A hybrid flow-shop energy-efficient scheduling method for parallel batch machines

Abstract

The present application relates to a kind of hybrid flow shop energy-saving scheduling method for parallel batch machine, compared with prior art, it solves the defect that hybrid flow shop energy-saving scheduling is difficult to realize.The present application includes the following steps: the setting of hybrid flow shop working state;Calculate the maximum completion time and total energy consumption of the set of workpieces to be processed;Build the hybrid flow shop energy-saving scheduling scene of multi-objective parallel batch machine;Generation of hybrid flow shop energy-saving scheduling scheme.The present application can efficiently obtain the best scheduling strategy that meets the requirements of multi-objective in complex scenarios by coordinating multiple populations and introducing adaptive mechanism, fully utilizing the useful information in the distribution characteristics of solution to guide the search direction.

Description

Technical Field

[0001] This invention relates to the field of hybrid pipeline workshop scheduling technology, specifically to an energy-saving scheduling method for hybrid pipeline workshops using parallel batch processing machines. Background Technology

[0002] Hybrid flow shop (FSP) is a typical manufacturing environment suitable for various production scenarios, such as small-batch customized industrial products in the semiconductor, electrical appliance, and steel industries. It represents a scheduling problem of significant research value in practical production. Hybrid flow shop scheduling (HFSP) is an extension of FSP, considering machine flexibility and making the scheduling model closer to actual production. Furthermore, with the continued growth of the global economy and the increase in population, the energy demand of manufacturing worldwide is constantly rising. According to statistics, manufacturing accounts for nearly one-third of global energy consumption. Therefore, more and more countries are exploring new technologies and methods to reduce energy consumption and pollution, and promote the sustainable use of energy. Balancing manufacturing efficiency and energy consumption has become one of the key issues facing enterprise decision-makers.

[0003] Existing technologies employ multi-objective optimization algorithms to schedule production in hybrid assembly lines. However, these solutions apply to overly simplistic scenarios, while current real-world production scenarios are far more complex, involving more realistic production environments, such as assembly lines with parallel batch processors. These batch processors can process multiple workpieces simultaneously without exceeding their capacity. This situation significantly complicates the problem, classifying it as a more complex NP-hard problem. Currently available algorithms struggle to find richer and more reasonable production and processing solutions within a limited search time. Furthermore, these algorithms fail to effectively handle the distribution characteristics of solutions, failing to fully utilize the useful information provided by these characteristics to guide the evolution of the population. Consequently, the resulting production and processing solutions often fail to meet the requirements of enterprise managers. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies in achieving energy-saving scheduling of hybrid pipeline workshops, and to provide an energy-saving scheduling method for hybrid pipeline workshops using parallel batch processors to solve the above problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A hybrid pipeline workshop energy-saving scheduling method for parallel batch processing machines includes the following steps:

[0007] 11) Setting up the working state of the mixed flow workshop: setting up the parallel batch processing mechanism and the set of workpieces to be processed;

[0008] 12) Calculate the maximum completion time and total energy consumption for constructing the set of workpieces to be processed;

[0009] 13) Construct a multi-objective hybrid production line energy-saving scheduling scenario with parallel batch processing machines: Based on the actual production situation, set constraints and construct a multi-objective hybrid production line energy-saving scheduling scenario with parallel batch processing machines;

[0010] 14) Generation of energy-saving scheduling scheme for hybrid assembly line workshop: Based on the set of workpieces to be processed, the adaptive multi-group cooperative evolution algorithm is used to solve the energy-saving scheduling scenario of hybrid assembly line workshop with parallel batch processing machine, and a set of production and processing schemes is obtained, namely the energy-saving scheduling scheme for hybrid assembly line workshop.

[0011] Setting the working status of the mixed flow workshop includes the following steps:

[0012] 21) Set up a parallel batch processing mechanism: The parallel batch processing mechanism processes each workpiece in two sequential stages, and only enters the second stage after the first stage is completed;

[0013] The first stage includes qualified parallel machines, and the second stage consists of parallel batch processing machines. In the first stage, machine qualification restrictions must be followed, and workpieces are only allowed to be processed on qualified machines. The second stage consists of multiple energy-intensive batch processing furnaces, each of which processes multiple workpieces simultaneously within its capacity. The first stage machines take qualification constraints into account, meaning that not all machines can process every workpiece. Machine processing qualifications are preset proportionally. Machines have three states: processing, idle, and off. The energy consumption of each state is different, and the size of each workpiece varies. All workpieces are ready at the initial time point.

[0014] 22) Based on actual production and processing needs, construct the workpiece set Ω as shown in equation (1).

[0015] Ω= {J1,J2,…,J j ,…,J n} (1)

[0016] In equation (1), j represents the index of the workpiece in the set of workpieces to be processed Ω; J j Let represent the j-th workpiece in the workpiece set Ω to be processed; n represents the total number of workpieces in the workpiece set Ω to be processed.

[0017] The method for calculating the maximum completion time and total energy consumption for constructing the set of workpieces to be processed is as follows:

[0018] The maximum completion time C of the set of workpieces to be processed Ω is constructed using equations (2) and (3) respectively. max Total Energy Consumption (TEC)

[0019]

[0020]

[0021] In equations (2) and (3), j represents the index of the workpiece; C j J represents the j-th workpiece. j The processing time is denoted by i; i represents the machine index; m1 and m2 represent the total number of machines in stage 1 and stage 2, respectively; T represents the total time period; f(t) represents the unit energy price within time period t.

[0022] and These represent the processing states of machines in stages 1 and 2, respectively. If machine i is in a processing state at time t, the value is 1; otherwise, it is 0.

[0023] and These represent the idle states of machines in phase 1 and phase 2, respectively. If machine i is idle at time t, the value is 1; otherwise, it is 0.

[0024] and These represent the shutdown states of machines in phase 1 and phase 2, respectively. If machine i is in the shutdown state at time t, the value is 1; otherwise, it is 0.

[0025] and These represent the processing energy consumption rate of machine i in stage 1 and stage 2, respectively;

[0026] and These represent the idle energy consumption rate of machine i in phase 1 and phase 2, respectively.

[0027] and These represent the power consumption rate of machine i during shutdown in phase 1 and phase 2, respectively.

[0028] The construction of a multi-objective hybrid pipeline workshop energy-saving scheduling scenario with parallel batch processing machines includes the following steps:

[0029] 41) Set the constraints as follows:

[0030] Constraint 1: That is, ensure that each workpiece j is processed on only one machine i in stage 1;

[0031] Constraint 2: a ij <<π ij That is, it is used for machine qualification assessment. If workpiece j cannot be processed on machine i in stage 1, it will not be assigned to that machine.

