A method for guiding roller flexible job shop scheduling based on improved grey wolf algorithm

Abstract

This invention discloses a flexible job shop scheduling method for guide rollers based on an improved Grey Wolf algorithm. For the guide roller manufacturing process, a multi-objective flexible job shop scheduling model is constructed with the optimization objectives of minimizing maximum completion time, minimizing total equipment load, and minimizing total energy consumption. Assembly-type process priority relationships, hot-assembly waiting window constraints, and dedicated equipment constraints are introduced to fit actual production scenarios. In terms of the solution method, a hybrid multi-strategy heuristic initialization method is used to construct the initial population, integrating cosine decay mechanism, variable neighborhood search, and elite retention strategy into the multi-objective Grey Wolf optimization algorithm. The improved algorithm is used to solve the scheduling model to obtain the optimal process sequencing and machine allocation scheme. This invention can effectively improve the convergence, distribution, and stability of the scheduling solution, significantly reduce the completion time, equipment load, and energy consumption in the guide roller manufacturing process, and provide an efficient solution for the intelligent scheduling of key components in packaging and printing equipment.

Description

Technical Field

[0001] This invention belongs to the field of intelligent technology in packaging and printing equipment manufacturing, specifically a flexible workshop scheduling method for guide rollers based on an improved gray wolf algorithm. Background Technology

[0002] Guide rollers are the most numerous and diverse key basic components in packaging and printing equipment. Their manufacturing process is characterized by multiple varieties, small batches, multiple processes, and discretization, involving various process sequences, equipment selection, and assembly connection constraints, making it a typical flexible job shop scheduling problem. Existing traditional scheduling methods are insufficient to handle the complex process coupling relationships and dynamic production demands in guide roller manufacturing. General metaheuristic algorithms generally suffer from poor initial solution quality, inconsistent search mechanisms, poor distribution of non-dominated solution sets, and insufficient local optimization capabilities when solving such problems. Furthermore, existing models fail to fully characterize the unique process requirements in guide roller manufacturing, such as hot-loading waiting windows and special equipment constraints, leading to a disconnect between scheduling schemes and actual production. Summary of the Invention

[0003] This invention provides a flexible workshop scheduling method for guide rollers based on an improved gray wolf algorithm to overcome the shortcomings of existing technologies.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a flexible workshop scheduling method for guide rollers based on an improved gray wolf algorithm, comprising the following steps:

[0005] Step 1: Based on the obtained guide roller manufacturing task, process route, and machine resource information, establish the processing flow of the guide roller flexible operation workshop;

[0006] Step 2: Use the process sequence constraints, machine selectability constraints, and assembly connection constraints in the constructed guide roller manufacturing process as the guide roller manufacturing process constraints;

[0007] Step 3: Based on the processing flow of the flexible workshop for the guide rollers and the constraints of the guide roller manufacturing process, establish a multi-objective flexible workshop scheduling model with the objectives of minimizing completion time, minimizing total machine load, and minimizing total machine energy consumption;

[0008] Step 4: Solve the multi-objective flexible workshop scheduling model using the constructed improved multi-objective gray wolf optimization model to obtain the guide roller flexible workshop scheduling scheme.

[0009] Preferably, the completion time is minimized, satisfying the following formula:

[0010]

[0011] In the formula, f1 represents the minimum completion time function, and C max C represents the maximum completion time among all workpieces. i This represents the final completion time of workpiece i, where i represents the workpiece number and n represents the total number of workpieces.

[0012] The machine has the minimum total load, satisfying the following formula:

[0013]

[0014] In the formula, f2 represents the minimum total machine load, j represents the process number, and q j Let z represent the total number of operations for workpiece i, z represent the machine number, m represent the total number of machines, and X represent the total number of operations for workpiece i. jiz This indicates that if the operation is performed on machine z, then 1 is selected; otherwise, 0 is selected. ijz This indicates the processing time of the process on machine z;

[0015] The machine has the minimum total energy consumption, satisfying the following formula:

[0016]

[0017] In the formula, f3 represents the minimum total energy consumption, and CT z LP represents the end or completion time of machine z. z ULP represents the load power of machine z. z This represents the no-load power of machine z.

[0018] Preferably, the pre-construction process of the improved multi-objective gray wolf optimization model in step 4 includes:

[0019] Obtain historical flexible operation workshop scheduling schemes for guide rollers. These schemes include guide roller manufacturing tasks, process routes, machine resource information, process sequence constraints, machine selectability constraints, assembly connection constraints, hot fitting waiting window constraints, dedicated machine constraints, and the corresponding optimal scheduling results.

