In this paper, a deterministic heuristic method is developed for obtaining an initial solution to an extremely large-scale capacitated vehicle routing problem (CVRP) having thousands of customers. The heuristic has three main objectives. First, it should be able to withstand the computational and memory problems normally associated with extremely large-scale CVRP. Secondly, the outputs should be reasonably accurate and should have a minimum number of vehicles. Finally, it should be able to produce the results within a short duration of time. The new method, based on the sweep algorithm, minimizes the number of vehicles by loading the vehicles nearly to their full capacity by skipping some of the customers as and when necessary. To minimize the total traveled distance, before the sweeping starts the customers are ordered based on both the polar angle and the distance of the customer from the depot. This method is tested on 10 sets of standard benchmark instances found in the literature. The results are compared with the results of the CW 100 method by Arnold et al. (2019a). The results indicate that the new modified sweep algorithm produces an initial solution with a minimum number of vehicles and with reasonable accuracy. The deviation of the output from the best-known solution (BKS) is within a reasonable limit for all the test instances. When compared with the CW 100 the modified sweep provides a better initial solution than CW 100 whenever the capacity of the vehicle is more and the depot is located eccentrically. The heuristic does not face any memory problems normally associated with the solving of an extremely large-scale CVRP.
Hybrid Modified Ant System with Sweep Algorithm and Path Relinking for the Capacitated Vehicle Routing Problem