[0032] Constraint 3: a ij >>pijt That is, if workpiece j is not assigned to machine i in stage 1, then the workpiece will not be processed on that machine at any time period t.

[0033] Constraint 4: That is: if workpiece j is assigned to machine i in stage 1, then machine i will be processing workpiece j for at least one time period t.

[0034] Constraints 5 and 6: and That is, ensure that the processing of workpiece j is not interrupted and that the workpiece cannot be preempted;

[0035] Constraint 7: That is, it is guaranteed that during phase 1, machine i can only be in one of three states during time period t: processing, idle, or off;

[0036] Constraint 8: That is: define the processing state of machine i during time period t in stage 1;

[0037] Constraint 9 and Constraint 10 and That is: Define the idle state of machine i in time period t of stage 1. If machine i is in an idle state in time period t, then at least one time period from time period 1 to t-1 and time period t+1 to T is in a processing state; otherwise, the machine is shut down.

[0038] Constraint 11 and Constraint 12:

[0039] and That is, the shutdown state of machine i in time period t of phase 1 is defined. If machine i is shut down in time period t, it cannot process any workpieces in time period from t+1 to T. This means that once the machine is shut down, it will not be restarted.

[0040] Constraint 13: That is, to ensure that any workpiece can only be processed in one batch on one batch processing machine in stage 2;

[0041] Constraint 14: That is, ensure that the size of the batch b formed does not exceed the capacity Q of the batch processing machine;

[0042] Constraint 15: y b >>y b+1 That is, it excludes the situation where batch b+1 is formed but batch b is not formed, that is, it does not allow empty batches in the middle;

[0043] Constraint 16: That is, if there are no workpieces in the current batch, the processing time for the current batch is 0.

[0044] Constraint 17: That is: if batch processing machine i is in a processing state during time period t in stage 2, then batch processing machine i will process one batch during time period t.

[0045] Constraint 18: That is, ensure that the processing time of batch b is the longest among all workpieces in that batch;

[0046] Constraint 19: That is, the start time of batch b must not be earlier than the completion time of all workpieces in that batch in stage 1;

[0047] Constraint 20: That is, ensure that the start time of the next batch on batch processing machine i does not exceed the completion time of the previous batch;

[0048] Constraint 21: That is: define the completion time of each batch on batch processing machine i;

[0049] Constraints 22 and 23: and That is: ensure that the processing of batch b on batch processing machine i is not interrupted;

[0050] Constraint 24: That is, ensure that batch processing machine i can only be in one of three states during time period t: processing, idle, or off;

[0051] Constraints 25 and 26: and That is: the idle state of batch processing machine i in time period t of stage 2 is defined. If machine i is idle in time period t, then at least one time period from time period 1 to t-1 and time period t+1 to T is in the processing state; otherwise, the batch processing machine is shut down.

[0052] Constraints 27 and 28:

[0053] and That is, the idle state of batch processing machine i in time period t of phase 2 is defined. If batch processing machine i is shut down in time period t, it cannot process any workpieces in time period from t+1 to T. This means that once the machine is shut down, it will not be restarted.

[0054] Constraint 29: That is, ensure that the processing time for all batches does not exceed the maximum completion time;

[0055] 42) Minimize the maximum completion time C max With the total energy consumption TEC as the target, a multi-objective hybrid flow workshop energy-saving scheduling scenario with parallel batch processing machine is constructed using Equation (4);

[0056]

[0057] In equation (4), f1 represents the first target value, and f2 represents the second target value; let the two-dimensional space where the first target value f1 and the second target value f2 are distributed be the target space; a ij This indicates that if workpiece j is assigned to machine i in stage 1, then π is 1; otherwise, it is 0. ij This indicates the qualification assessment of the machine in stage 1. If workpiece j is processed on machine i in stage 1, it is 1; otherwise, it is 0. ijt The value is 1 if workpiece j is processed on machine i during time period t, and 0 otherwise; L represents a positive number, an auxiliary variable. and These represent the processing time and completion time of workpiece j in stage 1, respectively. and α represents the auxiliary variables for stage 1 and stage 2 respectively; b represents the batch index; α represents the total number of batches; a ibj This indicates that if workpiece j is assigned to the b-th batch of batch processor i in stage 2, the value is 1; otherwise, it is 0. j Q represents the size of workpiece j; Q represents the capacity of the batch processor in stage 2; y b This indicates that if the b-th batch includes at least one workpiece, the value is 1; otherwise, it is 0. This indicates that at time t, if batch b is processed on machine i, then it is 1; otherwise, it is 0. This indicates the processing time of workpiece j in stage 2; and and These represent the start time, processing time, and completion time of batch b in stage 2 on batch processor i, respectively.

[0058] The generation of the energy-saving scheduling scheme for the hybrid flow workshop includes the following steps:

[0059] 51) Based on the energy-saving scheduling scenario of a hybrid flow workshop, define and initialize the current generation t = 0, and let the population of generation t be denoted as P. t Set the population size to N, the reference vector set to V, and the maximum number of iterations to t. max The reference vector set V is a uniformly distributed set of reference vectors, and the number of reference vectors in V is less than or equal to N.

[0060] 52) The population is initialized using heuristic rules, and a two-part encoding is used to represent chromosomes, including machine selection sequences and workpiece sequences, to generate N individuals, thus obtaining the 0th generation population.

[0061] Heuristic rules include Johnson's rule, shortest processing time priority, longest processing time priority, and random rules;

[0062] The encoding method uses a two-segment structure, consisting of a workpiece sequence vector and a machine selection vector. Each segment consists of two parts: the workpiece and machine vectors for stage 1 and stage 2. The elements in the workpiece sequence vector represent the workpiece number, which determines the processing order of all workpieces on the machine in each stage. The elements in the machine selection vector represent the machine number selected for the corresponding process.

