Multi-AGV scheduling model for fixed charging pile and solving algorithm thereof

Abstract

The invention discloses a multi-AGV scheduling model oriented to a fixed charging pile and a solving algorithm thereof, the model is constructed on a factory topology network, and uniquely assigning a sequence with the same vehicle, task starting and ending moments, a vehicle state and an SOC track, pile entering and pile exiting moments and session charging amounts and session occupation duration on the topology network are jointly decided; and minimizing the total energy consumption of the system, minimizing the maximum completion time and minimizing the economic cost are taken as optimization objectives. Transport organization and energy supply scheduling of the automatic guided vehicle (AGV) in a workshop and a storage environment are improved, multi-target collaborative scheduling modeling and solving under the condition of a fixed charging pile are emphasized, the total energy consumption of the result is reduced, the maximum construction period is stably converged within a threshold range, and the economic cost is effectively controlled.

Description

Technical Field

[0001] This invention provides a multi-AGV scheduling model for fixed charging piles and its solution algorithm. Background Technology

[0002] In discrete manufacturing and warehousing systems, multiple automated guided vehicles (AGVs) handle cross-workstation material transport and work-in-process transfers. The scheduling system needs to maintain stable operation under complex factors such as concentrated task arrivals, fluctuating cycle times, and network congestion. Factory roads are often abstracted as a topology consisting of work points, storage points, and pathway nodes. Accessibility and path costs vary significantly in space, with main pathways and bottleneck sections forming congestion hotspots during peak hours. Uneven distribution of transport distances and arrival times amplifies scheduling uncertainty. Fixed charging stations are widely used in industrial settings. When vehicles are low on power, they return to the charging station for a recharge session before continuing production. While this model is mature and reliable in terms of safety and maintenance, it can lead to increased empty return trips and non-productive time under conditions of high task density and path congestion, as well as charging station occupancy conflicts and queuing. The coupling between time windows and energy constraints can easily cause cascading delays and infeasible solutions.

[0003] Traditional methods often process task allocation, path planning, and energy replenishment in stages, making it difficult to simultaneously weigh energy consumption, maximum completion time, and monetization costs within a unified framework. They also rarely incorporate the relationship between charging volume and occupancy time into a mixed-integer linear model in a linear envelope manner for engineering solutions. Therefore, it is necessary to establish a multi-objective scheduling model that can uniformly describe task assignment and vehicle sequence, processing and transfer timing, path reachability, SOC dynamics, and fixed charging pile session mechanisms, and design scalable heuristic algorithms to generate stable and feasible scheduling schemes under large-scale task loads. Summary of the Invention

[0004] To address the aforementioned technical problems in existing technologies, the present invention aims to provide a multi-AGV collaborative scheduling model and solution algorithm for fixed charging pile conditions. This invention improves the transportation organization and energy replenishment scheduling of Automated Guided Vehicles (AGVs) in workshop and warehouse environments, focusing on multi-objective collaborative scheduling modeling and solution under fixed charging pile conditions.

[0005] The model of this invention jointly decides on the unique assignment of tasks and the order of vehicles on the topology network, the start and end times of tasks and vehicle states, SOC trajectory, entry and exit times of charging piles, session charging amount, and session duration, with the optimization objectives of minimizing total system energy consumption, minimizing maximum completion time, and minimizing economic cost. The solution algorithm adopts an improved genetic optimization framework, using two-stage encoding and decoding repair and thresholding evaluation, and performs local neighborhood fine-tuning on elite individuals to output high-quality solutions that satisfy the constraints. The fixed charging pile-specific constraints use a linear envelope based on the rate range to characterize the relationship between charging amount and session duration, and provide a temporal expression for the connection between the entry and exit points of charging piles and the approximate full charge.

