Effective neighborhood search with optimal splitting and adaptive memory for the team orienteering problem with time windows

The Team Orienteering Problem with Time Windows (TOPTW) is an extension of the well-known Orienteering Problem. Given a set of locations, each one associated with a profit, a service time and a time window, the objective of the TOPTW is to plan a set of routes, over a subset of locations, that maximizes the total collected profit while satisfying travel time limitations and time window constraints. Within this paper, we present an effective neighborhood search for the TOPTW based on (1) the alternation between two different search spaces, a giant tour search space and a route search space, using a powerful splitting algorithm, and (2) the use of a long term memory mechanism to keep high quality routes encountered in elite solutions. We conduct extensive computational experiments to investigate the contribution of these components, and measure the performance of our method on literature benchmarks. Our approach outperforms state-of-the-art algorithms in terms of overall solution quality and computational time. It finds the current best known solutions, or better ones, for 89% of the literature instances within reasonable runtimes. Moreover, it is able to achieve better average deviation than state-of-the-art algorithms within shorter computation times. Moreover, new improvements for 57 benchmark instances were found.