[0063] 53) Initialize a set R, which will be used as the non-dominated solution set;

[0064] 54) Obtain the population P of generation t. t All non-dominated individuals are added to set R;

[0065] Among them, any two individuals and Their target vectors are respectively represented as and If individual Pareto Dominant Individuals There are exactly two possibilities:

[0066] (1) and

[0067] (2) and

[0068] If individual An individual is not Pareto-dominated by any other individual. As a non-dominant individual;

[0069] 55) According to equation (5), the population P of generation t is... t The two objective values ​​of all individuals are normalized to obtain the normalized population of generation t. in, P′ represents the population of generation t after normalization. t The γth individual; the γth individual after normalization The two target values ​​are denoted as and The normalized γth individual Target vector Recorded as The sets of maximum and minimum values ​​for each objective value in generation t are respectively represented as: and

[0070]

[0071] 56) Divide the subpopulations and calculate the population P′ of the t-th generation after normalization in the target space according to equation (6). t The γth individual Target vector The reference vector V corresponding to the subpopulation s in the reference vector set V s The cosine value of the included angle The normalized population P′ of generation t t The γth individual The vector is assigned to the subpopulation of the reference vector with the smallest cosine value, thus normalizing the population P′ of generation t. t Divided into S subpopulations Where S is the number of subpopulations, s represents the index of the subpopulation, and the size of S is equal to the number of vectors in the reference vector set V;

[0072]

[0073] In equation (6), P′ represents the population of generation t after normalization. t The γth individual Target vector The modulus length; |V s | represents the reference vector V corresponding to the s-th subpopulation. s The modulus length;

[0074] 57) Calculate the cumulative new solution contribution value g(t) for the first t generations using individuals from the same subpopulation for cooperative pairing according to equation (7).

[0075]

[0076] Where: n1(t) represents the number of times individuals from the same subpopulation are used to generate offspring solutions through cooperative pairing in the first t generations, and n2(t) represents the number of times different populations are used to generate offspring solutions through cooperative pairing in the first t generations;

[0077] When traversing all individuals in the entire population, cooperative pairing within the same subpopulation selects only the current individual. Subgroup For other individuals, the cooperative pairing of different subpopulations selects individuals that do not contain the current individual. subpopulation Individuals are paired up;

[0078] 58) Calculate the selection probability p of the same-child population in the (t+1)th generation. t+1 If the value of g(t) is less than or equal to 0.2*t max Then p t+1 =p rmin If the value of g(t) is greater than or equal to 0.8*t max , will p t+1 =p rmax Otherwise, update p according to equation (8). t+1 The value;

[0079]

[0080] in: and The optimal value was determined based on the Taguchi experiment.

[0081] 59) For the current individual Select a pairing individual Generate a random number rd. If rd is less than p... t In the current individual Subgroup Randomly select another individual Otherwise, without the current individual subpopulation Randomly select an individual

[0082] 510) For the current individual The individuals selected in the above steps As two parents, the position-based crossover method PBX is used to perform crossover operations to generate the (t+1)th generation individuals.

[0083] The location-based crossover method operates as follows:

[0084] For two individuals, denoted as the parent individuals, a binary string of the same length as the chromosome of the processing order is first generated. The chromosome gene corresponding to the value at the specified position in the binary string is retained, along with the chromosome gene of the processing order and the machine-selected chromosome gene at the corresponding position. The remaining genes are placed into the newly generated offspring according to the order of the other chromosome, thus generating two offspring solutions. Two target values ​​for the two offspring solutions are then calculated, and the individual with the non-dominated solution is retained, denoted as... Proceed to the next mutation operation;

[0085] 511) Individuals retained by the crossover operation Perform a mutation operation, using positional mutation, and output the mutated individual of generation t+1.

[0086] Among them: the position variation step refers to two-stage variation, in which one workpiece number is randomly selected in each of the two stages, and the processing machine of the current workpiece is changed to another qualified processing machine.

[0087] 512) The x-axis is C max The target space with TEC as the vertical axis is evenly divided into three parts, which are denoted as Region I, Region II, and Region III from top to bottom;

[0088] 513) The mutated individuals Individuals are obtained by performing a local search in a region. First, determine the individual. The solution belongs to the region. If it belongs to region I, the LS2 search operator is used to reduce the total energy consumption; if it belongs to region III, the LS1 search operator is used to shorten the total completion time; if it belongs to region II, a random number rd is generated to select either the LS1 or LS2 search operator, and each operator has the same probability of being selected.

[0089] The two search operators are: the first search operator, denoted as LS1, reduces the total completion time by randomly changing the machine selection of the workpiece on the critical path; the second search operator, denoted as LS2, reduces the total energy consumption by adjusting the workpiece to be processed on a low-energy machine.

[0090] 514) Based on the characteristics of time-of-use pricing, the individual data after the regional search is... Make adjustments;

[0091] The adjustment strategy for time-of-use electricity pricing is based on the characteristics of time-of-use pricing. Firstly, without changing the maximum completion time, the start time of the workpiece is adjusted from the end to the beginning, moving the workpiece from a high-energy-consumption time to a low-energy-consumption time, thereby reducing total energy consumption. Secondly, with the maximum completion time increased, since the electricity price function is a periodic function (let's assume the increase time is one period of the electricity price function), the start time of the workpiece is adjusted from the end to the beginning, moving the workpiece from a high-energy-consumption time to a low-energy-consumption time, thereby reducing total energy consumption.

[0092] 515) Obtain the population P of generation t+1. t+1 All non-dominated individuals are selected and added to set R, while dominated individuals in set R are removed.

[0093] 516) If t = t max If the output is stored in set R, then all non-dominated individuals are stored in set R as a set of production and processing schemes. Otherwise, assign t+1 to t and return to step 55). Set R is the optimal scheduling scheme set, where each individual represents a feasible scheduling scheme.

[0094] 517) Select a solution from set R that meets the actual requirements and process the set of workpieces Ω to be processed; wherein: the solution that meets the actual requirements includes: the efficiency-first solution, the profit-first solution, and the efficiency-profit trade-off solution.

[0095] Beneficial effects

[0096] The present invention provides an energy-saving scheduling method for hybrid pipeline workshops for parallel batch processing machines. Compared with the prior art, this method coordinates multiple populations and introduces an adaptive mechanism to fully utilize the useful information in the distribution characteristics of the solution to guide the search direction. Even in complex scenarios, it can efficiently obtain the optimal scheduling strategy that meets multiple objectives.

[0097] This method employs a solution distribution feature to design an adaptive subpopulation cooperative search strategy. It uses adaptive learning based on differences within and outside the subpopulation to guide the generation of offspring individuals, thereby guiding the evolutionary direction of the population. Furthermore, it utilizes regional local search and adjustments based on time-of-use electricity pricing characteristics to further improve the quality of individuals, thus obtaining a more comprehensive and superior generation and processing scheme.

