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

Researchers have developed WeCon, a weight-conditioned neural solver that achieves comparable solution quality to state-of-the-art methods while reducing inference time by 40% across multiple multi-objective combinatorial optimization problems. The solver introduces Gated Residual Fusion blocks for weight-instance interaction and Efficient Preference Optimization to generate more informative training pairs. The approach addresses key limitations in existing neural solvers, including weight-signal dilution and ineffective training from random sampling.

arXiv:2605.22876v1 Announce Type: new Abstract: Existing neural solvers for Multi-Objective Combinatorial Optimization Problems MOCOPs commonly adopt decomposition-based strategies that scalarize an 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, 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 GRF 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 RF block in the decoder to alleviate weight-signal dilution. Finally, we propose Efficient Preference Optimization EPO , which constructs high-quality solutions, thereby generating more informative pairs to improve training effectiveness. Experiments on four MOCOP variants across different problem scales and distribution patterns demonstrate that WeCon achieves HyperVolume HV values comparable to SOTA solver POCCO-W, while reducing inference time by 40%. Ablation studies validate the contributions of all designs.