A quantum genetic algorithm for pickup and delivery problems with coalition formation

With the “last mile” of the delivery process being the most expensive phase, autonomous package delivery systems are gaining traction as they aim for faster and cheaper delivery of goods to city, urban and rural destinations. This interest is further fueled by the emergence of e-commerce, where many applications can benefit from autonomous package delivery solutions. However, the environment stochasticity, variability and task complexity for autonomous operation make it difficult to deploy such systems in real-world applications without the incorporation of advanced machine learning and optimization algorithms. Moving away from designing a “one size fits all” agent to solve the outdoor package delivery problem and considering ad-hoc teams of agents trained within a data-driven framework could provide the answer. In this work, we propose a delivery scheduling algorithm for heterogeneous multi-agent systems using the pickup and delivery problem (PDP) formulation. Specifically, a 3-index mixed integer program-based PDP that allows coalition formation (PDP-CF) among agents is derived to allow multi-agent PDP schedules. We propose a quantum genetic algorithm to solve for the schedule since it is can better handle the large computational complexity of PDP-CF. Multiple PDP scenario simulations show the merits of the proposed approach.