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. Theoretical results are established to show the expressive power of the proposed GCN, and explain the underlying mechanism of the size generalization ability. 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：组合优化旨在从可替代产品集合中选取受限子集以最大化期望收益。该问题因兼具组合与非线性特性而属于NP-hard问题，在电商等领域尤为常见——平台每分钟需求解数千个此类优化问题。本文提出基于图卷积网络（GCN）的框架高效求解约束组合优化问题。该方法首先构建问题的图表示，训练GCN学习从问题参数到最优组合的映射关系，并基于GCN输出开发三种推理策略。利用GCN跨实例规模泛化的能力，从样本中习得的模式可迁移至大规模问题。理论分析证明了所提GCN的表达能力，并阐释了规模泛化能力的内在机制。数值实验表明，在包含20个产品的实例上训练的GCN，可在数秒内对多达2000个产品的问题实现超过85%的最优收益，在准确率与效率上均优于现有启发式方法。我们进一步将框架扩展至基于交易数据的未知选择模型场景，验证了其相似的性能与可扩展性。