[0006] The technical solution adopted in this invention is as follows: A multi-AGV collaborative scheduling model for fixed charging piles is constructed on the factory topology network, with the optimization objectives of minimizing total system energy consumption, minimizing maximum completion time, and minimizing economic cost. 3.1 Symbol Definition A = {1, 2, ..., a}: a set of vehicles, index a, which represents the a-th automated guided vehicle in the system; T = {1, 2, ..., i}: a set of tasks, where index i represents the i-th transportation task in the system; N = {1, 2, ..., |i|}: a set of nodes, where index i represents the i-th work node in the factory area; F = {1, 2, ..., |f|}: a set of fixed charging stations, where index f represents the f-th fixed charging station; F1: The total system task completion time, which is the maximum value of the completion times of all tasks; F2: Total completion time of the multi-AGV system during the entire scheduling cycle; The overall cost associated with the configuration and operation of FCS for fixed charging stations; s i The starting node of task i; e j : The endpoint of task j; : The time window for task i; ET i : Indicates the earliest start time of task i; LT i : Indicates the latest start time for task i; Loading service time for task i; The time for uninstalling the service for task i; d ij Manhattan distance between nodes i and j; : Accessibility indicator. If it is passable between nodes i and j on the map, the accessibility indicator is 1; otherwise, it is 0. v AGV travel speed; c Energy consumption coefficient per unit distance of AGV under no-load conditions; Energy consumption coefficient per unit distance when fully loaded by AGV; Q: Rated load capacity of AGV; w j The weight of goods in task j; σ AGV battery capacity limit; θ : Lower limit threshold for AGV battery safety capacity; π e Electricity unit price; : Cost of operating and maintenance distance; : Fixed cost coefficient for each use of a fixed charging station; : Cost coefficient per unit time occupied by a fixed charging station; Construction cost coefficient per unit capacity of fixed charging piles; p a : The initial position node of the a-th AGV; : The node where the a-th AGV is located before task i begins; M A sufficiently large constant, for example, a value of 10. 6 The constant; ε 2 Construction period threshold; ε 3 Cost threshold; D ai The total distance traveled by the a-th AGV while performing task i; E ai : Total energy consumption of the a-th AGV performing task i; : The state of charge (SOC) of the a-th AGV at time t; Maximum completion time; The a-th AGV returns to the charging station after completing task i. f The power replenished at the location; After completing task i, the a-th AGV enters the charging station. f At that moment; The a-th AGV leaves the charging station after completing task i. f At that moment; Before executing task i, the a-th AGV moves from its current position to the task start point. s i The driving distance; From the end of the mission e i to charging station f The driving distance; The starting point of task i s i To the finish line e i The driving distance; The endpoint of task i e i To the starting point of task j s j The driving distance; The endpoint of task j e j To the starting point of task i s i The driving distance; Charging pile f To the starting point of task j s j The driving distance; AGV from position p a Drive to the starting point of mission i s i The distance; Decision variables: If the a-th AGV is performing task i, then set the value to 1; otherwise, set the value to 0. If task i precedes task j on the same AGV, then set the value to 1; otherwise, set the value to 0. : Indicates the time when the a-th AGV starts executing task i. If the a-th AGV has not been assigned task i, it is 0; otherwise, it is the time when the AGV actually starts serving task i. : Represents the time when the a-th AGV completes task i. If the a-th AGV has not been assigned task i, it is 0; otherwise, it is the time when the AGV actually completes service task i. If the a-th AGV moves directly from node i to node j, then set the value to 1; otherwise, set the value to 0. If the a-th AGV goes to the charging station after completing task i. f If the value is 1, then take 1; otherwise, take 0. 3.2 Model Objective Function Based on the above description of the multi-task-point scheduling problem for multiple automated guided vehicles (AGVs), the mathematical model for the AGV scheduling problem considering energy consumption, project duration, and economy, constructed in this invention, is as follows. The objective function is: ; Wherein: Equation (1) represents the objective function of minimizing the sum of total system energy consumption; Equation (2) represents the objective of minimizing the maximum completion time; Equation (3) represents the system cost minimization under the fixed charging pile model.

