A variable neighborhood search algorithm for the vehicle routing problem with multiple trips

The vehicle routing problem with multiple trips (VRPMT) is a variants of the standard (VRP), where each vehicle can be used more than once during the working period. For this NP-Hard problem, we propose a variable neighborhood search Algorithm in which four neighborhood structure are designed to find the planning of trips. The algorithm was tested over a set of benchmark problems and the obtained solutions were compared with five previously proposed algorithms. Encouraging results are obtained.