An industrial manufacturing multi-task intelligent optimization method based on constraint coupling strength index

Abstract

This invention addresses the challenge of complex scheduling tasks in industrial manufacturing, where multiple tasks exist simultaneously with coupled constraints, leading to high optimization difficulty. It proposes an intelligent multi-task optimization method based on constraint coupling strength indices. This method aims to minimize the number of vehicles used and the total transportation cost. First, a knowledge graph network is constructed to store task information and constraints. Then, a constraint coupling strength index is calculated based on the relationship between constraints and decision variables. Subsequently, during the multi-task differential evolution search, candidate solutions are grouped according to constraint coupling strength, and differentiated cross-tabulation, mutation, and cross-task knowledge transfer strategies are employed to guide the search process towards efficient convergence. This method effectively characterizes complex constraint structures, enhances multi-task collaborative optimization capabilities, and provides an efficient and feasible optimization solution for transportation scheduling in industrial manufacturing.

Description

Technical Field

[0001] This invention addresses the multi-task optimization and scheduling application scenario in industrial manufacturing. It proposes an intelligent multi-task optimization method for industrial manufacturing based on a constraint coupling strength index, addressing the problem of multiple industrial scheduling optimization tasks existing simultaneously in the scheduling network, with mutually influential constraints, complex coupling relationships, and a limited feasible solution space. This method guides the evolutionary search process and achieves cross-task information sharing by characterizing the degree of correlation between different constraints, thereby improving the feasibility, stability, and scheduling efficiency of scheduling schemes in industrial manufacturing. This invention belongs to the fields of intelligent optimization and computational intelligence, and is also applicable to the technical fields of logistics and transportation scheduling in industrial manufacturing. Background Technology

[0002] Traditional intelligent optimization methods in industrial manufacturing often address single scenarios or tasks. However, in actual industrial manufacturing, multiple scheduling tasks often exist simultaneously, such as transportation scheduling needs corresponding to different production areas, processes, or product categories. These tasks differ in their task objects, constraints, and operating rules, but share certain similarities in path planning and scheduling solution methods. Solving multiple tasks independently not only incurs high computational costs but also makes it difficult to fully utilize the common information between tasks, thus limiting overall scheduling efficiency and optimization results. Therefore, a multi-task optimization method can be used to collaboratively solve multiple vehicle routing problems in industrial manufacturing.

[0003] Multi-task optimization methods can achieve information sharing among multiple related tasks, thereby improving overall solution performance. Among them, the multi-task differential evolution method has advantages such as strong search capability and fast convergence speed, and has high application value in industrial scheduling and combinatorial optimization problems. However, in industrial manufacturing scheduling scenarios, there are usually multiple types of operational constraints, such as capacity constraints, service time scheduling constraints, and business constraints related to material handling processes. These constraints often influence each other and form coupling relationships, resulting in a complex feasible solution space structure. Existing multi-task optimization methods are prone to problems such as difficulty in generating feasible solutions, instability in the search process, and negative transfer caused by cross-task information migration when facing industrial scheduling scenarios with strong constraint coupling. These problems affect the convergence performance of the algorithm and the reliability of the scheduling results.

[0004] To address the aforementioned problems, this invention proposes an intelligent multi-task optimization method for industrial manufacturing based on constraint coupling strength indices. This method uses the number of vehicles used and total transportation cost as optimization objectives. It quantifies the coupling relationships between various constraints in the scheduling tasks of industrial manufacturing and introduces a guidance mechanism based on constraint coupling strength indices during evolutionary search and cross-task information sharing. This improves the search capability for feasible solutions, enhances the effect of multi-task collaborative optimization, and provides an effective technical solution for scheduling under complex industrial manufacturing constraints. Summary of the Invention

[0005] This invention proposes an intelligent optimization method for multiple tasks in industrial manufacturing based on constraint coupling relationship analysis. This method constructs a correlation structure between constraints and decision variables, quantifies the constraint coupling strength, and introduces a coupling guidance mechanism in the multi-task evolutionary search process to achieve collaborative solution of multiple industrial scheduling optimization tasks.

[0006] The present invention adopts the following technical solution and implementation steps:

[0007] 1. A multi-task intelligent optimization method for industrial manufacturing based on constraint coupling strength index, characterized by determining the optimization objective of each scheduling task and the optimal route for scheduling vehicles, employing a multi-task differential evolution algorithm to solve multiple vehicle routing problems, guiding the evolutionary search process by characterizing the correlation between different constraints and achieving cross-task information sharing, thereby improving the feasibility, stability, and scheduling efficiency of vehicle scheduling schemes, and simultaneously achieving the optimal number of vehicles used and total transportation cost, including the following steps:

[0008] Step 1: Determine the optimization objective and constraints for each industrial scheduling problem: Assume there are L tasks, each task has K... max The dispatch vehicles are parked at the industrial manufacturing center, serving N factories. Each vehicle has a maximum load capacity of Q. The opening and closing times of the industrial manufacturing center are A and E, respectively. Each factory is served by only one transport vehicle. Each vehicle departs from the industrial manufacturing center carrying the workpiece requirements of the factory it is serving, delivering the required workpieces to each factory in the service order, and finally returning to the industrial manufacturing center. Each factory to be served has the following attributes: factory number i, factory location coordinates (x, y, y). i , y i The weight q of the workpieces required by the i-th factory. i The expected earliest start time of service for the i-th factory, a i And the expected latest start time of service e i And the service time s of the vehicle at the i-th factory. i Where i=0 represents a station; 0 < K max < 50 vehicles, 0 < N < 150 units, 0 < Q < 30 tons, 0 < A < 1440 minutes, 0 < E < 1440 minutes, i = 0, ..., N, 0 < x i < 100, 0 < y i < 100, 0 < a i < 1440 minutes, 0 < e i < 1440 minutes, 0 < s i< 200 minutes;

[0009] Every industrial scheduling problem aims to minimize the number of vehicles used and the total transportation cost.

[0010]

[0011]

[0012] Here, f1(X) and f2(X) are two optimization objectives, namely the number of vehicles used and the total transportation cost of vehicles, respectively. <K ≤ K max h k Indicates whether the k-th vehicle is used, h k =1 means yes, h k =0 indicates no, w k This represents the maintenance cost coefficient per unit distance traveled by the k-th vehicle. This coefficient is pre-set based on one or more factors, including the vehicle's model, energy consumption level, maintenance costs, or depreciation costs. ijk L represents the transportation cost coefficient for the k-th vehicle traveling from factory i to factory j. This coefficient is determined based on one or more factors, including vehicle type, transportation distance, unit energy cost, and road toll cost. ij x is the distance between factory i and factory j, where i=0, …, N, j=0, …, N, i, j=0 represents an industrial manufacturing center, and i, j =1, …, N represents a factory. ijk Indicates whether the k-th vehicle travels from factory i to factory j, x ijk =1 means yes, x ijk =0 indicates no, k = 1,…, K, λ1 represents the unit time cost of the vehicle performing the task, which is predetermined based on one or more factors such as labor costs, equipment depreciation costs, energy consumption costs, or dispatching costs incurred during vehicle operation; λ2 represents the unit distance cost of the vehicle performing the task, which is determined based on one or more factors such as fuel consumption costs, energy consumption costs, road toll costs, or vehicle wear and tear costs incurred during vehicle transportation; T k D represents the total mission time for the k-th vehicle, where k = 1, ..., K, D k Let k represent the total distance traveled by the k-th vehicle, where k = 1, ..., K;

[0013] Based on the above optimization objectives, each industrial scheduling task must meet the following constraint: each factory is served only once by one scheduling vehicle:

[0014]

[0015] Every dispatch vehicle that is activated must depart from the industrial manufacturing center and ultimately return to the industrial manufacturing center:

[0016]

[0017] Service artifacts with incompatible types cannot be served by the same vehicle:

[0018]

[0019] Where z ik z is an auxiliary variable indicating whether the service job types of vehicle k and factory i are compatible. ik = 1 is true, z ik =0 indicates no, r i M represents the service workpiece type of factory i. rirj Indicates whether the service workpiece types of factory i and factory j are the same, M rirj =1 means yes, M rirj =0 means no;

[0020] The total weight of service items dispatched by each dispatch vehicle in its service route must not exceed the vehicle's maximum load capacity:

[0021]

[0022] Where, q i Q is the number of service workpieces that factory i needs to schedule. k This is the maximum load capacity of vehicle k;

[0023] The total task time for each dispatched vehicle within its service route must not exceed the maximum task time.

