Title: One Direction to Rule Them All: Toward Generalizable Solving Strategies Across Combinatorial Optimization Problems
Primary area: optimization
Keywords: Neural Combinatorial Optimization, Generalization

Abstract: Many combinatorial optimization problems (COPs) share latent structure despite differing in surface form, allowing classical heuristics to transfer with minimal adaptation. In contrast, most learning-based solvers are trained in isolation and fail to leverage cross-problem commonalities. This paper explores the possibility of learning generalized solving strategies that capture shared structures across different COPs, enabling easier adaptation to new tasks. We leverage a header-encoder-decoder architecture in which light problem-specific headers and decoders handle inputs and outputs, while a shared, heavy encoder is trained to capture problem-agnostic solving strategies. The key is to align the encoder’s optimization behavior across tasks by enforcing gradient consistency, making updates induced by different COP objectives point in similar directions with comparable magnitudes. We realize this via task-specific feature rotation matrices and loss weights that steer the encoder’s gradients, learned alongside the solver in a bi-level procedure: an inner loop optimizes each task with reinforcement learning on its true objective, and an outer loop tunes rotations and weights through a gradient consistency loss. Experiments on six COPs show that it enhances the model's ability to generalize COPs. The learned encoder on several problems can directly perform comparably on new problems to models trained from scratch, suggesting its potential to support developing the foundational model for combinatorial optimization.