Discrete choice experiments (DCEs) investigate the attributes that influence individuals' choices when selecting among various options. To enhance the quality of the estimated choice models, researchers opt for Bayesian optimal designs that utilize existing information about the attributes' preferences. Given the nonlinear nature of choice models, the construction of an appropriate design requires efficient algorithms. Among these, the coordinate-exchange (CE) algorithm is commonly employed for constructing designs based on the MNL model. However, as a hill-climbing method, the CE algorithm tends to quickly converge to local optima, potentially limiting the quality of the resulting designs. We propose the use of a simulated annealing (SA) algorithm to construct Bayesian optimal designs. This algorithm accepts both superior and inferior solutions, avoiding premature convergence and allowing a more thorough exploration of potential solutions. Consequently, it ultimately obtains higher-quality choice designs compared to the CE algorithm. Our work represents the first application of an SA algorithm in constructing Bayesian optimal designs for DCEs. Through extensive computational experiments, we demonstrate that the SA designs generally outperform the CE designs in terms of statistical efficiency, especially when the prior preference information is highly uncertain.

翻译：离散选择实验（DCEs）旨在探究个体在不同选项间进行选择时影响其决策的属性特征。为提高选择模型的估计质量，研究者倾向于采用贝叶斯最优设计，此类设计能够利用关于属性偏好的先验信息。鉴于选择模型固有的非线性特性，构建合适的设计方案需要高效的算法支持。其中，坐标交换（CE）算法常被用于基于MNL模型的设计构建。然而，作为爬山法的一种，CE算法容易快速收敛至局部最优解，这可能限制最终设计方案的质量。本文提出采用模拟退火（SA）算法构建贝叶斯最优设计。该算法能够同时接受更优解与次优解，避免早熟收敛现象，从而实现对解空间更充分的探索。因此，相较于CE算法，SA算法最终能获得更高质量的选择设计方案。本研究首次将SA算法应用于DCEs的贝叶斯最优设计构建。通过大量计算实验证明，SA设计在统计效率方面普遍优于CE设计，尤其在先验偏好信息具有高度不确定性时表现更为突出。