Nested particle swarm optimisation for multi‐depot vehicle routing problem

Vehicle routing problem (VRP) is a well‐known non‐deterministic polynomial hard problem in operations research. VRP is more suited for applications having one warehouse. A variant of VRP called as multi‐depot vehicle routing problem (MDVRP) has more than one warehouse. Cluster first and route second is the methodology used for solving MDVRP. An improved k‐means algorithm is proposed for clustering that reduces the MDVRP to multiple VRP. In this work, MDVRP is considered with more than one objective and nested particle swarm optimisation with genetic operators is proposed for solving each VRP. Master particle swarm optimisation forms the group within each cluster. Slave particle swarm optimisation generates the route for each group. The objective of MDVRP is to minimise the total travel length along with route and load balance among the depots and vehicles. The results obtained are better in balancing load, route length and the number of vehicles, rather than minimisation of total cost.