Hybrid MCMF–NSGA-II Framework for Energy-Aware Task Assignment in Multi-Tier Shuttle Systems

The rapid growth of robotic warehouses and smart logistics has increased the demand for efficient scheduling of multi-tier shuttle systems (MTSSs). MTSS scheduling is a complex robotic task allocation problem, where throughput, energy efficiency, and service quality must be jointly optimized under operational constraints. To address this challenge, this study proposes a hybrid optimization framework that integrates the Minimum-Cost Maximum-Flow (MCMF) algorithm with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The MTSS is modeled as a cyber–physical robotic system that explicitly incorporates task flow, energy flow, and information flow. The lower-layer MCMF ensures efficient and feasible task–robot assignments under state-of-charge (SOC) and deadline constraints, while the upper-layer NSGA-II adaptively tunes cost-function weights to explore Pareto-optimal trade-offs among makespan, energy consumption, and waiting time. Simulation results show that the hybrid framework outperforms baseline heuristics and static optimization methods and reduces makespan by up to 5%, the energy consumption by 2.8%, and the SOC violations by over 90% while generating diverse Pareto fronts that enable flexible throughput-oriented, service-oriented, or energy-conservative scheduling strategies. The proposed framework thus provides a practical and scalable solution for energy-aware robotic scheduling in automated warehouses, thus bridging the gap between exact assignment methods and adaptive multi-objective optimization approaches.