[0098] The present invention also has the following advantages:

[0099] 1. This invention addresses the actual production conditions of hybrid assembly line workshops containing parallel batch processors. Considering factors such as machine eligibility, machine status, different energy consumption rates, and time-of-use electricity pricing, it establishes a multi-objective optimization model aimed at minimizing total energy cost and maximizing completion time. This model is solved using an adaptive multi-population co-evolutionary algorithm, generating a set of optional production and processing schemes with short processing times and low energy consumption. This provides enterprise managers with a decision-making basis to improve the production efficiency and reduce energy consumption of hybrid assembly line workshops.

[0100] 2. In the adaptive multi-population co-evolutionary algorithm, this invention designs a dynamic cooperative search strategy based on population distribution characteristics. This strategy achieves targeted searching by coordinating information exchange between different subpopulations. Simultaneously, this strategy employs different selection probabilities at different evolutionary stages of the algorithm to balance global exploration and local exploitation, ensuring a balance between exploration and exploitation throughout the entire evolutionary process.

[0101] 3. This invention divides the search space into three regions based on the location characteristics of the solutions and designs two corresponding local optimization operators. The algorithm can adaptively select the local optimization operator according to the region where the solution is located. This improves the overall convergence of the algorithm and obtains a better solution.

[0102] 4. This invention considers the characteristics of time-of-use electricity pricing and proposes two adjustment strategies. These two strategies reduce total energy consumption by adjusting the processing time sequence of workpieces, shifting processing during high-energy-consuming periods to low-energy-consuming periods. This allows the algorithm to obtain a more optimized processing scheme while meeting the constraint of maximum completion time. Attached Figure Description

[0103] Figure 1 This is a sequence diagram of the method of the present invention;

[0104] Figure 2 This is a flowchart of the adaptive multi-population cooperative evolution algorithm involved in this invention. Detailed Implementation

[0105] To provide a better understanding of the structural features and effects achieved by the present invention, a detailed description is provided below, accompanied by preferred embodiments and accompanying drawings:

[0106] like Figure 1 As shown, the present invention provides an energy-saving scheduling method for a hybrid pipeline workshop using a parallel batch processing machine, comprising the following steps:

[0107] The first step is to set up the working state of the mixed production line workshop: set up the parallel batch processing mechanism and the set of workpieces to be processed.

[0108] (1) Set up a parallel batch processing mechanism: The parallel batch processing mechanism processes each workpiece through two sequential processing stages, and only enters the second stage after the first stage is completed.

[0109] The first stage includes qualified parallel machines, and the second stage consists of parallel batch processing machines. In the first stage, machine qualification restrictions must be followed, and workpieces are only allowed to be processed on qualified machines. The second stage consists of multiple energy-intensive batch processing furnaces, each of which processes multiple workpieces simultaneously within its capacity. The first stage machines take qualification constraints into account, meaning that not all machines can process every workpiece. Machine processing qualifications are preset proportionally. Machines have three states: processing, idle, and off. The energy consumption of each state is different, and the size of each workpiece varies. All workpieces are ready at the initial time point.

[0110] (2) Based on actual production and processing needs, construct the workpiece set Ω as shown in equation (1).

[0111] Ω= {J1,J2,…,J j ,…,J n} (1)

[0112] In equation (1), j represents the index of the workpiece in the workpiece set Ω; n represents the total number of workpieces in the workpiece set Ω.

[0113] The second step is to calculate the maximum completion time and total energy consumption for constructing the set of workpieces to be processed.

[0114] The maximum completion time C of the set of workpieces to be processed Ω is constructed using equations (2) and (3) respectively. max Total Energy Consumption (TEC)

[0115]

[0116]

[0117] In equations (2) and (3), j represents the index of the workpiece; C j J represents the j-th workpiece. j The processing time is denoted by i; i represents the machine index; m1 and m2 represent the total number of machines in stage 1 and stage 2, respectively; T represents the total time period; f(t) represents the unit energy price within time period t.

[0118] and These represent the processing states of machines in stages 1 and 2, respectively. If machine i is in a processing state at time t, the value is 1; otherwise, it is 0.

[0119] and These represent the idle states of machines in phase 1 and phase 2, respectively. If machine i is idle at time t, the value is 1; otherwise, it is 0.

[0120] and These represent the shutdown states of machines in phase 1 and phase 2, respectively. If machine i is in the shutdown state at time t, the value is 1; otherwise, it is 0.

[0121] and These represent the processing energy consumption rate of machine i in stage 1 and stage 2, respectively;

[0122] and These represent the idle energy consumption rate of machine i in phase 1 and phase 2, respectively.

[0123] and These represent the power consumption rate of machine i during shutdown in phase 1 and phase 2, respectively.

[0124] The third step is to construct an energy-saving scheduling scenario for a hybrid production line workshop with multiple objectives and a parallel batch processing machine: Based on the actual production situation, set constraints to construct an energy-saving scheduling scenario for a hybrid production line workshop with multiple objectives and a parallel batch processing machine.

[0125] (1) Set the constraints as follows:

[0126] Constraint 1: That is, ensure that each workpiece j is processed on only one machine i in stage 1;

[0127] Constraint 2: a ij <<π ij That is, it is used for machine qualification assessment. If workpiece j cannot be processed on machine i in stage 1, it will not be assigned to that machine.

[0128] Constraint 3: a ij >>p ijt That is, if workpiece j is not assigned to machine i in stage 1, then the workpiece will not be processed on that machine at any time period t.

[0129] Constraint 4: That is: if workpiece j is assigned to machine i in stage 1, then machine i will be processing workpiece j for at least one time period t.

[0130] Constraints 5 and 6: and That is, ensure that the processing of workpiece j is not interrupted and that the workpiece cannot be preempted;

[0131] Constraint 7: That is, it is guaranteed that during phase 1, machine i can only be in one of three states during time period t: processing, idle, or off;

[0132] Constraint 8: That is: define the processing state of machine i during time period t in stage 1;

[0133] Constraints 9 and 10: and That is: Define the idle state of machine i in time period t of stage 1. If machine i is in an idle state in time period t, then at least one time period from time period 1 to t-1 and time period t+1 to T is in a processing state; otherwise, the machine is shut down.

[0134] Constraint 11 and Constraint 12:

[0135] and That is, the shutdown state of machine i in time period t of phase 1 is defined. If machine i is shut down in time period t, it cannot process any workpieces in time period from t+1 to T. This means that once the machine is shut down, it will not be restarted.

