Adapted Ant Colony Optimization for Team Orienteering Problem

The Team Orienteering Problem (TOP) is to find multiple optimal subsets of nodes and the associated routes to visit these nodes with the objective to maximize the total profits and under the constraint that the traveling cost of each route does not exceed the given cost limit. Such a problem is very challenging and difficult to solve because it involves node selection optimization, route optimization, and cost constraints for multiple routes. Thanks to the significantly good performance of Ant Colony Optimization (ACO) algorithms in solving path planning problems, they are considered promising for addressing TOP. To this end, this paper takes the first attempt to adapt five classical ACO algorithms, namely the Ant System (AS), Elitist Ant System (EAS), Rank-based Ant System (AS rank), Min-Max Ant System (MMAS), and Ant Colony System (ACS), to solve TOP. To achieve this, we maintain an ant team consisting of multiple ants to construct a feasible solution containing multiple routes. Further, we design an ant selection scheme for the ant team to select the next node to visit in the route construction by considering the given cost constraints. To assess the optimization performance of the five adapted ACO algorithms in solving TOP, experiments are conducted on the classical TOP instances. The results reveal that all five ACO algorithms are promising for addressing TOP. Particularly, ACS excels in maximizing the overall team profit, while EAS demonstrates good stability in minimizing the profit differences between routes.