A Greedy Randomized Adaptive Search Procedure for the Orienteering Problem with Hotel Selection

Abstract The Orienteering Problem with Hotel Selection (OPHS) is one of the most recent variants of the Orienteering Problem (OP). The sequence of hotels has a significant effect on the quality of the OPHS solutions. According to prior studies, it is not efficient to consider all feasible sequences of hotels for constructing a tour. For this reason, solution methods for this problem should be independent of the Total Number of Feasible Sequences of hotels (TNFS). This paper proposes a novel approach based on a well-known metaheuristic called Greedy Randomized Adaptive Search Procedure (GRASP) to tackle the OPHS. In the previously introduced algorithms for this problem, the OP solutions among all feasible pairs of hotels are considered to construct a proper sequence of hotels. Our suggested GRASP algorithm does not follow this policy; instead, it uses a novel, potent, and fast dynamic programming method for hotel selection. This dynamic idea makes the introduced GRASP approach independent of the TNFS and solving the OPs. Considering 400 benchmark instances with and five instances without known optimal values, the proposed method in this article obtains the optimal solutions for 231 instances (57.75%), as opposed to 174 instances (43.5%) for the best formerly suggested algorithm. GRASP constructs better tours than the state-of-the-art algorithm for 142 instances (35.5%) and finds new best results for three out of five instances with unknown optimal values. Moreover, GRASP can produce high quality solutions for 76 new large instances constructed using the instances of a similar problem to the OPHS.