Adaptive gradient descent enabled ant colony optimization for routing problems

The design of Ant Colony Optimization (ACO) has been inspired by the foraging behavior of ant colonies. ACO is one of the most widely used metaheuristic algorithms applicable to various optimization problems. Nevertheless, the deficiency of ACO is early maturity and slow convergence, usually leading to dissatisfactory performance. In this research, a new type of ACO is proposed with innovative adaptive learning mechanism is devised (the algorithm is called ADACO). In the paper, first, the ACO algorithm for Traveling Salesman Problem (TSP) is modeled in the framework of reinforcement learning (RL) and learns a best policy by stochastic gradient descent (SGD). Then, an adaptive gradient descent strategy, which can exploit the update history of per-dimensional pheromones to achieve intelligent convergence, is integrated into the ACO algorithm as ADACO. A parallel computation process is implemented in the process to expedite computational efficiency. Finally, through case studies in TSP and Capacitated Vehicle Routing Problem (CVRP), ADACO is validated. ADACO is trialed on various sizes of TSP and CVRP instances and compared with other state-of-the-art algorithms. Results show that ADACO is competitive in terms of accuracy (better in most cases), stability (statistically significant) and adaptability (support various types of problems). The results also elucidate that the algorithm maintains good computational efficiency owing to its parallel implementation. It can be concluded that ADACO is effectively applicable to routing problems with good performance.