[0136] Constraint 13: That is, to ensure that any workpiece can only be processed in one batch on one batch processing machine in stage 2;

[0137] Constraint 14: That is, ensure that the size of the batch b formed does not exceed the capacity Q of the batch processing machine;

[0138] Constraint 15: y b >>y b+1 That is, it excludes the situation where batch b+1 is formed but batch b is not formed, that is, it does not allow empty batches in the middle;

[0139] Constraint 16: That is, if there are no workpieces in the current batch, the processing time for the current batch is 0.

[0140] Constraint 17: That is: if batch processing machine i is in a processing state during time period t in stage 2, then batch processing machine i will process one batch during time period t.

[0141] Constraint 18: That is, ensure that the processing time of batch b is the longest among all workpieces in that batch;

[0142] Constraint 19: That is, the start time of batch b must not be earlier than the completion time of all workpieces in that batch in stage 1;

[0143] Constraint 20: That is, ensure that the start time of the next batch on batch processing machine i does not exceed the completion time of the previous batch;

[0144] Constraint 21: That is: define the completion time of each batch on batch processing machine i;

[0145] Constraints 22 and 23: and That is: ensure that the processing of batch b on batch processing machine i is not interrupted;

[0146] Constraint 24: That is, ensure that batch processing machine i can only be in one of three states during time period t: processing, idle, or off;

[0147] Constraints 25 and 26: and That is: the idle state of batch processing machine i in time period t of stage 2 is defined. If machine i is idle in time period t, then at least one time period from time period 1 to t-1 and time period t+1 to T is in the processing state; otherwise, the batch processing machine is shut down.

[0148] Constraints 27 and 28:

[0149] and That is, the idle state of batch processing machine i in time period t of phase 2 is defined. If batch processing machine i is shut down in time period t, it cannot process any workpieces in time period from t+1 to T. This means that once the machine is shut down, it will not be restarted.

[0150] Constraint 29: That is, ensure that the processing time for all batches does not exceed the maximum completion time.

[0151] (2) Minimize the maximum completion time C max With the total energy consumption TEC as the target, a multi-objective hybrid flow workshop energy-saving scheduling scenario with parallel batch processing machine is constructed using Equation (4);

[0152]

[0153] In equation (4), f1 represents the first target value, and f2 represents the second target value; let the two-dimensional space where the first target value f1 and the second target value f2 are distributed be the target space; a ij This indicates that if workpiece j is assigned to machine i in stage 1, then π is 1; otherwise, it is 0. ij This indicates the qualification assessment for Stage 1. A value of 1 indicates that workpiece j can be processed on machine i in Stage 1; otherwise, a value of 0 indicates that it is not. ijt The value is 1 if workpiece j is processed on machine i during time period t, and 0 otherwise; L represents a positive number, an auxiliary variable. and These represent the processing time and completion time of workpiece j in stage 1, respectively. and α represents the auxiliary variables for stage 1 and stage 2 respectively; b represents the batch index; α represents the total number of batches; a ibj This indicates that if workpiece j is assigned to the b-th batch of batch processor i in stage 2, the value is 1; otherwise, it is 0. j Q represents the size of workpiece j; Q represents the capacity of the batch processor in stage 2; y b This indicates that if the b-th batch includes at least one workpiece, the value is 1; otherwise, it is 0. This indicates that at time t, if batch b is processed on machine i, then it is 1; otherwise, it is 0. This indicates the processing time of workpiece j in stage 2; and and These represent the start time, processing time, and completion time of batch b in stage 2 on batch processor i, respectively.

[0154] The fourth step is to generate an energy-saving scheduling scheme for the hybrid assembly line workshop: Based on the set of workpieces to be processed, an adaptive multi-population cooperative evolution algorithm is used to solve the energy-saving scheduling scenario of the hybrid assembly line workshop with parallel batch processing machines and a set of production and processing schemes are obtained, namely, the energy-saving scheduling scheme for the hybrid assembly line workshop.

[0155] Here, an adaptive collaborative search strategy is adopted to balance the global exploration and local development of the algorithm, ensuring the efficiency of the entire search process; local search operators for different solution distribution regions are designed to improve the convergence of the algorithm and obtain better solutions; at the same time, the time-of-use electricity price factor is considered to shift the processing of high-energy-consuming time to low-energy-consuming time, thereby reducing the total energy consumption.

[0156] like Figure 2 As shown, the generation of an energy-saving scheduling scheme for a hybrid flow workshop includes the following steps:

[0157] (1) Based on the energy-saving scheduling scenario of a hybrid flow workshop, define and initialize the current generation t=0, and let the population of generation t be denoted as P. t Set the population size to N, the reference vector set to V, and the maximum number of iterations to t. max The reference vector set V is a uniformly distributed set of reference vectors, and the number of reference vectors in V is less than or equal to N.

[0158] (2) The population is initialized using heuristic rules, and a two-part encoding is used to represent chromosomes, including machine selection sequences and workpiece sequences, to generate N individuals, thus obtaining the 0th generation population.

[0159] Heuristic rules include Johnson's rule, shortest processing time priority, longest processing time priority, and random rules;

[0160] The encoding method uses a two-segment structure, consisting of a workpiece sequence vector and a machine selection vector. Each segment consists of two parts: the workpiece and machine vectors for stage 1 and stage 2. The elements in the workpiece sequence vector represent the workpiece number, which determines the processing order of all workpieces on the machine in each stage. The elements in the machine selection vector represent the machine number selected for the corresponding process.

[0161] (3) Initialize a set R, which will be used as the non-dominated solution set;

[0162] (4) Obtain the population P of generation t t All non-dominated individuals are added to set R;

[0163] Among them, any two individuals and Their target vectors are respectively represented as and If individual Pareto Dominant Individuals There are exactly two possibilities:

[0164] and

[0165] and

[0166] If individual An individual is not Pareto-dominated by any other individual. As a non-dominant individual;

[0167] (5) According to equation (5), the population P of generation t is processed. t The two objective values ​​of all individuals are normalized to obtain the normalized population of generation t. in, P′ represents the population of generation t after normalization. t The γth individual; the γth individual after normalization The two target values ​​are denoted as and The normalized γth individual Target vector Recorded as The sets of maximum and minimum values ​​for each objective value in generation t are respectively represented as: and

[0168]

[0169] (6) Divide the subpopulations and calculate the population P′ of the t-th generation after normalization in the target space according to equation (6). t The γth individual Target vector The reference vector V corresponding to the subpopulation s in the reference vector set V s The cosine value of the included angle The normalized population P′ of generation t t The γth individual The vector is assigned to the subpopulation of the reference vector with the smallest cosine value, thus normalizing the population P′ of generation t. t Divided into S subpopulations Where S is the number of subpopulations, s represents the index of the subpopulation, and the size of S is equal to the number of vectors in the reference vector set V;

[0170]

[0171] In equation (6), P′ represents the population of generation t after normalization. t The γth individual Target vector The modulus length; |V s | represents the reference vector V corresponding to the s-th subpopulation. s The modulus length;

[0172] (7) Calculate the cumulative new solution contribution value g(t) for the first t generations of cooperative pairing using individuals from the same subpopulation according to equation (7).

