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

2026-03-22

AI Summary

Coordinate-exchange algorithms are widely employed to generate optimal experimental designs; however, the ordering of design points in their output exhibits an overlooked systematic bias, leading to significantly elevated frequencies of certain permutations and potentially compromising the statistical validity of experiments. This study is the first to uncover this non-randomness through order-statistic analysis, integrating principles from experimental design theory with algorithmic behavior research to demonstrate that the outputs of coordinate-exchange algorithms are not truly random. The findings underscore the necessity of introducing an explicit randomization step following the application of such algorithms and provide both theoretical justification and practical recommendations for enhancing the reliability of experimental designs.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• coordinate-exchange algorithm
• optimal experimental design
• design point order
• randomization

Innovation

• coordinate-exchange algorithm
• optimal experimental design
• design point ordering
• randomization