arXiv:2509.22557cs.LGmath.OC2025-09

用图神经网络高效筛选商品组合,大幅提升打包定价利润。

Self-Improving Neural-Guided Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing

  • 构建产品图结构,用GNN预测组合入选概率,压缩候选组合空间
  • 在100种商品下,利润比传统方法高13%-21%,耗时仅为2%
  • 支持大规模应用,适合电商、游戏等需动态定价的场景

混合打包定价是电商业、旅游和游戏等行业中的经典收益管理问题,旨在设计商品组合及定价以最大化预期利润。精确的混合打包模型虽能捕捉此结构,但候选组合数量随商品数呈指数增长,导致计算不可行。本文提出一种基于图神经网络(GNN)的剪枝-优化框架,将每实例表示为紧凑的段-产品图,预测段-产品包含概率,从而将指数级的组合空间压缩为小规模候选集;最终在保留的组合上求解混合打包优化问题,必要时通过GNN引导的局部搜索进一步优化。由于仅在小规模实例有精确标签,我们引入迭代自提升机制:当前GNN策略在大规模实例生成高质量解,作为更大规模训练的近似最优标签。理论上,在温和条件下,所提边输出型GNN可充分表达最优产品分配映射。数值实验表明,最快策略在含100个商品的实例上,利润比包尺寸定价高13%-21%,运行时间仅为后者的约2%。

原文摘要 · Abstract (English)

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed bundling models capture this structure but become computationally intractable because the number of candidate bundles grows exponentially with the number of products. We develop a graph neural network (GNN)-guided pruning-then-optimization framework for bundle pricing with (non-)additive valuations. The method represents each instance as a compact segment-product graph, predicts segment-product inclusion probabilities, and accordingly prunes the exponential bundle space into a small candidate family; the final prices and bundle offerings are obtained by solving the mixed bundling formulation over the retained bundles, possibly refined by a GNN-guided local search. Because exact labels are available only at small scales, we further propose an iterative self-improvement procedure: the current GNN policies generate high-quality solutions on large-scale instances, which serve as near-optimal labels for training a stronger model at larger scales. Theoretically, we show that under mild conditions the proposed edge-output GNN class is expressive enough to represent the optimal product-assignment mapping, justifying the edge-level learning target. Numerical experiments show that the fastest proposed policy delivers 13-21% higher profit than bundle-size pricing on instances with up to 100 products at about 2% of its runtime.

打包定价图神经网络收益管理

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