Enhancing Ant Colony Optimization by Adaptive Gradient Descent

Ant Colony Optimization (ACO) is one of the widely used metaheuristic algorithms applicable to various optimization problems. The ACO design has been inspired by the foraging behavior of ant colonies. The performance of the algorithm, however, is not satisfactory since the update stage of pheromones in the algorithm is static and less intelligent, leading to early maturity and slow convergence. To improve the algorithm, in this research, a new ACO algorithm with an innovative adaptive gradient descent strategy (ADACO) is designed, and the algorithm is applied to the Travelling Salesman Problems (TSP) problem for validation. In the chapter, first, the ACO algorithm for TSP is modeled in the framework of stochastic gradient descent (SGD). A new loss function aiming at minimizing the expectation of error ratio and its gradient is defined. 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 also implemented in the algorithm. Finally, ADACO was trialed on various sizes of TSP instances and benchmarked with the Max–Min Ant System (MMAS) algorithm, the Ant Colony System (ACS) algorithm, and the Iterated Local Search (ILS) algorithm. Results show that ADACO outperformed those comparative algorithms in terms of accuracy, stability and adaptability. Furthermore, the results also elucidate that ADACO maintained high-performance computational efficiency owing to its parallel implementation.