Agricultural machinery operation and fuel oil supply cooperative scheduling method based on multi-objective optimization

Abstract

The invention discloses an agricultural machinery operation and fuel oil supply cooperative scheduling method based on multi-objective optimization, belongs to the field of agricultural machinery scheduling, and aims to solve the problems of low operation efficiency and high operation cost caused by disjunction of agricultural machinery fuel oil supply and operation scheduling and lack of global dynamic cooperative planning. The method comprises the following steps: S1, constructing an agricultural machinery operation and fuel supply cooperative scheduling model; the collaborative scheduling model is based on the following sets: a farmland operation point set composed of all farmlands needing operation, an agricultural machine set composed of all agricultural machines, a fuel oil supply truck set composed of all fuel oil supply trucks and preset related constraint conditions; s2, constructing a comprehensive objective function integrating two optimization objectives of total scheduling time and total scheduling cost, and taking the comprehensive objective function as an optimization objective of the collaborative scheduling model; and S3, designing solving steps of the model based on a grey wolf heuristic algorithm, and finally outputting an optimal cooperative scheduling scheme of the agricultural machinery and the fuel supply vehicle.

Description

Technical Field

[0001] This invention belongs to the field of agricultural machinery scheduling, specifically involving a method for coordinated scheduling of agricultural machinery operations and fuel supply based on multi-objective optimization. Background Technology

[0002] With the continued growth of the global population and the increasing prominence of food security issues, agricultural production is facing enormous pressure to increase yields, reduce costs, and decrease resource consumption. Against this backdrop, smart agriculture, characterized by precision, intelligence, and automation, has emerged as an inevitable direction for the transformation and upgrading of modern agriculture. Smart agriculture deeply integrates modern information technologies such as the Internet of Things, big data, artificial intelligence, and GPS, aiming to achieve refined management and optimal resource allocation throughout the entire agricultural production process. As a key execution unit of smart agriculture, the operational efficiency and collaborative scheduling level of agricultural machinery directly affect the economic benefits and timeliness of agricultural production.

[0003] Currently, large-scale, cross-field collaborative agricultural machinery operations have become the main production mode of modern farms. However, when agricultural machinery operates for extended periods and under high intensity in vast fields, it faces the problem of limited fuel endurance. Due to the complex working environment and dispersed operating areas in farmland, it is common for agricultural machinery to be forced to stop midway to seek refueling due to fuel exhaustion. Such unplanned shutdowns not only interrupt individual agricultural machinery operations and delay farming time, but also disrupt the operating rhythm of the entire fleet, seriously affecting the overall efficiency and reliability of large-scale collaborative agricultural machinery operations. Therefore, how to provide timely and efficient fuel refueling for agricultural machinery in operation has become the core key to realizing intelligent management and collaborative scheduling of the entire process in smart agricultural operation systems. As an important component of the intelligent agricultural machinery platform, a scheduling system that can dynamically coordinate agricultural machinery operation paths and fuel refueling strategies plays a crucial role in improving the overall operational robustness of the platform and reducing operating costs.

[0004] Regarding the issue of fuel refueling for agricultural machinery, existing solutions and practices remain at a relatively rudimentary stage, broadly categorized into two types: The first is reactive refueling, where the operator calls for backup via walkie-talkie or mobile phone when fuel is low, and the refueling vehicle then proceeds to the designated location. This method suffers from delayed response, random routes, and a lack of overall planning, easily leading to excessive empty runs for the refueling vehicle and multiple machines queuing, resulting in low efficiency and high costs. The second type is simple rule-based refueling, such as setting fixed operating times or areas for each machine before returning to a fixed refueling point, or planning a fixed patrol route for the refueling vehicle covering all operating areas. While this method offers some planning, it lacks integration with the actual progress of agricultural machinery operations, dynamic fuel consumption, and the collaborative status of multiple vehicles, failing to adapt to real-time changes in field operations and still resulting in significant time and resource waste.

[0005] In recent years, vehicle routing problems and their extended models have been widely studied in logistics distribution, vehicle scheduling, and other fields, including route optimization with time windows and capacity constraints. However, directly applying such models to the collaborative scheduling scenario of agricultural machinery fuel replenishment faces several unique challenges: First, agricultural machinery is not only a fuel demand point but also a dynamically moving service provider (performing farming tasks). Its path is strongly correlated with fuel consumption, which means that the location and time of the demand point (the agricultural machinery needing refueling) change dynamically with the execution of the scheduling plan, fundamentally different from the traditional static demand point routing problem. Second, fuel replenishment is a meeting service process where both the service provider and the service recipient must be present simultaneously. This involves the precise spatiotemporal matching and coupling of the two moving paths of the agricultural machinery and the replenishment vehicle, with constraints far exceeding the complexity of traditional one-way delivery. Furthermore, the optimization objectives are multifaceted, requiring both minimizing the total operation time to seize farming opportunities and minimizing the total scheduling cost (fuel, manpower, vehicle wear and tear, etc.) to ensure economic efficiency, constituting a typical multi-objective optimization problem.

