A New Method for Generating Initial Solutions of Capacitated Vehicle Routing Problems

In vehicle routing problems, the initial solutions of the routes are important for improving the quality and solution time of the algorithm. For a better route construction algorithm, the obtained initial solutions must be basic, fast, and flexible with reasonable accuracy. In this study, initial solutions are introduced to improve the final solution of the Capacitated Vehicle Routing Problem based on a method from the literature. Using a different formula for addressing the gravitational forces, a new method is introduced and compared with the previous physics inspired algorithm. By using the initial solutions of the proposed method and using them as the initial routes of the Record-to-Record and Simulated Annealing algorithms, it is seen that better results are obtained when compared with various algorithms from the literature. Also, in order to fairly compare the algorithms executed on different machines, a new comparison scale for the solution quality of vehicle routing problems is proposed that depends on the solution time and the deviation from the best known solution. The obtained initial solutions are then input to Record-to-Record and Simulated Annealing algorithms to obtain final solutions. Various test instances and CVRP solutions from the literature are used for comparison. The comparisons with the proposed method have shown promising results.