[0007] Furthermore, the model of this invention includes the following constraints: ; ; Equation (4) indicates that each task must be performed by only one vehicle; Equation (5) indicates that the sequence variable and the assignment variable are linked and the order is forced when they are in the same vehicle; Equation (6) indicates that the bidirectional serialization of adjacent tasks in the same vehicle includes the transfer time; Equation (7) indicates that the task completion time at least covers the start time, travel time and loading / unloading time and is released by a sufficiently large constant M when not assigned; Equation (8) indicates that the task start and end times meet the given time window; Equation (9) indicates that the time and energy from the initial position of the vehicle to the starting point of the first task are feasible; Equation (10) indicates that the electricity at the start and end of the task is within the upper and lower bounds of the capacity; Equation (11) indicates that the energy income and expenditure are balanced during the execution of the task; Equation (12) indicates that the path reachability restriction does not allow unreachable node pairs to be selected; Equation (13) indicates that the maximum completion time is the lower bound of the completion time of all assigned tasks; Equation (14) indicates the range of values ​​of the binary decision variable; Equation (15) indicates the non-negativity of session energy supply; Equation (16) indicates that various time variables and project duration variables are non-negative.

[0008] In the constraints of the model of this invention, when the a-th AGV completes task i, if it chooses to conduct a charging session at a fixed charging pile f, then the binary variable... Indicate the choice, and with , These represent the times of entering and leaving the fixed charging station f, respectively. This represents the amount of electricity generated during the session. To depict the linear relationship between "charging amount and usage time," an equivalent charging rate parameter *r* for the fixed charging station is introduced, expressed as a linear envelope: In MILP, this is implemented using upper and lower bound envelopes. The timing between session initiation and task completion satisfies: The start time of the next task j after the session ends must satisfy the constraint of "transition time after exiting the stub": If the "fully charged approximation" method is used, the state of charge (SOC) of the AGV's battery can be brought close to the upper limit at the time of pile exit. : This is to ensure the energy feasibility of subsequent tasks. In terms of economics, the electricity consumption of a fixed charging station FCS session... Enter electricity bill item Session duration Entry time fee In addition to a one-time access fee Amortization with the number of equipment Total cost accounting. In light of the above description, the model of this invention also includes the following constraints: ; Equation (17) indicates that at most one fixed charging station session can be selected after each task is completed; Equation (18) indicates that the start time of the fixed charging station session is not earlier than the completion time of the corresponding task; Equation (19) indicates the linear lower bound of the charging amount and the duration of the fixed charging station session; Equation (20) indicates the linear upper bound of the charging amount and the duration of the fixed charging station session; Equation (21) indicates the linear lower bound of the session duration required to reach full charge; Equation (22) indicates the linear upper bound of the session duration required to reach full charge; Equation (23) indicates the approximate full charge when the vehicle's battery level approaches the upper bound of the capacity at the end of the session; Equation (24) indicates that if no charging is performed, the battery level at the end of the task must not be lower than the safety threshold; Equation (25) indicates that a transfer time from the charging station to the starting point of the next task must be reserved from the end of charging to the start of the next task.

[0009] The algorithm of this invention's model employs a heuristic solution framework that primarily uses an improved genetic algorithm and secondarily uses simulated annealing (SA). Its overall process is as follows: Figure 3As shown, the algorithm first reads the task parameters, AGV fleet parameters, and energy replenishment resource parameters such as fixed charging piles to initialize the problem instance. Then, an initial population is generated, and the initial individuals undergo a complete decoding and feasibility repair to obtain an initial scheduling scheme that satisfies the basic time window and energy constraints. For an AGV scheduling model that simultaneously includes three objectives—total system energy consumption, maximum completion time, and operating cost—and involves two types of energy replenishment mechanisms—fixed charging piles and mobile charging vehicles, the algorithm uses a two-segment chromosome encoding method to describe the solution space. The chromosome consists of two parts: a "task assignment segment" and a "charging session segment." The task assignment segment determines the AGV executing each transportation task, and the relative order of tasks within the same AGV is implicitly determined by the task's arrangement in the chromosome. The charging session segment describes whether an AGV triggers a energy replenishment behavior after completing a task and the corresponding energy replenishment resource type. This segment marks potential energy replenishment sessions with a charging intention variable, without directly giving the absolute start and end times of charging. In this process, the algorithm dynamically calculates the actual start and end times of each task based on the task time window constraints and the AGV's battery state of charge (SOC) constraints, and synchronously updates the AGV's energy evolution process on the time axis. SOC represents the AGV's current remaining battery power, ensuring that the AGV's battery level does not fall below a safe threshold during task execution and travel. For the energy replenishment resource side, the algorithm uniformly handles the port occupancy constraints of fixed charging piles, as well as the migration time of mobile charging vehicles between different service nodes, service session mutual exclusion relationships, and necessary migration buffer times during the decoding phase, thereby generating a complete scheduling table that can be directly used for objective function calculation. If a time window or energy constraint violation is found during decoding, the task start time, energy replenishment period, or resource allocation is adjusted through an in-decoding repair strategy; if the violation still cannot be repaired, a penalty is imposed on the individual.

