A multi-constraint task scheduling method for unmanned surface vehicle, electronic equipment, computer readable storage medium and program product

Abstract

The application discloses a multi-constraint task scheduling method for unmanned surface vehicles and relates to the technical field of intelligent task allocation. The initial state and task attributes of an unmanned surface vehicle are inputted, an initial population is generated, individuals of the initial population are decoded, the dynamic priority of a task to be executed at a current scheduling time is determined based on a dynamic priority updating mechanism, hard constraints are checked, soft constraints are adjusted through a flexible time window extension mechanism, individual fitness is calculated, fast non-dominated level ordering and congestion degree calculation are performed, and an initial Pareto front is recorded. Iteration is performed, individuals of a parent population are crossed and mutated to generate a child population, the parent population and the child population are combined to form a candidate set, a global Pareto front is updated, solutions in the Pareto front are subjected to 2-opt local search and priority heuristic interchange strategies, an optimal individual is selected from the global Pareto front, and an optimal scheduling scheme is decoded and outputted. The method has the advantages of good scheduling stability, reduced cost and less time consumption.

Description

Technical Field

[0001] This invention relates to the field of intelligent task allocation technology, and in particular to a multi-constraint task scheduling method for unmanned surface vessels, electronic equipment, computer-readable storage medium, and program products. Background Technology

[0002] In actual inspection processes, unmanned surface vessels (USVs) performing offshore wind farm inspections are constrained by various factors, including mission time windows, mission type, priority, service time, navigation energy consumption, and endurance. Existing technologies primarily focus on the shortest path and lowest navigation cost, making it difficult to ensure the priority execution of critical tasks and to reflect factors such as waiting costs, service costs, navigation costs, and delay penalty costs. Furthermore, existing technologies suffer from insufficient local search capabilities, weak scheduling stability, and a tendency to get trapped in local optima. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a multi-constraint task scheduling method for unmanned surface vessels, thereby solving the problems of existing technologies failing to prioritize the execution of critical tasks under the premise of shortest path and lowest navigation cost, and having weak local search capabilities, making them prone to getting trapped in local optima. The invention also provides an electronic device, a computer-readable storage medium, and a program product.

[0004] The technical solution of the present invention is as follows: A multi-constraint task scheduling method for unmanned surface vessels, comprising the following steps:

[0005] Step 1: Input the initial state and mission attributes of the unmanned surface vessel, and generate a unique execution sequence as the initial population using integer permutation encoding.

[0006] Step 2: Decode the individuals in the initial population, then use a dynamic priority update mechanism based on the cumulative scheduling time of tasks to determine the dynamic priority of the tasks to be executed at the current scheduling time, verify hard constraints and adjust soft constraints through a flexible time window expansion mechanism, calculate the fitness of the individuals in the initial population, evaluate the quality of individuals through fast non-dominated ranking and crowding calculation, and record the Pareto front. The flexible time window expansion mechanism relaxes the executable range of critical tasks according to task priority. The hard constraints include access uniqueness constraints, energy constraints, time continuity constraints, and initial and termination constraints. The soft constraints are time window constraints. The fitness is evaluated based on total cost and total time. The total cost includes delay penalty cost, which is calculated based on a penalty function. The penalty function is calculated based on the time window constraints. The elite profile is an external elite set stored independently of the current population.

[0007] Step 3: Iterate and mutate the individuals in the parent population to generate the offspring population;

[0008] Step 4: Merge the parent population and the offspring population to form a candidate set, perform non-dominated sorting on the candidate set, extract the non-dominated solutions of the current generation and merge them with the existing solutions in the elite archive, delete dominated solutions and duplicate solutions in the merged set, write the remaining non-dominated solutions back to the elite archive, and update the global Pareto front.

[0009] Step 5: When the maximum number of iterations is reached, output the global Pareto front solution set. Perform a 2-opt local search and priority heuristic swap strategy on the solutions in the global Pareto front to reverse the task execution order. The priority heuristic swap strategy is to swap the delayed high-priority task with the preceding low-priority task. Select the optimal individual from the Pareto front and decode to output the optimal scheduling scheme.

[0010] Furthermore, the formula for calculating the delay penalty cost in step 2 is as follows:

[0011] ,

[0012] in, The penalty function employs a five-segment nonlinear model, applying penalties of varying intensities based on the relative position of the arrival time and the time window. For the task The actual arrival time; For the task Priority-adjusted time window For the task Dynamic priority at arrival time For the task Task type.

[0013] Furthermore, the calculation formula for the penalty function in step 2 is as follows:

[0014] ,

[0015] in, This is the actual arrival time. This represents the optimal time window for the task after priority adjustment. This represents the current dynamic priority of the task. For task type, To delay the duration, The length of the time window. This is the baseline value for opportunity cost, expressed in yuan / hour. Indicates the start point of the time window. This represents the penalty coefficient for arriving early. This represents the penalty coefficient for a slight delay. This represents the penalty coefficient for moderate delay. This represents the penalty coefficient for severe delays. As the opportunity cost benchmark, This represents a combined weighting function determined by both the task type and the current priority. To delay the duration, A fixed additional penalty for moderate delay. Fixed additional penalties for severe delays.

[0016] Furthermore, the adjusted time window calculation formula for the flexible time window expansion mechanism in step 2 is as follows:

[0017] ,

[0018] in, This represents the adjusted time window for task i under its current priority. Indicates the start time of the original time window. Indicates the end time of the original time window. Indicates the time window expansion ratio. Indicates the original time window length.

[0019] Furthermore, the total cost in step 2 is calculated by summing the sailing fuel cost, sailing time cost, waiting cost, service operation cost and the delay penalty cost, and the total time consumption is calculated by summing the sailing time of each segment, the waiting time of each task, and the service time of each task.

[0020] Furthermore, the formula for calculating the aviation fuel cost is as follows:

[0021] ,

[0022] in, This represents the Euclidean distance between adjacent mission points or homeports, in meters. This is the cost coefficient per unit distance traveled.

[0023] The formula for calculating the travel time cost is as follows:

[0024] ,

[0025] in, This represents the maintenance cost coefficient per unit time.

[0026] The formula for calculating the waiting cost is:

[0027]

[0028] in, For idling energy costs, To cover maintenance costs, As for opportunity cost, This represents the dynamic priority of task πj at the corresponding arrival time, used to characterize the amplifying effect of task urgency on the loss of waiting opportunities. 1.5 is the priority scaling factor, used to adjust the weight of dynamic priority in the waiting opportunity cost.

