An integrated collaborative optimization method for process planning and scheduling based on the hybrid ZOA-VNS algorithm.

Abstract

This invention provides an integrated process planning and scheduling collaborative optimization method, system, storage medium, and electronic device based on the hybrid ZOA-VNS algorithm, relating to the field of process planning and production scheduling collaborative optimization. The invention first obtains the set of workpieces to be processed, the set of machines, and available resources. Second, under the constraint of the number of available resources, a hybrid integer linear programming model is constructed with the optimization objective of minimizing the maximum completion time. Then, a four-layer real-number encoding structure is used as the encoding scheme, and a hybrid zebra optimization-variable neighborhood search algorithm is employed to solve the model, outputting the optimal zebra individual, and decoding to obtain the optimal integrated process planning and scheduling collaborative optimization scheme. By introducing the realistic factor of continuous resource constraints into the traditional integrated process planning and production scheduling problem, the problem becomes more practically applicable. Furthermore, the proposed hybrid zebra optimization-variable neighborhood search algorithm effectively solves this problem, achieving good optimization results.

Description

Technical Field

[0001] This invention relates to the field of collaborative optimization of process planning and production scheduling, and specifically to an integrated collaborative optimization method, system, storage medium, and electronic device based on the hybrid ZOA-VNS algorithm for process planning and scheduling. Background Technology

[0002] Process planning and production scheduling are two indispensable parts of product research and development and manufacturing. Process planning is responsible for determining the materials and processes required for production, while scheduling is responsible for allocating the production processes to different machines and optimizing specific objectives while meeting the requirements of process planning.

[0003] Although process planning and scheduling are closely related, in traditional manufacturing models they are often treated as two independent processes performed sequentially. In reality, the separation between process planning and scheduling often leads to problems such as uneven machine load, lack of flexibility in process plans, and conflicts between process plans and scheduling plans.

[0004] Furthermore, modern manufacturing systems face the challenge of effectively utilizing bottleneck resources. The rational allocation of resources required for different machines to perform their tasks is one of the key issues in production. Since operations require resources to arrive before they can begin, improper resource allocation can lead to system unavailability and idle periods, further resulting in resource waste and increased costs. Summary of the Invention

[0005] (1) Technical problems solved

[0006] To address the shortcomings of existing technologies, this invention provides an integrated process planning and scheduling collaborative optimization method, system, storage medium, and electronic device based on the hybrid ZOA-VNS algorithm, which solves the technical problems of integrated process planning and shop floor scheduling with continuous resource constraints.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] An integrated process planning and scheduling collaborative optimization method based on the hybrid ZOA-VNS algorithm includes:

[0010] Obtain the set of workpieces to be processed, the set of machines, and the available resources;

[0011] Based on the set of workpieces and the set of machines, and under the constraint of the number of available resources, a mixed integer linear programming model is constructed with the optimization objective of minimizing the maximum completion time.

[0012] A four-layer real number encoding structure of feature-link-machine-process is adopted as the encoding scheme. All initial zebra individual positions are randomly generated as the initial zebra population. The mixed integer linear programming model is solved by the hybrid zebra optimization-variable neighborhood search algorithm to output the optimal zebra individual. Based on the corresponding decoding scheme, the optimal integrated process planning and scheduling collaborative optimization scheme is obtained.

[0013] Preferably, the mixed-integer linear programming model includes:

[0014] minC max (1)

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] Where J represents the set of workpieces; O i F represents the set of operations for workpiece i; i M represents the set of machining features for workpiece i; M represents the set of machines.

[0028] i, i′ represent workpieces i, i′, 1 ≤ i, i′ ≤ |J|; j, j′ represent processes j, j′, 1 ≤ j, j′ ≤ |O|. i |;f,f′ represents the feature f,f′,1≤f,f′≤|F i |;k,k′ represents machine k,kn,1≤k,k′≤|M|;l,l′ represents process link l,l′;

[0029] Equation (1) is the objective function; min is the minimization function, Cmax Indicates the maximum completion time;

[0030] Constraint (2) means that for any workpiece, each of its machining features must select a process link; F ifl For decision variables, if the l-th process link of the processing feature f of workpiece i is selected, then it is 1; otherwise, it is 0.

[0031] Constraint (3) means that for any workpiece, if the process link of a certain machining feature in which one of its operations is located is not selected, then that operation will not be selected either; X ij For decision variables, if o ij If selected, the value is 1; otherwise, it is 0; N is a sufficiently large positive number; E ijfl Indicates if o ij If it is located on the l-th process link of processing feature f, then it is 1; otherwise, it is 0.

[0032] Constraint (4) means that for any workpiece, if a certain process link of a certain processing feature is selected, then all processes on that process link will be selected.

[0033] Constraint (5) indicates that when a process is selected for a workpiece, a selectable machining machine needs to be assigned to it; otherwise, no machining machine needs to be assigned. ijk For decision variables, if o ij If the process is performed on machine k, the value is 1; otherwise, it is 0.

[0034] Constraint (6) states that for any workpiece, the priority relationship between any two operations selected from two machining features with a priority relationship must satisfy the priority relationship corresponding to their machining features; E ij′f′l Indicates if o ij′ If it is located on the l-th process link of processing feature f′, then it is 1; otherwise, it is 0. ij′ For decision variables, if o ij′ If selected, the value is 1; otherwise, it is 0. iji′j′ For decision variables, if o ij In o i′j′ If it's a pre-processing step, the value is 1; otherwise, it's 0. iff′ This indicates that if the machining feature f of workpiece i is the immediate preceding machining feature of machining feature f′, then it is 1; otherwise, it is 0.

[0035] Constraint (7) states that for any workpiece, the priority relationship between two operations on any process link of any machining feature should satisfy the priority relationship between their corresponding operations; E ij′fl Indicates if o ij′ If it is located on the l-th process link of processing feature f, then it is 1; otherwise, it is 0.ijij′ For decision variables, if o ij In o ij′ For pre-processing, the value is 1; This indicates that if the operation j on the machining feature f of workpiece i is the immediate preceding operation of j′, then it is 1; otherwise, it is 0.

