Integrating conflict-free routing and collision avoidance into AGV scheduling under the hybrid battery-swapping and opportunity-charging mode in automated container terminals

In automated container terminals (ACTs), battery-powered automated guided vehicles (AGVs) perform the horizontal transport of containers between the quay and the yard. Xiao, Huang, Hu and Gu (2024) formulated the AGV scheduling problem under a hybrid energy-replenishment mode — battery swapping at a swapping station combined with opportunity charging at the AGV mates (buffer positions with charging facilities) during loading and unloading waits — as a mixed-integer program minimizing energy cost plus delay cost, solved by adaptive large neighborhood search, but explicitly assumed known paths, a uniform travel speed, and no path conflicts. The authors left open the integration of AGV path planning and collision avoidance into this hybrid-mode scheduling model, since real terminal road networks impose intersection restrictions and lane capacities that affect feasibility and timing. The 2024–2026 literature addresses the swapping-only and charging-only variants of this integration — Huang and Zhu (2025) combine bidirectional conflict-free routing with battery swapping under a completion-time objective, and Guo, Hu, Sha, Lian and Yang (2025) combine route planning under path conflicts with a dual-threshold charging strategy — but no published work integrates conflict-free routing and collision avoidance with the hybrid swapping-plus-opportunity-charging scheduling model and its energy-plus-delay objective. The open problem is therefore to formulate and solve this joint scheduling, battery-management, and conflict-free-routing problem, together with an effective solution method for realistic instance sizes.

Background

An automated container terminal (ACT) is a container port in which quay cranes load and discharge vessels, yard cranes stack containers in the yard, and battery-powered automated guided vehicles (AGVs) — driverless vehicles following fixed guide paths — perform the horizontal transport of containers between the quay and the yard. The AGV scheduling problem assigns loading and unloading tasks to AGVs, sequences each AGV's tasks, and decides when each AGV must replenish its battery, subject to task time windows: each container task has a latest start time, and starting later delays the cranes and downstream tasks, incurring a delay cost. Because battery capacity limits AGV availability, two replenishment modes are used in practice. In battery swapping, an AGV with a depleted battery visits a swapping station, where the battery is exchanged for a fully charged one (the station serves one AGV at a time). In opportunity charging, an AGV tops up its battery during idle waiting time at AGV mates — the buffer brackets at which AGVs park to exchange containers with cranes, some of which are equipped with charging facilities — so that recharging overlaps with container handling. Xiao, Huang, Hu and Gu (2024) introduced a hybrid mode combining both mechanisms and modeled AGV scheduling under it as a mixed-integer program minimizing the sum of energy cost and delay cost, solved with adaptive large neighborhood search (ALNS), a metaheuristic that iteratively removes and re-inserts parts of a solution while adapting its operator choices to past success. Their model explicitly assumes task paths are known, all AGVs travel at a common speed, and path conflicts among AGVs are not considered; their simulation of the hybrid mode against swapping-only operation reported 43.48% fewer battery swaps and 7.20% lower total cost. A separate literature studies conflict-free routing in ACTs: ensuring that the paths and timing of all AGVs avoid collisions at intersections and respect lane capacities. Zhong, Guo, Zhang and Yang (2023) integrated conflict-free AGV path planning with quay-crane/yard-crane scheduling under an energy-consumption objective but without any battery state-of-charge or replenishment decisions, and Cao, Yang, Liu, Zeng and Chen (2023) studied AGV dispatching with bidirectional conflict-free routing on a terminal road network, likewise without battery management. On the battery side, scheduling studies without routing include Yang, Hu, Cheng and Wang (2023) (battery swapping with speed control), Li, Li, Liu, Zhou and Pan (2023) (two-stage stochastic programming with random tasks and swapping), Zhen, Zhang, Tan and Wang (2025) (charging–swapping mixed mode solved by column generation), and Xue, He, Zhou, Lee, Wang and Chen (2026) (a two-phase label-setting plus Benders decomposition framework for swapping-considered scheduling, where routes are task sequences rather than conflict-free paths). After the source paper appeared, two adjacent integrations were published: Huang and Zhu (2025) combined AGV scheduling, bidirectional conflict-free routing, and battery swapping (with a double-threshold swapping rule) in a bi-level mixed-integer program minimizing job completion time, explicitly citing Xiao et al. (2024) and noting that few battery-management studies address conflict-free routing; and Guo, Hu, Sha, Lian and Yang (2025) jointly optimized task scheduling, route planning under path conflicts, and a flexible dual-threshold opportunity charging strategy with nonlinear charging characteristics. The first covers swapping only, the second charging only; neither treats the hybrid swapping-plus-opportunity-charging mode, and neither uses the energy-plus-delay cost objective of the source model. The coupling that makes the full integration difficult is the feedback among its parts: path conflicts and lane capacities perturb travel and waiting times, waiting times change how much opportunity charging an AGV receives, and battery states in turn constrain which routes and swap times remain feasible, so neither the scheduling layer nor the routing layer can be fixed independently of the other.