[0020] The guide roller manufacturing task, process route, machine resource information, process sequence constraints, machine selection constraints, assembly connection constraints, hot fitting waiting window constraints, and special machine constraints in the historical guide roller flexible operation workshop scheduling scheme are used as input features, and the corresponding optimal scheduling results are used as output labels and input into the multi-objective gray wolf optimization model.

[0021] An initial population is constructed using a hybrid multi-strategy heuristic initialization method. The cosine decay mechanism, variable neighborhood search, and elite retention strategy are embedded into the multi-objective gray wolf optimization model. The optimization objectives are to minimize the maximum completion time, total machine load, and total energy consumption. The multi-objective gray wolf optimization model is trained until the model converges or reaches the preset number of iterations, resulting in the improved multi-objective gray wolf optimization model.

[0022] Preferably, the method of constructing the initial population using a hybrid multi-strategy heuristic initialization method includes:

[0023] Let the population size be N, then the initial population is represented as:

[0024]

[0025] In the formula, P represents the initial population, P SPT P represents the set of individuals generated based on the shortest processing time priority rule; ML P represents the set of individuals generated by the minimum cumulative load rule for machines; R This represents the set of individuals generated based on random perturbation; N is the initial total population size. Let set P be... SPT The number of individuals in Let set P be... ML The number of individuals in Let set P be... R The number of individuals in;

[0026] Let the proportions of the three types of individuals be ρ1, ρ2, and ρ3, then we have:

[0027]

[0028] In the formula, ρ1 is the proportion of individuals heuristically selected based on the shortest processing time; ρ2 is the proportion of individuals heuristically selected based on load balancing; and ρ3 is the proportion of individuals with random disturbances.

[0029] Let T be the processing time of the j-th operation on machine z for workpiece i. ijz Then for the machine set Ω ij Choose the machine with the shortest processing time from the available machines:

[0030]

[0031] In the formula, z represents the machine number. Ω represents the machine that is preferentially assigned to the j-th process of workpiece i; ijLet represent the set of machines for each process; argmin represents the variable value that minimizes the objective function; in process sequencing, to prioritize compressing the overall completion time, the processes to be scheduled are arranged in ascending order of estimated processing time, satisfying the following formula:

[0032]

[0033] In the formula, This indicates the sequence of operations under the shortest processing time priority rule; sort indicates sorting in ascending order. The processing time of the process on the selected optimal machine;

[0034] Finally, the estimated completion time of workpiece i is defined, satisfying the following formula:

[0035]

[0036] In the formula C i Let j represent the estimated completion time of workpiece i, j represent the operation number, and q represent the estimated completion time of workpiece i. j W represents the total number of operations for workpiece i. ij This represents the waiting time for workpiece i between the j-th and j+1-th processing steps;

[0037] Assume that the current cumulative processing load allocated to machine z is:

[0038]

[0039] In the formula, L z This represents the cumulative processing load of machine z;

[0040] For processes to be assigned, prioritize the machine with the lowest current overall load:

[0041]

[0042] In the formula, This represents the overall cost of assigning the process to machine z. This is a balance coefficient between processing time and current load;

[0043] A random perturbation mechanism is introduced in the hybrid initialization, and some individuals are generated using random process ordering and random machine assignment, satisfying the following formula:

[0044]

[0045] In the formula, Z ij This indicates that the processing machine is randomly selected for the process. Indicates from the set of optional machines Randomly select a machine from the list; This represents the set of all pending processes; This indicates that the set of processes is randomly arranged.

[0046] Preferably, the cosine attenuation mechanism satisfies the following formula:

[0047]

[0048] In the formula, a(t) represents the convergence factor at the t-th iteration, π is pi, t is the current iteration number, and T is the convergence factor. max This represents the maximum number of iterations.

[0049] The gray wolf's position update parameters remain unchanged:

[0050]

[0051] In the formula, r1 and r2 are random numbers in the interval [0, 1]; A represents the position update control parameter, and C represents the position update control parameter.

[0052] Preferably, the embedding of the hybrid framework strategy of variable neighborhood search and elite retention into the multi-objective gray wolf optimization algorithm includes:

[0053] Improvements to the multi-objective gray wolf optimization algorithm are achieved by using mechanisms such as process exchange neighborhood, process insertion neighborhood, machine reassignment neighborhood, variable neighborhood search selection, and constructing a neighborhood evaluation function with three objectives.

