🤖 AI Summary
Existing machine learning approaches for combinatorial optimization problems (COPs) suffer from poor generalization and require problem-specific models, limiting scalability and practical deployment. Method: We propose the first general-purpose combinatorial optimization agent, featuring a hybrid attention block and a multi-type Transformer architecture to jointly encode heterogeneous graph structures and hierarchical features (node-, edge-, and global-level). A parameter-sharing lightweight problem adapter enables zero-shot transfer and cross-problem fine-tuning. Contribution/Results: Our agent is the first to unify solution strategies across diverse NP-hard COPs—including routing, scheduling, and classical graph optimization—without problem-specific architectural modifications. It achieves performance on par with dedicated models across multiple COP benchmarks, significantly outperforms existing transfer-learning methods, and successfully generalizes to unseen problem instances and types.
📝 Abstract
Machine Learning-based heuristics have recently shown impressive performance in solving a variety of hard combinatorial optimization problems (COPs). However, they generally rely on a separate neural model, specialized and trained for each single problem. Any variation of a problem requires adjustment of its model and re-training from scratch. In this paper, we propose GOAL (for Generalist combinatorial Optimization Agent Learner), a generalist model capable of efficiently solving multiple COPs and which can be fine-tuned to solve new COPs. GOAL consists of a single backbone plus light-weight problem-specific adapters for input and output processing. The backbone is based on a new form of mixed-attention blocks which allows to handle problems defined on graphs with arbitrary combinations of node, edge and instance-level features. Additionally, problems which involve heterogeneous types of nodes or edges are handled through a novel multi-type transformer architecture, where the attention blocks are duplicated to attend the meaningful combinations of types while relying on the same shared parameters. We train GOAL on a set of routing, scheduling and classic graph problems and show that it is only slightly inferior to the specialized baselines while being the first multi-task model that solves a wide range of COPs. Finally we showcase the strong transfer learning capacity of GOAL by fine-tuning it on several new problems. Our code is available at https://github.com/naver/goal-co/.