An augmented large neighborhood search method for solving the team orienteering problem

In the Team Orienteering Problem (TOP), a team of vehicles attempts to collect rewards at a given number of stops within a specified time frame. Once a vehicle visits a stop and collects its reward, no other vehicles can collect the reward again. Typically, a team cannot visit all stops and therefore has to identify the “best” set of stops to visit in order to maximize total rewards. We propose a large neighborhood search method with three improvement algorithms: a local search improvement, a shift and insertion improvement, and replacement improvement. Our proposed approach can find the best known solutions for 386 of the 387 benchmark instances, for the one instance which our solution is not the current best it is only varies by one from the best. Our approach outperforms all the previous approaches in terms of solution quality and computation time.

► We propose an augmented large neighborhood method for team orienteering problem.
► A shift improvement and a replacement improvement algorithms are developed.
► The method identifies the best known solution for 386 of 387 benchmark problems.
► It outperforms 12 existing approaches.