Flexible job shop scheduling method and device under complex constraints based on INSGA-II

Abstract

The application discloses a flexible job shop scheduling method and device under complex constraints based on INSGA-II, and the method comprises the following steps: obtaining basic production information and scheduling constraints of a workshop, wherein the basic production information comprises one or more of order tasks, device resources and manual resources, process information and shift information, and the scheduling constraints comprise non-machine-changing constraints and elastic extended shift time constraints; taking total weighted delay loss minimization and total cost minimization as double optimization targets, modeling a flexible machine shop scheduling problem under complex constraints to obtain a scheduling model of the flexible machine shop; and inputting production information of the current workshop into the scheduling model to obtain an optimal scheduling scheme of the current workshop. The method accurately establishes an FJSP model in combination with specific production characteristics, and makes the generated scheduling scheme closer to the real situation and more applicable.

Description

Technical Field

[0001] This invention relates to the field of workshop scheduling technology, and in particular to a flexible workshop scheduling method and apparatus based on INSGA-II under complex constraints. Background Technology

[0002] The classic flexible job shop scheduling problem model is as follows: Based on Brucker's FJSP, this problem model can be described as follows: There are n tasks J1,…,J... to be processed. n and m different machines M1,…,M m Each task J i By n i Process O i,1 ,…,O i,ni Composed of, and this n i Each process must be processed in this order; each process O i,j Corresponding to an optional set of machines O i,j Processing can be done on any of these machines, and the processing time on each machine is t. i,j (In some FJSP models, any M machine in the selectable machine set) k Each of these will correspond to a processing time t. i,j,k Machines cannot process two or more tasks simultaneously. To simplify the problem, the following assumption is usually made:

[0003] (1) All machines are available at the initial time t=0;

[0004] (2) All workpieces are in a processable state at the initial time t=0;

[0005] (3) Process O i,j Only from set M i,j Choose one machine to process;

[0006] (4) There is no priority order restriction between different workpieces, so the workpieces are independent of each other;

[0007] (5) Processing steps that have already begun must not be interrupted;

[0008] (6) The time for transporting the workpiece between machines and the machine setup time required for this process are included in the processing time t. i,j,k Inside.

[0009] The main methods for solving the flexible job shop scheduling problem are exact algorithms and approximate algorithms.

[0010] 1. Precise Algorithm

[0011] Exact algorithms mainly include branch and bound, mixed integer programming model, enumeration method based on disjunctive graph model and Lagrange relaxation method. Exact algorithms can theoretically ensure that the global optimal solution is found, but the corresponding time cost is large, which makes them particularly difficult to apply to large-scale job shop scheduling problems.

[0012] Brucker et al. proposed an FJSP (flexible job shop scheduling problem) involving two jobs to be processed, where each process has a set of available machines, and proposed a polynomial graphical algorithm for solving the problem. Sawik developed a multi-level ILP model for flexible manufacturing systems, which is a hierarchical decision structure including part type selection, machine loading, part processing sequence, and process scheduling. Sawik also provided linear programming formulas for each level and algorithms for solving part scheduling schemes. Jiang et al. proposed an FJSP model with alternative process plans, considering both job scheduling and process plan selection problems, and used 0-1 integer programming to model the problem, solving for the scheduling scheme that minimizes the absolute value of the completion date deviation or the total completion time. Torabi et al. proposed a mixed integer nonlinear programming (MINLP) approach to solve the periodic multi-product batch scheduling problem in flexible workshops. They employed an efficient enumeration method to replace the computationally complex MINLP problem, thus simplifying the determination of the optimal solution. This approach is suitable for small-scale problems, but for larger-scale problems, it requires solving several computationally intensive mixed 0-1 integer programming problems, making the method more difficult to implement. Roshanaei et al. established two MINLP models—position-based and sequence-based—to describe the processing in flexible workshops, and numerically solved them using the maximum completion time as the optimization criterion.

[0013] Exact algorithms can theoretically find the optimal solution, but they are usually based on some simplifying assumptions and the scale of the problem they consider is not too large. For MOFJSP (multi-objective flexible job shopscheduling problem), especially MOFJSP in the high-dimensional domain, it is difficult to apply exact algorithms effectively due to their high computational complexity.

