Model and solution for the traveling salesman problem with multiple time windows

Abstract

This paper applies the multi-time window traveling salesman problem to not only optimize the logistics cost, but also effectively endow users with multiple discrete idle optional time periods to meet the time requirements of just-in-time production. In the process of problem solving, firstly, the dynamic penalty factor is introduced into the objective function and the penalty function is added to relax the constraints of multi-time window in order to construct the relaxation model. Secondly, while in solving the model, the compressed annealing algorithm, which has the property of probability convergence, is proposed on the basis of the simulated annealing algorithm with only temperature parameter. The dynamic penalty factor is added as a pressure parameter to control the probability of the transition to an infeasible route regarding the time windows. Finally, comparison through data experiments between multi-time windows and single-time windows verifies the practicability of the former and comparison between the solution algorithm and simulated annealing algorithm verifies the stability of compressed annealing algorithm. The result shows that the compressed annealing algorithm is a comparatively better method to solve multi-time window traveling salesman problem.