[0010] During the evolution process, the algorithm follows... Figure 3The process described follows an iterative loop of "selection—crossover—mutation—decoding and repair—fitness evaluation." In each generation, the current population is first constrained; individuals meeting the constraints are selected, while infeasible individuals have their selection probability reduced through a penalty mechanism. Crossover and mutation operations are then performed to generate new individuals, which are then decoded and their feasibility repaired, and their multi-objective weighted fitness value is calculated. If a better solution emerges in the current generation, the global optimal solution record is updated. At the end of each generation, for the elite individuals with the best fitness, the algorithm incorporates a simulated annealing (SA) neighborhood improvement process to refine their key structures locally. By slightly perturbing the task order on the critical path, cross-AGV task redistribution, and refueling session duration, neighborhood solutions are generated, and the acceptance of these solutions is determined based on the simulated annealing criterion, thereby enhancing local optimization while maintaining global search capabilities. When the number of iterations reaches a preset upper limit or no improvement is observed for several consecutive generations, the algorithm terminates and outputs the current optimal scheduling scheme. The multi-objective evaluation adopts a weighted aggregation method after interval normalization, and the constraint handling follows the principle of "mainly repairing within the decoding process and supplementing with the penalty mechanism", so that the search process can maintain stable progress near the boundary of the feasible region.

[0011] The beneficial effects of this invention are that total energy consumption is reduced, the maximum construction period is stably converged within the threshold range, and economic costs are effectively controlled. Attached Figure Description

[0012] Figure 1 AGV operation cycle diagram for fixed charging pile energy replenishment strategy; Figure 2 This is a heatmap of the shortest path distance in Manhattan, presented as a topological map. Figure 3 Flowchart for solving the algorithm; Figure 4 This is a Gantt chart showing the scheduling and execution results. Detailed Implementation

[0013] In a typical application scenario, this invention selects n=800 orders as test cases, forming a batch task set T={1,2,...,n}. The system is configured with A=4 automated guided vehicles. The number of fixed charging stations is F=1, located near the main road of the factory area to ensure efficient switching between transportation and charging. The initial position of each vehicle... They are respectively located at the factory entrance and near the core workstations, with initial power consumption. It covers high, medium, and low levels to reflect the vehicle's adaptability to different energy states during dispatch. For example... Figure 1 The diagram illustrates the cyclical operation of an AGV under a fixed charging station strategy. Using the time axis as the horizontal axis, the diagram shows the complete operational cycle of a single vehicle within a multi-task sequence.

[0014] The road network of the factory area is abstracted as a topology graph composed of workstations, warehouses, and passageways, where the shortest path distance d between nodes is represented. ij It is calculated from the road network length and speed, such as Figure 2 The heatmap visually reflects the accessibility differences between main routes, bottleneck sections, and edge areas. During algorithm initialization and neighborhood operations, shorter node pairs are more likely to be assigned to adjacent tasks within the same vehicle, while longer node pairs trigger energy-sensitive penalties, thus guiding the search to avoid high-cost paths.

[0015] In the vehicle operation cycle, each vehicle undergoes the entire process of task start and completion, transition from the endpoint of the previous task to the starting point of the next task, returning to a fixed charging station during task breaks, continuously charging during the session until the target charge level is reached, then exiting the station, and finally transitioning to the next task. This cyclical mechanism ensures the continuity of task execution, while clearly showing the times of entering and exiting the charging station, the occupied interval of the session, the consumption interval during the transition, and the loading and unloading process on the timeline. The vehicle's status at different stages is represented by different striped intervals, which can intuitively reflect the impact of energy recovery on task transition and return empty driving time.

