exchange algorithm, revealing certain orders are more common and recommending explicit randomization before experiment implementation.

Contribution

It identifies the non-uniform distribution of design point orders from the coordinate-exchange algorithm and suggests a necessary randomization step for unbiased experimental results.

Findings

Certain orders of design points occur more frequently.

Explicit randomization is recommended before experiment execution.

The study enhances understanding of the coordinate-exchange algorithm's output.

Abstract

The coordinate-exchange algorithm is commonly used to construct optimal experimental designs. Every execution of the coordinate-exchange algorithm produces a new, seemingly random, order of the selected design points. In this short communication, we study the order of the design points produced by the algorithm and conclude that certain orders appear much more often than others. As a result, an explicit randomization step of the design points is required before conducting an experiment using a design produced by a coordinate-exchange algorithm.