ACS-OPHS: Ant Colony System for the Orienteering Problem with hotel selection

Abstract In this paper, an algorithm, called ACS-OPHS, is proposed to tackle the Orienteering Problem with Hotel Selection (OPHS). This algorithm is strongly based on the Ant Colony System (ACS); however, it differs from the ACS in the way the paths are constructed, in tuning a parameter of the transition rule and in the pheromone trails updating rules. The ACS-OPHS uses a bi-directional search strategy and employs a novel and fast approach to identify all feasible intermediate hotels in an offline manner. Moreover, in the ACS-OPHS, the relative importance of exploitation versus exploration is determined according to the progress of the algorithm in approaching to the global optima. The ACS-OPHS is a simple and well-performing approach to solve the OPHS. Concerning the standard benchmark instances, it outperforms the state-of-the-art algorithms in several instances and produces competitive solutions in reasonable time. This algorithm also improves the best known results of four instances with unknown optimal solutions.