[0014] 2. Approximation Algorithm

[0015] As the problem size increases, the constraints become more diverse and complex, it is difficult to model and solve the problem accurately, and the huge computational overhead makes it difficult for the original exact algorithm to continue to be effectively applied. For such complex problems, instead of pursuing the optimal solution, approximate algorithms for finding suboptimal or better solutions have become a new research direction.

[0016] Heuristic algorithms are designed based on people's intuitive feelings or long-term accumulated historical experience for specific problems. When using heuristic algorithms to solve a specific problem, although it cannot guarantee to get the optimal solution, nor can it predict the deviation degree of the feasible solution from the optimal solution, but it can give a feasible solution within an acceptable time, so many heuristic methods are applied to the solution of complex FJSP.

[0017] The operation of scheduling rules is simple, and the computational complexity is not high, which can solve large-scale production scheduling problems in a short time, so it has been widely used in FJSP. Shao Binbin et al. proposed a heuristic algorithm based on comprehensive dispatching rules. The comprehensive dispatching rules in the paper include two parts. One part is the rule for determining the priority order of the workpiece, which is based on the classic S / LPT (shortest / longest processing time), M / LRW (most / least remaining work), FCFS (first come first served) and other rules, and defines a priority index. The larger the value is, the more priority it has to be selected for scheduling. The other part is the machine allocation rule, which uses a greedy way to allocate the process to the machine with the earliest process completion time in the selected machine set. Kacem et al. first used different scheduling rules such as S / LPT, FIFO (first in first out), LIFO (last in first out) to allocate resources to the process, and then used genetic algorithm to further optimize after converting FJSP to JSP. Wang et al. proposed a heuristic algorithm based on FBS (filtered beam search) for FJSP model containing maintenance activities and maintenance resource constraints, and designed a branching scheme to combine machine availability constraints and maintenance resource constraints. Sobeyko et al. discussed FJSP with total weighted tardiness as the objective, and proposed an efficient iterative local search method, and combined SBH (shifting bottleneck heuristic) with the local search method proposed in this paper and VNS (variable neighborhood search) method.

[0018] Metaheuristic algorithm combines random algorithm and local search algorithm, and it is not limited to specific application, as a general framework has strong versatility.

[0019] Genetic algorithm as a typical metaheuristic algorithm has been widely used in scheduling problem. Zhang et al. proposed an effective genetic algorithm to solve FJSP, combined with the use of global selection, local selection, random selection strategy to generate high-quality initial population in the population initialization stage, using improved chromosome expression mechanism and related operation operator, to ensure that the generated solution is a feasible solution to avoid the repair mechanism of infeasible solution. There are also many studies on using improved genetic algorithm to solve FJSP, Rooyani et al. proposed a two-stage genetic algorithm, the first stage provides a high-quality initial population for the second stage. Cheng et al. proposed a double population hybrid genetic algorithm, which is responsible for global search and local search respectively, and improves performance through co-evolution. Yang et al. used NSGA-II (Non-dominated Sorting Genetic Algorithm II, non-dominated sorting genetic algorithm with elite strategy) to solve the multi-objective scheduling optimization problem, with the optimization objectives of minimizing the maximum completion time, critical machine workload and total machine workload, the processing sequence was randomly generated when generating the initial population, and the machine selection part used random generation and the shortest processing time two rules to mix in different proportions to form different initial populations. The comparison of experimental results with greedy random adaptive search process and other algorithms proves the effectiveness of the algorithm performance. Li et al. embedded variable neighborhood search algorithm into genetic algorithm to solve FJSP, for different machines using critical process migration strategy based on machine idle time, finding suitable machine idle time period for critical process insertion to reduce the maximum completion time, the hybrid algorithm has strong global search ability and local search ability, and improves the speed and quality of solution. Simulated annealing algorithm can accept worse solutions than current solutions with a certain probability in the iteration process, so as to jump out of local optimum, has strong global search ability, Altoe et al. proposed a simulated annealing algorithm based on clustering search to generate scheduling scheme of double objective FJSP, with the optimization objectives of minimizing the maximum completion time and total delay, generating a set of non-dominated solutions to obtain Pareto boundary, providing a series of selectable high-quality solutions for decision makers.