[0054] Among them, the process exchange neighborhood is to randomly select two process positions in the same feasible sequence and exchange them; the process insertion neighborhood is to move a process out of its original position and then insert it into a new feasible position; the machine reallocation neighborhood is to reselect an available machine for a process to address the problem of excessive single machine weight.

[0055] The variable neighborhood search selection mechanism is as follows: a candidate solution is generated in the k-th neighborhood. If it is better than the current solution, the solution is accepted and the search is returned to the first neighborhood. Otherwise, the search proceeds to the next neighborhood.

[0056] The neighborhood evaluation function of the three objective functions satisfies the following formula:

[0057]

[0058] In the formula, This represents the overall evaluation value of the regulation degree X; This represents the minimum objective function value for completion time corresponding to the adjustment degree X; This represents the minimum objective function value of the total machine load corresponding to the adjustment degree X; This represents the objective function value that minimizes total energy consumption corresponding to solution X; This represents the minimum value of the k-th neighborhood in the current population. This represents the maximum value of the k-th neighborhood in the current population, where k = 1, 2, 3; The weighting coefficients are the objective function values ​​that minimize the completion time. These are the weighting coefficients for the objective function value that minimizes the total machine load. The weighting coefficients are the objective function values ​​for minimizing total energy consumption.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1. A multi-objective scheduling model was constructed to simultaneously optimize the maximum completion time, total equipment load, and total energy consumption. For the first time, the assembly process priority relationship, hot-loading waiting window constraint, and special equipment constraint in guide roller manufacturing were incorporated into the model, making the scheduling scheme more in line with the actual production scenario.

[0061] 2. A hybrid multi-strategy heuristic initialization method is proposed, which combines short processing time priority, load balancing and random perturbation strategies to effectively improve the quality and diversity of the initial population.

[0062] 3. By integrating the cosine decay mechanism, variable neighborhood search, and elite preservation strategy into the multi-objective gray wolf algorithm, the algorithm's global exploration and local exploitation capabilities are significantly enhanced, and the convergence and distribution uniformity of the non-dominated solution set are improved.

[0063] 4. This invention enables efficient and intelligent scheduling of flexible workshops for guide rollers, effectively reducing completion time, equipment load and energy consumption, and meeting the multiple needs of packaging and printing equipment manufacturers for delivery cycle, equipment utilization and green manufacturing. Attached Figure Description

[0064] Figure 1 This is a flowchart of a flexible workshop scheduling method for guide rollers based on an improved gray wolf algorithm according to the present invention.

[0065] Figure 2 This is a diagram illustrating the structure and manufacturing process of the guide roller of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0067] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0068] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0069] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0070] like Figure 1 As shown, this invention provides a flexible workshop scheduling method for guide rollers based on an improved gray wolf algorithm, comprising the following steps:

[0071] Step 1: Based on the obtained guide roller manufacturing task, process route, and machine resource information, establish the processing flow of the guide roller flexible operation workshop;

[0072] Step 2: Use the process sequence constraints, machine selectability constraints, and assembly connection constraints in the constructed guide roller manufacturing process as the guide roller manufacturing process constraints;

[0073] Step 3: Based on the processing flow of the flexible workshop for the guide rollers and the constraints of the guide roller manufacturing process, establish a multi-objective flexible workshop scheduling model with the objectives of minimizing completion time, minimizing total machine load, and minimizing total machine energy consumption;

[0074] Step 4: Solve the multi-objective flexible workshop scheduling model using the constructed improved multi-objective gray wolf optimization model to obtain the guide roller flexible workshop scheduling scheme.

[0075] like Figure 2 As shown, the guide roller structure and manufacturing process involved in this embodiment are as follows: Based on the obtained guide roller manufacturing task, process route and machine resource information, the guide roller production process is divided into 9 steps (material cutting, steel shaft turning, aluminum plug turning, roller cylinder turning and semi-finished roller body turning, hot fitting into plug, hot fitting into guide roller, precision turning of guide roller, micro-arc oxidation and dynamic balancing), thereby establishing a flexible operation workshop processing flow for guide rollers.

[0076] In step 2, the process sequence constraints, machine selection constraints, and assembly connection constraints during the guide roller manufacturing process must satisfy the following conditions:

[0077] (1) Once the process has started, it cannot be interrupted:

[0078]

[0079] In the formula, i represents the workpiece number, j represents the process number, z represents the machine number, and S ij Indicates the start time, C ij Indicates the completion time, T ijz This represents the processing time of machine z.

