Multi-objective dual-flexible job shop scheduling method and system based on hybrid algorithm

Abstract

The present invention provides a multi-objective dual-flexible job shop scheduling method and system based on a hybrid algorithm, and relates to the technical field of dual-flexible job shop scheduling. When the present invention constructs a multi-objective dual-flexible job shop scheduling model with a combined weighted function of the maximum completion time and the line side inventory time as the objective function, multiple constraints including processing time constraints and preparation time constraints are considered, and two different learning effect models are selected to process the two constraints of processing time constraints and preparation time constraints respectively, and the model is optimized; finally, the hybrid algorithm is used to solve the optimized model to obtain the optimal solution of the model, and a Gantt chart of the multi-objective dual-flexible job shop scheduling is drawn according to the optimal solution, thereby realizing scheduling. The technical solution of the present invention is closer to the actual workshop production situation, and its scheduling results are more reasonable and accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of dual-flexible job shop scheduling, and in particular to a multi-objective dual-flexible job shop scheduling method and system based on a hybrid algorithm. Background Art

[0002] The Dual Flexible Job-Shop Scheduling Problem (DFJSP) refers to the traditional Flexible Job-Shop Scheduling Problem (FJSP) which only considers the flexibility of processing equipment. After considering the single auxiliary time of transportation time with resource constraints, due to the performance differences of transportation machines, the transportation time consumed by the workpieces on different transportation machines is different. The workpieces need to choose appropriate transportation machines and determine the transportation order on the transportation machines. This is called the Dual Flexible Job-Shop Scheduling Problem. The research on DFJSP is the key to achieving high efficiency, high quality, high flexibility and low cost in enterprise production, and it is also a problem that needs to be solved urgently in this field.

[0003] In a dual-flexible workshop, processing operations and preparation operations are very common. However, in previous studies, scholars would default to considering the preparation operation time as processing time to ignore the impact of preparation time on dual-flexible operations. At the same time, during the processing operation, the processing time of different stages is assumed to be exactly the same. In addition, existing solutions for DFJSP generally use a single intelligent algorithm to solve it.

[0004] However, in actual production, on the one hand, both processing operations and preparation operations are human-machine collaborative working modes, so both work scenarios have learning effects. The existing technology schedules the dual-flexible job shop without considering this learning effect, and its scheduling results are bound to be inaccurate and not in line with the actual situation; on the other hand, when considering multiple constraints, when using the existing single intelligent algorithm to solve the global optimal solution of the objective function, there will be many deficiencies such as low solution quality and slow solution search speed. In summary, the existing multi-objective dual-flexible job shop scheduling method cannot accurately and efficiently obtain scheduling results, and cannot provide effective reference for the actual production of enterprises. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the deficiencies in the prior art, the present invention provides a multi-objective dual-flexible job shop scheduling method and system based on a hybrid algorithm, which solves the problem of inaccurate and inefficient scheduling results in the existing dual-flexible job shop scheduling method.

[0007] (II) Technical solution

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

[0009] In a first aspect, the present invention first proposes a multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm, the method comprising:

[0010] Constructing a multi-objective dual-flexible job shop scheduling model; the multi-objective dual-flexible job shop scheduling model includes an objective function and constraints; the objective function is a combined weighted function of maximum completion time and line side inventory time; the constraints include processing time constraints and preparation time constraints;

[0011] Solving the processing time constraint based on a learning effect model that considers workpiece position correlation and workpiece similarity to obtain the solved processing time constraint; solving the preparation time constraint based on a continuous exponential increasing learning effect model to obtain the solved preparation time constraint; optimizing a multi-objective dual-flexible job shop scheduling model based on the solved processing time constraint and the solved preparation time constraint;

[0012] The optimized multi-objective dual-flexible job shop scheduling model is solved based on a hybrid algorithm to obtain the optimal solution of the model, and a Gantt chart of the multi-objective dual-flexible job shop scheduling is drawn based on the optimal solution; the hybrid algorithm is a combined hybrid algorithm of a multi-population genetic algorithm and a simulated annealing algorithm; wherein the simulated annealing algorithm is used to solve the initial population generated by the multi-population genetic algorithm.

[0013] Preferably, the combined weighting function comprises:

[0014] minZ=ω1C max +ω2C edge

[0015] Among them, C max represents the maximum completion time, C edge represents the line-side inventory time; ω1 represents the optimization weight of the maximum completion time, and ω2 represents the optimization weight of the line-side inventory time.

[0016] Preferably, the workpiece position-related and workpiece similarity-considered learning effect model includes:

[0017] P j,r =P j (S[1,r]+S[2,r]+…+S[r,r]) α

[0018] Among them, P j represents the processing time of the process without considering the learning effect; P j,rrepresents the processing time of the workpiece at processing position r after considering the learning effect; S[r1,r2] represents the similarity between the workpieces at positions r1 and r2;

[0019] The continuous exponential learning effect model includes:

[0020] C max =R -1 (P+R(0))

[0021] Among them, C max represents the actual processing preparation time; P represents the normal processing preparation time before considering the learning effect, and R(0) is the function value of y=R(t) when t=0.

[0022] Preferably, solving the optimized multi-objective dual-flexible job shop scheduling model based on a hybrid multi-population genetic algorithm to obtain the optimal solution of the model, and drawing a Gantt chart of the multi-objective dual-flexible job shop scheduling based on the optimal solution includes the following steps:

[0023] Step 1 performs parameter initialization settings, including setting the initial temperature T0, final temperature T1, cooling rate q0, number of iterations c at each temperature, and maximum number of iterations L0 at each state in the simulated annealing algorithm; it also includes setting the population size N, initial temperature T0', cooling rate q0', and crossover rate p of each population in the multi-population genetic algorithm. c , mutation rate p m , the size of each population P size , iterative algebra gen, and the maximum number of iterations iterations;

[0024] Step 2 generates N initial populations of multi-population genetic algorithm based on simulated annealing algorithm;

[0025] Step3 Let the temperature T in the multi-population genetic algorithm = T0';

[0026] Step 4: Each population in the multi-population genetic algorithm begins to evolve independently, and the initial population is evolved based on a preset evolution rule;

[0027] Step 5: Let gen = gen + 1 and T = T × q0', and determine whether gen% 5 == 0 is true. If not, execute Step 4; if true, migrate each of the initial populations after evolution based on the preset migration strategy;

[0028] Step 6 determines whether gen%iterations==0 is true. If not, execute Step 4; if true, execute Step 7;

[0029] Step 7 Output the optimal individual and draw a Gantt chart for the multi-objective double flexible job shop scheduling according to the optimal individual.

[0030] Preferably, the Step 2 to generate N initial populations of the multi-population genetic algorithm based on the simulated annealing algorithm includes:

[0031] Step 2.1 Let the current temperature T = T0, generate an initial solution S1 and calculate the fitness R1 of the initial solution S1;

[0032] Step 2.2 Judge whether the current temperature T < T1 holds. If it holds, end the algorithm, output the optimal solution and draw a Gantt chart; if it does not hold, let c = 0 and execute Step 2.3;

[0033] Step 2.3 Randomly select any one of the mutation methods of PPS mutation, swap mutation, reverse mutation, and swap two sub-path mutations with the same probability to generate a new solution S2, and calculate the fitness R2 of the new solution S2;

[0034] Step 2.4 If R2 - R1 < 0 holds, let S1 = S2;

[0035] If R2 - R1 < 0 does not hold, calculate the acceptance probability exp(-(R2 - R1) / T) of S2, and randomly generate a random number rand uniformly distributed in the interval (0, 1). If exp(-(R2 - R1) / T) > rand holds, let S1 = S2; if exp(-(R2 - R1) / T) > rand does not hold, let S1 = S1;

[0036] Step 2.5 Let c = c + 1, judge whether c = L0 holds. If it holds, execute Step 2.6; if it does not hold, go to Step 2.3;

[0037] Step 2.6 Continue to cool down, let T = T × q0, and go to Step 2.2.

