A unified tabu search algorithm for vehicle routing problems with soft time windows

Abstract

The different ways of allowing time window violations lead to different types of the vehicle routing problems with soft time windows (VRPSTW). In this paper, different types of VRPSTW are analysed. A unified penalty function and a unified tabu search algorithm for the main types of VRPSTW are presented, with which different types of VRPSTW can be solved by simply changing the values of corresponding parameters in the penalty function. Computational results on benchmark problems are provided and compared with other methods in the literature. Some best known solutions for the benchmark problems in the literature have been improved with the proposed algorithm.