Team orienteering with possible multiple visits: Mathematical model and solution algorithms

Abstract

This study addresses a new team orienteering problem in which each point can be visited possibly multiple times with decreasing scores. The problem is to determine a set of routes from a starting to a finishing point within an allowed travel time limit for the objective of maximizing the total collected score. A mixed integer programming model is developed to represent the problem mathematically. Then, due to the complexity of the problem, a basic iterated local search (ILS) algorithm is proposed that incorporates the ordinary perturbation and local search operators. Then, it is improved in two ways: (a) an extended ILS algorithm with multi-visit based local search operators and (b) a hybrid ILS algorithm with a simulated annealing technique to permit non-improving moves in the local search step. To test the performance of the ILS algorithms, computational experiments were done on modified benchmark instances under the cases of linear, convex and concave score decreases, and the results show that the hybrid ILS algorithm improves the others significantly and also gives near optimal solutions for small sized test instances. Finally, a case study was done for a naval warship reconnaissance operation, and the results are reported.