[0038] Preferably, the preset evolution rules include: judge whether the current nth population satisfies n <= N / 2. If it satisfies, execute Step 4.1; otherwise, execute Step 4.2;

[0039] Step 4.1:

[0040] (1) Evaluate the population: Calculate the fitness value of each individual in the population; (2) Selection strategy: Use the binary tournament method to select operators from the previous generation population to form the parent population; (3) Crossover strategy: Perform crossover on the parent population to obtain new individuals, calculate the fitness values of the new individuals, and select the individuals with smaller fitness values among the new individuals and their parent individuals to inherit to the offspring population; (4) Mutation strategy: Perform mutation operations on the offspring population to achieve evolution;

[0041] Step 4.2:

[0042] (1) Evaluate the population: calculate the fitness value of each individual in the population; (2) Selection strategy: use the binary tournament method to select operators from the previous generation population to form the parent population; (3) Crossover strategy: cross the parent population to obtain new individuals, and calculate the fitness value of the new individuals, calculate the difference between the fitness value of the new individuals and the objective function value of the parent individuals, and use the Metropolis selection criterion to determine whether to accept the new individuals to be inherited to the next generation; (4) Mutation strategy: perform mutation operations on the offspring population to achieve evolution.

[0043] Preferably, the preset migration strategy includes:

[0044] According to the preset migration cycle, migration rate, and migration topology, the individuals ranked in the top 10% of fitness in the initial population after the previous evolution are used as migration operators and migrated to the initial population after the next evolution to replace the individuals ranked in the worst fitness.

[0045] Preferably, the migration period is 5, the mobility is 0.1, and the migration topology is a unidirectional ring topology.

[0046] In a second aspect, the present invention further proposes a multi-objective dual-flexible job shop scheduling system based on a hybrid algorithm, the system comprising:

[0047] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the steps of the method described above are implemented when the processor executes the computer program.

[0048] (III) Beneficial effects

[0049] The present invention provides a multi-objective dual-flexible job shop scheduling method and system based on a hybrid algorithm. Compared with the prior art, it has the following beneficial effects:

[0050] 1. The present invention constructs a multi-objective dual-flexible job shop scheduling model based on the consideration of processing time constraints and preparation time constraints, and then uses different learning effect models to process the processing time constraints and preparation time constraints respectively, and optimizes the multi-objective dual-flexible job shop scheduling model. Finally, the optimized multi-objective dual-flexible job shop scheduling model is solved to obtain the optimal solution of the model, and the Gantt chart of the multi-objective dual-flexible job shop scheduling is drawn based on the optimal solution. When performing multi-objective dual-flexible job shop scheduling, the present invention considers the processing time constraints and preparation time constraints on the one hand, and processes these two constraints respectively using different learning effect models, which is more in line with the actual situation of workshop production, and the scheduling result of the entire process corresponding to the optimal solution finally obtained is more reasonable and accurate; on the other hand, a hybrid algorithm is used to solve the objective function of the multi-objective dual-flexible job shop scheduling model considering multiple constraints, so as to improve the quality of the solution and the search speed. In general, the multi-objective dual-flexible job shop scheduling method based on the hybrid algorithm of the present invention improves the accuracy and efficiency of the scheduling results, optimizes the scheduling of resources such as workers, processing equipment, and transportation machines, makes the scheduling results of the entire process more reasonable, significantly reduces the maximum completion time and line-side inventory time, and improves the continuity and efficiency of production.

[0051] 2. Based on the characteristics of the two scenarios of processing operation and preparation operation, the present invention adopts a learning effect model that is related to the workpiece position and considers the workpiece similarity to solve the processing time after considering the learning effect, accurately expressing the learning effect relationship between the same processes, and at the same time clarifying that the learning effects of different processes on the same processing equipment are independent; a learning effect model in which work efficiency is a continuous exponential increase related to time is used to process the preparation time constraints, considering the impact of the worker's past work and work experience on the current work efficiency. The processing time constraints and preparation time constraints processed by the learning effect model are more in line with the actual production situation of the enterprise, making the scheduling results of the dual-flexible job shop more accurate.

[0052] 3. The present invention combines a multi-population genetic algorithm (MPGA) and a simulated annealing algorithm (SA) to form a hybrid multi-population genetic algorithm (HMPGA) for solving multi-objective dual-flexible job shop scheduling problems, which makes up for the shortcomings of a single optimization algorithm; in addition, the introduction of the simulated annealing algorithm can combine probability to randomly search for the global optimal solution of the objective function in the solution space, avoiding the genetic algorithm from falling into premature maturity, thereby improving the quality of the solution and the search speed.

[0053] 4. The present invention designs four new solution generation methods: PPS mutation, exchange mutation, inverse mutation, and exchange of two sub-paths mutation, and randomly selects one of the methods to generate a new solution in each iteration, avoiding poor population diversity caused by a single new solution generation method, thereby improving the algorithm's global optimization ability.

[0054] 5. According to the preset migration cycle, migration rate, and migration topology, the present invention uses the individuals ranked in the top 10% of the fitness in the initial population after the previous evolution as migration operators, and migrates them to the initial population after the next evolution to replace the individuals ranked the worst in fitness. This migration strategy utilizes the immigration operator to spread excellent genes among multiple populations, establishes connections between various populations, and ensures the associated evolution among multiple populations. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0056] Figure 1 A scenario diagram of dual flexible job shop scheduling considering multiple learning effects in the present invention;

[0057] Figure 2 Flow chart of a multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm in an embodiment of the present invention;

[0058] Figure 3 This is a working efficiency curve diagram considering the learning effect in an embodiment of the present invention;

[0059] Figure 4 A flow chart of solving a problem using a hybrid multi-population genetic algorithm in an embodiment of the present invention;

[0060] Figure 5 A schematic diagram of chromosome coding in an embodiment of the present invention;

[0061] Figure 6 Schematic diagram of PPS variation operation in an embodiment of the present invention;

[0062] Figure 7 A schematic diagram of an exchange variation operation in an embodiment of the present invention;

[0063] Figure 8 This is a schematic diagram of the reverse mutation operation in an embodiment of the present invention;

[0064] Fig. 9 A schematic diagram of a variation operation of exchanging two sub-paths in an embodiment of the present invention;

[0065] Fig.10 Schematic diagram of the effect of a process insertion on the preparation time of the next process before and after the process insertion in an embodiment of the present invention;

[0066] Fig.11Schematic diagram of migration of multiple population immigration operators in an embodiment of the present invention.

[0067] Fig.12 A Gantt chart of workshop scheduling corresponding to the optimal solution obtained without considering the preparation time in an embodiment of the present invention;

[0068] Fig.13 A Gantt chart of workshop scheduling corresponding to the optimal solution obtained by considering the preparation time in an embodiment of the present invention;

[0069] Fig.14 It is a fitness convergence diagram of four different solution algorithms in different use cases in the embodiments of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] The embodiment of the present application provides a multi-objective dual-flexible job shop scheduling method and system based on a hybrid algorithm, which solves the problem of inaccurate and inefficient scheduling results in the existing dual-flexible job shop scheduling method, and achieves the purpose of providing accurate reference for the efficient production of enterprises.