[0029] The formula for calculating the service operation cost is as follows:

[0030] ,

[0031] in, For the task Service duration, The basic cost coefficient per unit of service time. This is the task type coefficient.

[0032] Furthermore, the calculation formula for the dynamic priority update mechanism in step 2 is as follows:

[0033] ,

[0034] in, Let t be the dynamic priority corresponding to the current scheduling time t when task i performs a timing evaluation of the task during the decoding process. As the baseline priority for tasks, The moment of mission release. The length of the task time window. This is the priority growth factor corresponding to the task type. This is the upper limit of priority. To prevent small constants with zero denominators, t represents the current scheduling time.

[0035] Another technical solution of the present invention is: an electronic device, the electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor;

[0036] The memory stores a computer program that can be executed by the at least one processor, which is then executed by the at least one processor to enable the at least one processor to execute the aforementioned unmanned surface vessel multi-constraint task scheduling method.

[0037] Another technical solution of the present invention is: a computer-readable storage medium storing a computer program, the computer program being used to enable a processor to implement the aforementioned unmanned surface vessel multi-constraint task scheduling method when executed.

[0038] Another technical solution of the present invention is: a computer program product, including a computer program, which, when executed by a processor, implements the aforementioned unmanned surface vessel multi-constraint task scheduling method.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] By employing a dynamic priority update mechanism and a flexible time window expansion mechanism, the on-time rate of high-priority tasks can be increased to over 90%, and the total cost is reduced by approximately 30%-40% compared to traditional algorithms. The penalty ratio is significantly reduced, thus decreasing the total scheduling cost. Furthermore, by combining 2-opt local search, the task execution cycle can be shortened, reducing waiting time and redundant travel, thereby reducing the total task time. Through the combination of multi-objective optimization and local optimization, the solution set becomes more robust, improving scheduling stability. Attached Figure Description

[0041] Figure 1 The flowchart of the improved NSGA-II algorithm of this invention is shown.

[0042] Figure 2 This diagram illustrates the impact of each improved module of the present invention on the on-time performance of tasks.

[0043] Figure 3 The result diagram shows the task scheduling of the basic GA algorithm.

[0044] Figure 4 The graph shows the task scheduling results of the PSO algorithm.

[0045] Figure 5 The diagram shows the results of the basic NSGA-II task scheduling.

[0046] Figure 6 The task scheduling results are shown in the diagram for improving the NSGA-II algorithm.

[0047] Figure 7 This is a comparison chart of the cost, computation time, and on-time performance of different algorithms in this invention.

[0048] Figure 8 This is a radar chart showing the combined performance of different algorithms in this invention. Detailed Implementation

[0049] The specific technical solution of the present invention will be further described in detail below with reference to specific examples.

[0050] Combination Figure 1 As shown in the figure, the multi-constraint task scheduling method for unmanned surface vessels according to an embodiment of the present invention includes the following steps:

[0051] Within a given two-dimensional operational area, a single unmanned surface vessel (USV) departs from its base, sequentially visits a set of geographically dispersed task points, completes corresponding service tasks, and finally returns to the base. Each task has specific service time, time window constraints, and task priority, and the task types exhibit heterogeneity. Based on the differences in actual task characteristics, tasks are categorized into four types: time-sensitive, event-driven, dependent, and routine inspection. Time-sensitive tasks are responsible for blade crack detection, requiring urgent response and having high priority. Event-driven tasks are responsible for post-typhoon safety inspections, triggered by specific events. Dependent tasks are responsible for sea state data collection, dependent on environmental conditions. Routine inspection tasks are responsible for daily routine maintenance, with flexible timing.

[0052] The initial state of the unmanned surface vessel (USV) includes base coordinates, initial remaining battery power, rated battery capacity, safe depth of discharge coefficient, cruising speed, baseline cruising power, idle power, and power-speed index. The effective available battery power is the product of the rated battery capacity and the safe depth of discharge coefficient, used to limit the maximum allowable power consumption during scheduling. Idle power is the power required by the USV to maintain basic systems such as positioning, communication, navigation, and monitoring while waiting at the mission point. In this embodiment, the rated battery capacity is 15 kWh, the safe depth of discharge coefficient is 0.70, the effective available battery power is 10.5 kWh, the idle power is 0.15 kW, and the initial remaining battery power is taken as the rated battery capacity.

[0053] Task attributes include at least the task point coordinates, task type, baseline priority, task creation time, original time window set, and service duration. The task creation time is the moment the scheduling system receives the task request or generates the task record, and it serves as the starting point for dynamic priority updates over time. In this embodiment, the estimated total scheduling duration is T, and the task creation time is randomly determined within the range of 0 to 0.15T. The original time window set for each task is formed according to the task creation time, preparation time, window length, and window interval for the corresponding task type: the start time of the first time window is the sum of the task creation time and preparation time, and the end time is the sum of the start time and window length; when multiple time windows are set, the start time of the next time window is the sum of the end time of the previous time window and the window interval. In this embodiment, 1 to 2 original time windows are set for each task, with a window interval of 0.5 to 1.5 hours; the preparation time, window length, and service duration are determined within a preset range based on the task type.

[0054] The original time window set for each task is formed according to the task creation time, preparation time, window length, and window interval for the corresponding task type. Different task types correspond to different time parameter configurations. Specifically, Time-Sensitive Tasks (TS) are mainly used for urgent tasks such as blade crack detection, with a preparation time of 0.2–0.8 h, a time window length of 1.2–3.0 h, and a service duration of 0.25–0.45 h; Event-Driven Tasks (ED) are mainly used for emergency response tasks such as post-typhoon safety inspections, with a preparation time of 1.0–3.5 h, a time window length of 1.2–2.6 h, and a service duration of 0.25–0.35 h; Dependent Tasks (DP) are mainly used for tasks dependent on environmental conditions, such as sea state data acquisition, with a preparation time of 0.8–2.5 h, a time window length of 2.0–3.2 h, and a service duration of 0.18–0.28 h; and Regular Inspection Tasks (NM) are mainly used for periodic equipment inspection tasks, with a preparation time of 2.0–6.0 h, a time window length of 2.5–4.0 h, and a service duration of 0.10–0.30 h.

[0055] For each task, the system determines the preparation time, window length, and service time within the corresponding parameter range based on the task type, and generates the original time window set for the task accordingly. The service time represents the continuous operation time required for the unmanned surface vessel to perform detection, data acquisition, or inspection operations after arriving at the task point.

