International Journal of Computing and Mathematics

Some comparative studies in the latest years have studied the use of parallel ant colony optimization (ACO) algorithms over traditional sequential ACOs to fix the travelling salesman problem (TSP). These studies, however, did not take a systematic strategy to evaluate on a similar basis the efficiency of both algorithms. In this paper, as a result of the application of a sequential ACO and a parallel ACO to Eil51, Eil76, and KroA100, we aim to compare both the quality of the solutions and the running time on a standardized and therefore comparable ground. Our research reaffirmed that the parallel algorithm exceeds the sequential algorithm, especially for bigger TSPs, in computing effectiveness. We also discovered that if the size of TSPs continues to increase, such a comparison could be irrelevant. We discovered that the worst solution among 10 consecutive runs collected from the parallel ACO was still stronger than the strongest solution among 10 consecutive runs collected from the linear ACO, although within 300 iterations both did not achieve the appropriate worldwide solution. The suggested parallel ACO has a very elevated consistency because in every three runs for all three instances, at least one best solution was discovered within an error of 0.5 percent to the ideal worldwide solution.