[0072] The technical solution in the embodiment of the present application is to solve the above technical problems, and the overall idea is as follows:

[0073] In order to more accurately simulate and truly restore the real production situation of the dual-flexible job shop, the present invention takes the combined weighted function of the maximum completion time and the line inventory time as the objective function to construct a multi-objective dual-flexible job shop scheduling model, taking into account multiple constraints including processing time constraints and preparation time constraints, and selects two different learning effect models to process the two constraints of processing time constraints and preparation time constraints respectively, and optimizes the model; finally, the hybrid algorithm is used to solve the optimized model to obtain the optimal solution of the model, and the Gantt chart of the multi-objective dual-flexible job shop scheduling is drawn according to the optimal solution, thereby realizing scheduling. The technical solution of the present invention is closer to the real workshop production situation, and its scheduling results are more reasonable and accurate.

[0074] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0075] Dual-flexible job shop scheduling problem considering multiple learning effects Figure 1As shown in the figure, before being processed, the workpiece will be sent to the line-side inventory buffer area next to the processing equipment, waiting for the previous process on the processing equipment to be completed. After the processing equipment is idle, it will prepare for the next process to be processed, such as changing the mold or adjusting the production parameters. When the preparation operation is completed, the current process can select any processing equipment from the available processing equipment set for processing. The flexibility of the processing equipment is as follows Figure 1 As shown in the dashed box on the left, O 1,2 Optional in M1 p or M2 p After processing, the workpiece will enter the buffer area next to the processing equipment and wait for transportation. The flexibility of the transportation machine is as follows: Figure 1 As shown in the dashed box on the right, when workpiece 1 is processed in process 2, it is transferred to M2 p The process can be started from M1 t or M2 t Select one for transportation, and after the last process is completed, the workpiece will be transported to the warehouse for storage.

[0076] Preparation time. In dual-flexible job shop scheduling, preparation time refers to the time when different processing procedures are produced on the same processing equipment, which often requires adjusting the parameter settings of the processing equipment or changing the mold. This period of time is called preparation time. In previous studies that did not consider preparation time, preparation time was considered as processing time by default. However, preparation time and processing time have different characteristics and properties. Preparation time is often auxiliary time before actual processing. The condition for its generation only requires that the current processing equipment is idle. In addition to the equipment being idle, the condition for the generation of processing time also requires that the previous workpiece of the workpiece be processed and transported to the current workstation. Therefore, the preparation operation can often begin before the workpiece arrives at the current workstation.

[0077] Considering that the dual-flexible job shop scheduling problem becomes more complicated after considering the preparation time with learning effect, the present invention makes the following reasonable assumptions:

[0078] (1) All processing equipment and transport machines are idle at time 0.

[0079] (2) Transportation only considers one-way transportation time, and the transportation machine is idle after the workpiece is delivered.

[0080] (3) After each process is completed, the workpiece is transported to the next workstation, and after the last process is completed, the workpiece is transported to the warehouse.

[0081] (4) The processing and transportation process will continue without interruption.

[0082] (5) The workpiece process is fixed and the order cannot be reversed.

[0083] (6) Any processing equipment cannot process multiple processes in parallel, and any transport machine can only transport one workpiece at a time.

[0084] (7) The workpiece process can only select one processing equipment or transportation machine from the available equipment set.

[0085] (8) Due to the different performance of processing equipment, the time required to process the same process may not be the same.

[0086] (9)Only the same processes on a piece of processing equipment have a learning effect, and the learning effects between different processes are independent.

[0087] (10) The processing steps on different processing equipment follow the same learning curve.

[0088] (11) There is preparation time before the process is processed, and it is related to the current processing equipment and the previous process on the equipment.

[0089] (12) The preparation time for the first process on any processing equipment is 0 。

[0090] (13) The preparation operations on different processing equipment obey the same learning curve, namely, the universal continuous-time exponential function.

[0091] Based on the above assumptions,

[0092] Embodiment 1:

[0093] In the first aspect, the present invention first proposes a multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm, see Figure 2 , the method comprising:

[0094] S1. Construct a multi-objective dual-flexible job shop scheduling model; the multi-objective dual-flexible job shop scheduling model includes an objective function and constraints; the objective function is a combined weighted function of the maximum completion time and the line side inventory time; the constraints include processing time constraints and preparation time constraints;

[0095] S2. Solving the processing time constraint based on a learning effect model that considers workpiece position correlation and workpiece similarity to obtain a solved processing time constraint; solving the preparation time constraint based on a continuous exponentially increasing learning effect model to obtain a solved preparation time constraint; optimizing a multi-objective dual-flexible job shop scheduling model based on the solved processing time constraint and the solved preparation time constraint;

[0096] S3. Solve the optimized multi-objective dual-flexible job shop scheduling model based on a hybrid algorithm to obtain the optimal solution of the model, and draw a Gantt chart of the multi-objective dual-flexible job shop scheduling based on the optimal solution; the hybrid algorithm is a combined hybrid algorithm of a multi-population genetic algorithm and a simulated annealing algorithm; wherein the simulated annealing algorithm is used to solve the initial population generated by the multi-population genetic algorithm.

[0097] It can be seen that the multi-objective dual-flexible job shop scheduling method based on the hybrid algorithm of this embodiment builds a multi-objective dual-flexible job shop scheduling model based on the consideration of processing time constraints and preparation time constraints, and then uses different learning effect models to process the processing time constraints and preparation time constraints respectively. Finally, based on the solved processing time constraints and preparation time constraints, the multi-objective dual-flexible job shop scheduling model is solved to obtain the optimal solution of the model, and the Gantt chart of the multi-objective dual-flexible job shop scheduling is drawn based on the optimal solution. This embodiment considers the processing time constraints and preparation time constraints when performing multi-objective dual-flexible job shop scheduling, and uses the learning effect to process these two constraints, which is more in line with the actual situation of workshop production, optimizes the scheduling of resources such as workers, processing equipment, and transportation machines, and the scheduling result of the entire process corresponding to the optimal solution finally obtained is more reasonable, which significantly reduces the maximum completion time and line-side inventory time, and improves the continuity and efficiency of production.

[0098] The following is combined with Figure 1-14 , and explanations of the specific steps S1-S3 are provided to explain in detail the implementation process of an embodiment of the present invention. This embodiment proposes a multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm, and the specific steps are as follows:

[0099] S1. Construct a multi-objective dual-flexible job shop scheduling model; the multi-objective dual-flexible job shop scheduling model includes an objective function and constraints; the objective function is a combined weighted function of maximum completion time and line inventory time; the constraints include processing time constraints and preparation time constraints.

[0100] 1) Construct a multi-objective dual-flexible job shop scheduling model.

[0101] This embodiment uses a combined weighted function of the maximum completion time and the line-side inventory time as the objective function, and takes minimizing the sum of the maximum completion time and the line-side inventory time as the ultimate goal, and transforms the multi-objective problem into a single-objective problem through the weight vector ω.

[0102]

[0103] minZ=ω1C max +ω2C edge

[0104] Where Z represents the combined objective function value; C max represents the maximum completion time, C edge represents the line inventory time, ω1 represents the optimization weight of the maximum completion time, ω2 represents the optimization weight of the line inventory time; n is the total number of workpieces; i is the workpiece number, i=1,...,n. Specifically, when all workpieces are processed, it means that this scheduling is over. Therefore, C max is the maximum value of the end time of the production cycle of all workpieces, as shown in the following formula:

[0105]

[0106] Among them, C edge Indicates the line inventory time. When the workpiece is waiting for processing or waiting for transportation, it will be piled up in the buffer area of ​​the workstation to become the line inventory; k is the processing equipment number, k = 1,..., m; b is the transportation machine number, b = 1,..., a; x i,j,k is a 0-1 integer variable, x i,j,k =1 process O i,j On the device Upper processing; x i,j,k =0 means that the process is not in the equipment Upper processing; i,j,b is a 0-1 integer variable, y i,j,b =1 indicates process O i,j Use transport machine after processing Transportation i,j,b =0 means that the process does not use the machine transportation; For process O i,j Transporting machines Transportation time on For process O i,j In processing equipment The actual processing time after taking into account the learning effect; For process O i,j The set of available processing equipment; For process O i,j Available transport machine set; J i is the total number of processes for workpiece i; j is the process number, j = 1,...,J i ; C i is the completion time of job i;

[0107] 2) Set the constraints of the objective function of the above multi-objective dual-flexible job shop scheduling model.