[0020] Overall, the precise algorithm can solve the problem of smaller size, usually need to make considerable simplification of the actual problem, the calculation amount increases sharply with the problem size makes its application is limited; Heuristic algorithm using the design of scheduling rules to greatly improve the efficiency of the algorithm, the calculation amount is greatly reduced, can obtain the scheduling scheme with fast speed, but the scheduling rules have their own emphasis, will tend to optimize a certain index, it is difficult to find the global optimal solution, may exist shortsighted, one-sided defects, easy to fall into local optimal or even worse solution. Meta-heuristic algorithm balances the advantages and defects of the foregoing two kinds of methods to a certain extent, within the acceptable time and cost of calculation, as far as possible from the global perspective to find the approximate optimal solution, for larger scale problem also has good performance, in FJSP application is more widely.

[0021] But looking back at past research can be found that most research work focuses on the performance of the algorithm under the standard FJSP problem model, through the fusion of different algorithms, the proposal of new algorithm, the embedding of new strategy to improve the optimization performance of the algorithm, but the actual production process is often more complex, the factors affecting production, the constraints to be met are more diverse, different enterprises have their own unique production characteristics, and there is not small difference with the standard FJSP problem model, which increases the difficulty of directly applying the research results of the past to the actual production process. In the actual workshop production, the set of optional machines is often the same type of machine, and the time for processing a certain process is also roughly the same, and the difference can be ignored. If the process j (O i,j ) of a workpiece i is processed on machine M1, the set of optional machines of the next process O i,j+1 contains M1 (for example, {M1, M2, M3}), if other machines are used instead of M1, workpiece disassembly, transportation, installation and other processes will be required, which will cause waste of time and human resources; At the same time, the retooling step in the installation process will also affect the machining accuracy. Obviously, it is a better choice to continue using machine M1 to process process O i,j+1 , and most of the previous research has not paid attention to avoiding unnecessary machine change in the processing process. Secondly, the shift information is often simplified and ignored, making it difficult to accurately reflect the real production situation in a long period of time (one week, one month), and the actual task quantity is not considered to optimize the work time arrangement. SUMMARY

[0022] The present application aims to at least partially solve one of the problems in the related art.

[0023] To this end, one object of the present application is to provide a flexible job shop scheduling method under complex constraints based on INSGA-II, which is aimed at the scheduling problem of a flexible machine shop that needs to consider constraints such as shift replacement, flexible extension of shift time and non-machine replacement, accurately models and solves a reasonable scheduling scheme according to the actual production characteristics, and optimizes the objective of minimizing the total weighted tardiness loss and total cost.

[0024] Another object of the present application is to provide a flexible job shop scheduling device under complex constraints based on INSGA-II.

[0025] To achieve the above object, one aspect of the embodiments of the present application provides a flexible job shop scheduling method under complex constraints based on INSGA-II, comprising the following steps:

[0026] Obtaining basic production information and scheduling constraints of the workshop, wherein the basic production information includes one or more of order tasks, equipment resources and manual resources, process information and shift information, and the scheduling constraints include non-machine replacement constraints and flexible extension of shift time constraints;

[0027] Modeling the flexible machine shop scheduling problem under complex constraints with the dual optimization objectives of minimizing the total weighted tardiness loss and minimizing the total cost to obtain a scheduling model of the flexible machine shop; and

[0028] Inputting the production information of the current workshop into the scheduling model to obtain the optimal scheduling scheme of the current workshop.

[0029] To achieve the above object, another aspect of the embodiments of the present application provides a flexible job shop scheduling device under complex constraints based on INSGA-II, comprising:

[0030] The acquisition module is configured to obtain basic production information and scheduling constraints of the workshop, wherein the basic production information includes one or more of order tasks, equipment resources and manual resources, process information and shift information, and the scheduling constraints include non-machine replacement constraints and flexible extension of shift time constraints;

[0031] The modeling module is configured to model the flexible machine shop scheduling problem under complex constraints with the dual optimization objectives of minimizing the total weighted tardiness loss and minimizing the total cost to obtain a scheduling model of the flexible machine shop; and

[0032] The scheduling module is configured to input the production information of the current workshop into the scheduling model to obtain the optimal scheduling scheme of the current workshop.

