Improved tabu search algorithm for the open vehicle routing problem with soft time windows and satisfaction rate

The open vehicle routing problem (OVRP) has a wide range of applications in the field of logistics distribution. A model of OVRP with soft time windows and satisfaction rate is analyzed here in order to reduce the logistics distribution cost. The minimization of the number of vehicles required is taken as the primary objective, while the minimization of the traveling distance cost and the deviation cost of the time windows are used as secondary objectives. A corresponding mathematical model with bi-objective programming is established for the problem. Based on the coding rules of natural numbers, several strategies such as the adaptive penalty mechanism, multi-neighborhood structure and re-initialization rule are embedded in the tabu search algorithm (TSA), resulting in an improved TSA (ITSA). Computational results are provided and these are compared with other methods in the literature, demonstrating the effectiveness of the ITSA.