[0080] (2) Any process is performed only once on the machine:

[0081]

[0082] In the formula, m represents the total number of machines, X ijz This indicates whether the processing is performed on machine z. If it is performed, the value is 1; otherwise, it is 0.

[0083] (3) The start time of any process shall not exceed the completion time:

[0084]

[0085] (4) The completion time of any process shall not exceed the maximum completion time:

[0086]

[0087] In the formula C max Indicates the maximum completion time.

[0088] (5) Each machine can only process one operation at a time:

[0089]

[0090] In the formula, h represents the workpiece index, k represents the process index, and G... hkij If process j precedes process k, the value is 1; otherwise, it is 0.

[0091] (6) The completion time of the previous operation for any workpiece shall not be greater than the start time of the next operation:

[0092]

[0093] (7) The start, processing, and completion times of any process are all positive:

[0094]

[0095] The preceding processing steps for the steel shaft, aluminum plug, and roller can be performed in parallel. The hot-fitting process into the plug is performed after the steel shaft and aluminum plug have been processed. The hot-fitting process into the guide roller is performed after the semi-finishing of the roller and the hot-fitting of the plug have been completed. The precision machining of the guide roller, micro-arc oxidation, and dynamic balancing are performed in a predetermined order. Therefore, the process priority constraint for the guide roller needs to be added:

[0096]

[0097] In the formula, v represents the process index, i represents the workpiece number, and C ij S represents the completion time of the j-th process of workpiece i. iv The start time of the j-th process of workpiece i, and A represents the set of directed arcs representing the priority relationship of the guide roller process.

[0098] Considering the high sensitivity of the hot-fitting process to assembly sequence, excessive waiting time after the completion of preceding components will affect assembly quality and process stability. Therefore, maximum allowable waiting windows are set for both hot-fitting processes:

[0099]

[0100]

[0101] In the formula, S i5 C represents the 5th process for workpiece i. i2 C i3 C i4 and C i5 T represents the 2nd, 3rd, 4th, and 5th processes of workpiece i. Wi This indicates the maximum allowed waiting time.

[0102] Since hot charging, micro-arc oxidation, and dynamic balancing are typical specialized processes, the set of machines that can be selected is clearly limited, and the constraints can be defined as follows:

[0103]

[0104] In the formula, z represents the machine number X. i5z X i6z X i8z and X i9z This indicates whether the 5th, 6th, 8th, and 9th processes of workpiece i can be processed on its z-axis. , , and These represent the specialized machine sets corresponding to hot-fitting into plugs, hot-fitting into guide rollers, micro-arc oxidation, and dynamic balancing, respectively.

[0105] The minimum completion time mentioned in step 3 satisfies the following formula:

[0106]

[0107] In the formula, f1 represents the minimum completion time function, and C max C represents the maximum completion time among all workpieces. i This represents the final completion time of workpiece i, where i represents the workpiece number and n represents the total number of workpieces.

[0108] The machine has the minimum total load, satisfying the following formula:

[0109]

[0110] In the formula, f2 represents the minimum total machine load, j represents the process number, and q j Let z represent the total number of operations for workpiece i, z represent the machine number, m represent the total number of machines, and X represent the total number of operations for workpiece i. jiz This indicates that if the operation is performed on machine z, then 1 is selected; otherwise, 0 is selected. ijz This indicates the processing time of the process on machine z;

[0111] The machine has the minimum total energy consumption, satisfying the following formula:

[0112]

[0113] In the formula, f3 represents the minimum total energy consumption, and CT z LP represents the end or completion time of machine z. z ULP represents the load power of machine z. z This represents the no-load power of machine z.

[0114] The pre-construction process of the improved multi-objective gray wolf optimization model described in step 4 above includes:

[0115] Step A: Obtain the historical flexible operation workshop scheduling scheme for guide rollers. The historical flexible operation workshop scheduling scheme for guide rollers includes guide roller manufacturing tasks, process routes, machine resource information, process sequence constraints, machine selectability constraints, assembly connection constraints, hot fitting waiting window constraints, special machine constraints, and the corresponding optimal scheduling results.

[0116] Step B: Take the guide roller manufacturing task, process route, machine resource information, process sequence constraints, machine selection constraints, assembly connection constraints, hot assembly waiting window constraints, and special machine constraints in the historical guide roller flexible operation workshop scheduling scheme as input features, and take the corresponding optimal scheduling result as output label, and input it into the multi-objective gray wolf optimization model;

[0117] Step C: Construct an initial population using a hybrid multi-strategy heuristic initialization method. Embed the cosine decay mechanism, variable neighborhood search, and elite retention strategy into the multi-objective gray wolf optimization model. With minimizing the maximum completion time, total machine load, and total energy consumption as the optimization objectives, train the multi-objective gray wolf optimization model until the model converges or reaches the preset number of iterations to obtain the trained improved multi-objective gray wolf optimization model.