[0056] To facilitate subsequent model construction, the main symbols involved in this invention are defined as shown in Table 1.

[0057] Table 1 Definitions of Main Symbols

[0058]

[0059] To reflect the changing urgency of tasks as the cumulative waiting time for scheduling changes, this invention introduces a dynamic priority update mechanism based on the cumulative waiting time of tasks:

[0060] ,

[0061] in, Let t be the dynamic priority corresponding to the current scheduling time t when task i performs a timing evaluation of the task during the decoding process. As the baseline priority for tasks, The moment of mission release. The length of the task time window. This is the priority growth factor corresponding to the task type. This is the upper limit of priority. To prevent small constants with zero denominators, t represents the current scheduling time.

[0062] To meet the operational requirements of different tasks and achieve targeted control, this invention divides the configuration levels of four tasks to distinguish different control intensities. The corresponding relationship of the configuration levels matched to different task types is shown in Table 2.

[0063] Table 2 Task Type Parameter Table

[0064]

[0065] The task scheduling problem for unmanned surface vessels (USVs) in offshore wind farms needs to be optimized while satisfying multiple constraints. Based on the enforceability of these constraints, they can be divided into hard constraints and soft constraints. Hard constraints include access uniqueness constraints, energy constraints, time continuity constraints, and initial and termination condition constraints. Soft constraints include time window constraints and priority adaptive time expansion mechanisms. Hard constraints must be strictly satisfied, while soft constraints are reflected through penalty functions. Hard constraints are necessary conditions for a feasible solution; solutions that violate hard constraints are directly deemed infeasible and do not participate in subsequent selection and ranking. The formula for the access uniqueness constraint is:

[0066] ,

[0067] Where N={1,2,...,n} is the set of task node indices; i is the specific task node number; j is the position index of the task in the access sequence; This represents the j-th task that is visited in the sequence; Represents the task node numbered i; the symbol " The '+' signifies 'exists exactly once'. The overall meaning is: for each task i, there exists a unique position j in the access sequence corresponding to it, thus ensuring that each task is accessed only once. Each task must be accessed exactly once. This is a fundamental constraint of the vehicle routing problem, ensuring that all wind turbine detection points are completely covered, and that there are no duplicate operations or task omissions.

[0068] The formula for energy constraints is:

[0069]

[0070] Among them, E consumed E represents the cumulative energy consumption of the entire task execution sequence. travelj E represents the energy consumption of the j-th segment of the voyage. effective E represents the effective usable energy of the battery. capacity This refers to the battery's rated capacity; DOD safe This is the safe depth of discharge coefficient.

[0071] The navigation energy consumption is calculated based on a physical model, and the calculation formula is as follows:

[0072]

[0073] Where P(v) is the propulsion power of the unmanned surface vessel at speed v; Let j be the sailing time for the j-th segment; Reference cruise power; v is the baseline cruising speed; v is the current cruising speed. The power-speed index is used to characterize the nonlinear relationship between power and speed.

[0074] The total energy consumption of the unmanned surface vessel (USV) is the energy consumed during its round trip to all mission points. The total energy consumption of the USV must not exceed the effective capacity of its battery; otherwise, the battery will be depleted mid-journey, preventing the mission from being completed or the USV from returning to its home port. Using a safe depth of discharge of 70% instead of 100% is to reserve emergency power to deal with unforeseen circumstances and ensure the safety of the battery system.

[0075] The formula for the time continuity constraint is:

[0076]

[0077] in, The arrival time for executing the (j+1)th task, The departure time after performing the j-th task. This represents the time required to travel from the j-th visitor node to the (j+1)-th visitor node.

[0078] The formula for calculating the sailing time is as follows:

[0079]

[0080] Let j represent the sailing time of the j-th segment (the sailing time in the above formula represents the same physical quantity, only the subscript is different). This represents the Euclidean distance between adjacent visit mission points or home ports. The cruising speed of the unmanned surface vessel.

[0081] The arrival time of the next mission is equal to the departure time of the previous mission plus the travel time. This constraint ensures the continuity and causal relationship of the timeline, reflecting the physical process of the unmanned surface vessel moving in space.

[0082] The formulas for calculating the initial and final conditions are as follows:

[0083]

[0084] This indicates the arrival time of the unmanned surface vessel as it travels from base B to the first mission point. This indicates the distance the unmanned surface vessel travels from base B to the first mission point. The cruising speed of the unmanned surface vessel. This indicates the arrival time upon returning to base after completing all tasks. This indicates the departure time after the last task is completed. This represents the distance from the last mission point to base B.

[0085] Unmanned surface vessel from home port base After setting off and completing all tasks, the unmanned surface vessel (USV) must return to its home port. This is a fundamental requirement of the closed-loop path problem, ensuring that the USV can safely return for charging, maintenance, and data unloading.

[0086] The actual service start time of the task cannot be earlier than the start time of the time window. If the unmanned surface vessel arrives early, it must wait until the time window opens before it can begin operations. Soft constraints allow for delayed arrival, but a penalty function translates the degree of violation into cost increments, guiding the algorithm to find a better solution. The formula for the time window constraint is:

[0087] ,

[0088] in, This indicates the actual start time of the j-th task. This indicates the time when the unmanned surface vessel arrived at the mission point. For the task The start time of the time window after priority adjustment.

[0089] To address the issue of excessively high penalty costs for high-priority tasks due to overly restrictive time windows in traditional methods, this invention proposes a flexible time window expansion mechanism. High-priority tasks are more critical and should be given greater scheduling flexibility to reduce the risk of delayed execution of critical tasks. The expanded time window and penalty function form a dual guarantee: a more lenient window improves on-time performance, while the penalty function maintains the constraint strength. The formula for calculating the time window expansion ratio is as follows:

[0090] ,

[0091] in, This represents the time window expansion ratio calculated based on the current priority. This represents the basic flexibility coefficient for task i. This indicates the current dynamic priority of task i. This represents a range clipping function used to limit the expansion ratio to a preset upper and lower bound.

[0092] The adjusted time window calculation formula is as follows:

[0093] ,

[0094] in, This represents the adjusted time window for task i under its current priority. Indicates the start time of the original time window. Indicates the end time of the original time window. Indicates the time window expansion ratio. Indicates the original time window length.