[0006] In summary, existing technologies either lack systematic planning or fail to accurately characterize the dynamics, coupling, and multi-objective nature of agricultural machinery fuel replenishment coordination and scheduling. A comprehensive intelligent coordination and scheduling method capable of optimizing agricultural machinery operation paths and fuel replenishment strategies to achieve optimal overall time and cost has not yet been developed. Therefore, developing a technical solution that deeply integrates agricultural machinery operation and fuel replenishment processes for unified modeling and optimization decision-making is of significant theoretical value and urgent practical need for overcoming current bottlenecks in smart agriculture operation scheduling and improving the overall efficiency of agricultural production systems. Summary of the Invention

[0007] To address the problems of low operational efficiency and high operating costs caused by the disconnect between agricultural machinery fuel supply and operation scheduling, and the lack of global dynamic collaborative planning, this invention provides a collaborative scheduling method for agricultural machinery operation and fuel supply based on multi-objective optimization.

[0008] The multi-objective optimization-based coordinated scheduling method for agricultural machinery operations and fuel replenishment described in this invention includes the following steps:

[0009] S1. Construct a coordinated scheduling model for agricultural machinery operations and fuel replenishment; the coordinated scheduling model is based on the following set: a set of agricultural operation points consisting of all farmland requiring operations. A collection of agricultural machinery composed of all agricultural institutions A collection of all refueling vehicles. and the preset related constraints;

[0010] S2. Construct a comprehensive objective function that integrates the two optimization objectives of total scheduling time and total scheduling cost, as the optimization objective of the cooperative scheduling model;

[0011] S3. Based on the gray wolf heuristic algorithm, design the solution steps of the model and finally output the optimal collaborative scheduling scheme of agricultural machinery and fuel supply vehicle.

[0012] Preferably, in step S2, the comprehensive objective function The expression is:

[0013]

[0014] In the formula, Total scheduling time, For the total scheduling cost, This is the weighting coefficient for the total scheduling time. This is the weighting coefficient for the total scheduling cost.

[0015] Preferably, the total scheduling time The total travel time and total operating time of all agricultural machinery, as well as the total travel time of all fuel supply vehicles, are expressed as follows:

[0016]

[0017] In the formula, For the complete set of nodes, , For the initial starting point set, For the set of termination points;

[0018] For agricultural machinery From node To the node The travel time;

[0019] Decision variables Agricultural machinery From node To the node If yes, then it is 1; otherwise, it is 0.

[0020] For agricultural machinery At the node Time required to complete the assignment;

[0021] For supply vehicle From node To the node The travel time;

[0022] Decision variables Supply vehicle From node To the node If yes, it is 1; otherwise, it is 0.

[0023] Preferably, the total scheduling cost The total mobility cost and total operating cost of all agricultural machinery, as well as the total mobility cost of all fuel supply vehicles, are expressed as follows:

[0024]

[0025] In the formula, For agricultural machinery From node To the node The transfer cost;

[0026] For agricultural machinery At the node The costs incurred in completing the task;

[0027] For supply vehicle From node To the node The transfer costs.

[0028] Preferably, in step S1, the constraints of the model include dynamic constraints on fuel inventory, which ensure that the remaining fuel quantity of the agricultural machinery is correctly updated as it operates and moves, specifically including:

[0029] Fuel consumption constraints: agricultural machinery From node Move to node At that time, the remaining fuel quantity must meet the following requirements:

[0030]

[0031] Refueling reset constraints: If agricultural machinery At the node If you accept refueling, your remaining fuel level must meet the following requirements:

[0032]

[0033] Fuel tank capacity constraints: agricultural machinery At any node The remaining fuel quantity must meet the following requirements:

[0034]

[0035] In the formula, , Indicates agricultural machinery At the node ,node The amount of fuel remaining at that time; For agricultural machinery The maximum capacity of the fuel tank; For agricultural machinery At the node Fuel consumption during operation; For agricultural machinery From node To the node Fuel consumption during travel; decision variables Supply vehicle Is it at the node? agricultural machinery Replenish supplies; if so, return 1; otherwise, return 0. It is an infinite constant.