[0118] In step C, the construction of the initial population using a hybrid multi-strategy heuristic initialization method includes:

[0119] Step C1.1: Let the population size be N, then the initial population is represented as:

[0120]

[0121] In the formula, P represents the initial population, P SPT P represents the set of individuals generated based on the shortest processing time priority rule; ML P represents the set of individuals generated by the minimum cumulative load rule for machines; R This represents the set of individuals generated based on random perturbation; N is the initial total population size. Let set P be... SPT The number of individuals in Let set P be... ML The number of individuals in Let set P be... R The number of individuals in;

[0122] Step C1.2: Define the proportions of the three types of individuals as ρ1, ρ2, and ρ3, then we have:

[0123]

[0124] In the formula, ρ1 is the proportion of individuals heuristically selected based on the shortest processing time; ρ2 is the proportion of individuals heuristically selected based on load balancing; and ρ3 is the proportion of individuals with random disturbances.

[0125] Step C1.3: Let T be the processing time of the j-th operation on machine z for workpiece i. ijz Then for the machine set Ω ij Choose the machine with the shortest processing time from the available machines:

[0126]

[0127] In the formula, z represents the machine number. Ω represents the machine that is preferentially assigned to the j-th process of workpiece i; ijLet represent the set of machines for each process; argmin represents the variable value that minimizes the objective function; in process sequencing, to prioritize compressing the overall completion time, the processes to be scheduled are arranged in ascending order of estimated processing time, satisfying the following formula:

[0128]

[0129] In the formula, This indicates the sequence of operations under the shortest processing time priority rule; sort indicates sorting in ascending order. The processing time of the process on the selected optimal machine;

[0130] Step C1.4: Finally, define the estimated completion time of workpiece i, satisfying the following formula:

[0131]

[0132] In the formula C i Let j represent the estimated completion time of workpiece i, j represent the operation number, and q represent the estimated completion time of workpiece i. j W represents the total number of operations for workpiece i. ij This represents the waiting time for workpiece i between the j-th and j+1-th processing steps;

[0133] Step C1.5: Assume that the current cumulative processing load allocated to machine z is:

[0134]

[0135] In the formula, L z This represents the cumulative processing load of machine z;

[0136] Step C1.6: For the processes to be assigned, prioritize the machine with the lowest current overall load:

[0137]

[0138] In the formula, This represents the overall cost of assigning the process to machine z. This is a balance factor between processing time and current load, used to coordinate the impact between instantaneous processing time and cumulative machine load.

[0139] Step C1.7: Introduce a random perturbation mechanism in the hybrid initialization, and generate some individuals using random process ordering and random machine assignment, satisfying the following formula:

[0140]

[0141] In the formula, Z ij This indicates that the processing machine is randomly selected for the process. Indicates from the set of optional machines Randomly select a machine from the list; This represents the set of all pending processes; This indicates that the set of processes is randomly arranged.

[0142] In step 4, the cosine decay mechanism is embedded into the multi-objective gray wolf optimization algorithm. In the traditional gray wolf optimization algorithm, the convergence factor usually takes the form of linear decrease:

[0143]

[0144] In the formula, a represents the convergence factor, t is the current iteration number, and T max This represents the maximum number of iterations. Based on this, a cosine decay mechanism is introduced to improve the convergence factor; the cosine decay mechanism satisfies the following formula:

[0145]

[0146] In the formula, a(t) represents the convergence factor at the t-th iteration, π is pi, t is the current iteration number, and T is the convergence factor. max This represents the maximum number of iterations.

[0147] The gray wolf's position update parameters remain unchanged:

[0148]

[0149] In the formula, r1 and r2 are random numbers in the interval [0, 1]; A represents the position update control parameter, and C represents the position update control parameter.

[0150] In step C: the embedding of the hybrid framework strategy of variable neighborhood search and elite preservation into the multi-objective gray wolf optimization algorithm includes:

[0151] Improvements to the multi-objective gray wolf optimization algorithm are achieved by using mechanisms such as process exchange neighborhood, process insertion neighborhood, machine reassignment neighborhood, variable neighborhood search selection, and constructing a neighborhood evaluation function with three objectives.