[0024]

[0025] Where t ij It is the travel time for dispatched vehicles from factory i to factory j, s i The maximum task time refers to the longest duration during which a single dispatched vehicle is allowed to perform a task in a single dispatch process. This value is preset based on one or more factors, such as the working hours of the industrial manufacturing center, the vehicle's available running time, personnel scheduling requirements, or task scheduling rules.

[0026] The arrival time of each dispatched vehicle at each factory should be within the time window required by that factory, and the dispatched vehicle should return to the center within the time window required by the industrial manufacturing center:

[0027]

[0028] Among them, a i e represents the earliest time that the i-th factory is allowed to start service. i t represents the latest time that the i-th factory is allowed to start service. i This represents the time when the dispatched vehicle arrives at the i-th factory and begins providing service;

[0029]

[0030] Among them, A l E represents the earliest time that the vehicle is allowed to return to the industrial manufacturing center corresponding to the l-th task. l t represents the latest time that the vehicle is allowed to return to the industrial manufacturing center corresponding to the l-th task. k This represents the time it takes for the kth dispatched vehicle to return to the industrial manufacturing center after completing its service route.

[0031] Constraint violation degree of the comprehensive calculation solution:

[0032]

[0033] Wherein, CV(x) represents the comprehensive constraint violation degree of candidate solution x; This indicates the violation of the r-th inequality constraint function in the l-th task; This indicates the violation of the s-th equality constraint function in the l-th task; U represents the number of inequality constraints in this task, and V represents the number of equality constraints in this task; δ represents the tolerance threshold allowed for equality constraints, used to convert equality constraints into approximate constraints with tolerance, and its value is preset according to the computational accuracy requirements of the problem.

[0034] When a candidate solution satisfies all constraints, its comprehensive constraint violation degree CV(x) is 0; when a candidate solution violates any constraint, the degree of violation is accumulated using the above formula, which is then used to evaluate the feasibility of the candidate solution.

[0035] Step 2: Construct a knowledge graph network to store task information and constraints.

[0036] Before constructing the knowledge graph, the relevant data is first structured based on the task information, constraints, and decision variables of the industrial scheduling problem determined in step 1, and the types of nodes to be created in the knowledge graph and their attribute fields are determined accordingly.

[0037] Step 2.1 Define the node types and attribute fields of the knowledge graph:

[0038] Before constructing a knowledge graph, first determine the types of nodes to be created in the knowledge graph and set corresponding attribute fields for each type of node. The specific steps are as follows:

[0039] ① Create a Task node l : Used to represent the l-th industrial scheduling task determined in step 1, where l = 1, ..., L; when creating a task node, write the task number l and the number of scheduling nodes N contained in the task to it. l Available vehicle limit K max. l Vehicle load limit Q l Industrial Dispatch Center Time Window Parameter A l With E l ;

[0040] ② Create Constraint nodes p : Used to represent the p-th constraint in the industrial scheduling task determined in step 1, where p = 1,…, P; When creating a constraint node, write the constraint number p, constraint name, and constraint type identifier to it to distinguish different types of constraint conditions.

[0041] ③ Create a variable node m : Used to represent decision variables or intermediate variables involved in the calculation process in the industrial scheduling model established in step 1, where m = 1,…, M; when creating a variable node, write the variable number m, variable name, variable type identifier, and variable value range or domain to it;

[0042] Step 2.2 Define the relation types and relation attributes of the knowledge graph:

[0043] After creating the nodes, define the relationship types between them to describe the structural associations between tasks, constraints, and variables. The specific steps are as follows:

[0044] ① In the Task node l Constraint node p The task contains a constraint relationship HAS_CONSTRAINT, which indicates that the l-th task contains the p-th constraint. When creating this relationship, the relationship attributes are written, including the task number l and the constraint number p.

[0045] ② In the Task node l With the variable node m Create a task-variable relationship HAS_VARIABLE to indicate that the l-th task contains the m-th variable; when creating this relationship, write the relationship attributes, including the task number l and the variable number m;

[0046] ③ In the constraint node Constraint p With the variable node m Create a constraint association variable relationship RELATED_VARIABLE between them to indicate that a certain constraint depends on this variable when it is determined and calculated;

[0047] Step 2.3 Create a knowledge graph association structure for multi-task information and constraints:

[0048] For each task l Perform the following steps to write the task information into the knowledge graph:

[0049] ① Generate Task nodes l Write the task number and task parameters, including data such as the task's scheduling node, vehicle parameters, cost parameters, and time parameters;

[0050] ② Extract all decision variables and intermediate variables from the l-th task, and generate the corresponding variable nodes. m And connect to the Task via the HAS_VARIABLE relationship. l ;

[0051] For each task l Each constraint in p To establish the constraint variable association structure, follow these steps:

[0052] ① Generate constraint nodes (Constraint) based on the definition of the constraint. p Enter the constraint number and constraint name;

[0053] ② Use the HAS_CONSTRAINT relation to constrain p Connect to the corresponding task node. l ;

[0054] ③ For each relevant variable m Establish Constraint p →Variable m Create the RELATED_VARIABLE relationship and write it to the relationship attributes;

[0055] Step 3: Construction and calculation of constraint coupling strength index:

[0056] Step 3.1 Extract the set of constraint-variable relationships:

[0057] For any vehicle route optimization taskl Read the set of constraint nodes contained in the task from the knowledge graph: C l ={Constraint1, Constraint2,…,Constraint p}, and the corresponding set of variable nodes: V l ={Variable1, Variable2,…,Variable M By querying the RELATED_VARIABLE relation defined in the knowledge graph, the Constraint node for each constraint node is extracted. p The set of associated variables;

[0058] Step 3.2 Calculate the constraint coupling strength index using the formula:

[0059]

[0060] in This indicates the number of variables involved in both constraints p and q. This indicates the total number of variables involved between constraints p and q. This represents the degree of constraint violation of candidate solution x under constraint p. This represents the degree of constraint violation of candidate solution x under constraint q;

[0061] Step 3.3 Construct the constraint coupling strength index matrix:

[0062] Based on the above calculation rules, for Task l Calculate the constraint coupling strength index for any two types of constraints, and form a constraint coupling strength index matrix:

[0063]

[0064] The matrix is ​​a symmetric matrix with 0 elements on the main diagonal, which is used to indicate that the constraint itself does not participate in the coupled calculation.

[0065] Step 4: A multi-task evolutionary search guidance method based on constraint coupling strength indices:

[0066] Step 4.1 Initialize the multi-task evolutionary search population:

[0067] For each vehicle route optimization task l Initialize the corresponding evolutionary search population Pop l , represented as:

[0068]

[0069] Each individual in the population represents a candidate scheduling transportation path scheme, where This represents the nth individual solution of task l in the g-th generation; the individual encoding method is consistent with the task modeling stage and is used to represent vehicle allocation relationship and service order information;

[0070] Step 4.2 Grouping method of solutions based on constraint coupling strength index

[0071] For Task l The current population Pop l Based on the constraint coupling strength index matrix CCSM obtained in step 3 l The candidate solutions in the population are grouped using the following method:

[0072] For any candidate solution x i First, the fitness value of the solution on the objective is calculated to characterize the quality of the solution at the objective function level. The fitness value is defined as a weighted sum of the objective function values, and the calculation formula is as follows:

[0073]

[0074] Where, f1(x) i f2(x) and f2(x) i ) represent candidate solutions x i The values ​​to be taken for the two optimization objectives: the number of vehicles used and the total transportation cost of vehicles;

[0075] After obtaining the fitness values ​​of candidate solutions, the task is... l For any two constraints p and q in the equation: if their constraint coupling strength index CCSM pq If the value is greater than 0.5, then these two constraints are classified into a strongly coupled constraint group C. s Conversely, it is classified as a weakly coupled constraint group C. w Then, the constraint violation degree of the candidate solution on different constraint sets is calculated as follows:

[0076]

[0077] in, Indicates candidate solution x i The degree of constraint violation under constraint p;

[0078] Based on the above calculation results, the candidate solutions are divided according to the following rules:

[0079] When candidate solution x i Constraint violation CV on strongly coupled constraint groups s (xi The value is less than its constraint violation CV on the weakly coupled constraint group. w (x i ), classify the candidate solution as a strongly coupled dominant solution; when candidate solution x i Constraint violation CV on a loosely coupled constraint set w (x i The value is less than its constraint violation CV on the strongly coupled constraint group. s (x i The candidate solution is classified as a weakly coupled dominant solution.

