Adaptive Probabilistic Planning for the Uncertain and Dynamic Orienteering Problem

Abstract: The Orienteering Problem (OP) is a well-studied routing problem that has been extended to incorporate uncertainties, reflecting stochastic or dynamic travel costs, prize-collection costs, and prizes. Existing approaches may, however, be inefficient in real-world applications due to insufficient modeling knowledge and initially unknowable parameters in online scenarios. Thus, we propose the Uncertain and Dynamic Orienteering Problem (UDOP), modeling travel costs as distributions with unknown and time-variant parameters. UDOP also associates uncertain travel costs with dynamic prizes and prize-collection costs for its objective and budget constraints. To address UDOP, we develop an ADaptive Approach for Probabilistic paThs - ADAPT, that iteratively performs 'execution' and 'online planning' based on an initial 'offline' solution. The execution phase updates system status and records online cost observations. The online planner employs a Bayesian approach to adaptively estimate power consumption and optimize path sequence based on safety beliefs. We evaluate ADAPT in a practical Unmanned Aerial Vehicle (UAV) charging scheduling problem for Wireless Rechargeable Sensor Networks. The UAV must optimize its path to recharge sensor nodes efficiently while managing its energy under uncertain conditions. ADAPT maintains comparable solution quality and computation time while offering superior robustness. Extensive simulations show that ADAPT achieves a 100% Mission Success Rate (MSR) across all tested scenarios, outperforming comparable heuristic-based and frequentist approaches that fail up to 70% (under challenging conditions) and averaging 67% MSR, respectively. This work advances the field of OP with uncertainties, offering a reliable and efficient approach for real-world applications in uncertain and dynamic environments.