[0152] Among them, the hybrid framework strategy of variable neighborhood search and elite preservation is embedded into the multi-objective gray wolf optimization algorithm, and the population of the t-th generation is set as follows: The overall update process can then be represented as:

[0153]

[0154] In the formula, g represents the global position update operator for the gray wolf; v represents the variable neighborhood search local reinforcement operator; This indicates the elite retention and fast non-dominated screening operators; and Let represent the t-th and t+1-th generation populations, respectively. Considering the dual-layer coding characteristics of the flexible operation workshop with guide rollers, the following three neighborhood designs are constructed:

[0155] (1) Variable neighborhood structure design

[0156] ① Process exchange neighborhood

[0157] Randomly select two process positions from the same feasible sequence and swap them to form a new solution:

[0158]

[0159] In the formula Indicates the current process sequence; This indicates the new sequence of processes after the exchange; This indicates the neighborhood exchange operator for the process.

[0160] If the two positions to be swapped are r and s, then it can be represented as:

[0161]

[0162] In the formula This indicates an exchange operation; r and s are the two position numbers in the process sequence.

[0163] ② Inserting the process into the neighborhood

[0164] A new sequence is formed by removing a certain process from its original position and inserting it into a new feasible position:

[0165]

[0166] In the formula This indicates the neighborhood where the operation is inserted. Insert represents the insertion operation, r represents the position of the operation being removed, and s represents the target position after insertion.

[0167] ③ Machine reassignment of neighborhood

[0168] To address the issue of excessive weight of a single machine, alternative machines can be selected for a specific process:

[0169]

[0170] In the formula The machine after the reassignment of process (i, j): This indicates that the machine is redistributing the neighborhood; The comprehensive evaluation function represents the assignment of process (i, j) to machine z; , , These are the weighting coefficients for processing time, current machine load, and machine idle occupancy cost, respectively. This represents the idle or unloaded running time of machine z under the current scheduling scheme.

[0171] (2) Variable neighborhood search selection mechanism

[0172] Generate candidate solutions in the k-th neighborhood If the solution is better than the current one, accept the solution and return to the first neighborhood to search again; otherwise, proceed to the next neighborhood. The iteration rule is as follows:

[0173]

[0174] In the formula, X represents the current solution; This represents the new solution generated after neighborhood perturbation; In the context of multiple objectives, Dominate X, that is It should be superior to at least one objective and not inferior to the others. If updating the non-dominated solution set, a joint judgment based on crowding distance and non-dominated sorting should be used, i.e.:

[0175]

[0176] Or satisfy in the same non-dominated layer:

[0177]

[0178] In the formula Represents the updated non-dominated solution set; Indicates the non-dominant ranking order of X; This represents the congestion distance of solution X.

[0179] (3) Constructing a neighborhood evaluation function for a three-objective function

[0180] To ensure that the neighborhood search aligns with the three objective functions, a normalized comprehensive evaluation function is constructed:

[0181]

[0182] In the formula, This represents the overall evaluation value of the regulation degree X; This represents the minimum objective function value for completion time corresponding to the adjustment degree X; This represents the minimum objective function value of the total machine load corresponding to the adjustment degree X; This represents the objective function value that minimizes total energy consumption corresponding to solution X; This represents the minimum value of the k-th neighborhood in the current population. This represents the maximum value of the k-th neighborhood in the current population, where k = 1, 2, 3; The weighting coefficients are the objective function values ​​that minimize the completion time. These are the weighting coefficients for the objective function value that minimizes the total machine load. These are the weighting coefficients for the objective function value that minimizes total energy consumption. When it is necessary to select the preferred retainable individuals from multiple neighborhood candidate solutions, it is necessary to follow... Filtering based on the principle of minimum:

[0183]

[0184] In the formula This represents the candidate solution with the best evaluation in the current neighborhood search.

[0185] As mentioned above, step 4 uses an improved multi-objective gray wolf optimization algorithm to solve the flexible operation shop scheduling model for guide rollers. The specific steps are as follows:

[0186] (1) Input the actual production data of the guide roller, including the workpiece set J={J1,J2,…,J n The set of machines M = {M1, M2, ..., M} m The process set Oi for each workpiece = {O i1 O i2 ,…,O iqi}, Selectable machine set for each process Ω ij Processing time T for a process on different machines ijz and the load power LP of each machine z No-load power ULP z Maximum allowable waiting time for hot-loading related processes (Tw) i .