[0016] Algorithm framework such as Figure 3 As shown, the algorithm comprises an input layer, a modeling layer, a solution layer, and an output layer. The input layer includes the task set, the initial vehicle state, the topological distance matrix, and fixed charging pile parameters and cost parameters. The modeling layer maps the input to an objective function and constraints. The solution layer iteratively runs through steps including initialization, decoding and repair, fitness calculation, selection, crossover and mutation, elite merging, and local improvement. The output layer provides the scheduling scheme and performance metrics. The flowchart emphasizes the feedback mechanism between the model and the algorithm, especially how the insertion of charging sessions during the repair phase affects the task order, thus forming a closed-loop iteration.

[0017] The scheduling results are as follows Figure 4 As shown, Figure 4 The system uses color coding based on the project: "blue" represents loaded, "light" represents empty, "orange" represents waiting, and "green" represents charging. Figure 4 The results after 10 hours of operation are shown. A1-A4 are the numbers of the four AVG vehicles. The Gantt chart displays the operational status of each time period by vehicle dimension, with loaded transportation, empty transfer, waiting, and charging sessions represented by different color bands or textures. The chart marks the SOC transition range at several locations, from low battery to near full battery, indicating good coordination between charging and tasks. In the 800-unit scenario, the results show that sessions and tasks can be staggered during peak hours, significantly reducing empty return trips and avoiding congestion at charging stations. The three target indicators are: reduced total energy consumption, stable convergence of maximum project duration within the threshold range, and effective control of economic costs.

Claims

1. A multi-AGV collaborative scheduling model for fixed charging piles, characterized in that, The model is constructed on the plant topology network with the optimization objectives of minimizing total system energy consumption, minimizing maximum completion time, and minimizing economic cost. Symbol definition: A = {1, 2, ..., a}: a set of vehicles, index a, which represents the a-th automated guided vehicle in the system; T = {1, 2, ..., i}: a set of tasks, where index i represents the i-th transportation task in the system; N = {1, 2, ..., |i|}: a set of nodes, where index i represents the i-th work node in the factory area; F = {1, 2, ..., |f|}: a set of fixed charging stations, where index f represents the f-th fixed charging station; F1: The total system task completion time, which is the maximum value of the completion times of all tasks; F2: Total completion time of the multi-AGV system during the entire scheduling cycle; The overall cost associated with the configuration and operation of FCS for fixed charging stations; s i The starting node of task i; e j The endpoint of task j; : The time window for task i; ET i : Indicates the earliest start time of task i; LT i : Indicates the latest start time for task i; Loading service time for task i; The time it takes for task i to uninstall the service; d ij Manhattan distance between nodes i and j; : Accessibility indicator. If it is passable between nodes i and j on the map, the accessibility indicator is 1; otherwise, it is 0. v AGV travel speed; c Energy consumption coefficient per unit distance of AGV under no-load conditions; Energy consumption coefficient per unit distance when fully loaded by AGV; Q: Rated load capacity of AGV; w j The weight of goods in task j; σ AGV battery capacity limit; θ : Lower limit threshold for AGV battery safety capacity; π e Electricity unit price; : Cost of operating and maintenance distance; : Fixed cost coefficient for each use of a fixed charging station; : Cost coefficient per unit time occupied by a fixed charging station; Construction cost coefficient per unit capacity of fixed charging piles; p a : The initial position node of the a-th AGV; : The node where the a-th AGV is located before task i begins; M : A sufficiently large constant; ε 2 Construction period threshold; ε 3 Cost threshold; D ai The total distance traveled by the a-th AGV while performing task i; E ai : Total energy consumption of the a-th AGV performing task i; The battery level of the a-th AGV at time t; Maximum completion time; The a-th AGV returns to the charging station after completing task i. f The power replenished at the location; After completing task i, the a-th AGV enters the charging station. f At that moment; The a-th AGV leaves the charging station after completing task i. f At that moment; Before executing task i, the a-th AGV moves from its current position to the task start point. s i The driving distance; From the end of the mission e i to charging station f The driving distance; The starting point of task i s i To the finish line e i The driving distance; The endpoint of task i e i To the starting point of task j s j The driving distance; The endpoint of task j e j To the starting point of task i s i The driving distance; Charging pile f To the starting point of task j s j The driving distance; AGV from position p a Drive to the starting point of mission i s i The distance; Decision variables: If the a-th AGV is performing task i, then set the value to 1; otherwise, set the value to 0. If task i precedes task j on the same AGV, then set the value to 1; otherwise, set the value to 0. : Indicates the time when the a-th AGV starts executing task i. If the a-th AGV has not been assigned task i, it is 0; otherwise, it is the time when the AGV actually starts serving task i. : Represents the time when the a-th AGV completes task i. If the a-th AGV has not been assigned task i, it is 0; otherwise, it is the time when the AGV actually completes service task i. If the a-th AGV moves directly from node i to node j, then set the value to 1; otherwise, set the value to 0. If the a-th AGV goes to the charging station after completing task i. f If the value is 1, then take 1; otherwise, take 0. Based on the above description of the multi-task-point scheduling problem for multiple automated guided vehicles (AGVs), the mathematical model for AGV scheduling considering energy consumption, project duration, and economy constructed in this invention includes the following three objective functions: ； Wherein: Equation (1) represents the objective function of minimizing the sum of total system energy consumption; Equation (2) represents the objective of minimizing the maximum completion time; Equation (3) represents the system cost minimization under the fixed charging pile model.

