Parallelized Clustering-Based Optimization for CVRP: Leveraging Quantum Computing and GPU Acceleration

The Capacitated Vehicle Routing Problem is one of the most well-known issues in operations research and transportation logistics. It comprises optimizing a set of vehicle routes to serve a set of clients, subject to vehicle capacity restrictions. Reducing the total distance that the cars go is the aim of the challenge. The Capacitated Vehicle Routing Problem has been studied by academics for a very long time. This topic is receiving a lot of interest because it can be applied to almost every industry, including marketing, logistics, healthcare, and others. One of the main obstacles, though, is that when the problem is attempted to be solved for a greater number of clients and vehicles, the problem becomes so complex that standard computers are either unable to solve it or require several months or even years to generate an output. We proposed an approach for this restriction that enables the problem to be resolved with quantum computers. We use two algorithms in our methodology, Constrained Clustering and Fuzzy C-Means, to attain our results. Clustering and routing are the two phases each of these algorithms go through. This method involves grouping all connected consumers into different clusters and then conducting routing within each cluster. They work with notable efficiency, producing optimal solutions in a noticeably smaller span of time. The results show that the CC approach outperforms FCM in most instances, achieving an average optimality gap of 13.04%, compared to 16.5% for FCM. Furthermore, both approaches perform significantly better than non-clustered methods.