[0080] Step 4.3 Differentiated crossover and mutation strategy based on ungrouping

[0081] In the multi-task parallel evolutionary search process, for each task population Pop l Repeat the steps of ungrouping and differential evolution crossover:

[0082]

[0083]

[0084] in, Let represent the mutation vector generated by the i-th individual in the (g+1)-th generation of the task population. Let r1 represent three distinct individuals randomly selected from the population of generation g. These individuals are selected by uniform random sampling from the current population and satisfy r1≠r2≠r3≠i. Let Fi represent the adaptive mutation factor corresponding to the i-th individual in the g-th generation, and F0 represent the basic mutation factor, which is a pre-defined constant with a value ranging from 0.3 to 0.8, preferably 0.5. The function represents the adjustment function that dynamically changes with the iteration number g, used to control the dynamic adjustment of the variation factor. Its expression is:

[0085]

[0086] Where g represents the current iteration number, and G represents the maximum number of iterations;

[0087] Indicates with individual The corresponding weight coefficients related to the coupling constraint group; for strongly coupled dominant solutions, For weakly coupled advantageous solutions, , This represents the historical best solution in the g-th generation of the population, selected by the individual after sorting all candidate solutions in the current population according to their fitness values. Describing the vector norm, To prevent extremely small positive numbers with a denominator of zero.

[0088]

[0089] in, This represents the experimental vector component of the i-th individual in dimension j in the (g+1)-th generation. This represents the test vector components of the mutation vector in dimension j. This represents the component of the i-th individual in the g-th generation in dimension j; when the j-th dimension belongs to an individual... The corresponding coupling constraint group C(i), or the random number rand, is less than or equal to the crossover rate CR for the coupling constraint group. C(i) At that time, take As a component of the test vector, otherwise take As a component of the experimental vector, the crossover rate CR of the strongly coupled dominant solution C(i) ≥0.7, Crossover rate CR of weakly coupled dominant solutions C(i) ≤0.5;

[0090] Step 5: Cross-task knowledge transfer method based on constraint coupling strength index:

[0091] Step 5.1 Determine the set of tasks involved in knowledge transfer:

[0092] In the multi-task optimization process, let the set of vehicle routing optimization tasks to be solved simultaneously be:

[0093]

[0094] In any evolutionary generation, at least two different tasks are selected from the task set as the source task and target task for knowledge transfer;

[0095] Step 5.2 Evaluate inter-task transfer adaptability based on constraint coupling strength index:

[0096] For any two different tasks: source task l With the target task l’ Read the corresponding constraint coupling strength index matrix CCSM respectively. l With CCSM l’ ; Computation source task l With the target task l’ Task similarity between them:

[0097]

[0098] Based on the similarity of the constraint coupling structures in the two tasks, evaluate the transfer adaptability between the tasks; calculate the mobility rate:

[0099]

[0100] in: This represents the actual knowledge transfer rate between the source task and the target task. The initial mobility is represented by λ, which is the decay coefficient of the mobility as the number of iterations decreases. The decay coefficient is preset according to the expected change pattern of knowledge transfer intensity in the algorithm; g represents the current iteration number. Indicates Task l With Task l’ The task similarity between them is calculated based on the constraint coupling strength index matrix.

[0101] Step 5.3 Differentiated knowledge transfer method based on grouped solutions:

[0102] For the set of strongly coupled advantageous solutions in the target task, select feasible individual solutions from the source task. or its path structure fragment The path structure fragment is then mapped to the individual encoding of the target task to update the vehicle service order or node access sequence in the candidate solutions of the target task; for the set of weakly coupled advantageous solutions in the target task, parameter settings from the evolutionary process are selected from the source task.<F,CR> Information or elite solution for individual x best And use the information for crossover or mutation operations on the target task, where x best This indicates the optimal individual selected by the source task in the current generation based on its fitness value.

[0103] Step 6 Environment Selection:

[0104] For any task, merge its offspring population with the corresponding parent population to form a candidate solution set; for each individual in the candidate solution set, calculate its fitness value under the two objective functions;

[0105] The candidate solutions are sorted in ascending order based on their fitness values, and the top N solutions are selected from the sorted set. p Individuals constitute the population for this task in the next generation;

[0106] Step 7: Determine the algorithm termination condition:

[0107] Determine if the current iteration number g is less than the maximum iteration number G; if g < G, let g = g + 1 and repeat steps 3-6; if g = G, then stop the multi-task evolutionary search process.

[0108] After the algorithm terminates, the non-dominated solution set corresponding to each task is output. In the non-dominated solution set of each task, the element representing the industrial scheduling center or station in the encoding of each solution is uniformly set to 0, thus obtaining the vehicle scheduling scheme that satisfies the industrial process operation constraints, which serves as the final output result of the multi-task optimization scheduling of service workpiece scheduling.

[0109] The innovation of this invention is reflected in:

[0110] (1) This invention proposes a multi-task differential evolutionary optimization method based on the constraint coupling strength index for scheduling optimization problems in industrial processes. By constructing a knowledge graph to characterize the relationship between constraints and decision variables, and further quantifying the coupling strength between different constraints, the optimization algorithm can perceive complex constraint structures during the evolutionary search process, thereby improving the search efficiency of feasible solutions and the overall optimization performance under complex constraints.

[0111] (2) In the process of multi-task parallel optimization, this invention introduces a solution grouping and differentiated evolution strategy based on the constraint coupling strength index. By dividing candidate solutions into two categories, strong coupling dominant solutions and weak coupling dominant solutions, and adopting different crossover and mutation strategies for different types of solutions, the invention achieves key protection of decision variables related to key constraints and full exploration of non-key areas, effectively improving the optimality level of multi-task vehicle path optimization.

[0112] (3) The present invention further designs a cross-task knowledge transfer mechanism based on the constraint coupling strength index. By utilizing the similarity of the constraint coupling structure between different tasks, the effective solution information formed during the optimization process is selectively transferred between tasks, reducing the interference of invalid transfer on the search process, enhancing the effect of multi-task collaborative optimization, and thus improving the overall optimization quality of industrial process service workpiece scheduling.

[0113] Special Note:

[0114] This invention proposes a multi-task differential evolution optimization method based on a constraint coupling strength index. This method is applicable to multi-task optimization scenarios such as scheduling in industrial processes. Any research on multi-task industrial scheduling and optimization using the optimization method described in this invention or its equivalent improvements should be considered to fall within the protection scope of this invention. Attached Figure Description

[0115] Figure 1 This is the route map of the first industrial scheduling task in Task 1 of the optimization results of this invention.

[0116] Figure 2 This is the route map for the second industrial scheduling task in Task 1 of the optimization results of this invention.

[0117] Figure 3This is the industrial scheduling task roadmap for Task 2 in the optimization results of this invention. Detailed Implementation

[0118] The data samples used in this invention are R101 and RC101, which belong to the Solomon dataset, as shown in Tables 1 and 2. The first to eighth columns represent the customer number i and the x-coordinate of the customer's location, respectively. i and the vertical coordinate y i The required weight q of the workpiece in the factory i Expected earliest start time a i The expected latest start time of service e i Service duration s i In this context, i=0 corresponds to information about industrial manufacturing centers, and i=1,…,100 corresponds to information about factories. This invention addresses a two-task scheduling optimization problem, where task 1 uses the R101 dataset and task 2 uses the RC101 dataset.

