Distributed heterogeneous flow shop scheduling method based on improved hybrid memetic algorithm

Abstract

The application belongs to the field of workshop scheduling, and aims at solving the problem of low efficiency of the existing scheduling method of heterogeneous factories. The application comprises the following steps: S1, constructing a distributed heterogeneous flow shop scheduling model; S2, determining the value of the basic parameters of the algorithm, and generating an initial population by using a random strategy according to the coding rules; S3, evaluating the initial population, and performing a Pareto non-dominated sorting according to the fitness value; S4, performing an EOX crossover operation on the population with two-layer coding; S5, searching the solution space by using multiple operators; S6, adopting an elite reservation strategy, merging the parent population and the child population, and selecting half of the individuals as the evolution target of the next stage; S7, performing an evolution operation of local search on the selected individuals; S8, updating the population; S9, if the algorithm reaches the stopping condition, the algorithm is ended and the result is output, otherwise, the algorithm jumps to step S4 and continues to execute.

Description

Technical Field

[0001] This invention relates to a scheduling method for a flow workshop problem, belonging to the field of workshop scheduling. Background Technology

[0002] With the continuous development of economy and technology, manufacturing enterprises are facing unprecedented survival challenges. For these enterprises, only by improving competitiveness can they survive in the fierce competition. A high yield rate not only reduces factory production costs but also ensures product quality and improves customer satisfaction, thus having a positive impact on the enterprise's economic benefits and reputation. However, existing research on optimizing product yield rates is severely lacking.

[0003] With the continuous advancement of economic globalization, traditional single-unit production workshops are no longer suitable for current manufacturing scenarios, making distributed manufacturing a trend. Distributed manufacturing is more flexible than traditional production models, enabling the rational allocation of production resources and improving production efficiency, thus leading to a surge in research on distributed scheduling. Due to population growth and overconsumption, global environmental problems are becoming increasingly serious, and the "energy crisis" is intensifying. Manufacturing can consume 25%-50% of total energy consumption, making research on green scheduling of significant value. Existing research on distributed scheduling largely focuses on homogeneous factories; clearly, heterogeneous factories are more suitable for actual production scenarios. Currently, scheduling technology for homogeneous factories is relatively mature, but scheduling methods for heterogeneous factories are still in their early stages and inefficient. Summary of the Invention

[0004] To address the inefficiency of existing scheduling methods for heterogeneous factories, this invention provides a distributed heterogeneous flow shop scheduling method based on an improved hybrid meme algorithm.

[0005] The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm described in this invention includes the following steps:

[0006] Step S1: Construct a distributed heterogeneous workflow scheduling model;

[0007] Step S2: Given the fixed values ​​of the basic parameters of the algorithm, and using a random strategy according to the encoding rules, generate the initial population;

[0008] Step S3: Evaluate the initial population and perform Pareto non-dominated sorting based on fitness values;

[0009] Step S4: Perform a two-layer encoded EOX crossover operation on the population;

[0010] Step S5: Jointly search the solution space using multiple operators;

[0011] Step S6: Adopt the elite preservation strategy, merge the parent and offspring populations, and select half of the individuals as the next stage of evolution;

[0012] Step S7: Perform local search evolutionary operations on the selected individuals;

[0013] Step S8: Update the population;

[0014] Step S9: If the algorithm reaches the stopping condition, the algorithm ends and the result is output; otherwise, the algorithm jumps to step S4 to continue execution.

[0015] Preferably, the distributed heterogeneous flow shop scheduling model in step S1 is described as follows:

[0016] The entire manufacturing system consists of F factories located in different regions, and there are F factories in the F factories. p A replacement flow workshop with different processing capabilities and F h The system consists of several mixed production lines with varying processing capacities. Each stage of the mixed production line has M identical parallel machines, where M ≥ 1. All workpieces can be processed by any factory but only by one factory. Every step of a workpiece's processing must be completed, and the processing sequence of these steps is constrained. Each machine has five selectable speeds. The actual processing time of a workpiece is related to its standard processing time and the machine speed. The higher the machine speed, the shorter the actual processing time, but the more energy is consumed. Due to factors such as the production environment and technology of each factory, the standard processing time and yield of the same workpiece differ between different factories. The setup time of each process and the transportation time of the workpiece are included in the standard processing time. The buffer between machines is set to infinity. The optimization objective function includes the maximum completion time, total energy consumption, and total yield. The fitness value is calculated based on the following formula:

[0017] The fitness of the maximum completion time is obtained according to formula (1):

[0018] min f1=C max =max{C j,k} (1)

[0019] The fitness of total energy consumption is obtained according to equation (2):

[0020]

[0021]

[0022] The fitness of the total yield rate is obtained according to formula (4), and the total non-yield rate is used as the fitness value:

[0023]