[0108] According to the dual-flexible job shop production process, the constraints mainly consider the transportation time with resource constraints, preparation time and the processing order of each process of the workpiece, as well as the available equipment constraints for workpiece processing and transportation.

[0109] In the following formula, m is the total number of processing equipment; a is the total number of transportation equipment; M k p is the processing equipment, k = 1, ..., m, and the superscript p indicates that the parameter is related to the processing operation (the same below); is the transport equipment, b=1,...,a, and the superscript t indicates that the parameter is related to the transport operation (the same below); i,j is the j-th process of workpiece i.

[0110] Workpiece processing time constraints:

[0111] It means that the earliest processing time of the first process of any workpiece is 0, that is, it is assumed to be 1.

[0112] It indicates that the working efficiency of the equipment preparation operation obeys the universal continuous time exponential function, where R(t) is its original function and θ is the maximum learning efficiency of the learning effect of the equipment adjustment part; Adjust the learning rate for the partial learning effect for the device.

[0113] represents the preparation time after considering the learning effect, i.e., hypothesis 13, where;

[0114]

[0115] It means that the start time of the workpiece on the processing equipment is constrained by the transportation completion time of the previous process, that is, assumption 5, and is also constrained by the processing equipment resources. The current process can only be processed after the previous process and the equipment preparation operation are completed on the processing equipment, that is, assumption 6 and assumption 11; among them, For process O i,j In processing equipment is the earliest processing time on the workpiece; α is the learning coefficient of the learning effect of the workpiece processing part; λ is the learning rate of the learning effect of the workpiece processing part.

[0116]

[0117] The above formula indicates that the actual processing time of a process is related to the process of other workpieces that have been processed on the equipment, that is, assumption 9, where For process O i,j In processing equipment The original processing time on S j,k [r1, r2] is the processing equipment The similarity between the workpiece at position r1 and the workpiece at position r2 in the j-th process.

[0118] represents the completion time of the process, that is, assumption 4, where x i,j,k is the decision variable; For process O i,j In processing equipment Completion time on

[0119] Indicates that in process O i,j Available processing equipment sets Only one device is selected for processing, that is, assumption 7;

[0120] Workpiece transportation time constraints.

[0121] Transportation time refers to the time it takes to transport a workpiece between the processing equipment of two adjacent processes. If the processing equipment of two adjacent processes is the same, the transportation time is 0. After the last process of the workpiece is completed, it will be transported to the warehouse, and its time will be included in the transportation time of the last process. Process completion time refers to the time it takes for each process to be completed on its available processing equipment. Workpiece completion time refers to the time it takes for a workpiece to complete all operations, that is, the end time of the transportation of the last process of the workpiece. The maximum completion time refers to the time it takes for all workpieces to complete processing, that is, the end time of the transportation of the last process of the workpiece that is completed the latest. The constraints related to transportation time are as follows:

[0122] It means that the transportation start time of the first process of any workpiece is the completion time of the first process;

[0123] It means that the starting time of the workpiece on the transport machine is constrained by the process completion time, that is, assumption 3, and is also constrained by the transport machine resources and must be after the transport of the previous process by the transport machine is completed, that is, assumption 6; among them, For process O i,j Transporting machines The earliest delivery time on

[0124] represents the delivery time of workpiece i, which is the starting transportation time of workpiece i plus the transportation time of the workpiece, where y i,j,b is the decision variable, that is, hypothesis 4, where For process O i,j Transporting machines The earliest delivery time on For process O i,j Transporting machines The time of delivery on

[0125] Indicates that in process O i,j Available transport machine sets Choose a machine for transportation, that is, assumption 7;

[0126] It indicates the maximum value of the transportation completion time after each processing step of the workpiece is completed, which is the end time of the workpiece production cycle.

[0127] S2. Solve the processing time constraint based on the learning effect model that considers the workpiece position correlation and the workpiece similarity to obtain the solved processing time constraint; solve the preparation time constraint based on the continuous exponential increasing learning effect model to obtain the solved preparation time constraint; optimize the multi-objective dual-flexible job shop scheduling model based on the solved processing time constraint and the solved preparation time constraint.

[0128] Both processing operations and preparation operations are human-machine collaborative working modes, so both work scenarios have learning effects. This embodiment establishes different learning effect models based on the characteristics of the two scenarios. In this embodiment, the learning effect of processing time adopts a learning effect model that is related to the workpiece position and considers the workpiece similarity, and solves the processing time after considering the learning effect. The learning effect of preparation time adopts a continuous exponentially increasing learning effect model to solve the preparation time after considering the learning effect. Since the transportation process is mainly completed by the machine, the learning effect during the transportation process is not considered in this embodiment.

[0129] Learning effect of processing time. Based on the actual situation of multi-objective dual-flexible job shop scheduling, this embodiment obtains the following learning effect model considering workpiece similarity in a flexible job shop:

[0130] P j,r =P j (S[1,r]+S[2,r]+…+S[r,r]) α

[0131] Among them, P j represents the processing time of the process without considering the learning effect; P j,r represents the processing time of the workpiece at processing position r after considering the learning effect; S[r1,r2] represents the similarity of the workpieces at positions r1 and r2; where r represents the cumulative product production. α≤0 represents the learning factor of the workpiece α=lgλ / lg2, where λ represents the learning rate.

[0132] Unlike a mixed assembly line workshop (a mixed assembly line workshop is characterized by dedicated machines that are only used in a certain stage of workpiece processing), the processing equipment in a flexible operation workshop may process multiple different processes. On the same processing equipment, only the same processes have a learning effect, that is, the learning effects of different processes on the same processing equipment are independent.

[0133] Learning effects of preparation time.

[0134] Unlike the workpiece processing stage, where workers mainly operate various workpieces, in the equipment preparation stage, workers mainly operate processing equipment, and the operation objects are more single. The learning effect depends on the workers' familiarity with the operation of the processing equipment, and there is no need to consider the similarity between the workpieces. Therefore, in the equipment preparation stage, the use of a learning effect model in which work efficiency is continuously exponentially increased over time is more in line with the actual production situation of the enterprise. The continuous time model considers the impact of past workers' work on current work efficiency. Considering that workers' learning ability is limited, this embodiment does not consider the situation in which employees' work efficiency increases rapidly over time. This embodiment uses a continuous exponentially increasing learning effect model to simulate the learning effect of the preparation stage in DFJSP_MLE, see Figure 3 , Figure 3 In order to consider the work efficiency curve of the learning effect, the specific model is as follows:

[0135] r(t) represents a continuous monotonically increasing function of the worker's work efficiency over time after taking into account the learning effect. y=R(t) is the original function of r(t), that is, dR(t)=r(t)dt, where r(0)=1.

[0136] Assume t = R -1 (y) is the inverse function of function r(t), then the actual completion time is:

[0137] C max =R -1 (P+R(0))

[0138] Among them, C max represents the actual processing time; P represents the normal processing time before considering the learning effect, and R(0) is the function value of y=R(t) when t=0, that is, a constant.

[0139] S3. Solve the optimized multi-objective dual-flexible job shop scheduling model based on a hybrid algorithm to obtain the optimal solution of the model, and draw a Gantt chart of the multi-objective dual-flexible job shop scheduling based on the optimal solution; the hybrid algorithm is a combined hybrid algorithm of a multi-population genetic algorithm and a simulated annealing algorithm; wherein the simulated annealing algorithm is used to solve the initial population generated by the multi-population genetic algorithm.

[0140] 1) Construction of solution algorithm for multi-objective dual-flexible job shop scheduling model.