[0119] This invention uses the number of vehicles used and the total transportation cost as optimization objectives in the scheduling process, and adopts the following technical solution and implementation steps:

[0120] Step 1: Determine the optimization objective and constraints for each industrial scheduling problem. Assume there are two tasks, each with 40 dispatch vehicles parked at the industrial manufacturing center, serving 100 factories. Each vehicle has a maximum load capacity of 20 tons. The opening and closing times of the industrial manufacturing center are 0 and 1400 respectively. Each factory is served by only one transport vehicle. Each vehicle starts at the industrial manufacturing center carrying the workpiece requirements of the factory it is serving, and delivers the required workpieces to each factory in the service order, finally returning to the industrial manufacturing center. Each factory to be served has the following attributes: factory number i, factory location coordinates (x, y, y). i , y i The weight q of the workpieces required by the i-th factory. i The expected earliest start time of service for the i-th factory, a i And the expected latest start time of service e i And the service time s of the vehicle at the i-th factory. i Where i=0 represents a station;

[0121] Every industrial scheduling problem aims to minimize the number of vehicles used and the total transportation cost.

[0122]

[0123]

[0124] Here, f1(X) and f2(X) are two optimization objectives, namely the number of vehicles used and the total transportation cost of vehicles, respectively. <K ≤ K max h k Indicates whether the k-th vehicle is used, h k =1 means yes, h k =0 indicates no, w k This represents the maintenance cost coefficient per unit distance traveled by the k-th vehicle. This coefficient is pre-set based on one or more factors, including the vehicle's model, energy consumption level, maintenance costs, or depreciation costs. ijk L represents the transportation cost coefficient for the k-th vehicle traveling from factory i to factory j. This coefficient is determined based on one or more factors, including vehicle type, transportation distance, unit energy cost, and road toll cost. ij x is the distance between factory i and factory j, where i=0, …, N, j=0,…,N, i, j=0 represents an industrial manufacturing center, and i, j =1,…,100 represents a factory. ijk Indicates whether the k-th vehicle travels from factory i to factory j, x ijk =1 means yes, x ijk =0 indicates no, k = 1,…,40, λ1 represents the unit time cost of the vehicle performing the task, which is predetermined based on one or more factors such as labor costs, equipment depreciation costs, energy consumption costs, or dispatching operation costs incurred during vehicle operation; λ2 represents the unit distance cost of the vehicle performing the task, which is determined based on one or more factors such as fuel consumption costs, energy consumption costs, road toll costs, or vehicle wear and tear costs incurred during vehicle transportation; T k Let D represent the total mission time for the k-th vehicle, k=1,…,40. k Let k represent the total distance traveled by the k-th vehicle, where k = 1, ..., 40;

[0125] Based on the above optimization objectives, each industrial scheduling task must meet the following constraint: each factory is served only once by one scheduling vehicle:

[0126]

[0127] Every dispatch vehicle that is activated must depart from the industrial manufacturing center and ultimately return to the industrial manufacturing center:

[0128]

[0129] Service artifacts with incompatible types cannot be served by the same vehicle:

[0130]

[0131] Where z ik z is an auxiliary variable indicating whether the service job types of vehicle k and factory i are compatible. ik = 1 is true, z ik =0 indicates no, r i M represents the service workpiece type of factory i. rirj Indicates whether the service workpiece types of factory i and factory j are the same, M rirj =1 means yes, M rirj =0 means no;

[0132] The total weight of service items dispatched by each dispatch vehicle in its service route must not exceed the vehicle's maximum load capacity:

[0133]

[0134] Where, q i Q is the number of service workpieces that factory i needs to schedule. k This is the maximum load capacity of vehicle k;

[0135] The total task time for each dispatched vehicle within its service route must not exceed the maximum task time.

[0136]

[0137] Where t ij It is the travel time for dispatched vehicles from factory i to factory j, s i The maximum task time refers to the longest duration during which a single dispatched vehicle is allowed to perform a task in a single dispatch process. This value is preset based on one or more factors, such as the working hours of the industrial manufacturing center, the vehicle's available running time, personnel scheduling requirements, or task scheduling rules.

[0138] The arrival time of each dispatched vehicle at each factory should be within the time window required by that factory, and the dispatched vehicle should return to the center within the time window required by the industrial manufacturing center:

[0139]

[0140] Among them, a i e represents the earliest time that the i-th factory is allowed to start service. i t represents the latest time that the i-th factory is allowed to start service. i This represents the time when the dispatched vehicle arrives at the i-th factory and begins providing service;

[0141]

[0142] Among them, A l E represents the earliest time that the vehicle is allowed to return to the industrial manufacturing center corresponding to the l-th task. l t represents the latest time that the vehicle is allowed to return to the industrial manufacturing center corresponding to the l-th task. k This represents the time it takes for the kth dispatched vehicle to return to the industrial manufacturing center after completing its service route.

[0143] Constraint violation degree of the comprehensive calculation solution:

[0144]

[0145] Wherein, CV(x) represents the comprehensive constraint violation degree of candidate solution x; This indicates the violation of the r-th inequality constraint function in the l-th task; This indicates the violation of the s-th equality constraint function in the l-th task; U represents the number of inequality constraints in this task, and V represents the number of equality constraints in this task; δ represents the tolerance threshold allowed for equality constraints, used to convert equality constraints into approximate constraints with tolerance, and its value is preset according to the computational accuracy requirements of the problem.

[0146] When a candidate solution satisfies all constraints, its comprehensive constraint violation degree CV(x) is 0; when a candidate solution violates any constraint, the degree of violation is accumulated using the above formula, which is then used to evaluate the feasibility of the candidate solution.

[0147] Step 2: Construct a knowledge graph network to store task information and constraints.

[0148] Before constructing the knowledge graph, the relevant data is first structured based on the task information, constraints, and decision variables of the industrial scheduling problem determined in step 1, and the types of nodes to be created in the knowledge graph and their attribute fields are determined accordingly.

[0149] Step 2.1 Define the node types and attribute fields of the knowledge graph:

[0150] Before constructing a knowledge graph, first determine the types of nodes to be created in the knowledge graph and set corresponding attribute fields for each type of node. The specific steps are as follows:

[0151] ① Create a Task node lThis is used to represent the l-th industrial scheduling task determined in step 1, where l = 1, 2; when creating a task node, the task number l and the number of scheduling nodes N contained in the task are written to it. l Available vehicle limit K max. l Vehicle load limit Q k Industrial Dispatch Center Time Window Parameter A l With E l ;

[0152] ② Create Constraint nodes p : Used to represent the p-th constraint in the industrial scheduling task determined in step 1, where p = 1,…, P; When creating a constraint node, write the constraint number p, constraint name, and constraint type identifier to it to distinguish different types of constraint conditions.

[0153] ③ Create a variable node m : Used to represent decision variables or intermediate variables involved in the calculation process in the industrial scheduling model established in step 1, where m = 1,…, M; when creating a variable node, write the variable number m, variable name, variable type identifier, and variable value range or domain to it;

[0154] Step 2.2 Define the relation types and relation attributes of the knowledge graph:

[0155] After creating the nodes, define the relationship types between them to describe the structural associations between tasks, constraints, and variables. The specific steps are as follows:

[0156] ① In the Task node l Constraint node p The task contains a constraint relationship HAS_CONSTRAINT, which indicates that the l-th task contains the p-th constraint. When creating this relationship, the relationship attributes are written, including the task number l and the constraint number p.