[0036] Preferably, the constraints of the model also include a refueling synchronization constraint, which requires that the refueling operation only occurs when the agricultural machinery and the fuel supply vehicle are simultaneously located at the same node, specifically expressed as:

[0037]

[0038]

[0039] In the formula, decision variables Agricultural machinery From node To the node If yes, then it is 1; otherwise, it is 0.

[0040] Decision variables Supply vehicle From node To the node If yes, it is 1; otherwise, it is 0.

[0041] Preferably, in step S3, the solution process based on the gray wolf heuristic algorithm includes:

[0042] S31. Encoding of the solution: Encode a complete scheduling scheme into the position of a gray wolf individual; the encoding adopts an integer sequence encoding method, which includes: a farm machinery operation path segment indicating the order in which each farm machinery visits the field, a supply vehicle path segment indicating the order in which each fuel supply vehicle visits the node, and a supply operation point information segment indicating which nodes are refueled by which supply vehicle for which farm machinery.

[0043] S32. Population initialization: Randomly generate an initial scheduling scheme that satisfies the path closure constraint as the initial population individuals;

[0044] S33. Fitness Calculation: Based on the objective function And for the penalty items for violating the dynamic constraints on fuel inventory and the synchronous constraints on refueling, calculate the fitness value of each individual;

[0045] S34. Social Hierarchy and Position Update: Determine the positions of Alpha, Beta, and Delta wolves based on their fitness values ​​and guide population updates.

[0046] S35. Iterative Output: Repeat the iteration until the termination condition is met, and output the optimal scheduling scheme corresponding to Alpha Wolf.

[0047] The beneficial effects of the present invention: Compared with the prior art, the present invention has the following outstanding advantages:

[0048] 1. Significantly improves operational efficiency: By internalizing the fuel replenishment demand of agricultural machinery into scheduling constraints and performing global optimization, this invention can intelligently plan the optimal replenishment time and path, effectively reducing the downtime waiting time of agricultural machinery due to fuel shortage.

[0049] 2. Effectively Reduces Overall Costs: This invention optimizes time while minimizing the movement and operation costs of agricultural machinery and supply vehicles within a unified model. The optimized solution reduces vehicle mileage and balances task load, thereby lowering total fuel consumption and operating costs.

[0050] 3. Enhance system reliability: Through strict "dynamic constraints on fuel inventory", the mathematical model ensures that the fuel level of agricultural machinery is always within a safe range throughout the operation, fundamentally avoiding operation interruptions caused by fuel depletion, and improving the reliability and robustness of large-scale agricultural machinery collaborative operation plan execution.

[0051] 4. Provides intelligent decision support: The model and algorithm framework adopted in this invention is flexible and scalable. Decision-makers can flexibly balance time and cost preferences by adjusting the target weights; the algorithm can efficiently solve complex problems, providing feasible intelligent decision-making solutions for real-time scheduling in dynamic environments. Attached Figure Description

[0052] Figure 1 This is a flowchart of the agricultural machinery operation and fuel supply coordinated scheduling method based on multi-objective optimization described in this invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0056] Specific Implementation Method 1: The following is combined with... Figure 1 The following describes the implementation method in detail with reference to the accompanying drawings and embodiments. This invention abstracts a practical problem into a mathematical model, where the initial starting point, farmland operation point (i.e., the location of the field to be operated on), and termination point are collectively referred to as "nodes" to facilitate the description of network topology and path planning.

[0057] The multi-objective optimization-based coordinated scheduling method for agricultural machinery operations and fuel replenishment described in this invention includes the following three core steps:

[0058] S1. Construct a coordinated scheduling model for agricultural machinery operations and fuel replenishment; the coordinated scheduling model is based on the following set: a set of agricultural operation points consisting of all farmland requiring operations. A collection of agricultural machinery composed of all agricultural institutions A collection of all refueling vehicles. and the preset related constraints;

[0059] S2. Construct a comprehensive objective function that integrates the two optimization objectives of total scheduling time and total scheduling cost, as the optimization objective of the cooperative scheduling model;

[0060] S3. Based on the gray wolf heuristic algorithm, design the solution steps of the model and finally output the optimal collaborative scheduling scheme of agricultural machinery and fuel supply vehicle.