[0141] After solving the processing time constraint and the preparation time constraint, the objective function of the multi-objective dual flexible job shop scheduling model can be solved by using an intelligent algorithm (such as a genetic algorithm, a simulated annealing algorithm, and other heuristic optimization algorithms) to obtain the optimal solution of the model, and a Gantt chart of the multi-objective dual flexible job shop scheduling can be drawn based on the optimal solution. However, since the DFJSP_MLE problem is relatively complex, and considering that there are a large number of workpieces and processes in the actual production process, when using an intelligent algorithm to solve the model, in order to require the intelligent algorithm to still have a good effect when facing complex scheduling problems, in this embodiment, a preferred method is to use a multiple population genetic algorithm (Multiple Population GA, MPGA) and a simulated annealing algorithm (Simulated Annealing, SA) to combine to form a hybrid algorithm, that is, a hybrid multiple population genetic algorithm, and then use the hybrid multiple population genetic algorithm (Hybrid Multiple Population Genetic Algorithm, HMPGA) to solve the objective function.

[0142] This embodiment uses a multiple population genetic algorithm (Multiple Population GA, MPGA) to replace the standard genetic algorithm (Standard Genetic Algorithm, SGA) to avoid premature maturity; at the same time, in order to make up for the shortcomings of a single optimization algorithm, this embodiment also combines the multiple population genetic algorithm (MPGA) and the simulated annealing algorithm (SA) to form a hybrid multiple population genetic algorithm (HMPGA).

[0143] Multi-population genetic algorithm (MPGA) is an intelligent algorithm composed of multiple standard genetic algorithms (SGA). Each SGA population is controlled by setting different control parameters, crossover rate p c and mutation rate p m , to achieve the purpose of focusing on global search or local search. Among them, the crossover operator can change a large range of genes, which plays a decisive role in the generation of offspring, and represents the ability of the algorithm to search globally; while the mutation operator searches locally through small disturbances. The immigration operator plays the role of spreading excellent genes in multiple populations, that is, co-evolution is achieved by regularly sharing excellent individuals between populations. If there is no immigration operator to connect the various populations, the multiple populations will become several independently evolving standard genetic algorithms. Therefore, the population migration strategy is particularly important for MPGA.

[0144] The introduction of simulated annealing algorithm (SA) can combine probability to randomly search for the global optimal solution of the objective function in the solution space, avoiding the genetic algorithm from falling into premature maturity, thereby improving the quality of the solution and the search speed.

[0145] 2) Use a hybrid multi-population genetic algorithm to solve the objective function of the multi-objective dual-flexible job shop scheduling model.

[0146] First, the HMPGA algorithm uses the good global search ability of the simulated annealing algorithm to set a faster cooling rate to solve P chromosomes as the initial population of the multi-population genetic algorithm; then the P chromosomes are evenly divided into N populations, and each population performs independent genetic operations; secondly, when the N populations are performing genetic evolution, the idea of ​​simulated annealing is also introduced. Each population has two different selection strategies in the crossover operation. Half of the populations use the traditional binary tournament strategy. After the new individuals are obtained in the crossover operation, the fitness is compared with the parent chromosome, and the individuals with smaller fitness are selected to be inherited to the next generation; the other half of the population uses the idea of ​​simulated annealing to calculate the difference between the fitness of the individual and the parent chromosome, and then uses the Metropolis principle to select the inferior solution with a certain probability to be inherited to the next generation. See Figure 4 The specific operation process is as follows:

[0147] Step 1 performs parameter initialization settings, including setting the initial temperature T0, cooling rate q0, Markov chain length L0, etc. in the simulated annealing algorithm (SA); it also includes setting the population size N, initial temperature T0', cooling rate q0', crossover rate p of each population in the multi-population genetic algorithm (MPGA) c , mutation rate p m , the size of each population P size , iterative algebra gen, maximum number of iterations, etc.;

[0148] Step 2: Simulated annealing algorithm (SA) rapid cooling produces P = N × P size The number of individuals is evenly distributed to N populations as the initial population of the multi-population genetic algorithm (MPGA).

[0149] The simulated annealing algorithm (SA) sets a high initial temperature. As the temperature decreases, the probability of accepting new inferior solutions is adjusted through the Metropolis acceptance criterion. When the temperature is high, the algorithm is more likely to accept solutions with smaller objective function values, thereby fully searching for the optimal solution in the solution space. As the temperature decreases, the probability of accepting inferior solutions will become smaller and smaller until it approaches 0.

[0150] When using the SA algorithm to generate P individuals, this embodiment designs a three-layer encoding based on practical problems, dividing the chromosomes into the following three substrings:

[0151] 1) Process part: The first one is the process sequence string (JC). Its length is the sum of the processes of all workpieces. The gene of the process sequence string is the workpiece number, where the number of times the workpiece number appears j represents the jth process of the workpiece. i,j , the position index of the substring is the order of processing. Figure 5 As shown in the figure, the first square of the JC substring indicates that the first processing step is O 2,1 , the sixth square indicates that the sixth processing step is O 2,2 , and so on.

[0152] 2) Processing equipment part: The second one is the processing equipment selection string (MPC). Its length is the same as the process sequence string, where the gene is the available processing equipment number k of the process. The substring gene is arranged in sequence according to the process number. Its position index x2 (the right subscript 2 represents the second chromosome substring MPC) and process O i,j The mapping relationship is as follows:

[0153] The number of processes of the workpiece is J i ; 1≤i≤n.

[0154]

[0155] like Figure 5 As shown, Figure 5 The first square of the MPC substring in represents process O 1,1 The processing equipment is The second square represents process O 1,2 The processing equipment is

[0156] 3) Transport machine part: The third one is the transport machine selection string (MTC). Its length is the same as the first two substrings, where the gene is the available transport machine number b of the process, its index x3 (the right subscript 3 represents the third chromosome substring MTC) and process O i,j The mapping relationship is the same as the second substring. Figure 5 As shown, the first square of the MTC substring in the figure represents process O 1,1 The transport machine is The second square represents process O 1,2 Transport machines

[0157] The SA algorithm generates new solutions through certain mutation rules and randomly searches for the optimal solution of the objective function within the solution space. In this embodiment, the SA algorithm designs four different ways to generate new solutions for the JC substring in the chromosome and randomly selects one of them with the same probability to generate a new individual. The other two substrings, MPC and MTC, can generate new solutions in the conventional ways of uniform crossover and intelligent mutation, which will not be elaborated here. Specifically, when using the simulated annealing algorithm to generate new solutions during rapid cooling (independent evolution), the following steps are executed:

[0158] Step2.1 Let the current temperature T = T0, generate the initial solution S1, and calculate the fitness R1 of the initial solution S1;

[0159] Step2.2 Determine whether the current temperature T < T1 holds. If it holds, end the algorithm, output the optimal solution, and draw a Gantt chart; if it does not hold, let c = 0 and execute Step2.3;

[0160] Step2.3 Randomly select any one of the mutation methods of PPS mutation, swap mutation, reverse mutation, and swap two sub - paths mutation with the same probability to generate a new solution S2, and calculate the fitness R2 of the new solution S2.

[0161] Specifically, the four ways to generate new solutions of PPS mutation, swap mutation, reverse mutation, and swap two sub - paths mutation are described as follows:

[0162] 1) PPS mutation. PPS mutation (Precedence Preserving Shift Mutation, PPS) is a variant of insertion mutation. The main difference lies in the different insertion ranges. The traditional insertion mutation randomly searches for the insertion position within the entire chromosome, while PPS mutation randomly searches for the insertion position for insertion operations on the premise of ensuring the production sequence of a certain workpiece's processes to change the processing sequence of some processes. The specific operation steps are as follows:

[0163] S1.1 Randomly select a workpiece i and any process O i,j , and find the position x1 of this workpiece in the JC substring of the chromosome.

