Hybrid 2-stage Imperialist Competitive Algorithm with Ant Colony Optimization for Solving Multi-Depot Vehicle Routing Problem

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.