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

2026-05-20

AI Summary

Existing neural solvers struggle to effectively model weight information and suffer from inefficient preference optimization in multi-objective combinatorial optimization problems. This work proposes WeCon, a novel neural solver that enhances the interaction between weights and instance features through a triple-attention block and a Gated Residual Fusion (GRF) module in the encoder. To mitigate weight signal dilution, the decoder incorporates a Residual Fusion (RF) module. Furthermore, WeCon employs an Efficient Preference Optimization (EPO) strategy to generate highly informative training pairs. Evaluated on four multi-objective combinatorial optimization tasks, WeCon achieves hypervolume performance comparable to the state-of-the-art method POCCO-W while reducing inference time by 40%.

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.

Problem

• Multi-Objective Combinatorial Optimization
• Weight Conditioning
• Preference Optimization
• Neural Solver
• Solution Pair Sampling

Innovation

• Weight-Conditioned Neural Solver
• Gated Residual Fusion
• Residual Fusion Block
• Efficient Preference Optimization
• Multi-Objective Combinatorial Optimization