[0024] Where, function f1 is the fitness function for maximum completion time, function f2 is the fitness function for total energy consumption, function f3 is the fitness function for total yield, and C max TEC and TAYR are used as fitness values, C max The maximum completion time is represented by TEC, total energy consumption is represented by TEC, and total defect rate is represented by TAYR. j is the workpiece index, j = 1, ..., N, where N is the total number of workpieces; k is the process index, k = 1, ..., S, where S is the total number of processes; f is the factory index, f = 1, ..., F, where F is the total number of factories; and m is the machine index, m = 1, ..., M. f,k M f,k C represents the number of machines in the k-th process of factory f; j,k For process O j,k The completion time, O j,k EC represents the k-th process of workpiece j; f For the energy consumption of factory f, P j,f,k For process O j,k The standard processing time in factory f, v j,k For process O j,k Processing speed; For process O j,k Energy consumption per unit time during processing at factory f. The idle time of machine m for the k-th process in factory f. YR represents the energy consumption per unit time of machine m in idle mode during the k-th process of factory f; j,f Let x be the yield rate of workpiece j in factory f. If workpiece j is assigned to factory f, then x j,f =1, otherwise 0.

[0025] Preferably, the basic parameters of the algorithm in step S2 include the population size PS and the crossover probability P. Cr Cross-segment ratio α, stopping condition coefficient τ;

[0026] The algorithm's chromosome consists of three parts: factory arrangement, workpiece sorting, and speed selection.

[0027] In the factory arrangement section, the chromosome dimension is 1×F, the gene position represents the factory number, and the gene represents the number of workpieces; in the workpiece sorting section, the chromosome dimension is 1×N, the gene represents the workpiece number, and the gene position represents the processing order; in the speed selection section, the chromosome dimension is N×S, the row index represents the workpiece number, and the column index represents the process number.

[0028] Preferably, in step S3, the fitness value of each individual in the initial population is calculated according to the fitness value formula, and a fast non-dominated sort is performed to divide the population individuals into different dominance levels and calculate the crowding distance between individuals of the same dominance level.

[0029] Preferably, in step S4, a two-level encoded EOX crossover operation is performed on the population, and the probability of performing the EOX crossover operation on each individual in the population is P. Cr The specific process is as follows:

[0030] S4A-1: Transform the factory arrangement part of the chromosome and the workpiece sorting part of the chromosome into a two-layer coding method with consistent dimensions, and the genes at the same position of the factory arrangement part of the chromosome and the workpiece sorting part of the chromosome are all related to the same workpiece.

[0031] S4A-2: Randomly select an individual from the non-dominated solution set as parent individual 1, and parent individual 2 as the current individual;

[0032] S4A-3: Randomly select a gene segment from the chromosome of the workpiece sorting part of parent individual 1; then, delete the gene that is the same as segment from the chromosome of the workpiece sorting part of parent individual 2, and perform the same operation on the gene at the same position on the chromosome of the factory arrangement part.

[0033] S4A-4: Insert the segment into the first deleted gene position of the chromosome of the parent individual 2 workpiece sorting part to obtain the chromosome of the offspring workpiece sorting part. The factory arranges the same operation on the genes at the same position of the partial chromosome.

[0034] Preferably, the principle for using multiple operators to jointly search the solution space in step S5 is as follows:

[0035] The search is performed on all individuals using the TAYR optimization operator MU3;

[0036] Then, C is randomly selected for each individual. max Optimize operator MU1 or TEC optimization operator MU2 to perform the search;

[0037] Finally, each individual randomly selects either SA1 or SA2 to perform the search;

[0038] The C max The optimization operator MU1 includes FJ sc FJ sr FJ ic and FJ ir Search operators; TEC optimization operators MU2 include FJ se FJ ie FJ sr and FJ ir Search operators; TAYR optimization operators MU3 include FJ sy and FJ iy Search operators, and the operation methods of each search operator are as follows:

[0039] FJ sc : Swap a randomly selected workpiece and F from any non-critical factory c The position of a workpiece randomly selected from among the available positions;

[0040] FJ sr Randomly select any two workpieces from two different factories and swap their positions;

[0041] FJ ic Randomly select F c Inserting a workpiece into F e1 A randomly selected location;

[0042] FJ ir Factory F r1 ,F r2 These are two different randomly selected factories, F r1 A workpiece is randomly selected from the inputs and inserted into F. r2 Any position in the middle;

[0043] FJ se : A randomly selected non-critical factory with any workpiece and F e Exchange the positions of any one of the workpieces;

[0044] FJ ie Randomly select F e Inserting a workpiece into F e2 A location randomly selected from the data;

[0045] FJ sy Randomly select F y One of the workpieces and F e3 One of the randomly selected workpieces is exchanged;

[0046] FJ iy Randomly select F y One of the workpieces j inserts it into YR j,f Any location within the largest factory;

[0047] SA1: In F c Randomly select a workpiece and increase the processing speed of each of its processes by one level;

[0048] SA2: In F e1 Randomly select a workpiece and reduce the processing speed of each step of its operation by one level;

[0049] Among them, the factory with the longest completion time is the critical factory F. c The factory with the shortest completion time is the easiest factory, F. e1 The factory with the highest energy consumption is the key factory F.e The factory with the lowest energy consumption is the easiest factory, F. e2 The total defect rate of factory f divided by the number of parts is the average defect rate of factory f. The factory with the highest average defect rate is the critical factory F. y The factory with the lowest average defect rate is F. e3 .