[0164] S1.2 If the previous process O i,j of process O i,j-1 exists, then S_pos is equal to the position x1'+1 of O i,j-1 in the JC substring of the chromosome, otherwise S_pos = 1; if the subsequent process O i,j of process O i,j+1 exists, then E_pos is equal to the position x1”-1 of O i,j+1 in the JC substring of the chromosome, otherwise

[0165] S1.3 Randomly select a position in the interval [S_pos, E_pos] as process O i,j The insertion position forms a newly generated chromosome substring JC'.

[0166] like Figure 6 As shown, Figure 6 Schematic diagram of performing PPS mutation on JC substring to generate new substring JC'. 4,2 It is the second process of workpiece 3, and its position in the JC substring is x1=8. 4,1 The position x1' in the JC substring is 3, so S_pos is 4. 4,3 The position x1" in the JC substring is 11, so E_pos is 10. Finally, position 5 is randomly selected in the interval [4,10] as process O 4,2 The insertion position forms a new chromosome substring JC'.

[0167] 2) Swapping mutation: Swapping mutation is accomplished by exchanging genes at two random positions in the chromosome JC substring to generate a new substring JC'. The specific operation process is as follows.

[0168] S2.1 randomly selects two positions x1 and x2 in the chromosome JC substring.

[0169] S2.2 Exchange the genes at two positions to generate a new chromosome substring JC'.

[0170] like Figure 7 As shown, Figure 7 Schematic diagram of exchanging and mutating the JC substring to generate a new substring JC'. For example, two gene positions x1=5 and x2=8 are randomly selected and the genes at the two positions are exchanged to form a new chromosome substring JC'.

[0171] 3) Inversion mutation: Inversion mutation generates a new substring JC' by reversing the gene order between two gene positions. The specific operation process is as follows.

[0172] S3.1 randomly selects two positions x1 and x2 in the chromosome JC substring.

[0173] S3.2 Sort the genes from position x1 to position x2 in reverse order.

[0174] like Figure 8 As shown, Figure 8Schematic diagram of performing a reverse mutation on the JC substring to generate a new substring JC'. For example, two gene positions x1=5 and x2=9 are randomly selected, and the gene arrangement order between the two positions is reversed to form a new chromosome substring JC'. Reverse mutation will produce greater changes to chromosomes than PPS mutation and insertion mutation.

[0175] 4) Swap Two Sub Path Mutation: Swap Two Sub Path Mutation randomly selects two subpaths of equal length and swaps all genes of the two subpaths to generate a new substring JC'. The specific operation process is as follows.

[0176] S4.1 randomly selects two positions x1 and x2 in the chromosome JC substring as the starting points of the two subpaths.

[0177] S4.2 In the collection A random integer is generated in as the length of the two subpaths. In order to limit the impact of the mutation method on the chromosome, this paper chooses The subpath length is generated within the range of .

[0178] like Fig. 9 As shown, Fig. 9 Schematic diagram of exchanging two subpaths of the JC substring to generate a new substring JC'. For example, two gene positions x1 = 3 and x2 = 9 are randomly generated, and the length of the randomly generated subpath is 4. The genes of the subpaths at positions [3,7] and [9,13] are exchanged to form a new chromosome substring JC'.

[0179] Step 2.4 If R2-R1<0 holds, let S1=S2;

[0180] If R2-R1<0 does not hold, then calculate the acceptance probability of S2 exp(-(R2-R1) / T), and randomly generate a random number rand uniformly distributed in the interval (0,1). If exp(-(R2-R1) / T)>rand holds, then let S1=S2; if exp(-(R2-R1) / T)>rand does not hold, then let S1=S1.

[0181] Step 2.5 Let c = c + 1, and determine whether c = L0. If so, execute Step 2.6. If not, go to Step 2.3.

[0182] Step 2.6: Continue cooling, set T = T × q0, and go to Step 2.2.

[0183] After the above Step 2, a total of P = N × P sizeThe number of individuals is then P, and the P individuals are evenly distributed to N populations as the initial population of the multi-population genetic algorithm (MPGA).

[0184] Step 3: Let the temperature T in the multi-population genetic algorithm (MPGA) = T0'.

[0185] Step 4: Each population in the multi-population genetic algorithm (MPGA) begins to evolve independently, and the initial population is evolved based on the preset evolution rules. The preset evolution rules include: judging whether the current nth population satisfies n<=N / 2, if so, executing Step 4.1; otherwise, executing Step 4.2;

[0186] Step 4.1:

[0187] (1) Evaluate the population: calculate the fitness value of each individual in the population; (2) Select strategy: use the binary tournament method to select operators from the previous generation population to form the parent population; (3) Crossover strategy: perform crossover on the parent population to obtain new individuals, calculate the fitness value of the new individuals, and select the individual with the smaller fitness value between the new individuals and their parent individuals to be inherited to the offspring population; (4) Mutation strategy: perform mutation operations on the offspring population to achieve evolution;

[0188] Step 4.2:

[0189] (1) Evaluate the population: calculate the fitness value of each individual in the population; (2) Selection strategy: use the binary tournament method to select operators from the previous generation population to form the parent population; (3) Crossover strategy: cross the parent population to obtain new individuals, and calculate the fitness value of the new individuals, calculate the difference between the fitness value of the new individuals and the objective function value of the parent individuals, and use the Metropolis selection criterion to determine whether to accept the new individuals to be inherited to the next generation; (4) Mutation strategy: perform mutation operations on the offspring population to achieve evolution.

[0190] When calculating the fitness value of a new individual (i.e., the objective function of this embodiment), this embodiment designs a decoding rule. In the decoding process, the three substrings of each individual are decoded respectively. First, the genes are obtained from the JC substring in sequence, and the meaning of the process corresponding to the gene is determined; after each process is decoded, the process is obtained from the MPC substring through the index x2 and process O i,j The mapping relationship is used to find the processing equipment corresponding to the process, and read and calculate the processing time and preparation time of the process after considering the learning effect; finally, the MTC substring is obtained by index x3 and process O i,j The mapping relationship is used to find the corresponding transport machine after the process is completed, calculate the transport time of the process, and finally generate the activity schedule of the entire chromosome. The specific decoding steps are as follows:

[0191] Step 4-1 Get the x1th (initial x1=1)th bit of the JC substring and calculate the number of times the current workpiece appears. Then this process is the jth process of the i-th workpiece, denoted by O i,j .

[0192] Step 4-2 According to the formula Get process O i,j The corresponding index x2 in the MPC substring, read the gene at position x2 in the MPC substring, which is the processing equipment of this process. Get machining time from parameter set And calculate the actual processing time after the learning effect Specifically, it is calculated according to the following formula:

[0193]

[0194] Step 4-3 According to the formula Calculation process O i,j The earliest processing time

[0195] Step 4-4 Read the transport machines one by one The idle time period is used to determine whether the current process can be inserted into the idle time period for processing. The specific steps are as follows:

[0196] Step 4-4-1 Read The start and end time T1, T2 of the first (initial l = 0) idle time and the previous and next processes O i',j' ,O i”,j” ;

[0197] Step4-4-2 Judgment Is it less than T2? If yes, execute Step 4.3, otherwise l=l+1 and return to Step 4-4-1;

[0198] Step 4-4-3 According to the formula P j,r =P j (S[1,r]+S[2,r]+…+S[r,r]) α Get the current process preparation time from the parameter set And according to the formula Calculating preparation time after accounting for learning effects

[0199] Step 4-4-4 Inserting the current process will change the original preparation time of the next process after the idle time period According to the formula P j,r =P j (S[1,r]+S[2,r]+…+S[r,r]) αRe-obtain the preparation time of a process after the current idle time period The schematic diagram of the impact of the process insertion on the preparation time of the next process is as follows Fig.10 As shown, Fig.10 (a) Process O can be seen 1,3 Original preparation time In process O 2,1 Insert into processing equipment Afterwards, Fig.10 (b) as shown, process O 1,3 The preparation time is updated to

[0200] Step4-4-5 Judgment formula Is it true? If it is true, then O i,j You can insert this idle time period to process and calculate Otherwise l=l+1 and return to Step 4-4-1.