[0173]

[0174] Where: n1(t) represents the number of times individuals from the same subpopulation are used to generate offspring solutions through cooperative pairing in the first t generations, and n2(t) represents the number of times different populations are used to generate offspring solutions through cooperative pairing in the first t generations;

[0175] When traversing all individuals in the entire population, cooperative pairing within the same subpopulation selects only the current individual. Subgroup For other individuals, the cooperative pairing of different subpopulations selects individuals that do not contain the current individual. subpopulation Individuals are paired up;

[0176] (8) Calculate the selection probability p of the same-child population in the (t+1)th generation. t+1 If the value of g(t) is less than or equal to 0.2*t max Then p t+1 =p rmin If the value of g(t) is greater than or equal to 0.8*t max , will p t+1 =p rmax Otherwise, update p according to equation (8). t+1 The value;

[0177]

[0178] in: and The optimal value was determined based on the Taguchi experiment.

[0179] (9) For the current individual Select a pairing individual Generate a random number rd. If rd is less than p... t In the current individual Subgroup Randomly select another individual Otherwise, without the current individual subpopulation Randomly select an individual

[0180] (10) For the current individual The individuals selected in the above steps As two parents, the position-based crossover method PBX is used to perform crossover operations to generate the (t+1)th generation individuals.

[0181] The location-based crossover method operates as follows:

[0182] For two individuals, denoted as the parent individuals, a binary string of the same length as the chromosome of the processing order is first generated. The chromosome gene corresponding to the value at the specified position in the binary string is retained, along with the chromosome gene of the processing order and the machine-selected chromosome gene at the corresponding position. The remaining genes are placed into the newly generated offspring according to the order of the other chromosome, thus generating two offspring solutions. Two target values ​​for the two offspring solutions are then calculated, and the individual with the non-dominated solution is retained, denoted as... Proceed to the next mutation operation;

[0183] (11) Individuals retained by the crossover operation Perform a mutation operation, using positional mutation, and output the mutated individual of generation t+1.

[0184] Among them: the position variation step refers to two-stage variation, in which one workpiece number is randomly selected in each of the two stages, and the processing machine of the current workpiece is changed to another qualified processing machine.

[0185] (12) With C as the x-axis max The target space with TEC as the vertical axis is evenly divided into three parts, which are denoted as Region I, Region II, and Region III from top to bottom;

[0186] (13) The mutated individuals Individuals are obtained by performing a local search in a region. First, determine the individual. The solution belongs to the region. If it belongs to region I, the LS2 search operator is used to reduce the total energy consumption; if it belongs to region III, the LS1 search operator is used to shorten the total completion time; if it belongs to region II, a random number rd is generated to select either the LS1 or LS2 search operator, and each operator has the same probability of being selected.

[0187] The two search operators are: the first search operator, denoted as LS1, reduces the total completion time by randomly changing the machine selection of the workpiece on the critical path; the second search operator, denoted as LS2, reduces the total energy consumption by adjusting the workpiece to be processed on a low-energy machine.

[0188] (14) Based on the characteristics of time-of-use pricing, the individuals after the regional search are... Make adjustments;

[0189] The adjustment strategy for time-of-use electricity pricing is based on the characteristics of time-of-use pricing. Firstly, without changing the maximum completion time, the start time of the workpiece is adjusted from the end to the beginning, moving the workpiece from a high-energy-consumption time to a low-energy-consumption time, thereby reducing total energy consumption. Secondly, with the maximum completion time increased, since the electricity price function is a periodic function (let's assume the increase time is one period of the electricity price function), the start time of the workpiece is adjusted from the end to the beginning, moving the workpiece from a high-energy-consumption time to a low-energy-consumption time, thereby reducing total energy consumption.

[0190] (15) Obtain the population P of generation t+1. t+1 All non-dominated individuals are selected and added to set R, while dominated individuals in set R are removed.

[0191] (16) If t = t max If the output is stored in set R, then all non-dominated individuals are stored in set R as a set of production and processing schemes. Otherwise, assign t+1 to t and return to step 55). Set R is the optimal scheduling scheme set, where each individual represents a feasible scheduling scheme.

[0192] (17) Select a solution from set R that meets the actual requirements and process the set of workpieces Ω to be processed; where: the solutions that meet the actual requirements include: the efficiency-first solution, the profit-first solution, and the efficiency-profit compromise solution.

