WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems
Existing neural solvers for multi-objective combinatorial optimization problems (MOCOPs) suffer from limited weight-conditioned context modeling and inefficient training due to random sampling in preference optimization. WeCon introduces Gated Residual Fusion (GRF) in the encoder and Residual Fusion (RF) in the decoder to enhance weight-instance interaction, along with Efficient Preference Optimization (EPO) for higher-quality training pairs. Experiments show WeCon achieves comparable HyperVolume (HV) to state-of-the-art POCCO-W while reducing inference time by 40%.
Article intelligence
Key points
- WeCon uses Gated Residual Fusion (GRF) and Residual Fusion (RF) to improve weight-conditioned context modeling.
- The proposed Efficient Preference Optimization (EPO) constructs high-quality solution pairs for better training.
- WeCon achieves comparable HV to SOTA with 40% inference time reduction.
Why it matters
This matters because weCon uses Gated Residual Fusion (GRF) and Residual Fusion (RF) to improve weight-conditioned context modeling.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.22876] WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems
[Submitted on 20 May 2026]
Title:WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems
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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.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2605.22876 [cs.LG]
(or arXiv:2605.22876v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.22876
arXiv-issued DOI via DataCite
Submission history
From: Xuan Wu [view email] [v1] Wed, 20 May 2026 05:09:22 UTC (855 KB)
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