Assortment optimization seeks to select a subset of substitutable products, subject to constraints, to maximize expected revenue. The problem is NP-hard due to its combinatorial and nonlinear nature and arises frequently in industries such as e-commerce, where platforms must solve thousands of such problems each minute. We propose a graph convolutional network (GCN) framework to efficiently solve constrained assortment optimization problems. Our approach constructs a graph representation of the problem, trains a GCN to learn the mapping from problem parameters to optimal assortments, and develops three inference policies based on the GCN's output. Owing to the GCN's ability to generalize across instance sizes, patterns learned from small-scale samples can be transferred to large-scale problems. Numerical experiments show that a GCN trained on instances with 20 products achieves over 85% of the optimal revenue on problems with up to 2,000 products within seconds, outperforming existing heuristics in both accuracy and efficiency. We further extend the framework to settings with an unknown choice model using transaction data and demonstrate similar performance and scalability.

翻译：商品组合优化旨在从可替代产品集合中，在满足约束条件的前提下，选择一个子集以最大化期望收益。由于其组合性与非线性特征，该问题属于NP难问题，常见于电子商务等行业，平台每分钟需处理数千个此类问题。本文提出一种图卷积网络（GCN）框架，用于高效求解带约束的商品组合优化问题。该方法构建问题的图表示，训练GCN学习从问题参数到最优商品组合的映射，并基于GCN输出开发三种推理策略。得益于GCN在不同规模实例间的泛化能力，从小规模样本习得的模式可迁移至大规模问题。数值实验表明，在20种商品实例上训练的GCN，可在数秒内处理高达2000种商品的问题，获得超过最优收益85%的结果，在准确性与效率上均优于现有启发式算法。我们进一步将该框架扩展至选择模型未知的场景（利用交易数据），并验证了其相似的性能与可扩展性。