[0157] ② In the Task node l With the variable node m Create a task-variable relationship HAS_VARIABLE to indicate that the l-th task contains the m-th variable; when creating this relationship, write the relationship attributes, including the task number l and the variable number m;

[0158] ③ In the constraint node Constraint p With the variable node m Create a constraint association variable relationship RELATED_VARIABLE between them to indicate that a certain constraint depends on this variable when it is determined and calculated;

[0159] Step 2.3 Create a knowledge graph association structure for multi-task information and constraints:

[0160] For each task l Perform the following steps to write the task information into the knowledge graph:

[0161] ① Generate Task nodes l Write the task number and task parameters, including data such as the task's scheduling node, vehicle parameters, cost parameters, and time parameters;

[0162] ② Extract all decision variables and intermediate variables from the l-th task, and generate the corresponding variable nodes. m And connect to the Task via the HAS_VARIABLE relationship. l ;

[0163] For each task l Each constraint in p To establish the constraint variable association structure, follow these steps:

[0164] ① Generate constraint nodes (Constraint) based on the definition of the constraint. p Enter the constraint number and constraint name;

[0165] ② Use the HAS_CONSTRAINT relation to constrain p Connect to the corresponding task node. l ;

[0166] ③ For each relevant variable m Establish Constraint p →Variable m Create the RELATED_VARIABLE relationship and write it to the relationship attributes;

[0167] Step 3: Construction and calculation of constraint coupling strength index:

[0168] Step 3.1 Extract the set of constraint-variable relationships:

[0169] For any vehicle route optimization task l Read the set of constraint nodes contained in the task from the knowledge graph: C l ={Constraint1, Constraint2,…,Constraint p}, and the corresponding set of variable nodes: V l={Variable1, Variable2,…,Variable M By querying the RELATED_VARIABLE relation defined in the knowledge graph, the Constraint node for each constraint node is extracted. p The set of associated variables;

[0170] Step 3.2 Calculate the constraint coupling strength index using the formula:

[0171]

[0172] in This indicates the number of variables involved in both constraints p and q. This indicates the total number of variables involved between constraints p and q. This represents the degree of constraint violation of candidate solution x under constraint p. This represents the degree of constraint violation of candidate solution x under constraint q;

[0173] Step 3.3 Construct the constraint coupling strength index matrix:

[0174] Based on the above calculation rules, for Task l Calculate the constraint coupling strength index for any two types of constraints, and form a constraint coupling strength index matrix:

[0175]

[0176] The matrix is ​​a symmetric matrix with 0 elements on the main diagonal, which is used to indicate that the constraint itself does not participate in the coupled calculation.

[0177] Step 4: A multi-task evolutionary search guidance method based on constraint coupling strength indices:

[0178] Step 4.1 Initialize the multi-task evolutionary search population:

[0179] For each vehicle route optimization task l Initialize the corresponding evolutionary search population Pop l , represented as:

[0180]

[0181] Each individual in the population represents a candidate scheduling transportation path scheme, where This represents the nth individual solution of task l in the g-th generation; the individual encoding method is consistent with the task modeling stage and is used to represent vehicle allocation relationship and service order information;

[0182] Step 4.2 Grouping method of solutions based on constraint coupling strength index

[0183] For Task l The current population Pop l Based on the constraint coupling strength index matrix CCSM obtained in step 3 l The candidate solutions in the population are grouped using the following method:

[0184] For any candidate solution x i First, the fitness value of the solution on the objective is calculated to characterize the quality of the solution at the objective function level. The fitness value is defined as a weighted sum of the objective function values, and the calculation formula is as follows:

[0185]

[0186] Where, f1(x) i f2(x) and f2(x) i ) represent candidate solutions x i The values ​​to be taken for the two optimization objectives: the number of vehicles used and the total transportation cost of vehicles;

[0187] After obtaining the fitness values ​​of candidate solutions, the task is... l For any two constraints p and q in the equation: if their constraint coupling strength index CCSM pq If the value is greater than 0.5, then these two constraints are classified into a strongly coupled constraint group C. s Conversely, it is classified as a weakly coupled constraint group C. w Then, the constraint violation degree of the candidate solution on different constraint sets is calculated as follows:

[0188]

[0189] in, Indicates candidate solution x i The degree of constraint violation under constraint p;

[0190] Based on the above calculation results, the candidate solutions are divided according to the following rules:

[0191] When candidate solution x i Constraint violation CV on strongly coupled constraint groups s (x i The value is less than its constraint violation CV on the weakly coupled constraint group. w (x i ), classify the candidate solution as a strongly coupled dominant solution; when candidate solution x i Constraint violation CV on a loosely coupled constraint setw (x i The value is less than its constraint violation CV on the strongly coupled constraint group. s (x i The candidate solution is classified as a weakly coupled dominant solution.

[0192] Step 4.3 Differentiated crossover and mutation strategy based on ungrouping

[0193] In the multi-task parallel evolutionary search process, for each task population Pop l Repeat the steps of ungrouping and differential evolution crossover:

[0194]

[0195]

[0196] in, Let represent the mutation vector generated by the i-th individual in the (g+1)-th generation of the task population. Let r1 represent three distinct individuals randomly selected from the population of generation g. These individuals are selected by uniform random sampling from the current population and satisfy r1≠r2≠r3≠i. Let Fi represent the adaptive mutation factor corresponding to the i-th individual in the g-th generation, and F0 represent the basic mutation factor, which is a pre-defined constant with a value ranging from 0.3 to 0.8, preferably 0.5. The function represents the adjustment function that dynamically changes with the iteration number g, used to control the dynamic adjustment of the variation factor. Its expression is:

[0197]

[0198] Where g represents the current iteration number, and G represents the maximum number of iterations;

[0199] Indicates with individual The corresponding weight coefficients related to the coupling constraint group; for strongly coupled dominant solutions, For weakly coupled advantageous solutions, , This represents the historical best solution in the g-th generation of the population, selected by the individual after sorting all candidate solutions in the current population according to their fitness values. Describing the vector norm, To prevent extremely small positive numbers with a denominator of zero.

[0200]

[0201] in, This represents the experimental vector component of the i-th individual in dimension j in the (g+1)-th generation. This represents the test vector components of the mutation vector in dimension j. This represents the component of the i-th individual in the g-th generation in dimension j; when the j-th dimension belongs to an individual... The corresponding coupling constraint group C(i), or the random number rand, is less than or equal to the crossover rate CR for the coupling constraint group. C(i) At that time, take As a component of the test vector, otherwise take As a component of the experimental vector, the crossover rate CR of the strongly coupled dominant solution C(i) ≥0.7, Crossover rate CR of weakly coupled dominant solutions C(i) ≤0.5;

[0202] Step 5: Cross-task knowledge transfer method based on constraint coupling strength index:

[0203] Step 5.1 Determine the set of tasks involved in knowledge transfer:

[0204] In the multi-task optimization process, let the set of vehicle routing optimization tasks to be solved simultaneously be:

[0205]

[0206] In any evolutionary generation, at least two different tasks are selected from the task set as the source task and target task for knowledge transfer;

[0207] Step 5.2 Evaluate inter-task transfer adaptability based on constraint coupling strength index:

[0208] For any two different tasks: source task l With the target task l’ Read the corresponding constraint coupling strength index matrix CCSM respectively. l With CCSM l’ ; Computation source task l With the target task l’ Task similarity between them:

[0209]

[0210] Based on the similarity of the constraint coupling structures in the two tasks, evaluate the transfer adaptability between the tasks; calculate the mobility rate:

[0211]

[0212] in: This represents the actual knowledge transfer rate between the source task and the target task. The initial mobility is represented by λ, which is the decay coefficient of the mobility as the number of iterations decreases. The decay coefficient is preset according to the expected change pattern of knowledge transfer intensity in the algorithm; g represents the current iteration number. Indicates Task l With Task l’ The task similarity between them is calculated based on the constraint coupling strength index matrix.

[0213] Step 5.3 Differentiated knowledge transfer method based on grouped solutions:

[0214] For the set of strongly coupled advantageous solutions in the target task, select feasible individual solutions from the source task. or its path structure fragment The path structure fragment is then mapped to the individual encoding of the target task to update the vehicle service order or node access sequence in the candidate solutions of the target task; for the set of weakly coupled advantageous solutions in the target task, parameter settings from the evolutionary process are selected from the source task.<F,CR> Information or elite solution for individual x best And use the information for crossover or mutation operations on the target task, where x best This indicates the optimal individual selected by the source task in the current generation based on its fitness value.