Problem Statement

Formulate and solve the integrated AGV scheduling and conflict-free routing problem for an automated container terminal in which AGVs are subject to battery capacity limits and replenished by the hybrid mode of battery swapping and opportunity charging, replacing the source model's assumptions that task paths are known and that path conflicts among AGVs need not be considered, while retaining its assumptions that each AGV travels at a common speed between any two nodes (the fixed no-load and loaded speeds $v_1$ and $v_2$) and that opportunity charging is linear, the amount of charging being proportional to the charging time at rate $c$; conflicts are therefore resolved by collision-avoidance waiting or re-routing rather than by speed changes. Concretely, for a terminal with a road network of lanes and intersections, quay-side and yard-side task locations, a battery swapping station (one AGV served at a time), and AGV mates equipped with charging facilities, decide jointly: (1) the assignment of loading and unloading container tasks to AGVs and the sequence of each AGV's tasks under their time windows $[e_i, l_i]$; (2) when each AGV swaps its battery at the station and when it opportunistically charges at AGV mates during loading/unloading waits, tracking battery state of charge so that no AGV strands with a depleted battery; and (3) each AGV's route and traversal timing on the road network so that movement is conflict-free — no simultaneous occupation of an intersection or of a lane beyond its capacity, with collision-avoidance waiting or re-routing where conflicts would arise. The objective is the source's sum of energy cost and delay cost, $\min f = c_e(\sum_{i}\sum_{j}\sum_{k} z_{ijk} x_{ijk} + \sum_{i}\sum_{k} w_i y_{ik}) + c_t \sum_{i}\sum_{k} \tau_{ik}$, where $x_{ijk} = 1$ when AGV $k$ executes task $j$ immediately after task $i$, $y_{ik} = 1$ when AGV $k$ performs task $i$, $w_i$ is the loading energy consumption of task $i$ evaluated on the conflict-free loaded path actually taken for that task, $z_{ijk}$ is the no-load energy consumption of the empty movement from the end position of task $i$ to the start position of task $j$, and $\tau_{ik}$ is the time by which the start of task $i$ by AGV $k$ exceeds the latest start time $l_i$. Both energy terms are computed with the source's energy-consumption model (mechanical energy over the travelled distance at the corresponding speed, converted to electrical energy through the motor and battery-discharge efficiencies); the extension is that both the loading energy $w_i$ (on the conflict-free path chosen for the loaded leg of task $i$) and the no-load energy $z_{ijk}$ (on the empty path taken from the end position of task $i$ to the start position of task $j$) are evaluated on the conflict-free route actually taken, so that detours and the extra distance they add are charged, instead of on a single known path. As in the source, energy delivered during opportunity charging and time spent waiting are not themselves costed: they enter the objective through the state-of-charge balance and through the delays they induce. The problem is also to provide an exact or heuristic solution method, demonstrated on realistically sized instances of the scale used in the source study and in the adjacent conflict-free-routing literature, yielding feasible, conflict-free, battery-feasible schedules evaluated by the objective $\min f$.

References

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