[0036] Constraints (8) and (9) indicate that when the priority relationship of operations is determined, there should be a definite processing sequence for different operations on the same workpiece; ij o ij′ S represents the processes j and j′ of workpiece i, respectively; ij S ij′ They represent o respectively ij o ij′ Processing start time; Z ij′k For decision variables, if o ij′ If processed on machine k, the value is 1; otherwise, it is 0. ijk T ij′k They represent o respectively ij o ij′ Processing time on machine k;

[0037] Constraints (10) and (11) indicate that when the priority relationship of operations is determined, the operations processed on the same machine should have a definite processing order; S i′j′ o i′j′ Processing start time; Z i′j′k For decision variables, if o i′j′ If processed on machine k, the value is 1; otherwise, it is 0. ijk T i′j′k They represent o respectively ij o i′j′ Processing time on machine k;

[0038] Constraint (12) states that the cumulative resource consumption of all processes in operation at any given time cannot exceed the maximum available resource amount at the same time; O i (t) represents the set of processes being processed at time t; R ijk o ij Resource consumption on machine k; R max Indicates the maximum amount of resources available at any given time;

[0039] Constraint (13) clarifies the definition of maximum completion time.

[0040] Preferably, each layer of the encoding scheme is represented by a single vector, π. 1 Represents the feature sequence encoding, vector π 2 Represents the link sequence encoding, vector π 3Represents machine sequence encoding, vector π 4 This represents the process sequence encoding; the elements in the vector are random numbers between 0 and 1 that follow a uniform distribution, where the length of the feature sequence encoding and the link sequence encoding is equal to the sum of the number of processing features of all workpieces, and the length of the machine sequence encoding and the process sequence encoding is equal to the sum of the number of processes of all workpieces.

[0041] Preferably, the corresponding decoding scheme includes:

[0042] The first stage involves decoding the feature sequence: for the feature sequence encoding vector π 1 The number at the j-th position of the i-th workpiece in the sequence is used as the feature set to be assigned. All features of workpiece i that have no prior features or whose prior features have been assigned but have not yet been assigned are used as the feature set to be assigned. The number at the j-th position of the i-th workpiece in the feature sequence encoding vector is multiplied by the length of the feature set to be assigned and rounded down to obtain the feature index to be assigned. The corresponding feature in the feature set to be assigned is selected according to the index and added to the decoded feature sequence.

[0043] The second stage involves performing link sequence decoding: for the link sequence encoded vector π 2 Find the number at the j-th position of the i-th workpiece, and find the feature F of workpiece i. j The optional links are used as the set of links to be allocated. The number at the j-th position of the i-th workpiece in the link sequence encoding vector is multiplied by the length of the set of links to be allocated and rounded down to obtain the index of the link to be allocated. The corresponding link in the set of links to be allocated is selected according to the index and added to the decoded link sequence.

[0044] The third stage involves performing machine sequence decoding: for the machine sequence encoded vector π 3 The number at the j-th position of the i-th workpiece in the process O ij The selectable machines are used as the set of machines to be assigned. The number at the j-th position of the i-th workpiece in the machine encoding vector is multiplied by the length of the set of machines to be assigned and rounded down to obtain the index of the machine to be assigned. The corresponding machine in the set of machines to be assigned is selected according to the index and added to the decoded machine sequence.

[0045] The fourth stage involves decoding the process sequence: for the workpiece sequence encoding vector π 4 The j-th process of the i-th workpiece O ijIf the number is not in the process route of the i-th workpiece, then remove the number at the j-th position of the i-th workpiece from the process sequence encoding vector. Sort the encoded vector after removal in ascending order. If the number in the sorted encoded vector belongs to the number of the i-th workpiece in the encoded vector before sorting, then add the number i to the decoded process sequence. The number of numbers i in the decoded process sequence is equal to the number of processes in the process route of the i-th workpiece. The order of numbers i in the decoded process sequence corresponds to the order of processes in the process route of the i-th workpiece.

[0046] The fifth stage, based on the decoding rules of the embedded resource-based left-shift strategy, determines the start and end times of each process, including:

[0047] S100, for process O ij Find O in the process route of workpiece i ij The completion time (OT) of the previous process;

[0048] S200, for process O ij The assigned machine M i Find machine M i The completion time MT of the last assigned process and the machine M before MT. i Free time in It is machine M i The start time of the idle period in the i-th idle time segment. It is machine M i The idle end time of the i-th idle time period;

[0049] S300, if there is a free period satisfy So, process O ij The earliest possible start time Where PT represents process O ij In machine M i Processing time;

[0050] S400, Determine if Does a sub-time period of length PT exist within this period? Ensure that the remaining available resources during this sub-period are greater than or equal to those of process O. ij Resource consumption, if it exists, then process O ij Actual processing start time in These are the start and end times of a sub-time period of length PT, respectively.

[0051] Preferably, the step of using a hybrid zebra optimization-variable neighborhood search algorithm to solve the hybrid integer linear programming model and output the optimal zebra individual includes:

[0052] S31. Initialize the parameters of the hybrid zebra optimization-variable neighborhood search algorithm, including the number of zebras N, the maximum number of iterations T, the number of neighborhood structures k_max, and the maximum number of iterations l_max between two improvements of a single neighborhood.

[0053] S32. Randomly generate the positions of all initial zebra individuals as the initial zebra population. Each zebra individual is [π]. 1 ,π 2 ,π 3 ,π 4 ];

[0054] S33: Let i = 1, t = 1;

[0055] S34. Calculate and sort the fitness values ​​of all zebra individuals in the population, and select the individual with the best fitness as the initial position of the pioneer zebra PZ, where the fitness value is the maximum completion time.

[0056] S35. Simulate zebra foraging behavior: the i-th zebra in the population moves towards the lead zebra. The position of the i-th zebra is determined by the formula... renew;

[0057] S36. For the updated position of the i-th zebra, the elite retention strategy is adopted. That is, if the fitness of the updated i-th zebra is less than the fitness of the i-th zebra before the update, the updated position is retained; otherwise, the position of the i-th zebra remains unchanged.

[0058] S37. Randomly generate the location of predator AZ and simulate the defensive strategies a zebra adopts when facing a predator. Assume the zebra will choose either to flee to a nearby location or to fight back against the predator, and that the probabilities of each choice and strategy are equal. Let P... S = rand(0,1);

[0059] S38, If P S If the value is ≤0.5, then the zebra chooses the first strategy, and the position of the i-th zebra in the population is determined by the formula. Update; otherwise, the zebra chooses the second strategy, and the position of the i-th zebra in the population is determined by the formula. renew;

[0060] S39. For the updated position of the i-th zebra, the elite retention strategy is adopted. That is, if the fitness of the updated i-th zebra is less than the fitness of the i-th zebra before the update, the updated position is retained; otherwise, the position of the i-th zebra remains unchanged.

[0061] S310. If i < N, set i = i + 1, return to S34; otherwise, go to S311.

