WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems

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.