[0050] Preferably, the process of selecting half of the individuals as the next stage of evolution in step S6 is as follows: merge the parent population and the offspring population into a population of size 2PS, calculate the fitness value of each individual in the population, and perform non-dominated sorting. Prioritize individuals with low non-dominated levels, and select individuals with large crowding distances within the same dominance level, until PS individuals are selected for local search.

[0051] Preferably, the local search in step S7 refers to performing FJ on each individual in the population. ic operate.

[0052] Preferably, the population update process in step S8 is as follows: the PS individuals that have undergone the local search operation and the PS individuals that have not undergone the local search operation selected in step S6 are merged, and the PS individuals are selected to replace the original parent population to become the new generation parent population.

[0053] Preferably, the algorithm stopping condition in step S9 is that the CPU running time does not exceed τ×N×S×F seconds.

[0054] The beneficial effects of this invention are as follows: This invention establishes a distributed heterogeneous production line scheduling model, using maximum completion time, total energy consumption, and total yield as optimization objectives, which is a multi-objective optimization problem. Given the importance of product yield for production scheduling, this invention also designs a search operator to optimize yield. To find a reliable and feasible scheduling scheme for this problem, an improved hybrid meme algorithm is proposed. The algorithm first uses a random strategy to generate an initial population to ensure its diversity; then it performs a two-layer encoded EOX crossover operation; next, it uses multiple operators for joint search to ensure the algorithm searches the solution space in different directions; based on an elite strategy, it selects PS individuals for local search; finally, it selects PS individuals from the individuals that have undergone local search and the 2PS individuals that have not undergone local search to participate in the next generation of evolution. This invention's method is applied to the scheduling of heterogeneous factories, and its efficiency is significantly improved. Attached Figure Description

[0055] Figure 1 This is a flowchart of the algorithm of the present invention;

[0056] Figure 2 A scheduling Gantt chart for a problem example described in this invention;

[0057] Figure 3 A diagram illustrating individual coding;

[0058] Figure 4 A schematic diagram of a two-layer coding system for an individual;

[0059] Figure 5 This is a schematic diagram of the EOX crossover process in two layers of encoding;

[0060] Figure 6 This is a diagram illustrating HV values.

[0061] Figure 7 This is a schematic diagram of GD values. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0064] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0065] Specific Implementation Method 1: The following is combined with... Figures 1 to 7 This embodiment describes a distributed heterogeneous flow shop scheduling method based on an improved hybrid meme algorithm. The invention establishes a distributed heterogeneous flow shop scheduling model, using maximum completion time, total energy consumption, and total yield as optimization objectives, which is a multi-objective optimization problem. The improved hybrid meme algorithm first uses a random strategy to generate an initial population to ensure its diversity; then, it performs a two-layer encoded EOX crossover operation; next, it uses multiple operators for joint search to ensure the algorithm searches the solution space in different directions; based on an elite strategy, it selects PS individuals for local search; finally, it selects PS individuals from the individuals that have undergone local search and the 2PS individuals that have not, to participate in the next generation of evolution. This invention can provide a reliable and feasible scheduling scheme for the problem.

[0066] Specifically, the method includes the following steps:

[0067] Step S1: Construct a distributed heterogeneous workflow scheduling model;

[0068] Step S2: Given the fixed values ​​of the basic parameters of the algorithm, and using a random strategy according to the encoding rules, generate the initial population;

[0069] Step S3: Evaluate the initial population and perform Pareto non-dominated sorting based on fitness values;

[0070] Step S4: Perform a two-layer encoded EOX crossover operation on the population;

[0071] Step S5: Jointly search the solution space using multiple operators;

[0072] Step S6: Adopt the elite preservation strategy, merge the parent and offspring populations, and select half of the individuals as the next stage of evolution;

[0073] Step S7: Perform local search evolutionary operations on the selected individuals;

[0074] Step S8: Update the population;

[0075] Step S9: If the algorithm reaches the stopping condition, the algorithm ends and the result is output; otherwise, the algorithm jumps to step S4 to continue execution.

[0076] The distributed heterogeneous flow shop scheduling model described in step S1 is as follows:

[0077] The entire manufacturing system consists of F factories located in different regions, and there are F factories in the F factories. p A permutation flow shop (PFS) with different processing capacities and F h The system consists of several hybrid flow shops (HFS) with varying processing capacities. Each stage of the HFS has M identical parallel machines, where M ≥ 1. All workpieces can be processed by any factory but only by one factory. Every step of a workpiece's processing must be completed, and the processing sequence is subject to constraints. Each machine has five selectable speeds. The actual processing time of a workpiece is related to its standard processing time and the machine speed. Higher machine speeds result in shorter actual processing times but consume more energy. Due to factors such as the production environment and technology of each factory, the standard processing time and yield of the same workpiece differ between factories. The setup time and transport time of the workpiece are included in the standard processing time. The buffer between machines is set to infinity. The optimization objective function includes maximum completion time, total energy consumption, and total yield. The fitness value is calculated using the following formula:

[0078] The fitness of the maximum completion time is obtained according to formula (1):

[0079] min f1=C max =max{ Cj,k} (1)

