On taming large optimization problems : a machine learning approach for an improved performance of ad hoc teams of heterogeneous agents in package delivery.

Abstract

With the emergence of Internet of Things, cloud computing, and smart cities empowered by artificial intelligence and machine learning, transportation systems have witnessed improved operational performance from safety and sustainability to greener logistics and efficiency. Given that the “last mile” of the delivery process is 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 argue that heterogeneous multi-agent systems (MAS) can be leveraged to insure some efficient multimodal transport which uses vehicular and non-vehicular agent cooperation for task completion. While the pickup and delivery problem (PDP) is one of the most popular models of package delivery, it does not support MAS. Therefore, we present PDP formulations that allow coalition formation (CF), i.e. a constrained optimization problem is formulated to solve for the delivery schedule while considering teams of agents for task execution. Specifically, 3-index and 2-index mixed integer programming (MIP) approaches are derived. However, the large number of optimization variables in both formulations causes convergence issues when using branch and bound type optimization solvers, which led to adopting heuristic and data driven approaches. Multiple solvers are presented to find near-optimal schedules in