[0061] Step S1: Construction of the Cooperative Scheduling Model

[0062] 1. Definition of a set:

[0063] : A collection of farmland operation points, i.e., the location of all fields that need to be cultivated;

[0064] The initial starting point set, which is the common initial starting point set of all agricultural machinery and supply vehicles;

[0065] The set of termination points, that is, the set of termination points common to all agricultural machinery and supply vehicles;

[0066] : The complete set of nodes; In this invention, both path planning and resource allocation are performed within the node network. The above will be carried out.

[0067] Agricultural machinery assembly, composed of all agricultural machinery;

[0068] : A collection of fuel supply vehicles, consisting of all fuel supply vehicles;

[0069] 2. Parameter and variable definitions:

[0070] To accurately describe the problem, the following parameters and variables are defined:

[0071] Time and cost parameters:

[0072] Agricultural machinery From node To the node The travel time;

[0073] Agricultural machinery From node To the node The transfer cost;

[0074] Agricultural machinery At the node ( (Time) The time required to complete the task;

[0075] Agricultural machinery At the node ( The cost incurred in completing the task within a certain timeframe;

[0076] Supply vehicle From node To the node The travel time;

[0077] Supply vehicle From node To the node The transfer cost;

[0078] Fuel-related parameters (key):

[0079] Agricultural machinery The maximum capacity of the fuel tank;

[0080] Agricultural machinery At the node Fuel consumption during operation;

[0081] Agricultural machinery From node To the node Fuel consumption during travel;

[0082] : Infinite constant;

[0083] Decision variables:

[0084] Agricultural machinery From node To the node If yes, then it is 1; otherwise, it is 0.

[0085] Supply vehicle From node To the node If yes, then it is 1; otherwise, it is 0.

[0086] Supply vehicle Is it at the node? agricultural machinery Replenish supplies; if so, return 1; otherwise, return 0.

[0087] Agricultural machinery At the node The start time of the assignment;

[0088] Agricultural machinery Reaching the node The amount of fuel remaining at that time;

[0089] 3. Construction of comprehensive optimization objectives

[0090] This invention simultaneously aims to minimize both the total scheduling time and the total scheduling cost. To achieve efficient solution, a linear weighted method is used to transform it into a single-objective optimization problem, and the combined objective function is... for:

[0091]

[0092] This is the weighting coefficient for the total scheduling time. This is the weighting coefficient for the total scheduling cost.

[0093] Total scheduling time The expression is:

[0094]

[0095] Total scheduling cost The expression is:

[0096]

[0097] 4. Constraints of the Model

[0098] The constraints of the model include, but are not limited to, the following types:

[0099] (1) Path closure and flow balance constraints (conventional constraints):

[0100] Agricultural machinery and fuel supply vehicles must start from the initial point and eventually return to the terminal point, with the number of inflows and outflows at intermediate nodes being equal, and each field being served by at least one agricultural machine.

[0101] (2) Decision variable value constraints (conventional constraints):

[0102] , , for variable; , It is a non-negative continuous variable.

[0103] In addition to conventional constraints such as path flow balancing and task coverage, the core innovative constraints of this invention are as follows:

[0104] (3) Dynamic constraints on fuel inventory (core constraints):

[0105] This includes initial fuel level, fuel consumption update, refueling reset, and fuel tank capacity limit, specifically:

[0106] Initial fuel quantity: , Indicates agricultural machinery At the initial starting point The initial amount of oil.

[0107] Fuel consumption constraints:

[0108] Refueling and resetting constraints:

[0109] Fuel tank capacity constraints:

[0110] (4) Refueling synchronization constraint (core constraint):

[0111] Refueling operations require that the agricultural machinery and the refueling vehicle be located at the same node simultaneously.

[0112]

[0113]

[0114] These two inequalities ensure the refueling decision. The necessary condition for its establishment is: agricultural machinery. The path passes through the nodes And fuel supply vehicles The path also passes through nodes This precisely realizes the coordination mechanism between agricultural machinery and fuel supply vehicles.

[0115] II. Solution based on the gray wolf heuristic algorithm (corresponding to claim 6)

[0116] The above model is a complex mixed-integer programming problem. This invention employs the Grey Wolf Optimization Algorithm for an efficient approximate solution, the key being the specific encoding and fitness design tailored to this problem.

[0117] 1. Model conversion

[0118] The agricultural machinery operation and fuel supply scheduling problem is transformed into an optimization problem. The goal is to minimize the total working time and scheduling cost. By using integer sequence encoding, the route arrangement and refueling behavior are represented as a solution structure that can be handled by the Grey Wolf algorithm, while embedding all operation and fuel constraints.

