论文标题
用于搜索D-和A-最佳设计的差分演化变体
Differential evolution variants for Searching D- and A-optimal designs
论文作者
论文摘要
最佳实验设计是统计的重要子场，可最大程度地提高实验成功的机会。在最佳设计领域，D-和A-Aftimal设计是一个非常具有挑战性的问题，即最大程度地减少了逆Fisher信息矩阵的决定因素和痕迹。由于灵活性和易于实施，因此，传统的进化算法（EAS）用于处理一小部分实验优化设计问题，而无需数学推导和假设。但是，当前的EAS仍然是确定支持点数，处理不可行的重量解决方案以及实验不足的问题。为了解决上述问题，本文研究了用于在几种不同统计模型上查找D-和A-最佳设计的差异进化（DE）变体。提出了维修操作，以根据欧几里得距离将相似的支撑点与相应的权重相结合，并以较小的权重删除支撑点，从而自动确定支持点。此外，维修操作还将不可行的重量溶液固定到可行的重量解决方案中。为了丰富我们的最佳设计实验，我们利用所提出的DE变体来测试12个统计模型的D-和A-最佳设计问题。与其他竞争对手算法相比，模拟实验表明，Lshade可以在D-和A-最佳设计问题上实现更好的性能。
Optimal experimental design is an essential subfield of statistics that maximizes the chances of experimental success. The D- and A-optimal design is a very challenging problem in the field of optimal design, namely minimizing the determinant and trace of the inverse Fisher information matrix. Due to the flexibility and ease of implementation, traditional evolutionary algorithms (EAs) are applied to deal with a small part of experimental optimization design problems without mathematical derivation and assumption. However, the current EAs remain the issues of determining the support point number, handling the infeasible weight solution, and the insufficient experiment. To address the above issues, this paper investigates differential evolution (DE) variants for finding D- and A-optimal designs on several different statistical models. The repair operation is proposed to automatically determine the support point by combining similar support points with their corresponding weights based on Euclidean distance and deleting the support point with less weight. Furthermore, the repair operation fixes the infeasible weight solution into the feasible weight solution. To enrich our optimal design experiments, we utilize the proposed DE variants to test the D- and A-optimal design problems on 12 statistical models. Compared with other competitor algorithms, simulation experiments show that LSHADE can achieve better performance on the D- and A-optimal design problems.