[0062] S311. Obtain the top 10% individuals with the highest fitness in the zebra population as elite zebras, and perform variable neighborhood search on the positions of the elite zebras using k_max neighborhood structures. The maximum number of iterations between two improvements in a single neighborhood is l_max.

[0063] S312. If t < T, set t = t + 1 and i = 1, return to S34; otherwise, end the algorithm and output the zebra individual with the optimal fitness.

[0064] Preferably, design the following four neighborhood structures:

[0065] (1) Neighborhood structure N1:

[0066] For the operations on the critical path, randomly select one operation and assign it to another machine. The operations on the critical path are the operations on the processing route with the maximum completion time where the operations on different machines are connected end to end. Update the element value of the corresponding operation in the machine sequence encoding according to the above operation. The new element value is 1 - the original element value.

[0067] (2) Neighborhood structure N2:

[0068] Traverse the operations on the critical path in sequence. If two adjacent operations on the critical path are processed on the same machine and do not belong to the same workpiece, add these two operations to the pair of operations to be selected. Randomly select a pair of operations from the pair of operations to be selected and exchange the processing order of the two operations. Update the element value of the corresponding operation in the operation sequence encoding according to the above operation. First, arrange the element values corresponding to the operations of each workpiece in the operation sequence in ascending order, and exchange the element values at the corresponding positions of the two selected operations. (3) Neighborhood structure N3:

[0070] Randomly select an index from the feature sequence encoding, link sequence encoding, machine sequence encoding, and operation sequence encoding respectively, and change the element value at the index position. The new element value is a random number between [0, 1). **

[0071] (4) Neighborhood structure N4:

[0072] For each machine, calculate the load rate of the machine. For the machine with the highest load among all machines, randomly select an operation assigned to this machine, find all the alternative machines for this operation and arrange them in ascending order of load rate, and reassign the machine with the minimum load rate to the operation. The element value at the corresponding position of the operation O in the machine sequence encoding is ij corresponding to Where random represents a random function, and index represents process O. ij The machine with the lowest available load rate is indexed in its list of available machines, where N represents process O. ij The number of available machines.

[0073] An integrated process planning and scheduling collaborative optimization system based on the hybrid ZOA-VNS algorithm includes:

[0074] The acquisition module is used to acquire the set of workpieces to be processed, the set of machines, and available resources;

[0075] The construction module is used to construct a mixed integer linear programming model based on the set of workpieces and the set of machines, under the constraint of the number of available resources, with the optimization objective of minimizing the maximum completion time;

[0076] The solution module uses a four-layer real number encoding structure of feature-link-machine-process as the encoding scheme, randomly generates all initial zebra individual positions as the initial zebra population, and uses the hybrid zebra optimization-variable neighborhood search algorithm to solve the hybrid integer linear programming model, outputs the optimal zebra individual, and obtains the optimal integrated process planning and scheduling collaborative optimization scheme based on the corresponding decoding scheme.

[0077] A storage medium storing a computer program for integrated process planning and scheduling co-optimization based on a hybrid ZOA-VNS algorithm, wherein the computer program causes a computer to execute the integrated process planning and scheduling co-optimization method as described above.

[0078] An electronic device, comprising:

[0079] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including methods for performing integrated process planning and scheduling co-optimization as described above.

[0080] (III) Beneficial Effects

[0081] This invention provides an integrated method, system, storage medium, and electronic device for collaborative optimization of process planning and scheduling based on a hybrid ZOA-VNS algorithm. Compared with existing technologies, it has the following advantages:

[0082] This invention first obtains the set of workpieces to be processed, the set of machines, and available resources. Second, under the constraint of the number of available resources, a mixed-integer linear programming model is constructed with the optimization objective of minimizing the maximum completion time. Next, a four-layer real-number encoding structure (feature-link-machine-process) is used as the encoding scheme, and all initial zebra individual positions are randomly generated as the initial zebra population. A hybrid zebra optimization-variable neighborhood search algorithm is then used to solve the model, outputting the optimal zebra individual. Based on the corresponding decoding scheme, the optimal integrated process planning and scheduling collaborative optimization scheme is finally obtained. This invention introduces the realistic factor of continuous resource constraints into the traditional integrated process planning and production scheduling problem, making the problem more practically applicable. Furthermore, the proposed hybrid zebra optimization-variable neighborhood search algorithm effectively solves this problem, achieving good optimization results. Attached Figure Description

[0083] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0084] Figure 1 A block diagram illustrating an integrated process planning and scheduling collaborative optimization method based on a hybrid ZOA-VNS algorithm, provided in an embodiment of the present invention.

[0085] Figure 2 Network diagrams for three different workpiece instances provided in embodiments of the present invention;

[0086] Figure 3 This is an example diagram of a four-layer real number encoding structure of feature-link-machine-process provided in an embodiment of the present invention;

[0087] Figures 4-7 The following are sample diagrams, in sequence, of a feature sequence decoding scheme, a link sequence decoding scheme, a machine sequence decoding scheme, and a process sequence decoding scheme provided in the embodiments of the present invention;

[0088] Figure 8 The flowchart illustrates a hybrid zebra optimization-variable neighborhood search algorithm provided in an embodiment of the present invention.

[0089] Figure 9 A problem example scheduling Gantt chart is provided as an embodiment of the present invention;

[0090] Figure 10 This is a resource consumption diagram of a problem example provided in an embodiment of the present invention. Detailed Implementation

[0091] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] This application provides an integrated process planning and scheduling collaborative optimization method, system, storage medium, and electronic device based on the hybrid ZOA-VNS algorithm, which solves the technical problem of integrated process planning and shop floor scheduling with continuous resource constraints.

[0093] The technical solution in this application is to solve the above-mentioned technical problems, and the general idea is as follows:

[0094] To address integrated process planning and shop floor scheduling problems with continuous resource constraints, this invention designs a hybrid Zebra Optimization-Variable Neighborhood Search (ZOA-VNS) algorithm to solve the NP-hard main problem. The continuous resource constraint means that the resources consumed by each process at any given time cannot exceed the total resource limit. Zebra Optimization Algorithm (ZOA) is a metaheuristic search algorithm proposed by Trojovsky et al. (2022). It mathematically models the zebra's foraging strategy of following the lead zebra and its escape and counterattack strategies when facing predators as an optimization process, iteratively optimizing by continuously updating the positions of zebras in the population. Variable Neighborhood Search (VNS) is an improved local search algorithm. It uses neighborhood structures formed by different actions to perform alternating searches, achieving a good balance between concentration and dispersion.

