LM-GRASP: Instance-Specific Language Models for Combinatorial Construction via Online Imitation Learning

2026-07-30

AI Summary

This work addresses the limitations of traditional neural construction methods, which rely on costly offline pretraining and exhibit limited generalization. The authors propose an online learning framework that eliminates the need for pretraining by reformulating the random construction phase of GRASP as an instance-adaptive imitation learning task. For each problem instance, high-quality solutions generated via local search serve as expert demonstrations to train a decoder-only Transformer policy from scratch, discarding static heuristics and handcrafted features. The approach integrates behavioral cloning, dynamic elite trajectory archiving, and an iterative optimization loop to achieve fully data-driven constructive solving. Evaluated on the Taillard PFSP benchmark (ta51–ta60), the method yields an average makespan improvement of 28.4 units over GPU-GRASP, a gain comparable to that achieved through GPU acceleration.

Abstract

Machine learning for combinatorial optimization typically relies on neural constructors trained via reinforcement learning on large offline datasets for a fixed problem class-incurring high pretraining costs and generalizing poorly outside the training distribution. We propose an alternative: a metaheuristic framework that reformulates the randomized constructive phase of GRASP as an online imitation learning task, trained from scratch on each problem instance. A local search procedure acts as an expert oracle, while a decoder-only Transformer serves as the constructive policy. Unlike classical GRASP, which relies on static, myopic heuristic rules based on localized scalar costs, our approach is fully data-driven: the construction policy emerges from high-quality solutions discovered during the search itself, with no problem-specific feature engineering required. We instantiate this as LM-GRASP, a hybrid metaheuristic following an iterative learn-infer-improve cycle, training the policy online via behavioral cloning on a dynamic archive of elite trajectories-no external data or offline pretraining needed. The pipeline interfaces with the domain solely through the objective evaluator used by local search. Evaluated on the Taillard PFSP benchmark (ta51-ta60), the most discriminating block due to half its optima being unknown, LM-GRASP outperforms GPU-GRASP by 28.4 makespan units on average-comparable to the gain from GPU acceleration over sequential execution (27.2 units), though with overlapping standard deviations. This suggests instance-specific, online-trained language models are a promising, practical alternative to hand-engineered constructors, especially for landscapes resistant to classical greedy construction.

Problem

• combinatorial optimization
• offline pretraining
• generalization
• neural constructors
• high pretraining costs

Innovation

• online imitation learning
• instance-specific language models
• combinatorial optimization
• GRASP metaheuristic
• decoder-only Transformer