Integrated Optimization on Double-Side Cantilever Yard Crane Scheduling and Green Vehicle Path Planning at U-Shaped Yard

The U-shaped yard is an important part of the U-shaped automated container terminal (U-ACT), which consists of a set of blocks used for storing containers, I-lanes for automated guided vehicles (AGVs) travel, and U-lanes for external trucks (ETs) travel. Double-side cantilever yard cranes (DCYCs) perform stacking and unstacking operations for containers transported by AGVs and ETs. Managing and coordinating the operations of DCYC, AGVs, and ETs, not only improves the operation efficiency of U-ACTs but also helps to promote the development of green ports. This paper addresses the problem of scheduling DCYCs and path planning for AGVs and ETs in the U-ACT. To achieve this, we establish a bi-objective mixed integer programming model to minimize both the makespan and the energy consumption. The model considers conflicts between two DCYCs within each block, ensures workload balance for these DCYCs, optimizes parking slots for AGVs and ETs, and schedules appropriate entry times for AGVs and ETs into the yard to reduce conflicts. To solve this model, we develop an improved multi-objective particle swarm optimization (IMOPSO) algorithm, where a globally optimal heuristic search mechanism and several conflict avoidance strategies to plan conflict-free spatiotemporal paths are introduced to accelerate the convergence of the algorithm. Numerical experiments demonstrate the superiority of the IMOPSO approach in terms of multiple metrics, confirming the effectiveness of the optimized vehicle entry timing strategy, which improves efficiency by 7.33% and yields energy savings by 11.72%. These findings clearly highlight that our model and solution approach can effectively enhance the operational efficiency of DCYCs, AGVs, and ETs, contributing to the overall improvement of container terminal operations.