[0080] The fitness of total energy consumption is obtained according to equation (2):

[0081]

[0082]

[0083] The fitness of the total yield rate is obtained according to formula (4), and the total non-yield rate is used as the fitness value:

[0084]

[0085] Where, function f1 is the fitness function for maximum completion time, function f2 is the fitness function for total energy consumption, function f3 is the fitness function for total yield, and C max TEC and TAYR are used as fitness values, C max The maximum completion time is represented by TEC, total energy consumption is represented by TEC, and total defect rate is represented by TAYR. j is the workpiece index, j = 1, ..., N, where N is the total number of workpieces; k is the process index, k = 1, ..., S, where S is the total number of processes; f is the factory index, f = 1, ..., F, where F is the total number of factories; and m is the machine index, m = 1, ..., M. f,k M f,k C represents the number of machines in the k-th process of factory f; j,k For process O j,k The completion time, O j,k EC represents the k-th process of workpiece j; f For the energy consumption of factory f, P j,f,k For process O j,k The standard processing time in factory f, v j,k For process O j,k Processing speed; For process O j,k Energy consumption per unit time during processing at factory f. The idle time of machine m for the k-th process in factory f. YR represents the energy consumption per unit time of machine m in idle mode during the k-th process of factory f; j,f Let x be the yield rate of workpiece j in factory f. If workpiece j is assigned to factory f, then x j,f =1, otherwise 0.

[0086] The constraints of the distributed heterogeneous flow shop scheduling problem are:

[0087] This means that each workpiece must be assigned to a factory for processing;

[0088] This indicates that the workpiece must go through all processing stages;

[0089] This indicates that the completion time of a process is greater than or equal to the processing time of that process;

[0090] This means that the next process can only begin after the current process is completed;

[0091]

[0092] This means that only one workpiece can be processed by the same machine at any given time.

[0093] Constrain the range of values ​​for binary variables.

[0094] Where F represents the total number of factories, S represents the total number of processes, N represents the total number of workpieces, j and j' represent workpiece indices, j ≠ j', j = 1, ..., N, j' = 1, ..., N, k is the process index, k = 1, ..., S, f is the factory index, f = 1, ..., F, p j,k Indicates process O j,k Actual processing time, C j,k Indicates process O j,k The completion time, S j’,k Indicates process O j’,k The start time of processing; if workpiece j is assigned to factory f, then x j,f =1, otherwise x j,f =0; if process O j,k If the process is performed on machine m in the k-th step of the process in factory f, then y j,m,k,f =1, otherwise y j,m,k,f =0; if workpiece j is located in front of workpiece j' within factory f, then z j,j’,k,f =1, otherwise z j,j’,k,f =0, where U represents a sufficiently large integer.

[0095] To clearly explain the method for calculating the machine fitness function proposed in this invention, an example of the problem is given below. Figure 2 The Gantt chart for a scheduling scheme as an example.

[0096] Tables 1 and 2 contain the processing information for the examples.

[0097] Table 1

[0098]

[0099] Table 2

[0100]

[0101] As shown in Tables 1 and 2, there are a total of 3 factories and 10 workpieces. The processing times for the two processes of workpiece 1 are 2 and 3 in factory 1, 4 and 3 in factory 2, and 1 and 2 in factory 3. The unit energy consumption for the two processes of workpiece 1 is 5 and 7 in factory 1, 9 and 5 in factory 2, and 6 and 7 in factory 3. The yield rate of workpiece 1 processed in factory 1 is 0.98, in factory 2 it is 0.99, and in factory 3 it is 0.89. The same applies to other workpieces. Furthermore, the tables indicate that factories 1 and 2 are displacement-based flow workshops, and factory 3 is a mixed flow workshop. Process 1 has two machines, and process 2 has one machine. The unit idle energy consumption of the machine in the first process of factory 1 is 1, and the unit idle energy consumption of the machine in the second process is 2. The same applies to other factories.

[0102] The solution to the scheduling problem can be visually represented using a Gantt chart, and the above problem can be obtained as follows: Figure 2 The Gantt chart shown.

[0103] Gantt chart Figure 2 It can be calculated that the maximum completion time is equal to the completion time of factory 2, f1 = 15, the total energy consumption is f2 = (2×8 + 2×7 + 1×6) + 2×2 + (2×9 + 4×8 + 3×10) + 173 + 137 = 430, and the total non-performing rate is f3 = (1 - 0.98) + (1 - 1) + (0.99 - 0.91) + 0.02 + 0.16 = 0.28.

[0104] In step S2, this invention uses a random strategy to initialize the population, thus obtaining an initial population with rich diversity. The basic parameters of the algorithm in step S2 include the population size PS and the crossover probability P. Cr Cross-segment ratio α, stopping condition coefficient τ;

[0105] The algorithm's chromosome consists of three parts: factory arrangement, workpiece sorting, and speed selection.