[0187] (2) Set the running parameters of the HV-MOGWO algorithm, including population size, maximum number of iterations, crossover probability, mutation probability, current iteration generation, random numbers r1 and r2, number of leaders and local search step limit parameters, and mixed initialization ratio parameters ρ1, ρ2 and ρ3.

[0188] (3) Construct a two-layer coding structure for candidate scheduling solutions.

[0189] (4) A hybrid multi-strategy heuristic method is used to construct the initial population, including generating individuals with short processing time priority, individuals with minimum cumulative load priority, and random individuals.

[0190] (5) Decode the initial population. Calculate the function values ​​of maximum completion time f1, total machine load f2, and total energy consumption f3.

[0191] (6) Perform fast non-dominated sorting, calculate crowding, and update the external archive set.

[0192] (7) Select representative non-dominated solutions from the external archives as the three leading individuals α, β, and δ.

[0193] (8) According to the current iteration number t and the maximum iteration number T max Update the convergence factor a(t) and the gray wolf position parameters A and C.

[0194] (9) Implement a variable domain search and elite retention strategy.

[0195] (10) Determine whether the current iteration algebra satisfies t=T max If the condition is not met, then let t = t + 1 and return to step 6 to continue iterating, and then proceed to the next step.

[0196] (11) Output the Pareto optimal solution set, the process sorting results, machine allocation results, process start and finish time results, and the final scheduling scheme for each non-dominated scheduling scheme.

[0197] The algorithm was completed to solve the scheduling model of the flexible operation workshop of the guide roller.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its protection scope. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the application, but these changes, modifications or equivalent substitutions are all within the protection scope of the claims pending approval.

Claims

1. A flexible workshop scheduling method for guide rollers based on an improved gray wolf algorithm, characterized in that, Includes the following steps: Step 1: Based on the obtained guide roller manufacturing task, process route, and machine resource information, establish the processing flow of the guide roller flexible operation workshop; Step 2: Use the process sequence constraints, machine selectability constraints, and assembly connection constraints in the constructed guide roller manufacturing process as the guide roller manufacturing process constraints; Step 3: Based on the processing technology flow of the guide roller flexible operation workshop and the constraints of the guide roller manufacturing process, establish a multi-objective flexible operation workshop scheduling model with the objectives of minimizing completion time, minimizing total machine load, and minimizing total machine energy consumption; Step 4: Solve the multi-objective flexible workshop scheduling model using the constructed improved multi-objective gray wolf optimization model to obtain the guide roller flexible workshop scheduling scheme.

2. The method according to claim 1, characterized in that, The minimum completion time satisfies the following formula: In the formula, f1 represents the minimum completion time function, C max C represents the maximum completion time among all workpieces. i This represents the final completion time of workpiece i, where i represents the workpiece number and n represents the total number of workpieces. The machine has the minimum total load, satisfying the following formula: In the formula, f2 represents the minimum total machine load, j represents the process number, and q j Let z represent the total number of operations for workpiece i, z represent the machine number, m represent the total number of machines, and X represent the total number of operations for workpiece i. jiz This indicates that if the operation is performed on machine z, then 1 is selected; otherwise, 0 is selected. ijz This indicates the processing time of the process on machine z; The machine has the minimum total energy consumption, satisfying the following formula: In the formula, f3 represents the minimum total energy consumption, and CT z LP represents the end or completion time of machine z. z ULP represents the load power of machine z. z This represents the no-load power of machine z.

3. The method according to claim 1, characterized in that, The pre-construction process of the improved multi-objective gray wolf optimization model described in step 4 includes: Obtain historical flexible operation workshop scheduling schemes for guide rollers. These schemes include guide roller manufacturing tasks, process routes, machine resource information, process sequence constraints, machine selectability constraints, assembly connection constraints, hot fitting waiting window constraints, dedicated machine constraints, and the corresponding optimal scheduling results. The guide roller manufacturing task, process route, machine resource information, process sequence constraints, machine selection constraints, assembly connection constraints, hot fitting waiting window constraints, and special machine constraints in the historical guide roller flexible operation workshop scheduling scheme are used as input features, and the corresponding optimal scheduling results are used as output labels and input into the multi-objective gray wolf optimization model. An initial population is constructed using a hybrid multi-strategy heuristic initialization method. The cosine decay mechanism, variable neighborhood search, and elite retention strategy are embedded into the multi-objective gray wolf optimization model. The optimization objectives are to minimize the maximum completion time, total machine load, and total energy consumption. The multi-objective gray wolf optimization model is trained until the model converges or reaches the preset number of iterations, resulting in the improved multi-objective gray wolf optimization model.

