Algorithms for optimizing model-based incomplete block designs

2026-08-27

AI Summary

本文针对实验设计中因时间或参与负担导致的处理规模过大问题，提出一种基于模型的方法来优化参数，并通过局部搜索启发式算法解决计算难题。

Abstract

Because of time limitations or participation burden, the treatments in an experimental design can be too large for a single subject. Instead of addressing this using combinatorial incomplete block designs, we propose a model-based approach that optimizes model parameters. This offers distinct advantages: it incorporates subject-specific covariates to tailor treatment allocation to individual characteristics, allows for varying block sizes, and eliminates the equal-treatment replication requirement. Despite these benefits, model-based approaches are limited by a lack of software and prohibitively large search spaces, making exact optimization computationally intractable. Therefore, we present local search heuristic algorithms and compare them to existing methods. We evaluate first- and best-improvement algorithms, simulated annealing (SA), threshold accepting (TA), and two novel algorithms utilizing directional derivatives (dd) to guide exchanges. Serving as discrete versions of continuous gradient-based methods, these dd algorithms take smaller steps and avoid flat regions by prioritizing large-difference dd exchanges. Our broadly applicable approach uses item calibration in achievement tests as a comparative example to evaluate objective values and computational times. Results demonstrate that for larger problems, the dd algorithms achieve near-optimal solutions significantly faster than SA and TA. Due to computational efficiency, our algorithms offer a highly appealing approach for practical applications.

Problem

• model-based approach
• incomplete block designs
• subject-specific covariates
• varying block sizes
• equal-treatment replication

Innovation

• model-based approach
• directional derivatives (dd) algorithms
• local search heuristics
• incomplete block designs
• computational efficiency