[0106] A factory arranges chromosomes in a dimension of 1×F. The position of the chromosome gene in the factory arrangement is equal to the factory index, and the gene number represents the number of workpieces, such as... Figure 3 The factory's arrangement of the first gene "2" on the chromosome indicates that factory 1 needs to process 2 workpieces; the chromosome dimension for workpiece sorting is 1×N, the gene position represents the processing order of the workpiece in the first stage, and the gene number represents the workpiece sequence number, for example... Figure 3 The first gene "5" indicates that workpiece 5 is processed first in the first stage; a speed selection chromosome has a dimension of N×S, the row index of the gene equals the workpiece index, the column index equals the process index, and the gene number represents the speed level, such as... Figure 3The speed selection gene "1" in the first row and first column of the chromosome indicates that the first process of workpiece 1 selects the lowest speed level one.

[0107] It is worth noting that each stage of the hybrid assembly line workshop also requires the selection of processing machines for each process. In order to simplify coding, the processing machines for each stage of the hybrid assembly line workshop are determined during decoding based on the principles of "First Come First Processed (FCFP)" and "First Available Machine (FAM)".

[0108] The "first-come, first-served" principle means that the workpiece whose k-th process is completed first will start the k+1-th process first; the "earliest available machine" principle means that the earliest available machine will be selected from among multiple parallel machines to process the workpiece.

[0109] The algorithm uses a random strategy to obtain the initial population, resulting in a diverse initial population.

[0110] In step S3, the fitness values ​​of the obtained initial population are evaluated according to the fitness value formulas (1) to (4), and Pareto non-dominated sorting is performed, and crowding distance between individuals of the same level is calculated.

[0111] Quick nondominated sort mainly includes the following steps:

[0112] Step S3A-1: Scan every individual in the population and initialize two variables for each individual p: the number n of solutions that dominate individual p. p The solution set S of individuals dominated by individual p p ;

[0113] Step S3A-2: Let front = 1, n p The individual dominance level of 0 is equal to front, and n p Individuals with a value of 0 are assigned to set F_i;

[0114] Step S3A-3: For each individual in F_i, iterate through the solution set S for each individual. p The solution set S p n for each individual p Subtract one;

[0115] Step S3A-4: front = front + 1, set n p Individuals with a value of 0 are assigned to set F_i;

[0116] Step S3A-5: Repeat steps S3A-3 and S3A-4 until every individual in the population is assigned to a set F_i.

[0117] The formula for calculating congestion distance is as follows:

[0118]

[0119] Where n represents the target index for optimization, i is the index of individuals at the same level sorted by a certain fitness value, and f n min f is the minimum value of the nth objective function. n max This represents the maximum value of the nth optimization objective.

[0120] Individuals with lower dominance levels are given priority in participating in subsequent evolution, while individuals with higher crowding distances at the same dominance level are given priority in participating in subsequent evolution.

[0121] In step S4, a two-level EOX crossover operation is performed on the population, with the probability of performing the EOX crossover operation on each individual in the population being P. Cr Each individual in the population undergoes a process with probability P. Cr The EOX crossover operation of the two-layer encoding. A random number rand is generated; if rand... <P Cr If the condition is met, then the EOX crossover operation is performed; otherwise, the individual remains unchanged. The specific process is as follows:

[0122] S4A-1: Transform the factory arrangement part of the chromosome and the workpiece sorting part of the chromosome into a two-layer coding method with consistent dimensions, and the genes at the same position of the factory arrangement part of the chromosome and the workpiece sorting part of the chromosome are all related to the same workpiece.

[0123] S4A-2: Randomly select an individual from the non-dominated solution set as parent individual 1, and parent individual 2 as the current individual;

[0124] S4A-3: Randomly select a gene segment from the chromosome of the workpiece sorting part of parent individual 1; then, delete the gene that is the same as segment from the chromosome of the workpiece sorting part of parent individual 2, and perform the same operation on the gene at the same position on the chromosome of the factory arrangement part.

[0125] S4A-4: Insert the segment into the first deleted gene position of the chromosome of the parent individual 2 workpiece sorting part to obtain the chromosome of the offspring workpiece sorting part. The factory arranges the same operation on the genes at the same position of the partial chromosome.

[0126] Figure 4 A diagram illustrating the two-layer individual coding system:

[0127] It can be seen that the workpiece sorting chromosome and the factory arrangement chromosome have the same dimension. In this case, the gene on the factory arrangement chromosome refers to the processing factory, which can be regarded as the "identity number" of each workpiece. Genes at the same position describe the information of the same workpiece. For example, the first gene "5" on the workpiece sorting chromosome and the first gene "1" on the factory arrangement chromosome indicate that workpiece 5 is assigned to factory 1 for processing. This encoding method allows the two chromosomes to perform the same crossover operation.

[0128] Figure 5 A schematic diagram of the EOX crossover process with two layers of encoding:

[0129] Randomly select an individual 5718236411112222 from the non-dominated solution set of the population as parent individual 1, and the current individual 7458621311122222 as parent individual 2.

[0130] In parent individual 1, a segment is randomly selected from the workpiece sorting chromosome (segment 182 is selected here), and the factory arrangement chromosome segment is 112. Genes in parent individual 2 that are identical to the segment in the workpiece sorting chromosome are deleted. Genes at the same positions in the factory arrangement chromosome are also deleted, at positions 4, 6, and 7. The remaining gene sequence is 7456311122.