[0033] The flexible job shop scheduling method and device under complex constraints based on INSGA-II of the embodiment of the application have the following beneficial effects: the FJSP model is accurately established in combination with specific production characteristics, and the generated scheduling scheme is closer to the real situation and more usable; the improved non-dominated sorting genetic algorithm with an elite strategy is applied, high-quality scheduling schemes can be searched, and therefore the limited resources such as energy resources, equipment resources, human resources and time resources can be more efficiently and reasonably coordinated and utilized, so that the enterprise can improve the production system performance, save energy and reduce emissions, reduce product cost, reduce delay and improve market competitiveness.

[0034] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0035] The above and / or additional aspects and advantages of the application will become apparent and be readily understood from the following description, taken in conjunction with the accompanying drawings, in which:

[0036] Figure 1 A flow chart of the flexible job shop scheduling method under complex constraints based on INSGA-II according to one embodiment of the application;

[0037] Figure 2 A schematic diagram of adjacent equipment processes that need to use the same equipment according to one embodiment of the application;

[0038] Figure 3 A schematic diagram when one manual process is intervened according to one embodiment of the application;

[0039] Figure 4 A schematic diagram when one different group of equipment processes is intervened according to one embodiment of the application;

[0040] Figure 5 A schematic diagram of two-segment chromosome coding according to one embodiment of the application;

[0041] Figure 6 A schematic diagram of a greedy insertion decoding strategy according to one embodiment of the application

[0042] Figure 7 An example diagram of a crossover operation according to one embodiment of the application;

[0043] Figure 8 A flow chart of the INSGA-II algorithm according to one embodiment of the application;

[0044] Figure 9 A flow chart of dynamic shift adjustment according to one embodiment of the application;

[0045] Figure 10 Figure 1 is a structural schematic diagram of an INSGA-II based flexible job shop scheduling device under complex constraints according to an embodiment of the present application. DETAILED DESCRIPTION

[0046] Embodiments of the present application are described in detail below with reference to examples illustrated in the accompanying drawings, in which the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0047] The market demand is increasingly diversified and personalized today, and the production tasks in a period of time often contain many products with different production characteristics. The complex production tasks pose a considerable challenge to further improving production efficiency and intelligent manufacturing degree for enterprises. Therefore, the production optimization scheduling problem faced by modern manufacturing enterprises usually exhibits characteristics such as multi-objective, multi-constraint, and high nonlinearity. The present application is aimed at the production characteristics of a variety of products and small batch size in the machining workshop of an actual manufacturing enterprise. At the same time, due to the extremely high quality requirements of products, the required processing cycle is also relatively long, and there are some special constraints set in the processing process to ensure processing quality and processing stability. The complex production requirements make it extremely complex and tedious for on-site management personnel to manually develop scheduling tasks, the quality of the scheduling scheme is difficult to effectively guarantee, and the response speed cannot be well matched with the complex and changing production environment and production demand. Therefore, designing an efficient algorithm to automatically generate a scheduling scheme is a better choice than relying on experienced manual scheduling.

[0048] The existing technology mostly uses process level-based coding for chromosome coding to solve the flexible job shop scheduling problem, uses two equal-length chromosomes to represent the workpiece processing sequence and resource allocation, and fails to consider reducing unnecessary equipment replacement in the processing process. The present application defines a constraint process group, designs a constraint process group division algorithm, and an adaptive non-equal-length two-chromosome coding mode, which can reduce resource waste caused by unnecessary equipment replacement in the processing process.

[0049] The existing technology usually simplifies the work shift information, considers that all production resources are in an available state after zero time, and that the available time period is continuous and fixed. The present application considers that production and processing activities are carried out according to work shifts, which is more in line with the actual situation. The available time period of the production resource is a discontinuous time period after excluding the rest time, and the work shift is dynamically adjusted according to the task quantity. The work shift is no longer a fixed information but an information that can be optimized and adjusted, which can better match the task quantity at different periods.

[0050] A flexible job-shop scheduling method and device under complex constraints based on INSGA-II are provided according to an embodiment of the present application.

