论文标题
通过粒子群优化快速计算高度G-最佳的精确设计
Fast Computation of Highly G-optimal Exact Designs via Particle Swarm Optimization
论文作者
论文摘要
计算响应表面模型的精确$ g $ - 最佳设计是一个困难的计算，在过去的两个十年中，通过算法开发获得了增量的改进。这些最佳设计尚未在应用中被广泛考虑，部分原因是计算它们的困难和成本。 Three primary algorithms for constructing exact $G$-optimal designs are presented in the literature: the coordinate exchange (CEXCH), a genetic algorithm (GA), and the relatively new $G$-optimal via $I_λ$-optimality algorithm ($G(I_λ)$-CEXCH) which was developed in part to address large computational cost.粒子群优化（PSO）已在许多应用中实现了广泛的使用，但是迄今为止，尽管其广泛的成功，但在最佳设计问题中的应用相对较少。在本文中，我们开发了PSO的扩展，以使其适应最佳设计问题。然后，我们采用PSO来生成最佳设计，以涵盖$ k = 1、2、3、4、5 $设计因子，这是工业实验中常见的实验尺寸。我们将这些结果与过去二十年文献中发表的所有$ G $ - 最佳设计进行了比较。由GA以$ k = 1、2、3 $因素生成的$ G $ - 最佳设计未经挑战14年。我们证明，PSO发现了这些方案的$ G $ - 最佳设计，并且它以可比的计算成本与最先进的算法$ G（I_λ）$ -CEXCH进行了可比的计算成本。此外，我们表明PSO能够以$ k = 4，5 $的因素产生相等或更好的$ g $最佳设计。这些结果表明，PSO优于现有方法，可以有效地生成高度$ G $最佳的设计。
Computing proposed exact $G$-optimal designs for response surface models is a difficult computation that has received incremental improvements via algorithm development in the last two-decades. These optimal designs have not been considered widely in applications in part due to the difficulty and cost involved with computing them. Three primary algorithms for constructing exact $G$-optimal designs are presented in the literature: the coordinate exchange (CEXCH), a genetic algorithm (GA), and the relatively new $G$-optimal via $I_λ$-optimality algorithm ($G(I_λ)$-CEXCH) which was developed in part to address large computational cost. Particle swarm optimization (PSO) has achieved widespread use in many applications, but to date, its broad-scale success notwithstanding, has seen relatively few applications in optimal design problems. In this paper we develop an extension of PSO to adapt it to the optimal design problem. We then employ PSO to generate optimal designs for several scenarios covering $K = 1, 2, 3, 4, 5$ design factors, which are common experimental sizes in industrial experiments. We compare these results to all $G$-optimal designs published in last two decades of literature. Published $G$-optimal designs generated by GA for $K=1, 2, 3$ factors have stood unchallenged for 14 years. We demonstrate that PSO has found improved $G$-optimal designs for these scenarios, and it does this with comparable computational cost to the state-of-the-art algorithm $G(I_λ)$-CEXCH. Further, we show that PSO is able to produce equal or better $G$-optimal designs for $K= 4, 5$ factors than those currently known. These results suggest that PSO is superior to existing approaches for efficiently generating highly $G$-optimal designs.
