Hybrid modified ant system with sweep algorithm and path relinking for the capacitated vehicle routing problem

Vehicle routing problem is a widely researched combinatorial optimization problem. We developed a hybrid of three strategies—a modified ant system, a sweep algorithm, and a path relinking—for solving a capacitated vehicle routing optimization problem, a vehicle routing problem with a capacity constraint. A sweep algorithm was used to generate initial solutions and assign customers to vehicles, followed by a modified ant system to generate new generations of good solutions. Path relinking was used for building a better solution (candidate) from a pair of guiding and initial solutions. Finally, a local search method—swap, insert, reverse and greedy search operations—was used to prevent solutions from getting trapped in a local minimum. Performance of the proposed algorithm was evaluated on three datasets from CVRPLIB. Our proposed method was at least competitive to state-of-the-art algorithms in terms of the total route lengths. It even surpassed the best-known solution in the P-n55-k8 instance. Our findings can lower the transportation cost by reducing the travelling distance and efficiently utilizing the vehicle capacity.