[0131] Insert segment 182 into position 4 of the workpiece sorting chromosome of the parent individual 2 after gene deletion, and insert segment 112 into position 4 of the factory arrangement chromosome of the parent individual 2 after gene deletion, to obtain offspring individual 7451826311111222.

[0132] The principle for using multiple operators to jointly search the solution space in step S5 is as follows:

[0133] The search is performed on all individuals using the TAYR optimization operator MU3;

[0134] Then, C is randomly selected for each individual. max Optimize operator MU1 or TEC optimization operator MU2 to perform the search;

[0135] Finally, each individual randomly selects either SA1 or SA2 to perform the search;

[0136] The C max The optimization operator MU1 includes FJ sc FJ sr FJ ic and FJ ir Search operators; TEC optimization operators MU2 include FJ se FJ ie FJ sr and FJir Search operators; TAYR optimization operators MU3 include FJ sy and FJ iy Search operators, and the operation methods of each search operator are as follows:

[0137] FJ sc : Swap a randomly selected workpiece and F from any non-critical factory c The position of a workpiece randomly selected from among the available positions;

[0138] FJ sr Randomly select any two workpieces from two different factories and swap their positions;

[0139] FJ ic Randomly select F c Inserting a workpiece into F e1 A randomly selected location;

[0140] FJ ir Factory F r1 ,F r2 These are two different randomly selected factories, F r1 A workpiece is randomly selected from the inputs and inserted into F. r2 Any position in the middle;

[0141] FJ se : A randomly selected non-critical factory with any workpiece and F e Exchange the positions of any one of the workpieces;

[0142] FJ ie Randomly select F e Inserting a workpiece into F e2 A location randomly selected from the data;

[0143] FJ sy Randomly select F y One of the workpieces and F e3 One of the randomly selected workpieces is exchanged;

[0144] FJ iy Randomly select F y One of the workpieces j inserts it into YR j,f Any location within the largest factory;

[0145] SA1: In F c Randomly select a workpiece and increase the processing speed of each of its processes by one level;

[0146] SA2: In F e1 Randomly select a workpiece and reduce the processing speed of each step of its operation by one level;

[0147] Among them, the factory with the longest completion time is the critical factory F. c The factory with the shortest completion time is the easiest factory, F. e1 The factory with the highest energy consumption is the key factory F. e The factory with the lowest energy consumption is the easiest factory, F. e2 The total defect rate of factory f divided by the number of parts is the average defect rate of factory f. The factory with the highest average defect rate is the critical factory F. y The factory with the lowest average defect rate is F. e3 .

[0148] Step S6: Employ an elite preservation strategy, merge the parent and offspring populations, and select half of the individuals to enter the next stage of evolution. The process of selecting half of the individuals as the next stage of evolution in step S6 is as follows: merge the parent and offspring populations into a population of size 2PS, calculate the fitness value of each individual in the population, and perform non-dominance sorting. Prioritize individuals with lower non-dominance levels, and for individuals with the same dominance level, select individuals with larger crowding distances, until PS individuals are selected for local search.

[0149] The pseudocode for global search is shown in Algorithm1.

[0150]

[0151] The local search in step S7 refers to performing FJ on each individual in the population. ic operate.

[0152] The population update process in step S8 is as follows: merge the PS individuals that have undergone the local search operation with the PS individuals that have not undergone the local search selected in step S6, and select PS individuals to replace the original parent population to become the new generation parent population.

[0153] The algorithm stops in step S9 when the CPU runtime does not exceed τ×N×S×F seconds.

[0154] To verify the effectiveness and reliability of the distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm, this invention uses a computational example of size (F) p ,F h ,N,S)=(1,2,50,5),(F p ,F h ,N,S)=(2,1,50,8),(F p ,F h ,N,S)=(1,2,100,5),(F p ,F h A comparative experiment was conducted on the example N,S)=(2,1,100,8).

[0155] Among them, F p F represents the number of replacement flow workshops. h This indicates the number of mixed-flow workshops, where N represents the number of workpieces and S represents the total number of processes.

[0156] Since there are no existing examples relating to the problem to which this invention pertains, examples are generated based on the following numerical ranges: The standard processing time for a workpiece in different factories is a random, discrete, uniform integer between 10 and 100. The energy consumption per unit time of machine operation is a random, discrete, uniform integer between 15 and 40, and the energy consumption per unit time of machine idle is a random, discrete, uniform integer between 5 and 10. The yield rate of each workpiece in different factories is a decimal between 0.85 and 1. The number of parallel machines in each stage of the mixed assembly line is 1 to 5. There are 5 selectable speed levels, with a speed set U = {1, 1.3, 1.55, 1.75, 2.1}.

[0157] The problem described is a multi-objective optimization problem. The HV (Hyper volume) value, GD (Generation distance) value, and CM (C metric, solution set coverage) value are used to measure the algorithm comparison test results.