[0193] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A hybrid pipeline workshop energy-saving scheduling method for parallel batch processing machines, characterized in that, Includes the following steps: 11) Setting up the working state of the mixed flow workshop: setting up the parallel batch processing mechanism and the set of workpieces to be processed; Setting the working status of the mixed flow workshop includes the following steps: 111) Set up a parallel batch processing mechanism: The parallel batch processing mechanism processes each workpiece through two sequential processing stages, and only enters stage 2 after stage 1 is completed; Phase 1 consists of qualified parallel machines, while Phase 2 consists of parallel batch processing machines. In Phase 1, machine qualification restrictions must be followed, and workpieces are only allowed to be processed on qualified machines. Phase 2 consists of multiple energy-intensive batch processing furnaces, each of which processes multiple workpieces simultaneously within its capacity. In Phase 1, the machines take qualification constraints into account, meaning that not all machines can process every workpiece. Machine processing qualifications are preset proportionally, and machines have three states: processing, idle, and off. The energy consumption of each state is different, and the size of each workpiece varies. All workpieces are ready at the initial time point. 112) Based on actual production and processing needs, construct a set of workpieces to be processed as shown in equation (1). , In equation (1), j represents the workpiece in the set of workpieces to be processed. Index in; Represents the set of workpieces to be processed The j-th workpiece; n represents the set of workpieces to be processed. Total number of workpieces in the process; 12) Calculate the maximum completion time and total energy consumption for constructing the set of workpieces to be processed; 13) Construct an energy-saving scheduling scenario for a hybrid production line workshop with multiple objectives and a parallel batch processing machine: Set constraints based on actual production conditions and construct an energy-saving scheduling scenario for a hybrid production line workshop with multiple objectives and a parallel batch processing machine; 14) Generation of energy-saving scheduling scheme for hybrid assembly line workshop: Based on the set of workpieces to be processed, the adaptive multi-population cooperative evolution algorithm is used to solve the energy-saving scheduling scenario of hybrid assembly line workshop with parallel batch processing machine, and a set of production and processing schemes are obtained, namely the energy-saving scheduling scheme for hybrid assembly line workshop. The construction of a multi-objective hybrid pipeline workshop energy-saving scheduling scenario with parallel batch processing machines includes the following steps: 141) Set the constraints as follows: Constraint 1: That is, ensure that each workpiece j is processed on only one machine i in stage 1; Constraint 2: That is, it is used for machine qualification assessment. If workpiece j cannot be processed on machine i in stage 1, it will not be assigned to that machine. Constraint 3: That is, if workpiece j is not assigned to machine i in stage 1, then the workpiece will not be processed on that machine at any time period t. Constraint 4: That is: if workpiece j is assigned to machine i in stage 1, then machine i will be processing workpiece j for at least one time period t. Constraints 5 and 6: and That is, to ensure that the processing of workpiece j is not interrupted and that the workpiece cannot be preempted; Constraint 7: That is, it is guaranteed that during phase 1, machine i can only be in one of three states during time period t: processing, idle, or off; Constraint 8: That is, define the processing state of machine i during time period t in stage 1; Constraints 9 and 10: and That is: define the idle state of machine i in time period t of stage 1. If machine i is in the idle state in time period t, then at least one time period from time period 1 to t-1 and time period t+1 to T is in the processing state; otherwise, the machine is shut down. Constraint 11 and Constraint 12: and That is, it defines the shutdown state of machine i in time period t of phase 1. If machine i is shut down in time period t, it cannot process any workpieces in time period from t+1 to T. This means that once the machine is shut down, it will not be restarted. Constraint 13: That is, to ensure that any workpiece can only be processed in one batch on one batch processing machine in stage 2; Constraint 14: That is, to ensure that the size of the batch b formed does not exceed the capacity Q of the batch processing machine; Constraint 15: That is, it excludes the situation where batch b + 1 is formed but batch b is not formed, i.e., empty batches in the middle are not allowed; Constraint 16: That is, if there are no workpieces in the current batch, the processing time for the current batch is 0. Constraint 17: That is, if batch processing machine i is in a processing state during time period t in stage 2, then batch processing machine i will process one batch during time period t. Constraint 18: That is, to ensure that the processing time of batch b is the longest processing time among all workpieces in that batch; Constraint 19: That is, the start time of batch b is required to be no earlier than the completion time of all workpieces in that batch in stage 1; Constraint 20: That is, to ensure that the start time of the next batch on batch processing machine i does not exceed the completion time of the previous batch; Constraint 21: That is, define the completion time of each batch on batch processing machine i; Constraints 22 and 23: and That is, to ensure that the processing of batch b on batch processing machine i is not interrupted; Constraint 24: That is, to ensure that batch processing machine i can only be in one of three states during time period t: processing, idle or off; Constraints 25 and 26: and That is, the idle state of batch processing machine i in time period t of stage 2 is defined. If machine i is idle in time period t, then at least one time period from time period 1 to t-1 and time period t+1 to T is in processing state; otherwise, the batch processing machine is shut down. Constraints 27 and 28: and That is, it defines the idle state of batch processing machine i in time period t of phase 2. If batch processing machine i is shut down in time period t, it cannot process any workpieces in time period from t + 1 to T. This means that once the machine is shut down, it will not be restarted. Constraint 29: That is, to ensure that the processing time of all batches does not exceed the maximum completion time; 142) To minimize the maximum completion time Total energy consumption To achieve the goal, a multi-objective hybrid flow workshop energy-saving scheduling scenario with a parallel batch processing machine is constructed using equation (4), as follows: （4） In equation (4), This represents the first target value. Let the second objective value be denoted; let the first objective value be denoted. Second target value The distributed two-dimensional space is the target space; This indicates that if workpiece j is assigned to machine i in stage 1, then it is 1; otherwise, it is 0. This indicates the qualification assessment of the machine in stage 1. If workpiece j is processed on machine i in stage 1, it is 1; otherwise, it is 0. The value is 1 if workpiece j is processed on machine i during time period t, and 0 otherwise; L represents a positive number, an auxiliary variable. and These represent the processing time and completion time of workpiece j in stage 1, respectively. and ... Indicates the total number of batches; This indicates that if workpiece j is assigned to the bth batch of batch processor i in stage 2, it is 1; otherwise, it is 0. Indicates the dimension of workpiece j; This indicates the capacity of the batch processing machine in stage 2; This indicates that if the b-th batch includes at least one workpiece, the value is 1; otherwise, it is 0. This indicates that at time t, if batch b is processed on machine i, then it is 1; otherwise, it is 0. This indicates the processing time of workpiece j in stage 2; and and These represent the start time, processing time, and completion time of batch b in stage 2 on batch processor i, respectively.

2. The energy-saving scheduling method for a hybrid pipeline workshop using a parallel batch processing machine according to claim 1, characterized in that, The method for calculating the maximum completion time and total energy consumption for constructing the set of workpieces to be processed is as follows: The sets of workpieces to be processed are constructed using equations (2) and (3) respectively. Maximum completion time Total energy consumption , ， In equations (2) and (3), j represents the index of the workpiece; Represents the j-th workpiece The time it takes for the processing to be completed; i represents the machine index; and These represent the total number of machines in Phase 1 and Phase 2, respectively; T represents the total time period. This represents the unit energy price within time period t; and These represent the processing states of machines in stages 1 and 2, respectively. If machine i is in a processing state at time t, the value is 1; otherwise, it is 0. and These represent the idle states of machines in phase 1 and phase 2, respectively. If machine i is idle at time t, the value is 1; otherwise, it is 0. and These represent the shutdown states of machines in phase 1 and phase 2, respectively. If machine i is in the shutdown state at time t, the value is 1; otherwise, it is 0. and These represent the processing energy consumption rate of machine i in stage 1 and stage 2, respectively; and These represent the idle energy consumption rate of machine i in phase 1 and phase 2, respectively. and These represent the power consumption rate of machine i during shutdown in phase 1 and phase 2, respectively.

