The bi-objective orienteering problem with budget constraint: GRASP_ILS

In this paper, we introduce a new variant of the bi-objective orienteering problem (BOOP) called the bi-objective orienteering problem with budget constraint (BOOPBC) where an additional constraint is imposed on the budget of the tourist. In this problem, a set of points of interest (POIs) is given each with two profits and an entrance fee. The objective is to design routes visiting a set of POIs, so that the total profits of the visited POIs are maximized, while respecting the maximum length limit of the route and the limited budget of the tourist. To the best of our knowledge, this is the first study to address the BOOPBC. To find an approximation of the set of Pareto optimal solutions, we develop a hybrid metaheuristic based on the greedy randomized adaptive search procedure (GRASP) which uses an iterated local search (ILS) as an improvement phase. The proposed algorithm is tested on a set of benchmark instances extended from existing benchmarks. We also implement a simple multi-objective GRASP with Path Relinking procedure in order to verify the performance of the proposed method.