GTG-ACO: Graph Transformer Guided Ant Colony Optimization for learning heuristics and pheromone dynamics for combinatorial optimization

Abstract

Combinatorial optimization (CO) problems are fundamental to numerous real-world applications, ranging from logistics and scheduling to resource allocation. For solving CO problems, Ant Colony Optimization (ACO) is a widely used metaheuristic that simulates cooperative foraging behavior to iteratively construct high-quality solutions. However, traditional ACO suffers from handcrafted heuristic functions that fail to generalize across different instances and uniform pheromone initialization, which results in inefficient exploration and slow convergence.

To address these limitations, we introduce Graph Transformer Guided Ant Colony Optimization- GTG-ACO, a novel approach that jointly learns both heuristic and initial pheromone matrices, enabling the model to generalize across diverse problem instances without manual tuning. Additionally, GTG-ACO employs Graph Transformer augmented with Squeeze-and-Excitation (SE) network as the backbone for heuristic and pheromone learner. The Graph Transformers enable adaptive representation learning by leveraging attention mechanisms to dynamically capture structural relationships in graph representation of combinatorial optimization problems. Additionally, SE networks enhance the model by recalibrating feature importance, ensuring that critical information is amplified while suppressing less relevant features. Extensive evaluations on four combinatorial optimization problems—Traveling Salesman Problem (TSP), Capacitated Vehicle Routing Problem (CVRP), Single Machine Total Weighted Tardiness Problem (SMTWTP) and Bin Packing Problem (BPP)—demonstrate that GTG-ACO consistently outperforms state-of-the-art baselines achieving improvements ranging from 1% to 56%. Furthermore, we validate its real-world applicability by evaluating it on benchmark datasets TSPLIB and CVRPLIB. Thus, GTG-ACO establishes itself as a powerful and generalizable framework by jointly learning heuristic and pheromone matrices, enabling more informed exploration, which leads to superior solution quality in combinatorial optimization problems. Our code is publicly available at https://github.com/abrarrahmanabir/GTG-ACO.