[0095] Specifically, the following steps are taken: First, a MILP mathematical model is established with the goal of minimizing the maximum completion time. To address the proposed problem, a novel four-layer real-number integrated encoding and decoding scheme is designed based on the model. A left-shift strategy based on resource availability and machine idle time is then embedded into the decoding process. Furthermore, a hybrid Zebra Optimization-Variable Neighborhood Search (ZOA-VNS) algorithm framework is proposed, and four different neighborhood structures are designed and embedded into the ZOA algorithm, including a neighborhood structure that considers the critical path and machine load balancing, thereby enhancing the algorithm's local search capability.

[0096] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0097] Example 1:

[0098] like Figure 1 As shown, this embodiment of the invention provides an integrated process planning and scheduling collaborative optimization method based on the hybrid ZOA-VNS algorithm, including:

[0099] S1. Obtain the set of workpieces to be processed, the set of machines, and the available resources;

[0100] S2. Based on the set of workpieces and the set of machines, and under the constraint of the number of available resources, construct a mixed integer linear programming model with the optimization objective of minimizing the maximum completion time;

[0101] S3. A four-layer real number encoding structure of feature-link-machine-process is adopted as the encoding scheme. All initial zebra individual positions are randomly generated as the initial zebra population. The mixed integer linear programming model is solved by the hybrid zebra optimization-variable neighborhood search algorithm to output the optimal zebra individual. Based on the corresponding decoding scheme, the optimal integrated process planning and scheduling collaborative optimization scheme is obtained.

[0102] The embodiments of this invention introduce the realistic factor of continuous resource constraints into the traditional integrated process planning and production scheduling problem, making the problem more applicable to real-world situations. At the same time, the proposed hybrid zebra optimization-variable neighborhood search algorithm effectively solves the problem and achieves good optimization results.

[0103] The following will detail each step of the above solution:

[0104] First, let's describe the problem addressed in the embodiments of this invention:

[0105] This invention addresses an integrated process planning and shop floor scheduling problem considering continuous resource constraints, described below: This problem combines process planning and shop floor scheduling, aiming to simultaneously optimize the process plan and scheduling plan for a set of jobs. Specifically, the problem involves a set of n jobs, denoted as {J1, J2, ..., J...}. n The processing is carried out on m machines, denoted as {M1, M2, ..., M}. m Each workpiece has multiple machining features, denoted as {F1, F2, ..., F}. f Each feature can choose a different processing path. A workpiece's features can have different processing sequences under the constraint of feature priority relationships. Each operation of each workpiece can be processed on different machines, with different processing times and resource consumption. The number of continuous resources available to the factory at any given time is finite, and the resources consumed by a processing operation at any given time cannot exceed the total resources available at that time. The goal is to simultaneously determine the workpiece's process route, machine allocation, and processing sequence, minimizing the completion time while satisfying the workpiece's process route and resource constraints.

[0106] In step S1, the set of workpieces to be processed, the set of machines, and the available resources are obtained.

[0107] This step obtains data such as the set of workpieces to be processed, the set of machines, and available resources. To facilitate the explanation of subsequent model construction, the parameter symbols and explanations are further provided as shown in Table 1:

[0108] Table 1

[0109]

[0110]

[0111] In step S2, based on the set of workpieces and the set of machines, and under the constraint of the number of available resources, a mixed integer linear programming model is constructed with the optimization objective of minimizing the maximum completion time.

[0112] Before building the model, it is necessary to supplement the basic assumptions of the problem as follows:

[0113] (1) All workpieces can be processed at time zero;

[0114] (2) Once a process for processing a workpiece begins, it cannot be interrupted;

[0115] (3) A machine can only process one workpiece at a time;

[0116] (4) A workpiece can only be processed by one machine at a time.

[0117] (5) Once a workpiece has been processed in one step, it can be immediately sent to the next machine to process the next step.

[0118] Based on this, the mixed-integer linear programming model constructed in this step includes:

[0119] minC max (1)

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] in,

[0133] Equation (1) is the objective function; min is the minimization function;

[0134] Constraint (2) means that for any workpiece, each of its machining features must select a process link;

[0135] Constraint (3) means that for any workpiece, if the process link of a certain processing feature is not selected, then that process will not be selected either;

[0136] Constraint (4) means that for any workpiece, if a certain process link of a certain processing feature is selected, then all processes on that process link will be selected.

[0137] Constraint (5) means that when a process of a workpiece is selected, a selectable processing machine needs to be assigned to it; if a process is not selected, no processing machine needs to be assigned.

[0138] Constraint (6) means that for any workpiece, the priority relationship of any two operations selected from two processing features with priority relationship must satisfy the priority relationship corresponding to their processing features;

[0139] Constraint (7) means that for any workpiece, the priority relationship between two processes on any process link of any processing feature should satisfy the priority relationship between their processes;

[0140] Constraints (8) and (9) indicate that when the priority relationship of the operations is determined, there should be a definite processing sequence for different operations on the same workpiece;

[0141] Constraints (10) and (11) indicate that when the priority relationship of the operations is determined, the operations processed on the same machine should have a definite processing order;

[0142] Constraint (12) means that the cumulative resource consumption of all processes in operation at any given time cannot exceed the maximum available resources at the same time.

[0143] Constraint (13) clarifies the definition of maximum completion time.

[0144] In step S3, a four-layer real number encoding structure of feature-link-machine-process is adopted as the encoding scheme. All initial zebra individual positions are randomly generated as the initial zebra population. The mixed integer linear programming model is solved by the hybrid zebra optimization-variable neighborhood search algorithm to output the optimal zebra individual. Based on the corresponding decoding scheme, the optimal integrated process planning and scheduling collaborative optimization scheme is obtained.

[0145] Before introducing the hybrid zebra optimization-variable neighborhood search algorithm proposed in this embodiment of the invention, this step innovatively proposes the following encoding and decoding scheme:

[0146] (1) Encoding Scheme

[0147] As mentioned above, a four-layer real-number encoding structure—feature-link-machine-process—is used as the encoding scheme for this problem. Each layer of encoding is represented by a vector, π. 1 Represents the feature sequence encoding, vector π 2 Represents the link sequence encoding, vector π 3 Represents machine sequence encoding, vector π 4 This represents the process sequence encoding. The elements in the vector are random numbers between 0 and 1 that follow a uniform distribution. The lengths of the feature sequence encoding and link sequence encoding are equal to the sum of the number of processing features of all workpieces, and the lengths of the machine sequence encoding and process sequence encoding are equal to the sum of the number of processes of all workpieces.

