VRPDiv: A Divide and Conquer Framework for Large Vehicle Routing Problems

Abstract

The Vehicle Routing Problem (VRP) is an NP hard problem where we need to optimize itineraries for agents to visit multiple targets. When considering real-world travel (road-network topology, speed limits and traffic), modern VRP solvers can only process small instances with a few hundred targets. We propose a framework (VRPDiv) that can scale any solver to support larger VRP instances with up to ten thousand targets (10k) by dividing them into smaller clusters. VRPDiv supports the multiple VRP scenarios and contains a pool of clustering algorithms from which it chooses the ideal one depending on properties of the instance. VRPDiv assigns agents based on cluster demand and targets compatibility (i.e. realizable time-windows and capacity limitations). We incorporate the framework into the Bing Maps Multi-Itinerary Optimization (MIO)1 online service. This architecture allows MIO to scale up from solving instances with a few hundred to over 10k targets in under 10 minutes. We evaluate our framework on public datasets and publish a new dataset ourselves, as large enough instances supporting real-world travel were impossible to find. We investigate multiple clustering methods and show that choosing the correct one is critical with differences of up to 60% in quality. We compare with relevant baselines and report a 40% improvement in target allocation and a 9.8% improvement in itinerary durations. We compare with existing scores and report an average delta of 10%, with lower values (<5%) in instances with low workload (few targets per agent), which are acceptable for an online service.