[0051] Firstly, a flexible job-shop scheduling method under complex constraints based on INSGA-II according to an embodiment of the present application will be described with reference to the accompanying drawings.

[0052] Figure 1 A flow chart of the flexible job-shop scheduling method under complex constraints based on INSGA-II according to an embodiment of the present application is shown in FIG. 1.

[0053] As shown in FIG. 2, the flexible job-shop scheduling method under complex constraints based on INSGA-II includes the following steps: Figure 1

[0054] In step S101, basic production information and scheduling constraints of the workshop are acquired, wherein the basic production information includes one or more of order tasks, equipment resources and manual resources, and the scheduling constraints include non-machine changing constraints and flexible extended shift time constraints.

[0055] Firstly, the basic production information will be introduced.

[0056] 1. Order tasks

[0057] An order task contains the following information: order number, order priority, and delivery time. The order number is a unique number, which is used to establish a corresponding relationship with the process that needs to be performed for the product. The order priority is divided into four levels, which are represented by numbers 1, 2, 3 and 4 from high to low. Different priorities will correspond to different delay penalty weights.

[0058] 2. Equipment resources and manual resources

[0059] Two types of production resources are required during the processing of a product: equipment resources and manual resources. Correspondingly, processes can also be divided into two categories: equipment processes and manual processes. Equipment processes require the use of corresponding production equipment, and each piece of equipment is operated by a dedicated equipment operator. One person and one machine work together to complete the processing task of the equipment process. Manual processes do not require the use of special equipment and can be completed independently by manual workers with the corresponding manual skills. Equipment operators and manual workers are two different types of workers, and there is no intersection between them.

[0060] ​Both equipment resources and manual resources have the concept of resource group. Taking equipment resource group as an example, one equipment resource group number contains several pieces of equipment, and any equipment process Oij will specify an equipment resource group number, and any piece of equipment under the equipment resource group number can be selected to complete the process. The resource group is similar to the optional machine set in the classic FJSP, and the same manual resource group number is a number of manual workers.

[0061] 3. Process information

[0062] The process information includes order number, process number, resource group number, and processing time. Two processes with the same order number represent different processes under the same order task, and the process number indicates the current process is the first process of the order task. The resource group number represents the production resource required by the process, and if the resource group number belongs to the equipment resource group number, it represents the equipment sequence, and if it belongs to the manual resource group number, it represents the manual sequence.

[0063] 4. Shift information

[0064] Shift information is used to describe the working and resting time period of the day, which is also an information that is simplified by most FJSP researches. In these researches, the following assumptions are made: all machines are in an available state at the initial time t=0, and are in an available state or occupied state after that time, and there is no unavailable time period due to rest. However, in actual production, the daily processing and manufacturing work is often arranged according to the shift, and different shifts correspond to different working time periods. The time outside the working time cannot be processed. The shift information in the machine shop is shown in Table 1, where the end time of the large shift is 7:00, which means the next morning at 7:00.

[0065] Table 1 Shift information

[0066]

[0067] Secondly, the scheduling constraints are introduced.

[0068] 1. No machine change constraint

[0069] For any manual process, any one of the manual workers under the manual resource group number can be selected to complete the manual processing task. For equipment processes, the installation and removal of workpieces on corresponding equipment will bring about corresponding time and labor consumption, and will also affect the accuracy and stability of processing. In order to avoid frequent changes of the equipment used by a workpiece, according to the processing requirements of the aerospace structure machine shop, the selected equipment of two or more equipment processes that meet certain conditions needs to be consistent, i.e. no machine change constraint, which is explained as follows.

[0070] (1) If two or more adjacent processes of a product belong to equipment processes and have the same equipment resource group number, the same equipment must be selected for production, and no equipment replacement or other product insertion is allowed. An example of three consecutive equipment processes is shown in FIG. 3. Figure 2