[0148] For example, Table 2 and Figures 2-3 A sample encoding scheme is provided together:

[0149] Table 2

[0150]

[0151] (2) Decoding scheme

[0152] The decoding scheme here includes five stages: feature sequence decoding, link sequence decoding, machine sequence decoding, process sequence decoding, and determining the start and end times of each process. It's important to note that the fifth stage specifically utilizes a decoding rule that embeds a resource-based left-shift strategy to maximize machine utilization and minimize the maximum completion time, as detailed below:

[0153] The first stage involves decoding the feature sequence: for the feature sequence encoding vector π 1The number at the j-th position of the i-th workpiece in the feature sequence encoding vector is used as the feature set to be assigned. All features of workpiece i that have no prior features or whose prior features have been assigned but have not yet been assigned are used as the feature set to be assigned. The number at the j-th position of the i-th workpiece in the feature sequence encoding vector is multiplied by the length of the feature set to be assigned and rounded down to obtain the feature index to be assigned. The corresponding feature in the feature set to be assigned is selected according to the index and added to the decoded feature sequence.

[0154] For example, Figure 4 An example of a feature sequence decoding scheme is given.

[0155] The second stage involves performing link sequence decoding: for the link sequence encoded vector π 2 Find the number at the j-th position of the i-th workpiece, and find the feature F of workpiece i. j The optional links are used as the set of links to be allocated. The number at the j-th position of the i-th workpiece in the link sequence encoding vector is multiplied by the length of the set of links to be allocated and rounded down to obtain the index of the link to be allocated. The corresponding link in the set of links to be allocated is selected according to the index and added to the decoded link sequence.

[0156] For example, Figure 5 An example of a link sequence decoding scheme is given.

[0157] Understandably, based on the decoding in the first and second stages, the processing sequence for each workpiece can be determined. In this example, the processing sequence for workpiece 1 is O. 11 -O 12 -O 13 The processing steps for workpiece 2 are O 21 -O 25 -O 23 The machining process for workpiece 3 is O 31 -O 34 -O 32 -O 37 .

[0158] The third stage involves performing machine sequence decoding: for the machine sequence encoded vector π 3 The number at the j-th position of the i-th workpiece in the process O ij The selectable machines are used as the set of machines to be assigned. The number at the j-th position of the i-th workpiece in the machine encoding vector is multiplied by the length of the set of machines to be assigned and rounded down to obtain the index of the machine to be assigned. The machine corresponding to the set of machines to be assigned is selected according to the index and added to the decoded machine sequence.

[0159] For example, Figure 6 An example of a machine sequence decoding scheme is given.

[0160] Understandably, based on the decoding in the first three stages, the technological route for each workpiece can be determined, that is, the processing steps for each workpiece and the processing machine for each step. In this example, the technological route for workpiece 1 is O. 11 (M1)-O 12 (M4)-O 13 (M3), the process route for workpiece 2 is O 21 (M1)-O 25 (M4)-O 23 (M5), the process route for workpiece 3 is O 31 (M2)-O 34 (M2)-O 32 (M1)-O 37 (M4).

[0161] The fourth stage involves decoding the process sequence: for the workpiece sequence encoding vector π 4 The j-th process of the i-th workpiece O ij If the number is not in the process route of the i-th workpiece, then remove the number at the j-th position of the i-th workpiece from the process sequence encoding vector. Sort the encoded vector after removal in ascending order. If the number in the sorted encoded vector belongs to the number of the i-th workpiece in the encoded vector before sorting, then add the number i to the decoded process sequence. The number of numbers i in the decoded process sequence is equal to the number of processes in the process route of the i-th workpiece. The order of numbers i in the decoded process sequence corresponds to the order of processes in the process route of the i-th workpiece.

[0162] For example, Figure 7 An example of a process sequence decoding scheme is given.

[0163] Understandably, based on the decoding in the fourth stage, process O can be determined. ij The processing sequence, in this example, is O. 21 -O 25 -O 11 -O 12 -O 31 -O 34 -O 32 -O 37 -O 23 -O 13 .

[0164] After obtaining the processing sequence of all processes and the assigned machines, the fifth stage determines the start and end times of each process based on the decoding rules of the embedded resource-based left-shift strategy. The basic process is as follows:

[0165] S100, for process O ij Find O in the process route of workpiece iij The completion time (OT) of the previous process;

[0166] S200, for process O ij The assigned machine M i Find machine M i The completion time MT of the last assigned process and the machine M before MT. i Free time in It is machine M i The start time of the idle period i. It is machine M i The idle end time of the i-th idle time period;

[0167] S300, if there is a free period satisfy So, process O ij The earliest possible start time Where PT represents process O ij In machine M i Processing time;

[0168] S400, Determine if Does a sub-time period of length PT exist within this period? Ensure that the remaining available resources during this sub-period are greater than or equal to those of process O. ij Resource consumption, if it exists, then process O ij Actual processing start time in These are the start and end times of a sub-time period of length PT, respectively.

[0169] Based on the above encoding and decoding schemes, such as Figure 8 As shown, the process of the proposed hybrid zebra optimization-variable neighborhood search algorithm in this step is as follows:

[0170] S31. Initialize the parameters of the hybrid zebra optimization-variable neighborhood search algorithm, including the number of zebras N, the maximum number of iterations T, the number of neighborhood structures k_max, and the maximum number of iterations l_max between two improvements of a single neighborhood.

[0171] S32. Randomly generate the positions of all initial zebra individuals as the initial zebra population. Each zebra individual is [π]. 1 ,π 2 ,π 3 ,π 4 ];

[0172] S33: Let i = 1, t = 1;

[0173] S34. Calculate the fitness values of all zebra individuals in the population and sort them, and select the individual with the optimal fitness as the initial position of the pioneer zebra PZ, where the fitness value is the makespan;

[0174] S35. Simulate the foraging behavior of zebras. The i-th zebra in the population moves towards the pioneer zebra, and the position of the i-th zebra is updated using the formula Update;

[0175] S36. For the updated position of the i-th zebra, adopt the elite retention strategy, that is, if the fitness of the updated i-th zebra is less than the fitness of the i-th zebra before update, then retain the updated position, otherwise the position of the i-th zebra remains unchanged;

[0176] S37. Randomly generate the position of the predator AZ, and simulate the defense strategy adopted by zebras when facing predators. Assume that zebras will choose two strategies: running away nearby or counterattacking the predator, and the probabilities of choosing these two strategies are equal. Let P s = rand(0, 1);

[0177] S38. If P S ≤ 0.5, then the zebra chooses the first strategy, and the position of the i-th zebra in the population is updated using the formula Update, otherwise the zebra chooses the second strategy, and the position of the i-th zebra in the population is updated using the formula Update;

[0178] S39. For the updated position of the i-th zebra, adopt the elite retention strategy, that is, if the fitness of the updated i-th zebra is less than the fitness of the i-th zebra before update, then retain the updated position, otherwise the position of the i-th zebra remains unchanged;

[0179] S310. If i < N, let i = i + 1, return to S34, otherwise enter S311;

[0180] S311. Obtain the individuals with the top 10% fitness rankings in the zebra population as elite zebras, and perform variable neighborhood search on the positions of the elite zebras using k_max neighborhood structures. The maximum number of iterations between two improvements in a single neighborhood is l_max;

[0181] S312. If t < T, let t = t + 1, i = 1, return to S34, otherwise the algorithm ends and outputs the zebra individual with the optimal fitness.

