  The Multi-Depot Vehicle Routing Problem (MDVRP) is a real-world model of the
simplistic Vehicle Routing Problem (VRP) that considers how to satisfy multiple
customer demands from numerous depots. This paper introduces a hybrid 2-stage
approach based on two population-based algorithms - Ant Colony Optimization
(ACO) that mimics ant behaviour in nature and the Imperialist Competitive
Algorithm (ICA) that is based on geopolitical relationships between countries.
In the proposed hybrid algorithm, ICA is responsible for customer assignment to
the depots while ACO is routing and sequencing the customers. The algorithm is
compared to non-hybrid ACO and ICA as well as four other state-of-the-art
methods across 23 common Cordreaus benchmark instances. Results show clear
improvement over simple ACO and ICA and demonstrate very competitive results
when compared to other rival algorithms.