[0071] (2) If two equipment processes of a product have the same equipment resource group number but are not adjacent, and the intermediate process is one or more manual processes, since the manual process does not need to dismount the workpiece from the equipment during processing, there are objective conditions for realizing no equipment replacement. Whether the two equipment processes need to be arranged on the same equipment will depend on the total processing time of the intermediate manual process. If the cumulative processing time of the intermediate manual process (only considering the normal time in the process, not considering the waiting time caused by the occupation of manual personnel) is not more than 60 minutes, the two equipment processes must be completed on the same equipment, as shown in FIG. 4, and the equipment waits during the execution of the intermediate manual process, and no other product insertion is allowed (inserting other products will bring about dismounting, mounting, and other operations); if the cumulative processing time of the manual process exceeds 60 minutes, the two equipment processes are not required to be arranged on the same equipment. Figure 3

[0072] (3) If two equipment processes of a product have the same equipment resource group number but are not adjacent, and the intermediate process includes equipment processes with different equipment resource group numbers, the two equipment processes with the same equipment resource group number are not required to be arranged on the same equipment, and a corresponding example is shown in FIG. 5. Figure 4

[0073] 2. Flexible extension of shift time constraints

[0074] For shifts other than the reverse shift, if the remaining processing time required by a process does not exceed 30 minutes at the end of the scheduled shift on the same day, the equipment or manual operator responsible for processing can appropriately extend the shift working time to complete the process task before the shift ends; if the remaining processing time required by the process exceeds 30 minutes, the shift ends on time, and the processing task continues in the next shift. Since the end time of the reverse shift and the start time of the next reverse shift are continuous, the shift time cannot be extended, and the tasks not completed in the shift on the same day are left to the next shift for processing, and this constraint does not need to be considered.

[0075] In step S102, a flexible machine shop scheduling problem under complex constraints is modeled with total weighted tardiness loss minimization and total cost minimization as dual optimization objectives, to obtain a scheduling model for the flexible machine shop.

[0076] ​​​In step S103, the production information of the current workshop is input into the scheduling model to obtain an optimal scheduling scheme of the current workshop.

[0077] The double optimization objectives are introduced below.

[0078] 1. Minimization of total weighted tardiness loss

[0079] If the completion time of the last process of an order task is later than the delivery time of the order, tardiness loss will be generated, and the tardiness loss of a single order is defined as tardiness weight * tardiness duration (in hours). The tardiness weights of tasks of different priorities are shown in Table 2.

[0080] Table 2. Tardiness weight information of tasks of different priorities

[0081]

[0082] 2. Minimization of total cost

[0083] The cost considered here includes two parts: energy consumption cost and manual performance cost. The energy consumption cost here refers to the energy consumption of equipment resources, without considering the energy consumption of tools used by manual workers. The energy consumption of equipment resources consists of the following two parts:

[0084] (1) Processing energy refers to the energy consumed by equipment in the processing process to complete the corresponding processing task of a workpiece. Since the time required for starting and shutting down the equipment is short, the energy loss caused by the starting and shutting down of the equipment is not considered here, so the processing energy is equal to the power in the machine processing state multiplied by the processing duration.

[0085] (2) No load energy consumption refers to the energy consumed to maintain normal operation of the equipment during the period when the equipment needs to wait and is idle due to the non-arrival of the next processing task after completing the processing task of a workpiece. The no load energy consumption is equal to the power in the idle state of the machine multiplied by the idle duration.

[0086] The state of the equipment is divided into three types: shutdown state, processing state, and idle state. No energy is consumed when the equipment is in the shutdown state. The power in the processing state and the idle state of the equipment is related to the equipment group number, and the power of the equipment in the same equipment group is considered to be basically consistent. The switching rules of the three states of the equipment are as follows:

[0087] (1) If there is no processing task for the equipment on the day, the equipment is always in the shutdown state.

[0088] (2) If there is one or more processing tasks on the day, start at the beginning of the first processing task, start entering the processing state, and enter the shutdown state at the end of the last processing task on the day.

[0089] (3) The waiting time between the multiple processing time periods on the day is in the idle state, and the rest period in the shift is also in the idle state.

[0090] The artificial performance cost refers to the performance bonus obtained by the equipment operator according to the processing time length. The bonus per hour is related to the title of the equipment operator and the equipment resource group to which the equipment operator responsible for the equipment belongs, and the bonuses of the equipment operators in the same equipment resource group are relatively close. The titles of the operators from high to low can be divided into: special technician, senior technician, technician, assistant technician, senior worker, intermediate worker and junior worker. The bonus difference in the group is caused by the title difference of different operators.