[0182] Finally, based on the above decoding scheme, by decoding the optimal zebra individual, the optimal integrated process planning and scheduling collaborative optimization scheme can be obtained.

[0183] Exemplarily, Figures 9-10A Gantt chart for scheduling and a resource consumption chart for each problem instance are provided.

[0184] In one optional implementation, the present invention designs the following four neighborhood structures:

[0185] (1) Neighborhood structure N1:

[0186] For a process on the critical path, randomly select a process and assign it to another machine; the process on the critical path is the process on the processing route with the longest completion time that is connected end to end on different machines; update the element value of the corresponding process in the machine sequence code according to the above operation, the new element value is 1 - the original element value.

[0187] (2) Neighborhood structure N2:

[0188] Iterate through the processes on the critical path. If two adjacent processes on the critical path are processed on the same machine but do not belong to the same workpiece, add these two processes to the process pair to be selected. Randomly select a pair of processes from the process pair to be selected and swap the processing order of the two processes. Update the element values ​​of the corresponding processes in the process sequence code according to the above operations. First, arrange the element values ​​corresponding to the processes of each workpiece in the process sequence in ascending order, and swap the element values ​​of the corresponding positions of the two selected processes.

[0189] (3) Neighborhood structure N3:

[0190] Randomly select an index from feature sequence encoding, link sequence encoding, machine sequence encoding and process sequence encoding respectively, and change the element value at the index position. The new element value is a random number between [0,1).

[0191] (4) Neighborhood structure N4:

[0192] For each machine, calculate the machine's load rate. For the machine with the highest load, randomly select a process assigned to that machine. Find all available machines for that process and sort them in ascending order of load rate. Reassign the process to the machine with the lowest load rate. In the machine sequence encoding, process O... ij The value of the element at the corresponding position is Where random represents a random function, and index represents process O. ij The machine with the lowest available load rate is indexed in its list of available machines, where N represents process O. ij The number of available machines.

[0193] Thus, this embodiment of the invention completes the entire process of the integrated process planning and scheduling collaborative optimization method based on the hybrid ZOA-VNS algorithm.

[0194] Example 2:

[0195] This invention provides an integrated process planning and scheduling collaborative optimization system based on the hybrid ZOA-VNS algorithm, comprising:

[0196] The acquisition module is used to acquire the set of workpieces to be processed, the set of machines, and available resources;

[0197] The construction module is used to construct a mixed integer linear programming model based on the set of workpieces and the set of machines, under the constraint of the number of available resources, with the optimization objective of minimizing the maximum completion time;

[0198] The solution module uses a four-layer real number encoding structure of feature-link-machine-process as the encoding scheme, randomly generates all initial zebra individual positions as the initial zebra population, and uses the hybrid zebra optimization-variable neighborhood search algorithm to solve the hybrid integer linear programming model, outputs the optimal zebra individual, and obtains the optimal integrated process planning and scheduling collaborative optimization scheme based on the corresponding decoding scheme.

[0199] Example 3:

[0200] This invention provides a storage medium storing a computer program for integrated process planning and scheduling co-optimization based on a hybrid ZOA-VNS algorithm, wherein the computer program causes a computer to execute the integrated process planning and scheduling co-optimization method as described in Embodiment 1.

[0201] Example 4:

[0202] This invention provides an electronic device, comprising:

[0203] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including methods for performing integrated process planning and scheduling co-optimization as described in Example 1.

[0204] It is understood that the integrated process planning and scheduling collaborative optimization system, storage medium and electronic device based on the hybrid ZOA-VNS algorithm provided in the embodiments of the present invention correspond to the integrated process planning and scheduling collaborative optimization method based on the hybrid ZOA-VNS algorithm provided in the embodiments of the present invention. The explanation, examples and beneficial effects of the relevant contents can be referred to the corresponding parts of the integrated process planning and scheduling collaborative optimization method, and will not be repeated here.

[0205] In summary, compared with existing technologies, it has the following beneficial effects:

[0206] 1. The embodiments of the present invention introduce the realistic factor of continuous resource constraints on the basis of traditional integrated process planning and production scheduling problems, making the problem more applicable to reality. At the same time, the proposed hybrid zebra optimization-variable neighborhood search algorithm effectively solves the problem and achieves good optimization results.

[0207] 2. This invention aims to minimize the maximum completion time and studies the integrated process planning and shop floor scheduling problem considering continuous resource constraints. An integrated encoding and decoding scheme is designed for this problem. A resource-based left-shift strategy is embedded in the decoding stage to maximize machine utilization and shorten the maximum completion time. A hybrid ZOA-VNS algorithm is proposed to effectively solve the above problems.

[0208] 3. The hybrid ZOA-VNS algorithm proposed in this invention has both excellent global search and local search capabilities. It performs better than existing popular algorithms in solving large-scale integrated process planning and shop floor scheduling problems, and it is also highly applicable to solving other scheduling problems with NP-hard properties.

[0209] 4. This invention introduces the realistic factor of continuous resource constraints into the traditional integrated process planning and workshop scheduling problem, making the problem more applicable to reality. Furthermore, the problem can be extended to other problems by adding other constraints, which has strong theoretical research significance.

