In many choice modeling applications, people demand is frequently characterized as multiple discrete, which means that people choose multiple items simultaneously. The analysis and prediction of people behavior in multiple discrete choice situations pose several challenges. In this paper, to address this, we propose a random utility maximization (RUM) based model that considers each subset of choice alternatives as a composite alternative, where individuals choose a subset according to the RUM framework. While this approach offers a natural and intuitive modeling approach for multiple-choice analysis, the large number of subsets of choices in the formulation makes its estimation and application intractable. To overcome this challenge, we introduce directed acyclic graph (DAG) based representations of choices where each node of the DAG is associated with an elemental alternative and additional information such that the number of selected elemental alternatives. Our innovation is to show that the multi-choice model is equivalent to a recursive route choice model on the DAG, leading to the development of new efficient estimation algorithms based on dynamic programming. In addition, the DAG representations enable us to bring some advanced route choice models to capture the correlation between subset choice alternatives. Numerical experiments based on synthetic and real datasets show many advantages of our modeling approach and the proposed estimation algorithms.

翻译：在许多选择建模应用中，人们的需求常被描述为多重离散特征，即个体同时选择多个备选项。多重离散情境下个体行为的分析与预测面临诸多挑战。为解决此问题，本文提出基于随机效用最大化（RUM）的模型，将每个备选项子集视为复合选项，个体依据RUM框架选择子集。尽管该方法为多重选择分析提供了直观自然的建模途径，但公式中庞大的子集数量导致其估计与应用难以实现。为克服这一难题，我们引入基于有向无环图（DAG）的选择表示方法，其中DAG的每个节点关联一个基本备选项及选定基本备选项数量等附加信息。我们的创新在于证明多重选择模型等价于DAG上的递归路径选择模型，从而开发出基于动态规划的高效新估计算法。此外，DAG表示使我们能够引入先进的路径选择模型来捕捉子集选项间的相关性。基于合成与真实数据集的数值实验表明，本文提出的建模方法及估计算法具有显著优势。