[0201] Step 4-5 Get process O i,j The corresponding index x3 in the MTC substring, the gene reading x3 is the transport machine of this process. And get the shipping time from the parameter set

[0202] Step 4-6 Read the transport machines one by one Idle time period, and according to the formula formula Judgment process O i,j Whether it can be transported during this idle time period, and calculate

[0203] Step4-7Judge Is it true? If so, all processes are decoded and the iteration ends; otherwise, x1=x1+1, and go to Step 4-1.

[0204] Step 4-8 calculates the individual fitness value according to the calculation formula related to the combined objective function, and the chromosome decoding is completed. The calculation formula related to the combined objective function is as follows:

[0205]

[0206] Step 5: Let gen = gen + 1, T = T × q0'. Determine whether gen% 5 == 0. If not, return to Step 4 to start the next generation of evolution. If yes, select the top 10% of individuals in each SGA population as migration operators and migrate to the next SGA population to replace the individuals with the worst fitness.

[0207] The migration strategy mainly includes the migration scale, migration strategy and topological structure. In this embodiment, preferably, the migration cycle is selected as 5, that is, migration is performed once every 5 iterations, and the migration rate is set to 0.1. The migration strategy is to select the top 10% of individuals in each population to replace the individuals with the worst fitness in the next population, and the topological structure selects a unidirectional ring topological structure. The specific migration strategy of the immigration operator is as follows: Fig.11 shown.

[0208] Step 6 determines whether gen%iterations==0 is true. If not, return to Step 4 to start the next generation of evolution. If true, go to Step 7. Among them, gen%iterations==0 means to determine whether the current gen value is equal to iteration.

[0209] Step 7: Output the optimal individual and draw a Gantt chart based on the optimal individual.

[0210] Finally, draw a Gantt chart based on the optimal individual, such as Fig.13 As shown, the scheduling of multi-objective dual-flexible job shops is realized according to the Gantt chart.

[0211] At this point, the entire process of the multi-objective dual-flexible job shop scheduling method based on the hybrid algorithm of the present invention is completed.

[0212] In order to verify the actual effect of the multi-objective dual-flexible job shop scheduling method based on the hybrid algorithm proposed in this embodiment, this embodiment is proved through experiments.

[0213] 1) This example compares the impact of considering the preparation time constraint with the learning effect and not considering the preparation time constraint with the learning effect on the final scheduling result. The case of "not considering preparation time" is that only the transportation time with resource constraints is considered during optimization, and the preparation time actually exists, but it is not optimized; the case of "considering preparation time" is that the optimization considers both the transportation time with resource constraints and the preparation time, and both are optimized during the solution.

[0214] In order to make the experimental results more general, different chromosome sizes were selected for the experiment, with chromosome lengths of ρ = 54, 96, and 150 respectively, and different numbers of processing equipment m and transport machines a were set to form different use cases for experimental analysis. The results of each use case were the average of ten running results. The specific experimental results are shown in Table 1.

[0215] Table 1. The impact of multiple auxiliary times on scheduling results

[0216]

[0217] Note: ρ: total chromosome length; a: number of transport machines; m: number of processing equipment.

[0218] From Table 1, we can see that the optimization result considering preparation time is significantly better than the optimization result considering only transportation time with resource constraints. The combined objective function value is Z The optimization results of the line inventory C edge The optimization results have increased by up to 77.59% and by 69.8% on average. In the optimization results, the best optimization results of the combined objective function value and line inventory appeared in the case of ρ=150, a=5, m=10, indicating that the optimization effect on a larger scale will be more significant when the preparation time is taken into account, especially the optimization of line inventory, which has a significant improvement.

[0219] Fig.12 and Fig.13 The Gantt charts of the workshop scheduling are the optimal solutions without considering the preparation time and with considering the preparation time. By comparing the two figures, it can be found that the scheduling result of the entire process with the optimal solution considering the preparation time is more reasonable, and both the maximum completion time and the line inventory time are significantly reduced, which proves that it is necessary and positive to consider the impact of the preparation time on the scheduling results in the DFJSP_MLE problem.

[0220] 2) Compare the solution effects of the hybrid multi-population genetic algorithm (HMPGA) proposed in this embodiment and the existing single solution algorithms (mainly including multi-population genetic algorithm MPGA, standard genetic algorithm SGA, simulated annealing algorithm SA) in solving multi-objective dual-flexible job shop scheduling.

[0221] See also Fig.14 , Fig.14 The fitness convergence diagrams of the four algorithms under four use cases of ρ=54, a=3, m=4, ρ=96, a=4, m=6, ρ=96, a=4, m=8, and ρ=150, a=5, m=8 are given. The diagrams show that the convergence of HMPGA in each use case is optimal, especially in large-scale scheduling problems, where the convergence speed is faster and the optimal solution obtained is the best.

[0222] Embodiment 2:

[0223] In a second aspect, the present invention further provides a multi-objective dual-flexible job shop scheduling system based on a hybrid algorithm, the system comprising:

[0224] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the steps of the above method are implemented when the processor executes the computer program.

[0225] It can be understood that the multi-objective dual-flexible job shop scheduling system based on a hybrid algorithm provided in an embodiment of the present invention corresponds to the multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm mentioned above, and the explanations, examples, beneficial effects, etc. of the relevant contents can refer to the corresponding contents in the multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm, and will not be repeated here.

[0226] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0227] 1. The present invention constructs a multi-objective dual-flexible job shop scheduling model based on the consideration of processing time constraints and preparation time constraints, and then uses different learning effect models to process the processing time constraints and preparation time constraints respectively, and optimizes the multi-objective dual-flexible job shop scheduling model. Finally, the optimized multi-objective dual-flexible job shop scheduling model is solved to obtain the optimal solution of the model, and the Gantt chart of the multi-objective dual-flexible job shop scheduling is drawn based on the optimal solution. When performing multi-objective dual-flexible job shop scheduling, the present invention considers the processing time constraints and preparation time constraints on the one hand, and processes these two constraints respectively using different learning effect models, which is more in line with the actual situation of workshop production, and the scheduling result of the entire process corresponding to the optimal solution finally obtained is more reasonable and accurate; on the other hand, a hybrid algorithm is used to solve the objective function of the multi-objective dual-flexible job shop scheduling model considering multiple constraints, so as to improve the quality of the solution and the search speed. In general, the multi-objective dual-flexible job shop scheduling method based on the hybrid algorithm of the present invention improves the accuracy and efficiency of the scheduling results, optimizes the scheduling of resources such as workers, processing equipment, and transportation machines, makes the scheduling results of the entire process more reasonable, significantly reduces the maximum completion time and line-side inventory time, and improves the continuity and efficiency of production.

[0228] 2. Based on the characteristics of the two scenarios of processing operation and preparation operation, the present invention adopts the learning effect model related to the workpiece position and considering the workpiece similarity to solve the processing time after considering the learning effect, accurately expresses the learning effect relationship between the same processes, and clarifies that the learning effects of different processes on the same processing equipment are independent; the learning effect model in which the work efficiency is a continuous exponential increase related to time is adopted to process the preparation time constraint, considering the influence of the worker's past work and work experience on the current work efficiency. The processing time constraint and preparation time constraint processed by the learning effect model are more in line with the actual production situation of the enterprise, making the scheduling results of the dual-flexible job shop more accurate.