[0210] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0211] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. An integrated process planning and scheduling collaborative optimization method based on the hybrid ZOA-VNS algorithm, characterized in that, including: obtaining a set of workpieces to be processed, a set of machines, and available resources; constructing a mixed integer linear programming model based on the set of workpieces and the set of machines, with the objective of minimizing the makespan under the quantity limit of the available resources; adopting a four-layer real number coding structure of feature-link-machine-operation as the coding scheme, randomly generating the positions of all initial zebra individuals as the initial zebra population, and using a hybrid zebra optimization-variable neighborhood search algorithm to solve the mixed integer linear programming model, outputting the optimal zebra individual, and obtaining an optimal integrated process planning and scheduling collaborative optimization scheme based on the corresponding decoding scheme; the mixed integer linear programming model includes: minC max (1) Where J represents the set of workpieces; O i F represents the set of operations for workpiece i; i M represents the set of machining features for workpiece i; M represents the set of machines. i, i′ represent workpieces j, i′, 1 ≤ i, i′ ≤ |J|; j, j′ represent processes j, j′, 1 ≤ j, j′ ≤ |O|. i |;f,f′ represents the feature f,f′,1≤f,f′≤|F i |;k,k′ represents machine k,k′,1≤k,k′≤|M|;l,l′ represents process link l,l′; Equation (1) is the objective function; min is the minimization function, C max Indicates the maximum completion time; Constraint (2) means that for any workpiece, each of its machining features must select a process link; F ifl For decision variables, the value is 1 if the u-th process link of the processing feature j of workpiece i is selected, and 0 otherwise; Constraint (3) means that for any workpiece, if the process link of a certain machining feature in which one of its operations is located is not selected, then that operation will not be selected either; X ij For decision variables, if o ij If selected, the value is 1; otherwise, it is 0; N is a sufficiently large positive number; E ijfl Indicates if o ij If it is located on the l-th process link of processing feature f, then it is 1; otherwise, it is 0. Constraint (4) indicates that for any workpiece, if a certain process link of a certain processing feature of it is selected, then all operations on this process link will be selected; Constraint (5) indicates that when a process is selected for a workpiece, a selectable machining machine needs to be assigned to it; otherwise, no machining machine needs to be assigned. ijk For decision variables, if o ij If the process is performed on machine k, the value is 1; otherwise, it is 0. Constraint (6) states that for any workpiece, the priority relationship between any two operations selected from two machining features with a priority relationship must satisfy the priority relationship corresponding to their machining features; E ij′f′l Indicates if o ij′ If it is located on the l-th process link of processing feature f′, then it is 1; otherwise, it is 0. ij′ For decision variables, if o ij′ If selected, the value is 1; otherwise, it is 0. iji′j′ For decision variables, if o ij In o i′j′ If it's a pre-processing step, the value is 1; otherwise, it's 0. iff′ This indicates that if the machining feature f of workpiece i is the immediate preceding machining feature of machining feature f′, then it is 1; otherwise, it is 0. Constraint (7) states that for any workpiece, the priority relationship between two operations on any process link of any machining feature should satisfy the priority relationship between their corresponding operations; E ij′fl Indicates if o ij′ If it is located on the l-th process link of processing feature f, then it is 1; otherwise, it is 0. ijij′ For decision variables, if o ij In o ij′ For pre-processing, the value is 1; This indicates that if the operation j on the machining feature f of workpiece i is the immediate preceding operation of j′, then it is 1; otherwise, it is 0. Constraints (8) and (9) indicate that when the priority relationship of operations is determined, there should be a definite processing sequence for different operations on the same workpiece; ij o ij′ S represents the processes j and j′ of workpiece i, respectively; ij S ij′ They represent o respectively ij o ij′ Processing start time; Z ij′k For decision variables, if o ij′ If processed on machine k, the value is 1; otherwise, it is 0. ijk T ij′k They represent o respectively ij o ij′ Processing time on machine k; Constraints (10) and (11) indicate that when the priority relationship of operations is determined, the operations processed on the same machine should have a definite processing order; S i′j′ o i′j′ Processing start time; Z i′j′k For decision variables, if o i′j′ If processed on machine k, the value is 1; otherwise, it is 0. ijk T i′j′k They represent o respectively ij o i′j′ Processing time on machine k; Constraint (12) states that the cumulative resource consumption of all processes in operation at any given time cannot exceed the maximum available resource amount at the same time; O i (t) represents the set of processes being processed at time t; R ijk o ij Resource consumption on machine k; R max Indicates the maximum amount of resources available at any given time; Constraint (13) clarifies the definition of the makespan.

2. The integrated process planning and scheduling collaborative optimization method as described in claim 1, characterized in that, Each layer of the encoding scheme is represented by a single vector, π. 1 Represents the feature sequence encoding, vector π 2 Represents the link sequence encoding, vector π 3 Represents machine sequence encoding, vector π 4 This represents the process sequence encoding; the elements in the vector are random numbers between 0 and 1 that follow a uniform distribution, where the length of the feature sequence encoding and the link sequence encoding is equal to the sum of the number of processing features of all workpieces, and the length of the machine sequence encoding and the process sequence encoding is equal to the sum of the number of processes of all workpieces.

3. The integrated process planning and scheduling collaborative optimization method as described in claim 2, characterized in that, the corresponding decoding scheme includes: The first stage involves decoding the feature sequence: for the feature sequence encoding vector π 1 The number at the j-th position of the i-th workpiece in the sequence is used as the feature set to be assigned. All features of workpiece i that have no prior features or whose prior features have been assigned but have not yet been assigned are used as the feature set to be assigned. The number at the j-th position of the i-th workpiece in the feature sequence encoding vector is multiplied by the length of the feature set to be assigned and rounded down to obtain the feature index to be assigned. The corresponding feature in the feature set to be assigned is selected according to the index and added to the decoded feature sequence. The second stage involves performing link sequence decoding: for the link sequence encoded vector π 2 Find the number at the j-th position of the i-th workpiece, and find the feature F of workpiece i. j The optional links are used as the set of links to be allocated. The number at the j-th position of the i-th workpiece in the link sequence encoding vector is multiplied by the length of the set of links to be allocated and rounded down to obtain the index of the link to be allocated. The corresponding link in the set of links to be allocated is selected according to the index and added to the decoded link sequence. The third stage involves performing machine sequence decoding: for the machine sequence encoded vector π 3 The number at the j-th position of the i-th workpiece in the process O ij The selectable machines are used as the set of machines to be assigned. The number at the j-th position of the i-th workpiece in the machine encoding vector is multiplied by the length of the set of machines to be assigned and rounded down to obtain the index of the machine to be assigned. The corresponding machine in the set of machines to be assigned is selected according to the index and added to the decoded machine sequence. The fourth stage involves decoding the process sequence: for the workpiece sequence encoding vector π 4 The j-th process of the i-th workpiece O ij If the number is not in the process route of the i-th workpiece, then remove the number at the j-th position of the i-th workpiece from the process sequence encoding vector. Sort the encoded vector after removal in ascending order. If the number in the sorted encoded vector belongs to the number of the i-th workpiece in the encoded vector before sorting, then add the number i to the decoded process sequence. The number of numbers i in the decoded process sequence is equal to the number of processes in the process route of the i-th workpiece. The order of numbers i in the decoded process sequence corresponds to the order of processes in the process route of the i-th workpiece. In the fifth stage, according to the decoding rule embedded with a resource-based left shift strategy, determine the processing start time and end time of each operation, including: S100, for process O ij Find O in the process route of workpiece i ij The completion time (OT) of the previous process; S200, for process O ij The assigned machine M i Find machine M i The completion time MT of the last assigned process and the machine M before MT. i Free time in It is machine M i The start time of the idle period in the i-th idle time segment. It is machine M i The idle end time of the i-th idle time period; S300, if there is a free period satisfy So, process O ij The earliest possible start time Where PT represents process O ij In machine M i Processing time; S400, Determine if Does a sub-time period of length PT exist within this period? Ensure that the remaining available resources during this sub-period are greater than or equal to those of process O. ij Resource consumption, if it exists, then process O ij Actual processing start time in These are the start and end times of a sub-time period of length PT, respectively.