[0215] Step 6 Environment Selection:

[0216] For any task, merge its offspring population with the corresponding parent population to form a candidate solution set; for each individual in the candidate solution set, calculate its fitness value under the two objective functions;

[0217] The candidate solutions are sorted in ascending order based on their fitness values, and the top N solutions are selected from the sorted set. p Individuals constitute the population for this task in the next generation;

[0218] Step 7: Determine the algorithm termination condition:

[0219] Determine if the current iteration number g is less than the maximum iteration number 1000; if g < 1000, let g = g + 1 and repeat steps 3-6; if g = 1000, then stop the multi-task evolutionary search process.

[0220] After the algorithm terminates, the non-dominated solution set corresponding to each task is output. In the non-dominated solution set of each task, the element representing the industrial scheduling center or station in the encoding of each solution is uniformly set to 0, thus obtaining the vehicle scheduling scheme that satisfies the industrial process operation constraints, which serves as the final output result of the multi-task optimization scheduling of service workpiece scheduling.

[0221] Table 1. R101 Industrial Scheduling Optimization Data

[0222] Customer Number x-axis of customer location Customer location ordinate Demand Earliest start time Latest start time of service Service Hours 0 35 35 0 0 230 0 1 41 49 10 161 171 10 2 35 17 7 50 60 10 3 55 45 13 116 126 10 4 55 20 19 149 159 10 5 15 30 26 34 44 10 6 25 30 3 99 109 10 7 20 50 5 81 91 10 8 10 43 9 95 105 10 9 55 60 16 97 107 10 10 30 60 16 124 134 10 11 20 65 12 67 77 10 12 50 35 19 63 73 10 13 30 25 23 159 169 10 14 15 10 20 32 42 10 15 30 5 8 61 71 10 16 10 20 19 75 85 10 17 5 30 2 157 167 10 18 20 40 12 87 97 10 19 15 60 17 76 86 10 20 45 65 9 126 136 10 21 45 20 11 62 72 10 22 45 10 18 97 107 10 23 55 5 29 68 78 10 24 65 35 3 153 163 10 25 65 20 6 172 182 10 26 45 30 17 132 142 10 27 35 40 16 37 47 10 28 41 37 16 39 49 10 29 64 42 9 63 73 10 30 40 60 21 71 81 10 31 31 52 27 50 60 10 32 35 69 23 141 151 10 33 53 52 11 37 47 10 34 65 55 14 117 127 10 35 63 65 8 143 153 10 36 2 60 5 41 51 10 37 20 20 8 0 198 10 38 5 5 16 83 93 10 39 60 12 31 44 54 10 40 40 25 9 85 95 10 41 42 7 5 97 107 10 42 24 12 5 31 41 10 43 23 3 7 132 142 10 44 11 14 18 69 79 10 45 6 38 16 32 42 10 46 2 48 1 117 127 10 47 8 56 27 51 61 10 48 13 52 36 0 192 10 49 6 68 30 108 118 10 50 47 47 13 0 203 10 51 49 58 10 88 98 10 52 27 43 9 0 208 10 53 37 31 14 95 105 10 54 57 29 18 140 150 10 55 63 23 2 136 146 10 56 53 12 6 130 140 10 57 32 12 7 101 111 10 58 36 26 18 200 210 10 59 21 24 28 0 202 10 60 17 34 3 162 172 10 61 12 24 13 76 86 10 62 24 58 19 58 68 10 63 27 69 10 34 44 10 64 15 77 9 73 83 10 65 62 77 20 51 61 10 66 49 73 25 127 137 10 67 67 5 25 83 93 10 68 56 39 36 142 152 10 69 37 47 6 50 60 10 70 37 56 5 182 192 10 71 57 68 15 77 87 10 72 47 16 25 0 197 10 73 44 17 9 78 88 10 74 46 13 8 149 159 10 75 49 11 18 0 192 10 76 49 42 13 73 83 10 77 53 43 14 179 189 10 78 61 52 3 96 106 10 79 57 48 23 92 102 10 80 56 37 6 182 192 10 81 55 54 26 94 104 10 82 15 47 16 0 196 10 83 14 37 11 0 198 10 84 11 31 7 101 111 10 85 16 22 41 0 196 10 86 4 18 35 94 104 10 87 28 18 26 93 103 10 88 26 52 9 74 84 10 89 26 35 15 176 186 10 90 31 67 3 95 105 10 91 15 19 1 0 194 10 92 22 22 2 18 28 10 93 18 24 22 188 198 10 94 26 27 27 0 207 10 95 25 24 20 0 205 10 96 22 27 11 0 204 10 97 25 21 12 133 143 10 98 19 21 10 0 198 10 99 20 26 9 83 93 10 100 18 18 17 185 195 10

[0223] Table 2. RC101 Industrial Scheduling Optimization Data

[0224] Customer Number x-axis of customer location Customer location ordinate Demand Earliest start time Latest start time of service Service Hours 0 1 40 50 0 0 240 1 2 25 85 20 71 191 2 3 22 75 30 30 150 3 4 22 85 10 64 184 4 5 20 80 40 151 161 5 6 20 85 20 40 160 6 7 18 75 20 96 123 7 8 15 75 20 35 155 8 9 15 80 10 101 111 9 10 10 35 20 101 111 10 11 10 40 30 123 144 11 12 8 40 40 69 79 12 13 8 45 20 32 152 13 14 5 35 10 152 162 14 15 5 45 10 35 117 15 16 2 40 20 68 78 16 17 0 40 20 59 114 17 18 0 45 20 147 180 18 19 44 5 20 79 124 19 20 42 10 40 58 115 20 21 42 15 10 111 162 21 22 40 5 10 45 165 22 23 40 15 40 94 119 23 24 38 5 30 75 85 24 25 38 15 10 128 194 25 26 35 5 20 171 181 26 27 95 30 30 58 171 27 28 95 35 20 60 93 28 29 92 30 10 55 120 29 30 90 35 10 52 112 30 31 88 30 10 75 102 31 32 88 35 20 50 170 32 33 87 30 10 116 175 33 34 85 25 10 51 85 34 35 85 35 30 62 182 35 36 67 85 20 138 169 36 37 65 85 40 43 78 37 38 65 82 10 69 189 38 39 62 80 30 85 95 39 40 60 80 10 36 74 40 41 60 85 30 87 112 41 42 58 75 20 92 121 42 43 55 80 10 33 66 43 44 55 85 20 117 168 44 45 55 82 10 74 84 45 46 20 82 10 37 72 46 47 18 80 10 98 157 47 48 2 45 10 38 109 48 49 42 5 10 64 184 49 50 42 12 10 109 128 50 51 72 35 30 71 191 51 52 55 20 19 69 126 52 53 25 30 3 25 145 53 54 20 50 5 101 111 54 55 55 60 16 127 180 55 56 30 60 16 150 160 56 57 50 35 19 130 159 57 58 30 25 23 82 139 58 59 15 10 20 172 182 59 60 10 20 19 42 162 60 61 15 60 17 137 202 61 62 45 65 9 55 106 62 63 65 35 3 62 72 63 64 65 20 6 39 108 64 65 45 30 17 53 82 65 66 35 40 16 11 43 66 67 41 37 16 134 161 67 68 64 42 9 80 90 68 69 40 60 21 144 173 69 70 31 52 27 51 61 70 71 35 69 23 172 210 71 72 65 55 14 52 107 72 73 63 65 8 27 147 73 74 2 60 5 65 118 74 75 20 20 8 151 161 75 76 5 5 16 57 172 76 77 60 12 31 85 95 77 78 23 3 7 163 173 78 79 8 56 27 90 119 79 80 6 68 30 99 109 80 81 47 47 13 190 222 81 82 49 58 10 80 121 82 83 27 43 9 14 134 83 84 37 31 14 19 139 84 85 57 29 18 106 116 85 86 63 23 2 42 162 86 87 21 24 28 77 126 87 88 12 24 13 100 110 88 89 24 58 19 67 96 89 90 67 5 25 105 177 90 91 37 47 6 74 127 91 92 49 42 13 97 217 92 93 53 43 14 15 25 93 94 61 52 3 173 208 94 95 57 48 23 50 170 95 96 56 37 6 20 140 96 97 55 54 26 87 207 97 98 4 18 35 112 157 98 99 26 52 9 14 134 99 100 26 35 15 87 97 100 101 31 67 3 200 210

