在搜索混料模型$D$-最优设计的计算机算法领域, 主流算法包 括经典的Fedorov算法, 以及元启发类算法, 但两者在一些特定的优化问 题上, 分别在收敛速度和收敛精度方面有进一步提升的空间. 文章分别探讨了可能造成这种情况的两类算法各自的局限性, 并采取优势互补的策略, 构建了交换点式门限接受算法, 即ETA (exchange threshold accepting)算法. 以含倒数项混料模型为例, 文章验证了ETA算法生成设计的$D$-最优性, 并分别与Fedorov算法和元启发类的ProjPSO算法作比较. 结果表明, 至少在某些特殊的混料模型$D$-最优设计的搜索方面, ETA算法在收敛速度和精度方面均具有一定的优势.

In this paper, we discuss disadvantages of the classical algorithms which may affect the convergence speed and accuracy in finding $D$-optimal designs of certain mixture models, taking the Fedorov algorithm and the threshold accepting type algorithm for optimal designs of mixture models, which we construct in this paper for multiple purposes, as examples. Based on these discussions, the ETA (exchange threshold accepting) algorithm is given, which overcomes those shortcomings to some extend, by using meta-heuristic type sub-algorithms to improve the convergence speed, and by insisting on the idea of Fedorov algorithm to retain the convergence accuracy simultaneously. Detailed evaluation and comparison with the Fedorov algorithm and the ProjPSO algorithm based on mixture models with inverse terms are also given.