A Novel Method for Solving the Orienteering Problem with Hotel Selection

The Orienteering Problem with Hotel Selection (OPHS) is a variant of the Orienteering Problem (OP). There are two vertex types in the OPHS: nodes with specific scores and hotels without scores. The goal is finding a contiguous time-limited path with a maximum score that has a predefined origin and destination and consists of a certain number of trips. Each trip must begin from and terminate in one of the hotels. In this paper, an approach based on a well-known metaheuristic called Greedy Randomized Adoptive Search Procedure (GRASP) is presented for solving this problem. We also propose a novel local search method for improving the sequence of hotels. The algorithm was tested on 405 available benchmark instances. Considering 400 instances with known optimal solutions, it could find the optimal values for 205 instances while state-of-the-art algorithm produced the optimal solutions for 174 instances. It provided better solutions than stateof- the-art algorithm in 137 instances. It also improved the best known results of three instances among the five instances with unknown optimal solutions.