[0095] The core of the unmanned surface vessel (USV) multi-task scheduling problem lies in finding the optimal task access sequence to maximize scheduling efficiency. In practical applications, decision-makers typically need to balance operating costs and operational efficiency. On the one hand, excessively pursuing low costs may lead to excessively long task completion times, affecting overall operational efficiency; on the other hand, unilaterally pursuing the shortest time may result in high operating costs and time window violation penalties. Based on these considerations, this invention establishes a dual-objective optimal scheduling model to collaboratively optimize the two conflicting objectives of minimizing overall operating costs and minimizing total time. Overall operating costs encompass all expenses incurred by the USV during the entire scheduling process, including fuel costs, travel time costs, waiting costs, service operation costs, and delay penalty costs. The objective function formula for minimizing overall operating costs is:

[0096] ,

[0097] in, For the cost of aviation fuel, For the cost of travel time, Due to waiting costs, For service operation costs, To delay the cost of punishment.

[0098] Fuel cost reflects the direct energy consumption incurred by an unmanned surface vessel (USV) due to spatial displacement during mission execution. Fuel cost is directly proportional to the Euclidean distance between mission points and is the most fundamental cost component in scheduling optimization. The formula for calculating fuel cost is:

[0099] ,

[0100] in, This represents the Euclidean distance between adjacent mission points or homeports, in meters. This is the cost coefficient per unit distance traveled, expressed in yuan / km.

[0101] Voyage time cost reflects the time value loss and equipment maintenance costs incurred by an unmanned surface vessel (USV) during its voyage. Even while in motion, the USV's mechanical components, such as propulsion systems, navigation equipment, and communication modules, continue to operate, experiencing wear and tear and requiring regular maintenance. The formula for calculating the navigation time cost is:

[0102] ,

[0103] in, The cruising speed of the unmanned surface vessel is set based on actual sea conditions and safe navigation requirements. This is the maintenance cost coefficient per unit time, including mechanical wear and tear depreciation costs, and labor costs for manual monitoring and remote operation.

[0104] The formula for calculating the sailing time is:

[0105] ,

[0106] in, This represents the Euclidean distance between adjacent mission points or homeports, in meters. This refers to the cruising speed of the unmanned surface vessel.

[0107] Waiting costs reflect the multi-dimensional losses incurred when an unmanned surface vessel (USV) arrives at the mission point ahead of schedule but cannot immediately execute the mission due to time window constraints. Waiting costs consist of three sub-items: energy consumption, equipment maintenance, and opportunity cost. The formula for calculating waiting costs is as follows:

[0108]

[0109] in, The idling energy cost indicates that while in a standby state, the unmanned surface vessel (USV) still needs to maintain basic system operation to sustain positioning, communication, and monitoring functions. To cover maintenance costs, the equipment is still subject to wave impacts and other factors during the waiting period, thus creating a maintenance requirement. As for opportunity cost, This represents the dynamic priority of task πj at its corresponding arrival time, used to characterize the amplifying effect of task urgency on the opportunity cost of waiting. 1.5 is the priority scaling factor, used to adjust the weight of dynamic priority in the opportunity cost of waiting. The higher the dynamic priority, the greater the opportunity cost per unit of waiting time. For example, if the blade crack detection task is delayed, it may lead to further crack propagation; therefore, the opportunity cost per unit of waiting time is usually higher than that of a regular inspection task.

[0110] The formula for calculating the waiting time is:

[0111] ,

[0112] in, For the task The start time of the time window after priority adjustment This refers to the moment when the unmanned surface vessel arrives at the mission point.

[0113] Service operation costs reflect the costs incurred by unmanned surface vessels (USVs) when performing specific tasks at mission sites, such as data acquisition, equipment testing, and image capture. Different types of missions exhibit significant differences in unit time costs due to variations in operational complexity, equipment usage intensity, and data processing requirements. The formula for calculating service operation costs is as follows:

[0114] ,

[0115] in, For the task The service duration, in hours, is randomly assigned based on the task type during generation. The basic cost coefficient per unit of service time. This is the task type coefficient, reflecting the operational complexity of different tasks.

[0116] The delay penalty cost is the most critical cost component in this model. It quantifies the negative impact of task execution time deviating from the optimal time window through an economic penalty mechanism. The delay penalty cost reflects not only direct economic losses, such as increased equipment failure and safety risks, but also implicit costs such as decreased customer satisfaction and degraded service quality. The formula for calculating the delay penalty cost is as follows:

[0117] ,

[0118] in, As the penalty function, a five-segment nonlinear model is adopted, applying penalties of varying intensities based on the relative position of the arrival time and the time window. For the task The actual arrival time; For the task Priority-adjusted time window For the task Dynamic priority at arrival time For the task Task type.

[0119] The formula for the penalty function is:

[0120] ,

[0121] in, This is the actual arrival time. This represents the optimal time window for the task after priority adjustment. This represents the current dynamic priority of the task. For task type, To delay the duration, The length of the time window. This is the baseline value for opportunity cost, expressed in yuan / hour. Indicates the start point of the time window. This represents the penalty coefficient for arriving early. This represents the penalty coefficient for a slight delay. This represents the penalty coefficient for moderate delay. This represents the penalty coefficient for severe delays. As the opportunity cost benchmark, This represents a combined weighting function determined by both the task type and the current priority. To delay the duration, A fixed additional penalty for moderate delay. Fixed additional penalties for severe delays.

[0122] Total time reflects the total time required for the unmanned surface vessel to complete all tasks and return to its home port, and is a direct indicator of scheduling efficiency. There is a certain conflict between minimizing total time and minimizing total cost; their optimal solutions form a Pareto front, requiring a trade-off through multi-objective optimization algorithms. The formula for calculating total time is:

[0123] ,

[0124] in, This represents the sum of the travel times for each segment of the voyage. This represents the sum of the waiting times for all tasks. This represents the sum of the service times for all tasks.

[0125] This invention employs an improved NSGA-II algorithm to jointly optimize both total cost and total time, obtaining the Pareto front solution set. To facilitate subsequent comparison with the algorithm, the experimental section further constructs a comprehensive evaluation function to rank and evaluate candidate solutions across different algorithms.

[0126]

[0127] F is the comprehensive evaluation value used to rank the Pareto candidate solutions. , These are the two weighting coefficients for the comprehensive evaluation. This represents the corresponding total cost. Indicates the total completion time

[0128] In this embodiment, considering both the economy and execution efficiency of offshore wind farm inspection tasks, w1=0.4 and w2=0.6 are preferred. However, in practical applications, the above weights can be adjusted according to operation and maintenance needs.

