Vehicle routing is an important combinatorial optimization problem. In real transport networks,the travel speed and travel time of roads have large time-variability and randomness. The study of vehicle routing problem in time-dependent network has even more practical value than static network VRP problem. This paper combines the features of time-dependent networks and gives the mathematical models of the time-dependent vehicle routing problem. On this basis, the traditional ant colony optimization algorithm is improved. A new path transfer strategy of ants and new dynamic pheromone update strategy applicable to time-dependent network are proposed. Based on these strategies, the improved ant colony algorithm is given for solving the vehicle routing problem in time-dependent networks. The simulation results show that the algorithm can effectively solve the vehicle routing problem in time-dependent network and has better computational efficiency and convergence speed.

Research of the shortest path problem in time-dependent networks has important practical value. An improved pheromone update strategy suitable for time-dependent networks was proposed. Under this strategy, the residual pheromone of each road can accurately reflect the change of weighted value of each road. An improved selection strategy between adjacent cities was used to compute the cities' transfer probabilities, as a result, the amount of calculation is greatly reduced. To avoid the algorithm converging to the local optimal solution, the ant colony algorithm was combined with genetic algorithm. In this way, the solutions after each traversal were used as the initial species to carry out single-point crossover. An improved ant colony algorithm for the shortest path problem in time-dependent networks based on these improved strategies was presented. The simulation results show that the improved algorithm has greater probability to get the global optimal solution, and the convergence rate of algorithm is better than traditional ant colony algorithm.