2. The multi-AGV collaborative scheduling model for fixed charging piles as described in claim 1, characterized in that, The model includes the following constraints: ； Equation (4) indicates that each task must be performed by only one vehicle; Equation (5) indicates that the sequence variable and the assignment variable are linked and the order is forced when they are in the same vehicle; Equation (6) indicates that the bidirectional serialization of adjacent tasks in the same vehicle includes the transfer time; Equation (7) indicates that the task completion time at least covers the start time, travel time and loading / unloading time and is reduced by a sufficiently large constant M when not assigned; Equation (8) indicates that the task start and end times satisfy a given time window.

3. The multi-AGV collaborative scheduling model for fixed charging piles as described in claim 1, characterized in that, The model also includes the following constraints: ； Equation (9) indicates the time and energy feasibility from the vehicle's initial position to the starting point of the first task; Equation (10) indicates that the electricity at the start and end of the task is within the upper and lower bounds of the capacity; Equation (11) indicates the energy balance during the execution of the task; Equation (12) indicates that unreachable node pairs are not allowed to be selected due to path reachability restrictions; Equation (13) indicates that the maximum completion time is the lower bound of the completion time of all assigned tasks; Equation (14) indicates the range of values ​​for the binary decision variables; Equation (15) indicates the non-negativity of session energy supply; Equation (16) indicates the non-negativity of various time variables and project duration variables.

4. The multi-AGV collaborative scheduling model for fixed charging piles as described in claim 1, characterized in that, The model also includes the following constraints: ； ； Equation (17) indicates that at most one fixed charging station session can be selected after each task is completed; Equation (18) indicates that the start time of the fixed charging station session is not earlier than the completion time of the corresponding task; Equation (19) indicates the linear lower bound of the charging amount and the duration of the fixed charging station session; Equation (20) indicates the linear upper bound of the charging amount and the duration of the fixed charging station session; Equation (21) indicates the linear lower bound of the session duration required to reach full charge; Equation (22) indicates the linear upper bound of the session duration required to reach full charge; Equation (23) indicates the approximate full charge when the vehicle's battery level approaches the upper bound of the capacity at the end of the session; Equation (24) indicates that if no charging is performed, the battery level at the end of the task must not be lower than the safety threshold; Equation (25) indicates that a transfer time from the charging station to the starting point of the next task must be reserved from the end of charging to the start of the next task.