[0129] This invention's algorithm, within a multi-objective optimization framework, focuses on redesigning the encoding method and fitness evaluation. Since this invention studies the scheduling and ordering problem of a single unmanned surface vessel (USV), no target allocation is required; therefore, it employs an integer permutation encoding based on the task sequence. Assuming the total number of tasks is n, a chromosome consists of a unique sequence of integers from 1 to n. For example, with 6 tasks, the encoding of a particular individual can be represented as [3, 1, 5, 2, 6, 4], indicating that the USV sequentially executes tasks 3, 1, 5, etc.

[0130] During the decoding phase, the system performs a sequential simulation of the unmanned surface vessel's execution process according to the gene sequence. This includes: starting from the base according to the access sequence, calculating the Euclidean distance, travel time, and energy consumption between adjacent nodes segment by segment; updating remaining battery power and arrival time; updating the dynamic priority of tasks based on the current time and flexibly expanding the time window; selecting the window with the minimum "waiting cost + penalty cost" from the available time windows; then calculating the waiting time, actual service start time, service end time, departure time, and corresponding travel cost, time cost, waiting cost, service cost, and penalty cost; after all tasks are completed, calculating the return time and return energy consumption, ultimately obtaining the total cost and total time for that individual. To balance the algorithm's global search capability in the early iterations with its local exploitation capability in the later iterations, the crossover probability P_c and mutation probability P_m adaptively change with the number of iterations and population diversity to improve optimization efficiency and reduce the risk of getting trapped in local optima.

[0131] While the classic NSGA-II algorithm possesses powerful global search capabilities, it lacks efficiency in fine-grained order adjustments of adjacent task nodes. Therefore, this invention introduces a local search strategy for the Pareto front set, i.e., the optimal solution set, in the final stage of the genetic algorithm's optimization process. The 2-opt reverse search shortens the total journey by eliminating "crossings" in the task execution path. Specifically, it randomly selects two nodes from the current task sequence. and ,Will arrive The order of task execution is reversed. If the new sequence after reversal can reduce the objective function value without violating the power constraint, then the new solution is accepted.

[0132] Considering the unique nature of wind field tasks, some high-risk tasks, such as post-typhoon inspections, may be relegated to the back of the sequence, resulting in high penalties. Therefore, this invention designs a priority-based heuristic swapping strategy. This strategy scans the sequence, attempting to swap high-priority tasks that are currently delayed with lower-priority tasks preceding them. If the overall fitness improves after the swap, the sequence is updated. In this way, GA (Global Algorithm) handles global space exploration, while local search improves the accuracy of the solution, thereby further approximating the true Pareto optimal front.

[0133] The specific algorithm flow is as follows:

[0134] (1) Input data: Input the initial state and mission attributes of the unmanned surface vessel. The initial state of the unmanned surface vessel includes the base coordinates, initial remaining power, rated battery capacity, safe discharge depth coefficient, effective available power determined by the rated battery capacity and safe discharge depth coefficient, cruise speed, baseline cruise power, idle power, power-speed index, unit distance navigation cost, unit time maintenance cost and opportunity cost baseline value. The mission attributes include the mission point coordinates, original time window set, baseline priority, mission type, mission creation time and service duration. The original time window set is formed according to the mission creation time, preparation time corresponding to the mission type, window length and window interval.

[0135] (2) Initialize the algorithm parameters, setting the population size, maximum number of iterations, basic crossover probability P_c=0.75, basic mutation probability P_m=0.12, and local search parameters. The local search parameters include at least: the maximum number of iterations for 2-opt local search, the maximum number of executions for priority heuristic swaps, and the forward search range and minimum improvement threshold corresponding to different task types; in this embodiment, the maximum number of 2-opt iterations is 100, and the maximum number of priority swaps is 3.

[0136] (3) Initialize the population. Pop_Size unique task execution sequences are randomly generated using an integer permutation encoding method as the initial population.

[0137] (4) Decode each individual in the initial population, adopt a dynamic priority update mechanism based on the cumulative scheduling time of tasks, determine the dynamic priority of the tasks to be executed at the current scheduling time, verify hard constraints and adjust soft constraints through a flexible time window expansion mechanism, and calculate the fitness value of the individuals in the initial population. Decoding refers to simulating the execution process of the unmanned surface vessel task by task according to the task sequence, calculating the distance between adjacent nodes, travel time, travel energy consumption, arrival time, waiting time, service start time, departure time and return process in sequence, and accumulating the total cost and total time based on these. Then, perform fast non-dominated sorting and congestion calculation on all individuals to form the initial Pareto front; establish an elite archive and write the non-dominated solutions in the initial Pareto front into the elite archive. The elite archive is an external elite set stored independently of the current population, used to store the non-dominated solutions obtained during the iteration process; when writing a new solution, compare the dominance relationship between the new solution and the existing solutions in the elite archive, delete dominated solutions and duplicate solutions, and retain solutions that are not mutually dominated. Fast non-dominated sorting divides the population into multiple hierarchical fronts based on the dominance relationships between individuals; crowding calculation estimates the sparsity of solutions around an individual within the same front. The greater the crowding, the more preferentially it is retained to maintain the diversity of the solution set distribution.

[0138] (5) Adaptive evolution. Iterative loop, dynamically adjusting the crossover probability P_c and mutation probability P_m based on population diversity and stagnation generation. Population diversity is defined as the ratio of the number of individuals with distinct task sequences in the current population to the population size; stagnation generation refers to the number of consecutive generations in which the historical best comprehensive target value has not been improved. Parent population selection uses the NSGA-II selection operator to select individuals from the current population based on non-dominance level and crowding degree; crossover uses partial mapping crossover PMX, that is, selecting mapping intervals in two parent permutations and repairing duplicate genes according to the mapping relationship to generate legal offspring sequences; mutation uses exchange mutation, that is, randomly selecting two gene positions with a given position probability and exchanging their task numbers; then the fitness of offspring individuals generated by crossover and mutation is recalculated to form the offspring population.

[0139] (6) Elite retention. The parent population is merged with the offspring population generated by crossover and mutation to form a candidate set of size 2×Pop_Size; the non-dominated sorting is re-executed on the candidate set, and the top Pop_Size individuals are retained for the next generation according to the frontier level and crowding degree; the non-dominated solutions of the current generation are extracted and merged with the existing solutions in the elite archive, the dominated solutions and duplicate solutions in the merged set are deleted, and the remaining non-dominated solutions are written back to the elite archive to update the global Pareto front generation by generation.