[0225] Table 3. Optimal Industrial Scheduling Scheme for Each Task

[0226]

Claims

1. A multi-task intelligent optimization method for industrial manufacturing based on constraint coupling strength index, characterized in that, Includes the following steps: Step 1: Determine the optimization objective and constraints for each industrial scheduling problem: Assume there are L tasks, each task has K... max The dispatch vehicles are parked at the industrial manufacturing center, serving N factories. Each vehicle has a maximum load capacity of Q. The opening and closing times of the industrial manufacturing center are A and E, respectively. Each factory is served by only one transport vehicle. Each vehicle departs from the industrial manufacturing center carrying the workpiece requirements of the factory it is serving, delivering the required workpieces to each factory in the service order, and finally returning to the industrial manufacturing center. Each factory to be served has the following attributes: factory number i, factory location coordinates (x, y, y). i , y i The weight q of the workpieces required by the i-th factory. i The expected earliest start time of service for the i-th factory, a i And the expected latest start time of service e i And the service time s of the vehicle at the i-th factory. i Where i=0 represents a station; 0 < K max < 50 vehicles, 0 < N < 150 units, 0 < Q < 30 tons, 0 < A < 1440 minutes, 0 < E < 1440 minutes, i = 0, ..., N, 0 < x i < 100, 0 < y i < 100, 0 < a i < 1440 minutes, 0 < e i < 1440 minutes, 0 < s i < 200 minutes; Every industrial scheduling problem aims to minimize the number of vehicles used and the total transportation cost. ; Here, f1(X) and f2(X) are two optimization objectives, namely the number of vehicles used and the total transportation cost, respectively, where 0 < K ≤ K. max h k Indicates whether the k-th vehicle is used, h k =1 means yes, h k =0 indicates no, w k This represents the maintenance cost coefficient per unit distance traveled by the k-th vehicle. This coefficient is pre-set based on one or more factors, including the vehicle's model, energy consumption level, maintenance costs, or depreciation costs. ijk L represents the transportation cost coefficient for the k-th vehicle traveling from factory i to factory j. This coefficient is determined based on one or more factors, including vehicle type, transportation distance, unit energy cost, and road toll cost. ij x is the distance between factory i and factory j, where i=0, …, N, j=0, …, N, i, j=0 represents an industrial manufacturing center, and i, j =1, …, N represents a factory. ijk Indicates whether the k-th vehicle travels from factory i to factory j, x ijk =1 means yes, x ijk =0 indicates no, k = 1,…, K, λ1 represents the unit time cost of the vehicle performing the task, which is predetermined based on one or more factors such as labor costs, equipment depreciation costs, energy consumption costs, or dispatching costs incurred during vehicle operation; λ2 represents the unit distance cost of the vehicle performing the task, which is determined based on one or more factors such as fuel consumption costs, energy consumption costs, road toll costs, or vehicle wear and tear costs incurred during vehicle transportation; T k Let D represent the total mission time for the k-th vehicle, where k = 1, ..., K. k Let k represent the total distance traveled by the k-th vehicle, where k = 1, ..., K; Based on the above optimization objectives, each industrial scheduling task must meet the following constraint: each factory is served only once by one scheduling vehicle: Every dispatch vehicle that is activated must depart from the industrial manufacturing center and ultimately return to the industrial manufacturing center. Service artifacts with incompatible types cannot be served by the same vehicle. ;where z ik z is an auxiliary variable indicating whether the service job types of vehicle k and factory i are compatible. ik = 1 is true, z ik =0 indicates no, r i M represents the service workpiece type of factory i. rirj Indicates whether the service workpiece types of factory i and factory j are the same, M rirj =1 means yes, M rirj =0 means no; The total weight of service items dispatched by each dispatch vehicle in its service route must not exceed the vehicle's maximum load capacity: ; where q i Q is the number of service workpieces that factory i needs to schedule. k This is the maximum load capacity of vehicle k; The total task time for each dispatched vehicle within its service route must not exceed the maximum task time. ; where t ij It is the travel time for dispatched vehicles from factory i to factory j, s i The maximum task time refers to the longest duration during which a single dispatched vehicle is allowed to perform a task in a single dispatch process. This value is preset based on one or more factors, such as the working hours of the industrial manufacturing center, the vehicle's available running time, personnel scheduling requirements, or task scheduling rules. The arrival time of each dispatched vehicle at each factory should be within the time window required by that factory, and the dispatched vehicle should return to the center within the time window required by the industrial manufacturing center: ; where a i e represents the earliest time that the i-th factory is allowed to start service. i t represents the latest time that the i-th factory is allowed to start service. i This represents the time when the dispatched vehicle arrives at the i-th factory and begins providing service; Among them, A l E represents the earliest time that the vehicle is allowed to return to the industrial manufacturing center corresponding to the l-th task. l t represents the latest time that the vehicle is allowed to return to the industrial manufacturing center corresponding to the l-th task. k This represents the time it takes for the kth dispatched vehicle to return to the industrial manufacturing center after completing its service route. Constraint violation degree of the comprehensive calculation solution: Where CV(x) represents the comprehensive constraint violation degree of candidate solution x; This indicates the violation of the r-th inequality constraint function in the l-th task; This indicates the violation of the s-th equality constraint function in the l-th task; U represents the number of inequality constraints in this task, and V represents the number of equality constraints in this task; δ represents the tolerance threshold allowed for equality constraints, used to convert equality constraints into approximate constraints with tolerance, and its value is preset according to the computational accuracy requirements of the problem. When a candidate solution satisfies all constraints, its comprehensive constraint violation degree CV(x) is 0; when a candidate solution violates any constraint, the degree of violation is accumulated using the above formula to evaluate the feasibility of the candidate solution. Step 2: Construct a knowledge graph network to store task information and constraints. Before constructing the knowledge graph, the relevant data is first structured based on the task information, constraints, and decision variables of the industrial scheduling problem determined in step 1, and the types of nodes to be created in the knowledge graph and their attribute fields are determined accordingly. Step 2.1 Define the node types and attribute fields of the knowledge graph: Before constructing the knowledge graph, first determine the types of nodes to be created in the knowledge graph, and set corresponding attribute fields for each type of node; the specific steps are as follows: ① Create a Task node l : Used to represent the l-th industrial scheduling task determined in step 1, where l = 1,…,L; when creating a task node, write the task number l and the number of scheduling nodes N contained in the task to it. l Available vehicle limit K max. l Vehicle load limit Q l Industrial Dispatch Center Time Window Parameter A l With E l ; ② Create Constraint nodes p : Used to represent the p-th constraint in the industrial scheduling task determined in step 1, where p = 1,…, P; When creating a constraint node, write the constraint number p, constraint name, and constraint type identifier to it to distinguish different types of constraint conditions. ③ Create a variable node m : Used to represent decision variables or intermediate variables involved in the calculation process in the industrial scheduling model established in step 1, where m = 1,…, M; when creating a variable node, write the variable number m, variable name, variable type identifier, and variable value range or domain to it; Step 2.2 Define the relation types and relation attributes of the knowledge graph: After creating the nodes, define the relationship types between them to describe the structural associations between tasks, constraints, and variables; the specific steps are as follows: ① In the Task node l Constraint node p The task contains a constraint relationship HAS_CONSTRAINT, which is used to indicate that the l-th task contains the p-th constraint. When creating this relationship, the relationship attributes are written, including the task number l and the constraint number p. ② In the Task node l With the variable node m Create a task-variable relationship HAS_VARIABLE to indicate that the l-th task contains the m-th variable; when creating this relationship, write the relationship attributes, including the task number l and the variable number m; ③ In the constraint node Constraint p With the variable node m Create a constraint association variable relationship RELATED_VARIABLE between them to indicate that a certain constraint depends on this variable when it is determined and calculated; Step 2.3 Create a knowledge graph association structure for multi-task information and constraints: For each task l Perform the following steps to write the task information into the knowledge graph: ① Generate Task nodes l Write the task number and task parameters, including data such as the task's scheduling node, vehicle parameters, cost parameters, and time parameters; ② Extract all decision variables and intermediate variables from the l-th task, and generate the corresponding variable nodes. m And connect to the Task via the HAS_VARIABLE relationship. l ; For each task l Each constraint in p To establish the constraint variable association structure, follow these steps: ① Generate constraint nodes (Constraint) based on the definition of the constraint. p Enter the constraint number and constraint name; ② Use the HAS_CONSTRAINT relation to constrain p Connect to the corresponding task node. l ; ③ For each relevant variable m Establish Constraint p →Variable m Create the RELATED_VARIABLE relationship and write it to the relationship attributes; Step 3: Construction and calculation of constraint coupling strength index: Step 3.1 Extract the set of constraint-variable relationships: For any vehicle route optimization task l Read the set of constraint nodes contained in the task from the knowledge graph: C l ={Constraint1, Constraint2,…,Constraint p }, and the corresponding set of variable nodes: V l ={Variable1, Variable2,…,Variable M By querying the RELATED_VARIABLE relation defined in the knowledge graph, the Constraint node for each constraint node is extracted. p The set of associated variables; Step 3.2 Calculate the constraint coupling strength index using the formula: ;in This indicates the number of variables involved in both constraints p and q. This indicates the total number of variables involved between constraints p and q. This represents the degree of constraint violation of candidate solution x under constraint p. This represents the degree of constraint violation of candidate solution x under constraint q; Step 3.3 Construct the constraint coupling strength index matrix: Based on the above calculation rules, for Task l Calculate the constraint coupling strength index for any two types of constraints, and form a constraint coupling strength index matrix: The matrix is ​​a symmetric matrix with 0 elements on the main diagonal, which indicates that the constraint itself does not participate in the coupled calculation. Step 4: A multi-task evolutionary search guidance method based on constraint coupling strength indices: Step 4.1 Initialize the multi-task evolutionary search population: For each vehicle route optimization task l Initialize the corresponding evolutionary search population Pop l , is represented as: Each individual in the population represents a candidate scheduling and transportation route scheme, where This represents the nth individual solution of task l in the g-th generation; the individual encoding method is consistent with the task modeling stage and is used to represent vehicle allocation relationship and service order information; Step 4.2 Grouping method of solutions based on constraint coupling strength index For Task l The current population Pop l Based on the constraint coupling strength index matrix CCSM obtained in step 3 l The candidate solutions in the population are grouped using the following method: For any candidate solution x i First, the fitness value of the solution on the objective is calculated to characterize the quality of the solution at the objective function level. The fitness value is defined as a weighted sum of the objective function values, and the calculation formula is as follows: ;where, f1(x i f2(x) and f2(x) i ) represent candidate solutions x i The values ​​to be taken for the two optimization objectives: the number of vehicles used and the total transportation cost of vehicles; After obtaining the fitness values ​​of candidate solutions, the task is... l For any two constraints p and q in the equation: if their constraint coupling strength index CCSM pq If the value is greater than 0.5, then these two constraints are classified into a strongly coupled constraint group C. s Conversely, it is classified as a weakly coupled constraint group C. w Then, the constraint violation degree of the candidate solution on different constraint sets is calculated as follows: ;in, Indicates candidate solution x i The degree of constraint violation under constraint p; Based on the above calculation results, the candidate solutions are divided according to the following rules: When candidate solution x i Constraint violation CV on strongly coupled constraint groups s (x i The value is less than its constraint violation CV on the weakly coupled constraint group. w (x i ), classify the candidate solution as a strongly coupled dominant solution; when candidate solution x i Constraint violation CV on a loosely coupled constraint set w (x i The value is less than its constraint violation CV on the strongly coupled constraint group. s (x i The candidate solution is classified as a weakly coupled dominant solution. Step 4.3 Differentiated crossover and mutation strategy based on ungrouping In the multi-task parallel evolutionary search process, for each task population Pop l Repeat the steps of ungrouping and differential evolution crossover: ; ;in, Let represent the mutation vector generated by the i-th individual in the (g+1)-th generation of the task population. Let r1 represent three distinct individuals randomly selected from the population of generation g. These individuals are selected by uniform random sampling from the current population and satisfy r1≠r2≠r3≠i. Let Fi represent the adaptive mutation factor corresponding to the i-th individual in the g-th generation, and F0 represent the basic mutation factor, which is a pre-defined constant with a value ranging from 0.3 to 0.8, preferably 0.