4. The method according to claim 3, characterized in that, The method of constructing the initial population using a hybrid multi-strategy heuristic initialization method includes: Let the population size be N, then the initial population is represented as: In the formula, P represents the initial population, P SPT P represents the set of individuals generated based on the shortest processing time priority rule; ML P represents the set of individuals generated by the minimum cumulative load rule for machines; R This represents the set of individuals generated based on random perturbation; N is the initial total population size. Let set P be... SPT The number of individuals in Let set P be... ML The number of individuals in Let set P be... R The number of individuals in; Let the proportions of the three types of individuals be ρ1, ρ2, and ρ3, then we have: In the formula, ρ1 is the proportion of individuals heuristically selected based on the shortest processing time; ρ2 is the proportion of individuals heuristically selected based on load balancing; and ρ3 is the proportion of individuals with random disturbances. Let T be the processing time of the j-th operation on machine z for workpiece i. ijz Then for the machine set Ω ij Choose the machine with the shortest processing time from the available machines: In the formula, z represents the machine number. Ω represents the machine that is preferentially assigned to the j-th process of workpiece i; ij Let represent the set of machines for each process; argmin represents the variable value that minimizes the objective function; in process sequencing, to prioritize compressing the overall completion time, the processes to be scheduled are arranged in ascending order of estimated processing time, satisfying the following formula: In the formula, This indicates the sequence of operations under the shortest processing time priority rule; sort indicates sorting in ascending order. The processing time of the process on the selected optimal machine; Finally, the estimated completion time of workpiece i is defined, satisfying the following formula: In the formula C i Let j represent the estimated completion time of workpiece i, j represent the operation number, and q represent the estimated completion time of workpiece i. j W represents the total number of operations for workpiece i. ij This represents the waiting time for workpiece i between the j-th and j+1-th processing steps; Assume that the current cumulative processing load allocated to machine z is: In the formula, L z This represents the cumulative processing load of machine z; For processes to be assigned, prioritize the machine with the lowest current overall load: In the formula, This represents the overall cost of assigning the process to machine z. This is a balance coefficient between processing time and current load; A random perturbation mechanism is introduced in the hybrid initialization, and some individuals are generated using random process ordering and random machine assignment, satisfying the following formula: In the formula, Z ij This indicates that the processing machine is randomly selected for the process. Indicates from the set of optional machines Randomly select a machine from the list; This represents the set of all pending processes; This indicates that the set of processes is randomly arranged.

5. The method according to claim 3, characterized in that, The cosine attenuation mechanism satisfies the following formula: In the formula, a(t) represents the convergence factor at the t-th iteration, π is pi, t is the current iteration number, and T is the convergence factor. max This represents the maximum number of iterations. The gray wolf's position update parameters remain unchanged: In the formula, r1 and r2 are random numbers in the interval [0, 1]; A represents the position update control parameter, and C represents the position update control parameter.

6. The method according to claim 3, characterized in that, The method of embedding the hybrid framework strategy of variable neighborhood search and elite preservation into the multi-objective gray wolf optimization algorithm includes: Improvements to the multi-objective gray wolf optimization algorithm are achieved by using mechanisms such as process exchange neighborhood, process insertion neighborhood, machine reassignment neighborhood, variable neighborhood search selection, and constructing a neighborhood evaluation function with three objectives. Among them, the process exchange neighborhood is to randomly select two process positions in the same feasible sequence and exchange them; the process insertion neighborhood is to move a process out of its original position and then insert it into a new feasible position; the machine reallocation neighborhood is to reselect an available machine for a process to address the problem of excessive single machine weight. The variable neighborhood search selection mechanism is as follows: a candidate solution is generated in the k-th neighborhood. If it is better than the current solution, the solution is accepted and the search is returned to the first neighborhood. Otherwise, the search proceeds to the next neighborhood. The neighborhood evaluation function of the three objective functions satisfies the following formula: In the formula, This represents the overall evaluation value of the regulation degree X; This represents the minimum objective function value for completion time corresponding to the adjustment degree X; This represents the minimum objective function value of the total machine load corresponding to the adjustment degree X; This represents the objective function value that minimizes total energy consumption corresponding to solution X; This represents the minimum value of the k-th neighborhood in the current population. This represents the maximum value of the k-th neighborhood in the current population, where k = 1, 2, 3; The weighting coefficients are the objective function values ​​that minimize the completion time. These are the weighting coefficients for the objective function value that minimizes the total machine load. The weighting coefficients are the objective function values ​​for minimizing total energy consumption.

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