[0229] 3. The present invention combines a multi-population genetic algorithm (MPGA) and a simulated annealing algorithm (SA) to form a hybrid multi-population genetic algorithm (HMPGA) for solving multi-objective dual-flexible job shop scheduling problems, which makes up for the shortcomings of a single optimization algorithm; in addition, the introduction of the simulated annealing algorithm can combine probability to randomly search for the global optimal solution of the objective function in the solution space, avoiding the genetic algorithm from falling into premature maturity, thereby improving the quality of the solution and the search speed.

[0230] 4. The present invention designs four new solution generation methods: PPS mutation, exchange mutation, inverse mutation, and exchange of two sub-paths mutation, and randomly selects one of the methods to generate a new solution in each iteration, avoiding poor population diversity caused by a single new solution generation method, thereby improving the algorithm's global optimization capability.

[0231] 5. According to the preset migration cycle, migration rate, and migration topology, the present invention uses the individuals ranked in the top 10% of the fitness in the initial population after the previous evolution as migration operators, and migrates them to the initial population after the next evolution to replace the individuals ranked the worst in fitness. This migration strategy utilizes the immigration operator to spread excellent genes among multiple populations, establishes connections between various populations, and ensures the associated evolution among multiple populations.

[0232] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0233] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective dual-flexible job shop scheduling method based on a hybrid algorithm, characterized in that: The method comprises: Constructing a multi-objective dual-flexible job shop scheduling model; the multi-objective dual-flexible job shop scheduling model includes an objective function and constraints; the objective function is a combined weighted function of maximum completion time and line side inventory time; the constraints include processing time constraints and preparation time constraints; Solving the processing time constraint based on a learning effect model that considers workpiece position correlation and workpiece similarity to obtain the solved processing time constraint; solving the preparation time constraint based on a continuous exponential increasing learning effect model to obtain the solved preparation time constraint; optimizing a multi-objective dual-flexible job shop scheduling model based on the solved processing time constraint and the solved preparation time constraint; Solving the optimized multi-objective dual-flexible job shop scheduling model based on a hybrid algorithm to obtain the optimal solution of the model, and drawing a Gantt chart of the multi-objective dual-flexible job shop scheduling based on the optimal solution; the hybrid algorithm is a combination of a multi-population genetic algorithm and a simulated annealing algorithm; wherein the simulated annealing algorithm is used to solve the initial population generated by the multi-population genetic algorithm; The workpiece position-related and workpiece similarity-considered learning effect model includes: P j,r =P j (S[1,r]+S[2,r]+...+S[r,r]) α Among them, P j represents the processing time of the process without considering the learning effect; P j,r represents the processing time of the workpiece at processing position r after considering the learning effect; S[r1,r2] represents the similarity between the workpieces at positions r1 and r2; The continuous exponentially increasing learning effect model includes: C max =R -1 (P+R(0)) Among them, C max represents the actual processing preparation time; P represents the normal processing preparation time before considering the learning effect, and R(0) is the function value of y=R(t) when t=0.

2. The method according to claim 1, characterized in that The combined weighting function comprises: minZ=ω1C max +ω2C edge Among them, C max represents the maximum completion time, C edge represents the line-side inventory time; ω1 represents the optimization weight of the maximum completion time, and ω2 represents the optimization weight of the line-side inventory time.

3. The method according to claim 1, characterized in that The method of solving the optimized multi-objective dual-flexible job shop scheduling model based on a hybrid multi-population genetic algorithm to obtain an optimal solution of the model, and drawing a Gantt chart of the multi-objective dual-flexible job shop scheduling based on the optimal solution, includes the following steps: Step 1 performs parameter initialization settings, including setting the initial temperature T0, final temperature T1, cooling rate q0, number of iterations c at each temperature, and maximum number of iterations L0 at each state in the simulated annealing algorithm; it also includes setting the population size N, initial temperature T0', cooling rate q0', and crossover rate p of each population in the multi-population genetic algorithm. c , mutation rate p m , the size of each population P size , iterative algebra gen, and the maximum number of iterations iterations; Step 2 generates N initial populations of multi-population genetic algorithm based on simulated annealing algorithm; Step3 Let the temperature T in the multi-population genetic algorithm = T0'; Step 4: Each population in the multi-population genetic algorithm begins to evolve independently, and the initial population is evolved based on a preset evolution rule; Step 5: Let gen = gen + 1 and T = T × q0', and determine whether gen% 5 == 0 is true. If not, execute Step 4; if true, migrate each of the initial populations after evolution based on the preset migration strategy; Step 6 determines whether gen%iterations==0 is true. If not, execute Step 4; if true, execute Step 7; Step 7 outputs the optimal individual and draws the Gantt chart of multi-objective dual-flexible job shop scheduling based on the optimal individual.

4. The method according to claim 3, characterized in that The N initial populations of the multi-population genetic algorithm generated by the simulated annealing algorithm in Step 2 include: Step 2.1 Let the current temperature T = T0, generate the initial solution S1 and calculate the fitness R1 of the initial solution S1; Step 2.2 determines whether the current temperature T<T1 is established. If so, the algorithm is terminated to output the optimal solution and draw a Gantt chart; if not, set c=0 and execute Step 2.3; Step 2.3 Randomly select any one of the mutation modes, PPS mutation, exchange mutation, reverse mutation, and exchange of two subpaths, with the same probability to generate a new solution S2, and calculate the fitness R2 of the new solution S2; Step 2.4 If R2-R1<0, let S1=S2; If R2-R1<0 does not hold, then calculate the acceptance probability of S2 exp(-(R2-R1) / T), and randomly generate a random number rand uniformly distributed in the interval (0,1). If exp(-(R2-R1) / T)>rand holds, then let S1=S2; if exp(-(R2-R1) / T)>rand does not hold, then let S1=S1; Step 2.5 Let c = c + 1, and determine whether c = L0. If so, execute Step 2.

6. If not, go to Step 2.

3. Step 2.6: Continue cooling, set T = T × q0, and go to Step 2.

2.

5. The method according to claim 3, characterized in that The preset evolution rule includes: judging whether the current nth population satisfies n<=N / 2, if so, executing Step 4.1; otherwise, executing Step 4.2; Step 4.1: (1) Evaluate the population: calculate the fitness value of each individual in the population; (2) Selection strategy: Use the binary tournament method to select operators from the previous generation population to form the parent population; (3) Crossover strategy: Cross the parent population to obtain new individuals, calculate the fitness value of the new individuals, and select the individual with the smaller fitness value between the new individuals and their parent individuals to be inherited to the offspring population; (4) Mutation strategy: perform mutation operations on the offspring population to achieve evolution; Step 4.2: (1) Evaluate the population: calculate the fitness value of each individual in the population; (2) Selection strategy: Use the binary tournament method to select operators from the previous generation population to form the parent population; (3) Crossover strategy: Cross the parent population to obtain new individuals, calculate the fitness value of the new individuals, calculate the difference between the fitness value of the new individuals and the objective function value of the parent individuals, and use the Metropolis selection criterion to determine whether to accept the new individuals to be inherited to the next generation; (4) Mutation strategy: perform mutation operations on the offspring population to achieve evolution.

6. The method according to claim 3, characterized in that The preset migration strategy includes: According to the preset migration cycle, migration rate, and migration topology, the individuals ranked in the top 10% of fitness in the initial population after the previous evolution are used as migration operators and migrated to the initial population after the next evolution to replace the individuals ranked in the worst fitness.

7. The method according to claim 6, characterized in that The migration period is 5, the mobility is 0.1, and the migration topology is a unidirectional ring topology.

8. A multi-objective dual-flexible job shop scheduling system based on a hybrid algorithm, characterized in that: The system includes: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method according to any one of claims 1 to 7 when executing the computer program.

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