基于模型的不完全区组设计优化算法
Algorithms for optimizing model-based incomplete block designs
AI总结：
针对实验设计中处理因素过多的问题，提出基于模型的局部搜索启发式算法，其中含两种方向导数引导的新型算法，经项目校准示例验证，其在大规模问题上比模拟退火等方法更快得到近优解，具实用价值。
AI中文摘要：
由于时间限制或参与负担，实验设计中的处理因素可能过多，单个受试者无法全部参与。我们没有采用组合不完全区组设计来解决这个问题，而是提出了一种基于模型的方法，用于优化模型参数。该方法具有明显优势：它能纳入受试者特异性协变量，根据个体特征定制处理分配；允许区组大小变化；且消除了等处理重复的要求。尽管有这些优势，基于模型的方法受限于缺乏软件和过大的搜索空间，使得精确优化在计算上难以实现。因此，我们提出了局部搜索启发式算法，并将其与现有方法进行比较。我们评估了一阶改进算法、最优改进算法、模拟退火（SA）、阈值接受（TA），以及两种利用方向导数（dd）指导交换的新型算法。作为连续梯度方法的离散版本，这些dd算法步长更小，通过优先选择大差值的dd交换来避免平坦区域。我们以成就测验中的项目校准作为比较示例，评估目标值和计算时间。结果表明，对于较大规模的问题，dd算法比SA和TA能显著更快地达到接近最优的解。由于计算效率高，我们的算法为实际应用提供了极具吸引力的方法。
英文摘要：
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.