[0158] The HV value calculates the volume of the hypercube enclosed by the Pareto non-dominated solution set of the population and the reference point. Taking a two-dimensional target as an example... Figure 6 As shown, the HV value is the area enclosed between the Pareto front individual and the reference point. This paper selects (1,1,1) as the reference point after normalization of the Pareto front individual. Clearly, the larger the HV value, the richer the diversity of the Pareto non-dominated solution set and the better the convergence.

[0159] This represents the average minimum distance from each individual in the solution set E to the reference set E*.

[0160]

[0161] In the formula, dis represents the Euclidean distance between x and y, where x and y represent two individuals in space. This paper selects the Pareto solution set obtained by a single algorithm as the solution set E, and the Pareto solution set composed of the Pareto fronts obtained by all algorithms as the reference set E*. Figure 7 This is a schematic diagram of the GD value. The smaller the GD value, the better the convergence of the solution set.

[0162] The CM value calculates the dominance relationship between individuals in two solution sets E1 and E2.

[0163]

[0164] Here, E1 and E2 are two different solution sets.

[0165] The larger the value of C(E1,E2), the more individuals in solution set E1 can dominate solution set E2.

[0166] If C(E1,E2)=0, it means that there is no individual in solution set E2 that can be dominated by solution set E1. Conversely, if C(E1,E2)=1, it means that all individuals in solution set E2 can be dominated by solution set E1.

[0167] To demonstrate the effectiveness of the algorithm (HMOMA) of this invention, the HMOMA algorithm, the decomposition-based multi-objective algorithm (MOEA / D), and the non-dominated sorting genetic algorithm (NSGA-Ⅱ) were run independently 10 times on each example, and the average HV value, GD value, and CM value of each algorithm on different examples were compared.

[0168] The parameters for MOMA are set as follows: population size PS = 200, crossover probability P Cr =0.4, cross segment ratio α =0.05, stopping condition coefficient τ =0.05.

[0169] The experimental results are shown in Tables 3 and 4.

[0170] Table 3

[0171]

[0172] Table 4

[0173]

[0174] Where A1 is HMOAM, A2 is MOEA / D, and A3 is NSGA-Ⅱ.

[0175] As shown in Tables 3 and 4, the average HV value of HMOMA is significantly greater than that of MOEA / D and NSGA-II; the average GD value of HMOMA is significantly smaller than that of MOEA / D and NSGA-II; and C(HMOAM, MOEA / D) and C(HMOAM, NSGA-II) are both greater than C(MOEA / D, HMOAM) and C(NSGA-II, HMOAM). This indicates that the overall performance of the population obtained by HMOMA is superior to the other two algorithms. Furthermore, in terms of dominance relationships, the proportion of individuals dominated by the non-dominated solution set of HMOMA is higher than the proportion of individuals dominated by the compared algorithms. This means that HMOMA is better able to obtain individuals with shorter maximum completion time, lower total energy consumption, and higher overall yield than the compared algorithms. In conclusion, the distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm described in this invention can provide an efficient scheduling scheme.

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

Claims

1. A distributed heterogeneous flow shop scheduling method based on an improved hybrid meme algorithm, characterized in that, The method includes the following steps: Step S1: Construct a distributed heterogeneous workflow scheduling model; Step S2: Given the fixed values ​​of the basic parameters of the algorithm, and using a random strategy according to the encoding rules, generate the initial population; Step S3: Evaluate the initial population and perform Pareto non-dominated sorting based on fitness values; Step S4: Perform a two-layer encoded EOX crossover operation on the population; Step S5: Jointly search the solution space using multiple operators; Step S6: Adopt the elite preservation strategy, merge the parent and offspring populations, and select half of the individuals as the next stage of evolution; Step S7: Perform local search evolutionary operations on the selected individuals; Step S8: Update the population; Step S9: If the algorithm reaches the stopping condition, the algorithm ends and the result is output; otherwise, the algorithm jumps to step S4 to continue execution. The distributed heterogeneous flow shop scheduling model described in step S1 is as follows: The entire manufacturing system consists of components distributed in different regions. It consists of several factories. There are factories A replacement flow workshop with different processing capabilities and It consists of several mixed assembly lines with different processing capacities; each stage of the mixed assembly line has Two identical parallel machines All workpieces can be processed by any factory but only by one factory. Every process step of a workpiece must be completed, and the processing sequence of these processes is subject to constraints. Each machine has five selectable speeds. The actual processing time of a workpiece is related to its standard processing time and the machine speed. The higher the machine speed, the shorter the actual processing time, but the more energy is consumed. Due to the production environment and technological factors of each factory, the standard processing time and yield of the same workpiece differ in different factories. The process setup time and workpiece transportation time are included in the standard processing time. The buffer between machines is set to infinity. The optimization objective function includes maximum completion time, total energy consumption, and total yield. Its fitness value is calculated based on the following formula: The fitness of the maximum completion time is obtained according to formula (1): （1） The fitness of total energy consumption is obtained according to equation (2): （2） （3） The fitness of the total yield rate is obtained according to formula (4), and the total non-yield rate is used as the fitness value: （4） Among them, the function The fitness function is the function for the maximum completion time. Let be the fitness function of total energy consumption, and let be the function. Let be the fitness function of the overall yield rate. , , As a fitness value, Indicates the maximum completion time. Total energy consumption, This indicates the total non-performing product rate; For workpiece index, , The total number of workpieces. For process index, , The total number of processes, For factory indexing, , The total number of factories, For machine indexing, , Indicates factory No. The number of machines in each process step; For process The completion time, Indicates workpiece The One process; For the factory Energy consumption, For process At the factory Standard processing time in the middle, For process Processing speed; For process At the factory Energy consumption per unit time during processing For the factory No. Processing machines for each step During free time, For the factory No. Processing machines for each step Energy consumption per unit time in idle mode; For workpiece At the factory The yield rate, if the workpiece Assigned to factory but =1, otherwise 0.

2. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 1, characterized in that, The basic parameters of the algorithm in step S2 include the population size. Crossover probability Cross segment ratio α, stopping condition coefficient ; The algorithm's chromosome consists of three parts: factory arrangement, workpiece sorting, and speed selection. Among them, the factory arranges part of the chromosome dimension as follows: Gene position represents the factory sequence number, and gene represents the number of workpieces; the chromosome dimension of the workpiece sorting part is... Genes represent workpiece serial numbers, and gene positions indicate processing order; the speed selection part has chromosome dimensions of [missing information]. The row index represents the workpiece number, and the column index represents the process number.

3. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 1, characterized in that, In step S3, the fitness value of each individual in the initial population is calculated according to the fitness value formula, and a fast non-dominated sort is performed to divide the population individuals into different dominance levels and calculate the crowding distance between individuals in the same dominance level.

4. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 1, characterized in that, In step S4, a two-level encoded EOX crossover operation is performed on the population. The probability of performing the EOX crossover operation on each individual in the population is... The specific process is as follows: S4A-1: Transform the factory arrangement part of the chromosome and the workpiece sorting part of the chromosome into a two-layer coding method with consistent dimensions, and the genes at the same position of the factory arrangement part of the chromosome and the workpiece sorting part of the chromosome are all related to the same workpiece. S4A-2: Randomly select an individual from the non-dominated solution set as parent individual 1, and parent individual 2 as the current individual; S4A-3: Randomly select a gene segment from the chromosome of the workpiece sorting part of parent individual 1. Then, sort the chromosomes of parent individual 2 that are related to... The same gene is deleted, and the same operation is performed on genes at the same position on some chromosomes that are arranged by the factory; S4A-4: Will Insert the first deleted gene position of the chromosome in the sorted part of the parent individual 2 to obtain the sorted part of the chromosome in the offspring. The factory arranges the same operation on the genes at the same position on the sorted part of the chromosome.

5. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 1, characterized in that, The principle for using multiple operators to jointly search the solution space in step S5 is as follows: For all individuals Optimization Operator Perform a search; Then, randomly select each individual. Optimization Operator or Optimization Operator Perform a search; Finally, each individual randomly selects or Perform a search; The Optimization Operator include , , , and Search operators; Optimization Operator include , , , and Search operators; Optimization Operator include and Search operators, and the operation methods of each search operator are as follows: : Swap a randomly selected workpiece from any non-critical factory and The position of a workpiece randomly selected from among the available positions; Randomly select any two workpieces from two different factories and swap their positions; Random selection Inserting a workpiece A randomly selected location; :factory These are two different randomly selected factories, Insert a workpiece randomly selected from the middle Any position in the middle; : To combine any one workpiece from a randomly selected non-critical factory with Exchange the positions of any one of the workpieces; Random selection Inserting a workpiece A location randomly selected from the data; Random selection One of the workpieces and One of the randomly selected workpieces is exchanged; Random selection One of the workpieces Insert it Any location within the largest factory; :exist Randomly select a workpiece and increase the processing speed of each of its processes by one level; :exist Randomly select a workpiece and reduce the processing speed of each step of its operation by one level; Among them, the factory with the longest completion time is the key factory. The factory with the shortest completion time is the easiest factory. The factory with the highest energy consumption is the key factory. The factory with the lowest energy consumption is the easiest factory. ;factory The total defective rate divided by the number of parts is the factory's percentage. The average defect rate is the highest, and the factory with the highest average defect rate is the critical factory. The factory with the lowest average defect rate is .

6. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 2, characterized in that, The process of selecting half of the individuals as the next evolutionary target in step S6 is as follows: The parent and offspring populations are merged into a group of size [missing information]. For a population, calculate the fitness value of each individual and perform non-dominance ranking, prioritizing individuals with lower non-dominance levels, and within the same dominance level, selecting individuals with larger crowding distances, until a suitable individual is selected. Each individual performs a local search.

7. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 5, characterized in that, The local search in step S7 refers to performing a search on each individual in the population. operate.

8. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 6, characterized in that, The population update process in step S8 is as follows: The population that has undergone local search operations... Individuals and those selected in step S6 that have not undergone local search Individuals are merged and selected. Each individual replaces the original parent population to become the parent population of the new generation.

9. The distributed heterogeneous flow shop scheduling method based on the improved hybrid meme algorithm according to claim 2, characterized in that, The algorithm stopping condition in step S9 is that the CPU running time does not exceed [a certain value]. Second.

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