[0119] (1) The solution is encoded using an integer sequence encoding method:

[0120] ① One chromosome represents a complete scheduling scheme.

[0121] ② The sequence consists of multiple segments: agricultural machinery operation path, supply vehicle path, and supply operation point. The agricultural machinery operation path represents the order of operation nodes for each agricultural machine; the supply vehicle path represents the order of nodes visited by each supply vehicle; and the supply operation point represents which nodes the supply vehicle resupplyes at and which agricultural machine it resupplyes (which can be represented by an auxiliary vector).

[0122] (2) Specify the basic parameters of the algorithm

[0123] Gray wolf population size;

[0124] Maximum number of iterations;

[0125] The convergence factor decreases linearly with the number of iterations.

[0126] : Random numbers in the interval [0,1] are used for exploration control of position updates;

[0127] : Current position of the gray wolf (indicating the scheduling scheme);

[0128] Alpha Wolf's position (optimal solution);

[0129] : The position of the Beta wolf (suboptimal solution);

[0130] : The position of the Delta wolf (third best solution);

[0131] Total working time (objective function 1);

[0132] Total scheduling cost (objective function 2);

[0133] The weight of total working time within the objective function;

[0134] The weight of the total scheduling cost within the objective function;

[0135] 2. Algorithm Initialization

[0136] Initialize a gray wolf population, with each individual representing a scheduling scheme. Set the population size, iteration limit, and decay coefficient. Randomly generate initial paths and refueling decisions that meet basic feasibility requirements to conduct a global search. Initialize the following:

[0137] Gray wolf population size;

[0138] Maximum number of iterations;

[0139] Location (Solution) Initialization: Generate a random but feasible path combination for each gray wolf (ensuring that the basic constraints are satisfied).

[0140] The convergence factor decreases linearly with the number of iterations.

[0141] 3. Fitness Calculation

[0142] By evaluating the total working time and scheduling cost of the scheduling scheme represented by each gray wolf, and imposing penalties for constraint violations, a comprehensive fitness value is calculated to guide the next search direction. A lower fitness value indicates a better scheme.

[0143] (1) Objective function part:

[0144]

[0145] 4. Social class division

[0146] Based on fitness ranking, the three optimal gray wolves are defined as Alpha, Beta, and Delta. The remaining wolves adjust their positions according to the information from these three, simulating the cooperative hunting behavior of gray wolves, thereby guiding the population towards a better solution.

[0147] (1) Definition of the "Grey Wolf" role

[0148] Alpha ): The current optimal solution;

[0149] Beta ): Suboptimal solution;

[0150] Delta ( Third optimal solution;

[0151] 5. Location update mechanism

[0152] The gray wolves continuously update their positions using a mathematical model that moves closer to the three leader wolves. This position update is represented at the coding level as an adjustment of the scheduling path, requiring the continuous values ​​to be discretized into a sequence of visits. This step ensures continuous optimization of the population.

[0153] The position update for each wolf consists of the following formula:

[0154] (1) Surround the prey:

[0155]

[0156]

[0157] in:

[0158] : Represents the position of the three individuals: Alpha, Beta, and Delta.

[0159] : The position of the current individual in generation t+1.

[0160] : Exploration factor, controls the current wolf pack's stride and direction when approaching prey.

[0161] Weighting factor: Increases the randomness of the exploration.

[0162] The parameter decreases linearly from 2 to 0 with the number of iterations (controlling the transition from global search to local convergence).

[0163] : Random numbers within an interval.

[0164] (2) The final position is the average of the three close positions.

[0165] Each gray wolf will approach one of the three leaders, and the update formula is as follows:

[0166]

[0167]

[0168]

[0169] The final update location is:

[0170]

[0171] 6. Local search and perturbation mechanism

[0172] To avoid getting trapped in local optima, some individual paths are optimized after each update to increase the diversity of solutions.

[0173] 7. Termination and Output

[0174] The algorithm stops when the iteration reaches its limit or after several consecutive rounds without improvement, and outputs the current optimal individual's scheduling path, refueling point, and performance indicators. This scheme is the optimal collaborative scheduling strategy for agricultural machinery and supply vehicles.

[0175] This invention establishes an accurate model that includes dynamic fuel constraints and synchronous refueling constraints, and designs a matching intelligent solution algorithm. For the first time, it achieves deep collaborative optimization of agricultural machinery operation and fuel replenishment at the global level, providing effective technical support for the efficient management of smart agriculture.