[0140] (7) Determine whether the algorithm termination condition is met. If the maximum number of iterations is reached, output the global Pareto front solution set stored in HoF and proceed to step 8; otherwise, return to step 5 and continue to update the population and HoF.

[0141] (8) Local depth search: traverse each Pareto front solution saved in the elite archive output in step 7, and perform 2-opt reversal operation and priority heuristic swap operation in sequence; recalculate the fitness of the solutions before and after the local search, retain the solutions with better comprehensive evaluation values, and form an improved Pareto candidate solution set.

[0142] (9) Output the optimal solution. Based on decision preference, select the optimal individual from the improved Pareto candidate solution set formed in step 8, and decode and output the detailed task scheduling sequence, time nodes and cost details.

[0143] To verify the effectiveness of the proposed improved NSGA-II and local search hybrid algorithm in the scheduling of unmanned surface vessels (USVs) in offshore wind farms, we conducted a series of simulation experiments in the Python environment. In this embodiment, a 2-meter-class small USV was selected as the execution platform. The speed, service time, time window, and algorithm parameters were set according to Table 3, while the task point location and task type information were set according to Table 4. These parameter configurations are only for illustrating the feasible implementation of the method of this invention; in actual applications, they can be adjusted according to the USV model, wind farm scale, and operation and maintenance strategy. The sea area to be inspected was set as a 3000 m × 3000 m rectangular area, with the home port located at the center of the area, which has a range of 1500 x 1500 m. The scheduling object was one USV. Task points were generated using a concentric circle hierarchical distribution method, with random perturbations superimposed in the angular and radial directions to balance spatial uniformity and scene realism. The USV departed from the home port, visited each task point sequentially according to the optimized sequence, completed the service, and finally returned to the home port.

[0144] After completing the parameter configuration, the scheduling system reads information such as task location, task type, service duration, original time window, baseline priority, task creation time, as well as the unmanned surface vessel's base coordinates, initial remaining battery power, rated battery capacity, safe discharge depth coefficient, effective available battery power, cruise speed, baseline cruise power, and idle power. It then generates scheduling results in the order of task sequence encoding, path decoding, dynamic priority update, flexible time window expansion, multi-objective optimization, local correction, and scheme output.

[0145] Specifically, the system first uses integer permutation encoding to represent the task access order; then it calculates the travel time and energy consumption based on the distance between adjacent task points, and verifies the unique access of tasks, time continuity, energy constraints, and home port round-trip constraints; it calculates the comprehensive operating cost and total time for feasible individuals, and searches for Pareto candidate solutions by improving NSGA-II; finally, it performs 2-opt reversal and high-priority task exchange on the candidate solutions, and outputs the task execution sequence, arrival time, waiting time, service time, and cost composition.

[0146] Table 3 Parameter Settings for Example

[0147]

[0148] Table 4. Task location and task type information

[0149]

[0150] To illustrate the roles of the flexible time window expansion mechanism, dynamic priority, and 2-opt local search in this invention, four module combinations are set up under the same task scenario. The flexible time window expansion mechanism is used to widen the executable range of critical tasks according to task priority; the dynamic priority is used to update the current priority of the task to be executed according to the current scheduling time, task creation time, and task type, and the update result is used for time window adjustment, waiting cost, and delay penalty calculation; and the 2-opt local search is used to correct the local path order of Pareto candidate solutions.

[0151] All four combination schemes use the same task points, unmanned surface vessel parameters, and constraint verification rules. The only difference is the activation of different improvement modules, as shown in Table 5.

[0152] Table 5 Improved Module Combination Settings

[0153]

[0154] Among them, +TimeWin indicates that only the priority adaptive flexible time window expansion mechanism is enabled; +DynPrio indicates that only dynamic priority update is enabled; +2-opt indicates that only 2-opt local path optimization is enabled; and Full indicates that all three modules are enabled simultaneously.

[0155] Depend on Figure 2 The results show that the Full scheme provides a more significant guarantee for high-priority tasks. Time-sensitive tasks such as blade crack detection can enter the execution sequence earlier, and the on-time rate is higher than that of other single-module schemes.

[0156] In schemes without flexible time window expansion, high-priority tasks are more prone to delay penalties due to overly tight time windows. In schemes without dynamic priority or 2-opt local search, although some tasks can still be completed, waiting time, detour distance, and overall cost all increase. These results demonstrate that the three modules constrain and modify the scheduling scheme from three levels: time window, task weight, and path order.

[0157] Table 6 shows the time composition and cost under different module combinations. The total time of the Full scheme is 14.75 h, which is lower than that of the w / o FlexTW, w / o DynPrio and w / o 2-opt schemes; the waiting time is reduced to 1.46 h, indicating that the dynamic priority and flexible time window expansion mechanism can reduce the waiting time of critical tasks, and the 2-opt local search can reduce redundant flight range.

[0158] Table 6. Time Composition and Costs for Different Module Combinations

[0159]

[0160] As shown in Table 7, the Full scheme prioritizes high-priority or event-driven tasks such as post-typhoon safety inspections and blade crack detection in the task sequencing process to avoid them being postponed outside the strict time window; in other combined schemes, low-priority tasks are often executed in advance, which can easily cause delays in critical tasks.

[0161] Therefore, in this embodiment, the dynamic priority mechanism is used to determine the dynamic priority of the task to be executed at the current scheduling time based on the cumulative waiting time from the task release time to the current scheduling time, the task time window length, and the task type. It also influences the evaluation of candidate solutions through time window adjustment, waiting costs, and delay penalties. The flexible time window expansion mechanism provides a more reasonable executable interval for high-priority tasks, and the 2-opt local search shortens the navigation path between task points. Combined, these three mechanisms enable the scheduling system to meet energy and time continuity constraints while also considering cost, time consumption, and the timeliness of critical tasks.

[0162] When all three modules are activated simultaneously, the overall cost is significantly reduced compared to the single-module approach, and the on-time performance of high-priority tasks is improved to a high level. This result demonstrates that the module combination of the present invention is not simply an additive process, but rather creates a synergistic effect between task urgency identification, time window processing, and path order correction.

[0163] Table 7 Examples of task execution order under different module combinations

[0164]

[0165] In another embodiment, to illustrate the improvement of the scheduling method of the present invention compared with common algorithms, the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), the basic NSGA-II, and the improved NSGA-II of the present invention are compared in the same scenario. The main parameter settings of each algorithm are shown in Table 8. All algorithms use the task points shown in Table 4 and the unmanned surface vessel parameters shown in Table 3, and adopt the same time window, priority, and constraint verification rules.