4. The integrated process planning and scheduling collaborative optimization method as described in claim 3, characterized in that, using the hybrid zebra optimization-variable neighborhood search algorithm to solve the mixed integer linear programming model and output the optimal zebra individual; including: S31. Initialize the parameters of the hybrid zebra optimization-variable neighborhood search algorithm, including the number of zebras N, the maximum number of iterations T, the number of neighborhood structures k_max, and the maximum number of iterations l_max between two improvements of a single neighborhood; S32. Randomly generate the positions of all initial zebra individuals as the initial zebra population. Each zebra individual is [π]. 1 ,π 2 ,π 3 ,π 4 ]; S33: Let i = 1, t = 1; S34. Calculate the fitness values of all zebra individuals in the population and sort them, and select the individual with the optimal fitness as the initial position of the pioneer zebra PZ, where the fitness value is the makespan; S35. Simulate zebra foraging behavior: the i-th zebra in the population moves towards the lead zebra. The position of the i-th zebra is determined by the formula... renew; S36. For the updated position of the i-th zebra, adopt an elitist retention strategy, that is, if the fitness of the updated i-th zebra is less than the fitness of the i-th zebra before update, then retain the updated position, otherwise the position of the i-th zebra remains unchanged; S37. Randomly generate the location of predator AZ and simulate the defensive strategies a zebra adopts when facing a predator. Assume the zebra will choose either to flee to a nearby location or to fight back against the predator, and that the probabilities of each choice and strategy are equal. Let P... S = rand(0,1); S38, If P S If the value is ≤0.5, then the zebra chooses the first strategy, and the position of the i-th zebra in the population is determined by the formula. Update; otherwise, the zebra chooses the second strategy, and the position of the i-th zebra in the population is determined by the formula. renew; S39. For the updated position of the i-th zebra, adopt an elitist retention strategy, that is, if the fitness of the updated i-th zebra is less than the fitness of the i-th zebra before update, then retain the updated position, otherwise the position of the i-th zebra remains unchanged; S310. If i < N, let i = i + 1, return to S34, otherwise enter S311; S311. Obtain the individuals with the top 10% fitness rankings in the zebra population as elite zebras, and perform variable neighborhood search on the positions of the elite zebras using k_max neighborhood structures, with the maximum number of iterations l_max between two improvements of a single neighborhood; S312. If t < T, let t = t + 1, i = 1, return to S34, otherwise the algorithm ends and outputs the zebra individual with the optimal fitness.

5. The integrated process planning and scheduling collaborative optimization method as described in claim 4, characterized in that, Design the following four neighborhood structures: (1) Neighborhood structure N1: For a process on the critical path, randomly select a process and assign it to another machine; the process on the critical path is the process on the processing route with the longest completion time that is connected end to end on different machines; update the element value of the corresponding process in the machine sequence code according to the above operation, the new element value is 1 - the original element value. (2) Neighborhood structure N2: Iterate through the processes on the critical path. If two adjacent processes on the critical path are processed on the same machine but do not belong to the same workpiece, add these two processes to the process pair to be selected. Randomly select a pair of processes from the process pair to be selected and swap the processing order of the two processes. Update the element values ​​of the corresponding processes in the process sequence code according to the above operations. First, arrange the element values ​​corresponding to the processes of each workpiece in the process sequence in ascending order, and swap the element values ​​of the corresponding positions of the two selected processes. (3) Neighborhood structure N3: Randomly select an index from feature sequence encoding, link sequence encoding, machine sequence encoding and process sequence encoding respectively, and change the element value at the index position. The new element value is a random number between [0,1). (4) Neighborhood structure N4: For each machine, calculate the machine's load rate. For the machine with the highest load, randomly select a process assigned to that machine. Find all available machines for that process and sort them in ascending order of load rate. Reassign the process to the machine with the lowest load rate. In the machine sequence encoding, process O... ij The value of the element at the corresponding position is Where random represents a random function, and index represents process O. ij The machine with the lowest available load rate is indexed in its list of available machines, where N represents process O. ij The number of available machines.

6. An integrated process planning and scheduling collaborative optimization system based on a hybrid ZOA-VNS algorithm, characterized in that, The method for performing integrated process planning and scheduling collaborative optimization as described in claim 1 includes: The acquisition module is used to acquire the set of workpieces to be processed, the set of machines, and available resources; The construction module is used to construct a mixed integer linear programming model based on the set of workpieces and the set of machines, under the constraint of the number of available resources, with the optimization objective of minimizing the maximum completion time; The solution module uses a four-layer real number encoding structure of feature-link-machine-process as the encoding scheme, randomly generates all initial zebra individual positions as the initial zebra population, and uses the hybrid zebra optimization-variable neighborhood search algorithm to solve the hybrid integer linear programming model, outputs the optimal zebra individual, and obtains the optimal integrated process planning and scheduling collaborative optimization scheme based on the corresponding decoding scheme.

7. A storage medium, characterized in that, It stores a computer program for integrated process planning and scheduling co-optimization based on the hybrid ZOA-VNS algorithm, wherein the computer program causes the computer to execute the integrated process planning and scheduling co-optimization method as described in any one of claims 1 to 5.

8. An electronic device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including methods for performing the integrated process planning and scheduling co-optimization method as described in any one of claims 1 to 5.

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