[0176] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization, characterized in that, Includes the following steps: S1. Construct a coordinated scheduling model for agricultural machinery operations and fuel replenishment; the coordinated scheduling model is based on the following set: a set of agricultural operation points consisting of all farmland requiring operations. A collection of agricultural machinery composed of all agricultural institutions A collection of all refueling vehicles. and the preset related constraints; S2. Construct a comprehensive objective function that integrates the two optimization objectives of total scheduling time and total scheduling cost, as the optimization objective of the cooperative scheduling model; S3. Based on the gray wolf heuristic algorithm, design the solution steps of the model and finally output the optimal collaborative scheduling scheme of agricultural machinery and fuel supply vehicle.

2. The method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization according to claim 1, characterized in that, In step S2, the comprehensive objective function The expression is: In the formula, Total scheduling time, For the total scheduling cost, This is the weighting coefficient for the total scheduling time. This is the weighting coefficient for the total scheduling cost.

3. The method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization according to claim 2, characterized in that, The total scheduling time The total travel time and total operating time of all agricultural machinery, as well as the total travel time of all fuel supply vehicles, are expressed as follows: In the formula, For the complete set of nodes, , For the initial starting point set, For the set of termination points; For agricultural machinery From node To the node The travel time; Decision variables Agricultural machinery From node To the node If yes, then it is 1; otherwise, it is 0. For agricultural machinery At the node Time required to complete the assignment; For supply vehicle From node To the node The travel time; Decision variables Supply vehicle From node To the node If yes, it is 1; otherwise, it is 0.

4. The method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization according to claim 3, characterized in that, The total scheduling cost The total mobility cost and total operating cost of all agricultural machinery, as well as the total mobility cost of all fuel supply vehicles, are expressed as follows: In the formula, For agricultural machinery From node To the node The transfer cost; For agricultural machinery At the node The costs incurred in completing the task; For supply vehicle From node To the node The transfer costs.

5. The method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization according to claim 4, characterized in that, In step S1, the constraints of the model include dynamic fuel inventory constraints, which ensure that the remaining fuel quantity of the agricultural machinery is correctly updated as it operates and moves. Specifically, these constraints include: Fuel consumption constraints: agricultural machinery From node Move to node At that time, the remaining fuel quantity must meet the following requirements: Refueling reset constraints: If agricultural machinery At the node If you accept refueling, your remaining fuel level must meet the following requirements: Fuel tank capacity constraints: agricultural machinery At any node The remaining fuel quantity must meet the following requirements: In the formula, , Indicates agricultural machinery At the node ,node The amount of fuel remaining at that time; For agricultural machinery The maximum capacity of the fuel tank; For agricultural machinery At the node Fuel consumption during operation; For agricultural machinery From node To the node Fuel consumption during travel; decision variables Supply vehicle Is it at the node? agricultural machinery Replenish supplies; if so, return 1; otherwise, return 0. It is an infinite constant.

6. The method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization according to claim 5, characterized in that, The model also includes a refueling synchronization constraint, which requires that the refueling operation only occurs when the agricultural machinery and the fuel supply vehicle are simultaneously located at the same node, specifically expressed as: In the formula, decision variables Agricultural machinery From node To the node If yes, then it is 1; otherwise, it is 0. Decision variables Supply vehicle From node To the node If yes, it is 1; otherwise, it is 0.

7. The method for coordinated scheduling of agricultural machinery operations and fuel replenishment based on multi-objective optimization according to claim 1, characterized in that, In step S3, the solution process based on the gray wolf heuristic algorithm includes: S31. Encoding of the solution: Encode a complete scheduling scheme into the position of a gray wolf individual; the encoding adopts an integer sequence encoding method, which includes: a farm machinery operation path segment indicating the order in which each farm machinery visits the field, a supply vehicle path segment indicating the order in which each fuel supply vehicle visits the node, and a supply operation point information segment indicating which nodes are refueled by which supply vehicle for which farm machinery. S32. Population initialization: Randomly generate an initial scheduling scheme that satisfies the path closure constraint as the initial population individuals; S33. Fitness Calculation: Based on the objective function And for the penalty items for violating the dynamic constraints on fuel inventory and the synchronous constraints on refueling, calculate the fitness value of each individual; S34. Social Hierarchy and Position Update: Determine the positions of Alpha, Beta, and Delta wolves based on their fitness values ​​and guide population updates. S35. Iterative Output: Repeat the iteration until the termination condition is met, and output the optimal scheduling scheme corresponding to Alpha Wolf.

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