[0166] Figure 3The graph shows the task scheduling results of the basic GA algorithm. Figure 4 The task scheduling result diagram of the PSO algorithm is shown. To ensure consistency in the comparison process, GA and PSO use a unified comprehensive evaluation function as the fitness for single-objective search. At the same time, PSO is mapped to a discrete task sequence through random key encoding. Figure 5 Based on the NSGA-II task scheduling results diagram Figure 6 To improve the task scheduling results of the NSGA-II algorithm, the basic NSGA-II and the improved NSGA-II of this invention are optimized with total cost and total time as dual objectives. Representative schemes are selected from the Pareto front according to the same comprehensive evaluation function so as to make a horizontal comparison with single-objective algorithms.

[0167] This invention improves upon the non-dominated sorting and congestion maintenance mechanism of the basic NSGA-II by adding dynamic priority updates, flexible time window expansion mechanism adjustments, 2-opt local search, and high-priority task swapping, thereby enhancing the handling of the timeliness of critical tasks and the local structure of paths.

[0168] To facilitate a unified comparison of results from different algorithms, this embodiment uses the following comprehensive evaluation function to rank representative schemes. This function is only used for effect illustration and does not change the search mechanism of each algorithm itself:

[0169] F = w1·Cnorm + w2·Tnorm + w3·Pnorm + w4·(1 - Rhp)

[0170] In the formula, Cnorm represents the normalized total cost, Tnorm represents the total time consumption, Pnorm represents the delay penalty, Rhp represents the on-time rate of high-priority tasks, and w1, w2, w3, and w4 are weighting coefficients. The smaller the F value, the better the overall scheduling effect. Specifically, w1 is the normalized overall cost evaluation weighting coefficient, w2 is the normalized total time evaluation weighting coefficient, w3 is the normalized delay penalty evaluation weighting coefficient, and w4 is the high-priority task on-time rate loss evaluation weighting coefficient. Preferably, in this embodiment, w1=0.30, w2=0.20, w3=0.30, w4=0.20, and w1+w2+w3+w4=1. The above weights can be adjusted according to actual operation and maintenance needs.

[0171] Table 8. Main parameter settings for each algorithm

[0172]

[0173] Figure 7Table 9 shows a comparison of the costs, computation time, and on-time performance of different algorithms. As can be seen, under the same task and parameter conditions, the improved NSGA-II achieves a comprehensive cost of 1187.9 yuan, lower than the basic NSGA-II, GA, and PSO schemes, representing reductions of approximately 17.8%, 39.0%, and 43.5%, respectively. This result demonstrates that the present invention can achieve a more reasonable trade-off between flight costs, waiting costs, service costs, and delay penalties.

[0174] In terms of mission timeliness, the improved NSGA-II achieves a 90% on-time rate for high-priority missions. For time-sensitive missions such as blade crack detection and post-typhoon safety inspections, the dynamic prioritization mechanism allows them to receive higher ranking weights as waiting time increases, while the flexible time window expansion mechanism reduces the risk of critical missions being judged as delayed due to overly strict windows.

[0175] In terms of penalty cost, the improved NSGA-II has a penalty ratio of 67.9%, lower than the other three algorithms; combined with comprehensive cost calculation, its absolute penalty cost is approximately 806 yuan, lower than the basic NSGA-II, GA, and PSO. This result demonstrates that the time window adaptive processing of this invention can mitigate the increased costs caused by delays in critical tasks.

[0176] Table 9 Performance Comparison of Representative Schemes for Different Algorithms

[0177]

[0178] Table 10 shows the execution time breakdown for each algorithm. The improved NSGA-II has a total execution time of 14.75 h, with a flight time of 2.95 h and a waiting time of 1.46 h, both lower than most of the comparison schemes. Although its computation time increases due to local search and priority adjustment, this computation process usually occurs in the offline planning or near real-time decision-making stage before mission execution, in exchange for a shorter execution cycle and more stable time window satisfaction capability.

[0179] Therefore, this embodiment shows that the improved NSGA-II is suitable for unmanned surface vessel mission scheduling scenarios with multiple priorities, multiple time windows, and energy constraints, and can take into account the timeliness of critical missions, path economy, and overall completion time.

[0180] Table 10 Comparison of Time Composition of Representative Schemes for Different Algorithms

[0181]

[0182] Table 11 shows that after 30 runs under the same input conditions, the average cost of the improved NSGA-II is 1413.39, the lowest cost is 1187.90, and the highest cost is 1638.88, which is lower than that of GA, the basic NSGA-II, and PSO. This result indicates that the present invention can still maintain good solution stability even with differences in random initialization and evolutionary processes.

[0183] The reason for the above differences is that GA and PSO mainly rely on a single search mechanism, which is prone to premature convergence when faced with problems where time windows, dynamic priorities, and path order are coupled. Although the basic NSGA-II has multi-objective search capabilities, it lacks specific modifications for task timeliness and local path structure. This invention adds a flexible time window expansion mechanism, dynamic priorities, and 2-opt local search in addition to global search, enabling candidate solutions to be adjusted simultaneously towards low cost, short time consumption, and high on-time rate.

[0184] Table 11 Statistical analysis of results from 30 repeated runs

[0185]

[0186] To further illustrate the overall effect under multiple indicators, this embodiment normalizes the on-time rate of high-priority tasks, the on-time rate of low-priority tasks, total cost, penalty ratio, and computation time. For indicators such as total cost, penalty ratio, and computation time, which are generally considered to be "the smaller the better," reverse normalization is used to ensure that each indicator in the radar chart satisfies the principle that "the larger the value, the better the performance."

[0187] Depend on Figure 8 It is evident that the improved NSGA-II has a wide coverage of key indicators such as on-time performance of high-priority tasks, on-time performance of low-priority tasks, total cost, and penalty ratio. This indicates that it does not only achieve an advantage in a single indicator, but also achieves a relatively balanced effect between task on-time performance, scheduling economy, and penalty control.

[0188] It should be noted that the improved NSGA-II scores lower than some of the comparison algorithms in terms of computation time. This is because it adds steps such as flexible time window expansion adjustment, dynamic priority calculation, and 2-opt local search. For unmanned surface vessel inspection missions in offshore wind farms, this computational overhead is generally acceptable and can be traded for lower scheduling costs and higher mission-critical support capabilities.

