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

Background

The article discusses the challenges faced by existing neural solvers for MOCOPs, which often rely on decomposition-based strategies that either inject weights only during decoding or primarily during encoding. These methods suffer from limitations such as limited weight-conditioned context modeling and signal dilution during decoding. Additionally, preference optimization methods use random sampling to construct solution pairs, leading to less informative training data.

Key Points

WeCon addresses these issues through several innovative design elements:

• Encoder Design: A custom encoder layer with three attention blocks and a Gated Residual Fusion (GRF) block that facilitates interaction between instance features and weights. This mechanism generates more informative weight-conditioned context.

  • The GRF block helps in harmonious interaction, ensuring that the model effectively captures the relationship between instance features and weights.

• Decoder Design: An Introduction of a plug-and-play Residual Fusion (RF) block in the decoder to alleviate weight-signal dilution during decoding. This ensures that the signal from weights is not lost or diluted as it passes through the network.

  • The RF block helps in maintaining the integrity of the weight signals, ensuring they are preserved and utilized effectively throughout the decoding process.

• Efficient Preference Optimization (EPO): A method for generating high-quality solutions to construct more informative solution pairs for training. This approach significantly improves the quality of training data, leading to better model performance.

  • EPO constructs high-quality solutions that provide more useful information during the training phase, enhancing overall model effectiveness.

Significance

WeCon’s contributions are significant because they address key limitations in existing MOCOP solvers:

• Improved Context Modeling: By integrating weights more effectively throughout the network, WeCon enhances context modeling and leads to better decision-making.
• Reduced Inference Time: The approach demonstrates a 40% reduction in inference time while maintaining or even surpassing the performance of state-of-the-art methods like POCCO-W.
• Better Training Effectiveness: Through EPO, WeCon generates more informative solution pairs for training, leading to higher training effectiveness and better generalization.

Key Insights:

• The GRF block is crucial as it ensures that weights are effectively integrated into the model, providing a richer context during both encoding and decoding.
• The RF block in the decoder prevents signal dilution, ensuring that important weight information is preserved throughout the network’s operations.
• Efficient Preference Optimization (EPO) significantly improves training data quality, leading to better model performance.

Overall, WeCon represents a substantial advancement in neural solvers for MOCOPs by addressing critical limitations and demonstrating superior performance through empirical validation on multiple problem instances.