A note on the time travel approach for handling time windows in vehicle routing problems

In this paper, we identify two cases in which the proposition for calculating time window penalties presented in Nagata, Y., Bräysy, O. and Dullaert, W. A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows, Computers & Operations Research 2010;37(4): 724-37 yields incorrect results. We derive the corrected proposition and use numerical studies to show that a significant proportion of the evaluations performed by a Tabu Search for VRPTW falls under the two incorrect cases. Moreover, we demonstrate that the incorrect time window handling has a significant negative impact on the solution quality of the Tabu Search.