3. The energy-saving scheduling method for a hybrid pipeline workshop using a parallel batch processing machine according to claim 1, characterized in that, The generation of the energy-saving scheduling scheme for the hybrid flow workshop includes the following steps: 31) Based on the energy-saving scheduling scenario of a hybrid flow workshop, define and initialize the current algebra. = 0, let the first Generation population is recorded as Set the population size to The reference vector set is and the maximum number of iterations ;wherein the reference vector set A uniformly distributed reference vector set is used. The number is less than or equal to N; 32) The population is initialized using heuristic rules, and a two-part encoding is used to represent chromosomes, including machine selection sequences and workpiece sequences, to generate N individuals, thus obtaining the 0th generation population. = , t = 0; Heuristic rules include Johnson's rule, shortest processing time priority, longest processing time priority, and random rules; The encoding method uses a two-segment structure, consisting of a workpiece sequence vector and a machine selection vector. Each segment consists of two parts: the workpiece and machine vectors for stage 1 and stage 2. The elements in the workpiece sequence vector represent the workpiece number, which determines the processing order of all workpieces on the machine in each stage. The elements in the machine selection vector represent the machine number selected for the corresponding process. 33) Initialize a collection Used as a non-dominated solution set; 34) Obtain the t-th generation population All non-dominated individuals are added to the set. middle; Among them, any two individuals and Their target vectors are respectively represented as ( )and( If an individual Pareto Dominant Individuals There are exactly two possibilities: (1) ,and ; (2) ,and ; If individual An individual is not Pareto-dominated by any other individual. As a non-dominant individual; 35) According to formula (5), the first Generation population The two objective values ​​of all individuals are normalized to obtain the normalized population of generation t. ;in, Indicates the normalized i-th Generation population The Individual; the normalized i-th individual The two target values ​​are denoted as and ; after normalization, the first individual Target vector Recorded as The sets of maximum and minimum values ​​for each objective value in generation t are respectively represented as: and ; ； 36) Divide into subpopulations, and calculate the number of subpopulations after normalization in the target space according to equation (6). Generation population The Middle individual Target vector With reference vector set Reference vector corresponding to neutron population s The cosine value of the included angle And the normalized first Generation population The Middle individual The vector is assigned to the subpopulation of the reference vector with the smallest cosine value, thus normalizing the i-th... Generation population Divided into S subpopulations , where S is the number of subpopulations, s represents the index of the subpopulation, and the size of S is equal to the number of vectors in the reference vector set V; ， In equation (6), Indicates the normalized i-th Generation population The Middle individual Target vector The modulus length; Represents the reference vector corresponding to the s-th subpopulation. The modulus length; 37) Calculate the cumulative new solution contribution value of individuals from the same subpopulation for the first t generations using equation (7) for cooperative pairing. , ， in: This represents the number of times individuals from the same subpopulation were used to collaboratively pair up and generate offspring solutions in the first t generations. This represents the number of times that different populations cooperated to generate offspring solutions in the first t generations; When traversing all individuals in the entire population, cooperative pairing within the same subpopulation selects only the current individual. Subgroup For other individuals, the cooperative pairing of different subpopulations selects individuals that do not contain the current individual. subpopulation Individuals are paired up; 38) Calculate the selection probability of same-child population in generation t+1. ;if The value is less than or equal to Then ;if The value is greater than or equal to ,Will Otherwise, update according to formula (8). The value; ， in: and The optimal value was determined based on the Taguchi experiment. 39) For the current individual Select a pairing individual Generate a random number ,if Less than In the current individual Subgroup Randomly select another individual Otherwise, without the current individual subpopulation Randomly select an individual ; 310) For the current individual The individuals selected in the above steps As two parent generations, the position-based crossover method PBX is used to perform crossover operations to generate the (t+1)th generation individuals. ; The location-based crossover method operates as follows: For two individuals, denoted as the parent individuals, a binary string of the same length as the chromosome of the processing order is first generated. The chromosome gene corresponding to the value at the specified position in the binary string is retained, along with the chromosome gene of the processing order and the machine-selected chromosome gene at the corresponding position. The remaining genes are placed into the newly generated offspring according to the order of the other chromosome, thus generating two offspring solutions. Two target values ​​for the two offspring solutions are then calculated, and the individual with the non-dominated solution is retained, denoted as... Proceed to the next mutation operation; 311) Individuals retained by the crossover operation Perform a mutation operation, using positional mutation, and output the mutated individual of generation t+1. ; Among them: the position variation step refers to two-stage variation. In each of the two stages, one workpiece number is randomly selected and the processing machine of the current workpiece is changed to another qualified processing machine. 312) The x-axis will be... and the vertical axis are The target space is evenly divided into three parts, which are denoted as Region I, Region II, and Region III from top to bottom; 313) The mutated individuals Individuals are obtained by performing a local search in a region. First, determine the individual. The solution belongs to the region. If it belongs to region I, the LS2 search operator is used to reduce the total energy consumption; if it belongs to region III, the LS1 search operator is used to shorten the total completion time; if it belongs to region II, a random number rd is generated to select either the LS1 or LS2 search operator, and each operator has the same probability of being selected. The two search operators are: the first search operator, denoted as LS1, reduces the total completion time by randomly changing the machine selection of the workpiece on the critical path; the second search operator, denoted as LS2, reduces the total energy consumption by adjusting the workpiece to be processed on a low-energy machine. 314) Based on the characteristics of time-of-use pricing, the individual data after the regional search is... Make adjustments; The adjustment strategy for time-of-use electricity pricing is based on the characteristics of time-of-use pricing. Firstly, without changing the maximum completion time, the start time of the workpiece is adjusted from the end to the beginning, moving the workpiece from a high-energy-consumption time to a low-energy-consumption time, thereby reducing total energy consumption. Secondly, with the maximum completion time increased, since the electricity price function is a periodic function (let's assume the increase time is one period of the electricity price function), the start time of the workpiece is adjusted from the end to the beginning, moving the workpiece from a high-energy-consumption time to a low-energy-consumption time, thereby reducing total energy consumption. 315) Obtain the population of generation t+1. All non-dominated individuals are then added to the set. In the middle, remove the set The dominated individual; 316) If The output is then stored in the set. All non-dominated individuals are treated as a set of production and processing schemes; otherwise, let... Assign to Then, return to step 35), set It is the optimal set of scheduling schemes, where each individual represents a feasible scheduling scheme; 317) From the set Choose a solution that meets the actual needs from the set of workpieces to be processed. Processing is carried out; among which, solutions for actual needs include: solutions that consider efficiency, solutions that consider profit, and solutions that compromise between efficiency and profit.

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