提出高效权重条件神经求解器WeCon,提升多目标组合优化求解速度与效果。
WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems

- 通过三注意力块和门控残差融合,实现实例特征与权重的深度融合。
- 在四种问题变体上达到SOTA的超体积性能,推理时间减少40%。
- 适合需要快速求解多目标组合优化的工业场景应用。
现有神经求解器常采用分解策略,将多目标组合优化问题(MOCOPs)转化为多个与不同权重向量相关的子问题。然而,它们要么仅在解码阶段注入一次权重,限制了权重条件上下文建模;要么主要在编码阶段注入,导致解码阶段权重信号衰减。此外,其偏好优化方法依赖纯随机采样构建解对,往往生成信息量不足的解对,训练效率低。为此,我们提出高效权重条件神经求解器WeCon。设计包含三个注意力模块及门控残差融合块的编码器层,促进实例特征与权重的和谐交互,生成富含信息的权重条件上下文。在解码器中引入可插拔残差融合块,缓解权重信号衰减。最后提出高效偏好优化,生成高质量解对,提升训练有效性。在四个不同规模与分布模式的MOCOP变体上的实验表明,WeCon在超体积(HV)性能上接近当前最优(POCCO-W),但推理时间减少约40%。其中,采用增强解码器的WeCon-CCO版本在整体HV表现最佳,虽推理时间略增。消融实验验证了各项设计的有效性。
原文摘要 · Abstract (English)
Existing neural solvers for Multi-Objective Combinatorial Optimization Problems (MOCOPs) commonly adopt decomposition-based strategies that scalarize a MOCOP into multiple subproblems associated with distinct weight vectors. However, they either inject weights only once during decoding, limiting weight-conditioned context modeling, or primarily during encoding, causing weight-signal dilution during decoding. Moreover, their preference optimization methods rely on purely random sampling to construct solution pairs for training solvers, which often produces less informative pairs and thus leads to low training effectiveness. To better address these limitations, we propose an efficient Weight-Conditioned neural solver (WeCon). Specifically, we design an encoder layer with three attention blocks and our proposed Gated Residual Fusion block to facilitate harmonious interaction between instance features and weights, thereby generating informative weight-conditioned context. We further introduce a plug-and-play Residual Fusion block in the decoder to alleviate weight-signal dilution. Finally, we propose Efficient Preference Optimization, which constructs high-quality solutions, thereby generating more informative pairs to improve training effectiveness. Experimental results on four MOCOP variants across different problem scales and distribution patterns demonstrate that WeCon achieves HyperVolume (HV) performance comparable to the state-of-the-art (SOTA) solver POCCO-W, while requiring approximately 40% less inference time. Moreover, the variant WeCon-CCO, which adopts an enhanced decoder, achieves the best overall HV performance with increased inference time. Ablation studies validate the contributions of all proposed designs.
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