GOAL: A Generalist Combinatorial Optimization Agent Learner

TL;DR

GOAL tackles the fragmentation of combinatorial optimization by introducing a single backbone with lightweight task adapters capable of solving diverse COPs via mixed-attention and a multi-type transformer. It frames COP as tail-recursive constructive MDPs and trains on eight problems through imitation, while enabling efficient fine-tuning to new tasks in supervised or unsupervised modes. The results show competitive performance with specialized baselines on training tasks, strong zero-shot generalization to larger instances, and meaningful gains from ablation studies, including codebook sparsification for robust fine-tuning. This work points toward a foundation-model-like direction for COP, enabling rapid adaptation to new problems with reduced data and computation, and highlighting interesting avenues for scalable attention and larger-scale COPs.

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/.

Figures (19)

• Figure 1: GOAL - a single neural model to solve a variety of routing, scheduling, packing and graph problems.
• Figure 2: Left: Architecture of GOAL for single-type problems; the green components are task-specific, while the others belong to the backbone. The codebook is a shared $\ell{\times}D$ (resp. $\bar{\ell}{\times}\bar{D}$) matrix (with $\ell{\ll}D,\bar{\ell}{\ll}\bar{D}$) applied to the node (resp. edge) representations produced by the input adapters. Right: Architecture of GOAL for multi-type problems (with here 2 node types T1,T2); it uses multiple mixed attention blocks ("MMA"), some in self- and some in cross-attention mode, but they all share the same parameters (per layer); so do the two Feed Forward blocks ("FF"). For the edges, all the type combinations are shown (here T11,T12,T21,T22) but those which have no meaning in a task are simply omitted. The same set of parameters is used for the two architectures.
• Figure 3: Unsupervised fine-tuning of GOAL to eight diverse new tasks. We report the best results over 10 runs both for training from scratch and fine-tuning.
• Figure 4: (left) Performance with different variants of mixed-attention. (middle) Performance of single- vs multi-type GOAL. (right) Fine-tuning of GOAL with and without the codebook.
• Figure 5: Comparison of the (supervised) fine-tuning of the single- versus multi-task GOAL on four new problems.