5. The algorithm for a multi-AGV collaborative scheduling model for fixed charging piles as described in claim 1, characterized in that, The algorithm is a hybrid heuristic method that combines an improved genetic algorithm with simulated annealing neighborhood search, and it is further improved in terms of domain. The algorithm framework includes an input layer, a modeling layer, a solution layer, and an output layer. The input layer includes a task set, the initial state of the AGV vehicle, a topology distance matrix, fixed charging pile parameters, and cost parameters; the modeling layer maps the input layer into an objective function and constraints; the topology distance matrix is ​​generated by combining the position coordinates of the AGV vehicle. The solution layer iterates through the steps of initialization, decoding and repair, fitness calculation, selection, crossover and mutation, elite merging and domain improvement; the output layer provides the scheduling scheme and performance indicators, and outputs the scheduling scheme and optimization indicators when the termination condition is met.

6. The algorithm as described in claim 5, characterized in that, The algorithm first reads the task parameters, AGV vehicle parameters, cost parameters, and fixed charging pile parameters from the input layer to initialize the problem; then it generates an initial population and performs a complete decoding and feasibility repair on the initial individuals to obtain an initial scheduling scheme that satisfies the basic time window and energy constraints. For an AGV scheduling model that simultaneously includes three objective functions—total system energy consumption, maximum completion time, and economic cost—and involves two types of energy replenishment mechanisms—fixed charging piles and mobile charging AGVs—the algorithm uses a two-segment chromosome coding method to describe the solution space. The chromosome consists of two parts: a "task assignment segment" and a "charging session segment." The task assignment segment is used to determine the AGV that will execute each transportation task, and the relative order of tasks within the same AGV is implied by the order of tasks in the chromosome; the charging session segment is used to describe whether the AGV triggers an energy replenishment behavior after completing a task and the corresponding energy replenishment resource type. In this process, the algorithm dynamically calculates the actual start and end times of each task based on the task time window constraints and the AGV's battery state of charge (SOC) constraints, and synchronously updates the energy evolution process of the AGV on the time axis; where SOC represents the current remaining power state of the AGV, which is used to ensure that the AGV's power does not fall below the safety threshold during task execution and driving. For the energy replenishment resource side, the algorithm uniformly handles the port occupancy constraints of fixed charging piles, as well as the migration time of mobile charging vehicles (AGVs) between different service nodes, service session mutual exclusion relationships, and necessary migration buffer time during the decoding phase, thereby generating a complete scheduling table that can be directly used for objective function calculation. If a time window or energy constraint is found to be violated during the decoding process, the task start time, energy replenishment period, or resource allocation is adjusted through the decoding repair strategy. If it still cannot be repaired, a penalty is imposed on the individual. During the evolutionary process, the algorithm enters an iterative loop of "selection-crossover-mutation-decoding and repair-fitness evaluation". During the iteration process, decoding and repair are used to maintain the feasibility of individuals under time windows and energy constraints. When the number of iterations reaches the preset upper limit or no improvement is seen for several consecutive generations, the algorithm terminates and outputs the current optimal scheduling scheme. Multi-objective evaluation adopts a weighted aggregation method after interval normalization, and constraint handling follows the principle of "decoding and repair as the main method and penalty mechanism as the auxiliary method", so that the search process can maintain stable progress near the boundary of the feasible region.

7. The algorithm as described in claim 6, characterized in that, During the algorithm's iteration process, in each generation, the current population is first constrained. Individuals that meet the constraints are selected, while infeasible individuals have their selection probability reduced through a penalty mechanism. Subsequently, crossover and mutation operations are performed to generate new individuals, and the new individuals are decoded and their feasibility is repaired, and their multi-objective weighted fitness value is calculated. If a better solution appears in the current generation, the record of the global optimal solution is updated. At the end of each generation, for the elite individuals with the best fitness, the algorithm embeds a simulated annealing (SA) neighborhood improvement process to refine their key structures locally, generate neighborhood solutions, and decide whether to accept the neighborhood solution based on the simulated annealing criterion, thereby enhancing the local optimization effect while maintaining global search capabilities.

8. The algorithm as described in claim 5, characterized in that, The neighborhood improvement operation includes fine-tuning the task order on the critical path, the task redistribution across AGVs, and the duration of the refueling session. The initialization phase adopts a combination of heuristic and random methods to improve population diversity.

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