5. The function represents the adjustment function that dynamically changes with the iteration number g, used to control the dynamic adjustment of the variation factor. Its expression is: Where g represents the current iteration number and G represents the maximum number of iterations; Indicates with individual The corresponding weight coefficients related to the coupling constraint group; for strongly coupled dominant solutions, For weakly coupled advantageous solutions, , This represents the historical best solution in the g-th generation of the population, selected by the individual after sorting all candidate solutions in the current population according to their fitness values. Describing the vector norm, To prevent extremely small positive numbers with a denominator of zero; ;in, This represents the experimental vector component of the i-th individual in dimension j in the (g+1)-th generation. This represents the test vector components of the mutation vector in dimension j. This represents the component of the i-th individual in the g-th generation in dimension j; when the j-th dimension belongs to an individual... The corresponding coupling constraint group C(i), or the random number rand, is less than or equal to the crossover rate CR for the coupling constraint group. C(i) At that time, take As a component of the test vector, otherwise take As a component of the experimental vector, the crossover rate CR of the strongly coupled dominant solution C(i) ≥0.7, Crossover rate CR of weakly coupled dominant solutions C(i) ≤0.5; Step 5: Cross-task knowledge transfer method based on constraint coupling strength index: Step 5.1 Determine the set of tasks involved in knowledge transfer: In the multi-task optimization process, let the set of vehicle routing optimization tasks to be solved simultaneously be: In any evolutionary generation, at least two different tasks are selected from the task set as the source task and target task for knowledge transfer. Step 5.2 Evaluate inter-task transfer adaptability based on constraint coupling strength index: For any two different tasks: source task l With the target task l’ Read the corresponding constraint coupling strength index matrix CCSM respectively. l With CCSM l’ ; Computation source task l With the target task l’ Task similarity between them: Based on the similarity of the constraint coupling structures in the two tasks, evaluate the transfer adaptability between the tasks; calculate the mobility rate: ;in: This represents the actual knowledge transfer rate between the source task and the target task. The initial mobility is represented by λ, which is the decay coefficient of the mobility as the number of iterations decreases. The decay coefficient is preset according to the expected change pattern of knowledge transfer intensity in the algorithm; g represents the current iteration number. Indicates Task l With Task l’ The task similarity between them is calculated based on the constraint coupling strength index matrix; Step 5.3 Differentiated knowledge transfer method based on grouped solutions: For the set of strongly coupled advantageous solutions in the target task, select feasible individual solutions from the source task. or its path structure fragment The path structure fragment is then mapped to the individual encoding of the target task to update the vehicle service order or node access sequence in the candidate solutions of the target task; for the set of weakly coupled advantageous solutions in the target task, parameter settings from the evolutionary process are selected from the source task.<F,CR> Information or elite solution for individual x best And use the information for crossover or mutation operations on the target task, where x best This indicates the optimal individual selected by the source task in the current generation based on its fitness value. Step 6 Environment Selection: For any task, merge its offspring population with the corresponding parent population to form a candidate solution set; for each individual in the candidate solution set, calculate its fitness value under the two objective functions; The candidate solutions are sorted in ascending order based on their fitness values, and the top N solutions are selected from the sorted set. p Individuals constitute the population for this task in the next generation; Step 7: Determine the algorithm termination condition: Determine if the current iteration number g is less than the maximum iteration number G; if g < G, let g = g + 1 and repeat steps 3-6; if g = G, then stop the multi-task evolutionary search process. After the algorithm terminates, the non-dominated solution set corresponding to each task is output. In the non-dominated solution set of each task, the element representing the industrial scheduling center or station in the encoding of each solution is uniformly set to 0, so as to obtain the vehicle scheduling scheme that satisfies the industrial process operation constraints, which is the final output result of the multi-task optimization scheduling of service workpiece scheduling.

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