[0189] In summary, under the input conditions shown in the above embodiments, the present invention can output a task execution sequence that satisfies the requirements of home port departure and return, unique task access, energy constraints, and time continuity constraints, and achieves good overall results in terms of on-time performance of critical tasks, overall cost, waiting time, and total time consumption.

[0190] It is readily understood that the implementation of the methods in the above embodiments can be based on a computer program, which is a set of instructions that can be executed by a computer (i.e., by a processor). When the computer program is executed by the processor, it implements a multi-constraint task scheduling method for unmanned surface vessels.

[0191] Furthermore, at least some of the computer programs associated with the methods of the embodiments can be distributed in a computer program product including a computer-readable medium carrying computer-usable instructions for one or more processors. This computer-readable storage medium can be provided in various forms, including non-transitory forms, such as, but not limited to, one or more disks, optical discs, magnetic tapes, chips, and magnetic and electronic storage. Further, the computer program can also be stored in a memory, which is part of an electronic device that also has a processor electrically connected to the memory. The computer program stored in the memory can be executed by the processor, thereby realizing the multi-constraint task scheduling method for unmanned surface vessels.

Claims

1. A multi-constraint task scheduling method for unmanned surface vessels, characterized in that, Includes the following steps: Step 1: Input the initial state and mission attributes of the unmanned surface vessel, and generate a unique execution sequence as the initial population using integer permutation encoding. Step 2: Decode the individuals in the initial population, then use a dynamic priority update mechanism based on the cumulative scheduling time of tasks to determine the dynamic priority of the tasks to be executed at the current scheduling time, verify hard constraints and adjust soft constraints through a flexible time window expansion mechanism, calculate the fitness of the individuals in the initial population, evaluate the quality of individuals through fast non-dominated ranking and crowding calculation, form an initial Pareto front, and write the non-dominated solutions in the initial Pareto front into the elite archive. The flexible time window expansion mechanism relaxes the executable range of critical tasks according to task priority. The hard constraints include access uniqueness constraints, energy constraints, time continuity constraints, and initial and termination constraints. The soft constraints are time window constraints. The fitness is evaluated based on total cost and total time. The total cost includes delay penalty cost, which is calculated based on a penalty function. The penalty function is calculated based on the time window constraints. The elite archive is an external elite set stored independently of the current population. Step 3: Iterate and mutate the individuals in the parent population to generate the offspring population; Step 4: Merge the parent population and the offspring population to form a candidate set, perform non-dominated sorting on the candidate set, extract the non-dominated solutions of the current generation and merge them with the existing solutions in the elite archive, delete dominated solutions and duplicate solutions in the merged set, write the remaining non-dominated solutions back to the elite archive, and update the global Pareto front. Step 5: When the maximum number of iterations is reached, output the global Pareto front solution set. Perform a 2-opt local search and priority heuristic swap strategy on the solutions in the global Pareto front to reverse the task execution order. The priority heuristic swap strategy is to swap the delayed high-priority task with the preceding low-priority task. Select the optimal individual from the Pareto front and decode to output the optimal scheduling scheme.

2. The multi-constraint task scheduling method for unmanned surface vessels according to claim 1, characterized in that, The formula for calculating the delay penalty cost in step 2 is as follows: ， in, The penalty function employs a nonlinear model, applying penalties of varying intensities based on the relative position of the arrival time and the time window. For the task The actual arrival time; For the task Priority-adjusted time window For the task Dynamic priority at arrival time For the task Task type.

3. The multi-constraint task scheduling method for unmanned surface vessels according to claim 1, characterized in that, The formula for calculating the penalty function in step 2 is as follows: ， in, This is the actual arrival time. This represents the optimal time window for the task after priority adjustment. This represents the current dynamic priority of the task. For task type, To delay the duration, The length of the time window. This is the baseline value for opportunity cost, expressed in yuan / hour. Indicates the start point of the time window. This represents the penalty coefficient for arriving early. This represents the penalty coefficient for a slight delay. This represents the penalty coefficient for the case of moderate delay. This represents the penalty coefficient for severe delays. As the opportunity cost benchmark, This represents a combined weighting function determined by both the task type and the current priority. To delay the duration, A fixed additional penalty for moderate delay. Fixed additional penalties for severe delays.

4. The multi-constraint task scheduling method for unmanned surface vessels according to claim 1, characterized in that, The adjusted time window calculation formula for the flexible time window expansion mechanism in step 2 is as follows: ， in, This represents the adjusted time window for task i under its current priority. Indicates the start time of the original time window. Indicates the end time of the original time window. Indicates the time window expansion ratio. Indicates the original time window length.

5. The multi-constraint task scheduling method for unmanned surface vessels according to claim 1, characterized in that, The total cost in step 2 is calculated by adding up the cost of navigation fuel, navigation time, waiting time, service operation cost and the delay penalty cost. The total time consumption is calculated by adding up the sum of the navigation time of each segment, the waiting time of each task, and the service time of each task.

6. The multi-constraint task scheduling method for unmanned surface vessels according to claim 5, characterized in that, The formula for calculating the cost of aviation fuel is as follows: ， in, This represents the Euclidean distance between adjacent mission points or homeports, in meters. This is the cost coefficient per unit distance traveled. The formula for calculating the travel time cost is as follows: , in, This represents the maintenance cost coefficient per unit time. The formula for calculating the waiting cost is: ， in, For idling energy costs, To cover maintenance costs, As for opportunity cost, This represents the dynamic priority of task πj at the corresponding arrival time, used to characterize the amplification effect of task urgency on the loss of waiting opportunities. 1.5 is the priority scaling factor, used to adjust the weight of dynamic priority in the waiting opportunity cost. The formula for calculating the service operation cost is as follows: ， in, For the task Service duration, The basic cost coefficient per unit of service time. This is the task type coefficient.

7. The multi-constraint task scheduling method for unmanned surface vessels according to claim 1, characterized in that, The calculation formula for the dynamic priority update mechanism in step 2 is as follows: ， in, Let t be the dynamic priority corresponding to the current scheduling time t when task i performs a timing evaluation of the task during the decoding process. As the baseline priority for tasks, The moment of mission release. The length of the task time window. This is the priority growth factor corresponding to the task type. This is the upper limit of priority. To prevent small constants with zero denominators, t represents the current scheduling time.

8. An electronic device, characterized in that, The electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; The memory stores a computer program that can be executed by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the unmanned surface vessel multi-constraint task scheduling method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the multi-constraint task scheduling method for unmanned surface vessels as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the multi-constraint task scheduling method for unmanned surface vessels as described in any one of claims 1 to 7.

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