[0091] Optionally, in an embodiment of the present application, a flexible machine shop scheduling problem under complex constraints is modeled, including: modifying the non-dominated sorting genetic algorithm NSGA-II according to the characteristics of the production process and constraint conditions in the machine shop, generating an improved non-dominated sorting genetic algorithm with an elite strategy INSGA-II; solving the problem model based on the improved non-dominated sorting genetic algorithm with an elite strategy INSGA-II.

[0092] After determining the optimization target, the flexible machine shop scheduling problem under complex constraints is modeled to obtain the scheduling model of the flexible machine shop. First, the symbols and meanings used in the model are described, as shown in Table 3.

[0093] Table 3 Symbols and explanations in the scheduling problem model

[0094]

[0095]

[0096] In this model, the following assumptions are made: the model is a static scheduling model, the production task information to be processed is known and has not started processing, the information of all production equipment and operators is determined and is in an available state at the beginning of the scheduling, random events such as existing order changes, urgent insertions, equipment failures, and unqualified workpiece quality are not considered; the raw materials required for the processing process are sufficient, and there is no waiting time caused by insufficient raw materials; although the device calendar, manual worker calendar and other information are known at the beginning, the off-duty time can be appropriately adjusted according to the flexible extension of the shift end time constraint. On the basis of these assumptions, based on the analysis of the production characteristics and special constraints and requirements of the machine shop, the production scheduling problem can be modeled as follows:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] The problem model is a bi-objective optimization problem aiming at minimizing the total weighted tardiness loss and the total cost, and the definitions of the two objectives are given in equations (2-1) and (2-2); equation (2-3) indicates that the total processing time of a machine is the sum of the processing time of the machine each day; equation (2-4) indicates that the total idle time of a machine is also the sum of the idle time each day, and the idle time of a machine each day is the time period between the start time ts i,d and the end time te i,d of the machine in a day after the processing time is removed; equation (2-5) indicates that all tasks are in the state of waiting for processing at the start time of scheduling, and all processing can only start after the start time of scheduling; equation (2-6) indicates that the completion time of a workpiece is the completion time of the last process; equation (2-7) indicates that a process can and can only be completed by selecting one resource from the optional production resources; equation (2-8) indicates the process constraint of a task, which must be completed in a series of processes according to the process flow; equation (2-9) indicates the capacity constraint of a production resource, which can only process one workpiece at most at any time; and equation (2-10) indicates that the extension time of a day shift cannot exceed the preset upper limit of the flexible time.

[0109] In the flexible job shop scheduling problem, with the increase of the number of production equipment and production tasks and corresponding process, the feasible solution space of the problem will increase sharply, which belongs to NP problem. The machine shop researched in the present application has other constraint conditions, and the consideration of shift replacement, rest time period and other actual situations also makes the calculation of the available time of equipment and personnel more complex, and the state switching of daily processing, idling and shutdown of equipment also increases more calculation cost. If an accurate algorithm is used to solve the problem, it will bring unbearable calculation cost and need to consume a lot of time, which is difficult to apply in actual production scheduling. Under such a problem model, an approximate algorithm can find an approximate optimal solution with relatively small calculation cost, which will be a better choice. In the present application, on the basis of a meta-heuristic algorithm, i.e. non-dominated sorting genetic algorithm with elitist strategy (NSGA-II), corresponding modifications are made according to the characteristics of the production process and constraint conditions in the machine shop, and the improved non-dominated sorting genetic algorithm with elitist strategy (INSGA-II) is used to solve the problem model, so that a better scheduling scheme can be found within an acceptable calculation time.

[0110] Optionally, in an embodiment of the present application, the non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and constraint conditions in the machine shop, including that in the chromosome representing the processing sequence, each gene represents a constraint process group of any task, and the constraint process group contains one or more processes.

[0111] The improved non-dominated sorting genetic algorithm with elitist strategy is introduced.

[0112] 1. Non-equal-length two-section chromosome coding

[0113] The flexible job shop scheduling problem is composed of two sub-problems, one is the process sequence problem, and the other is the production resource (equipment or personnel) allocation problem, so two-section chromosomes can be used to express the two parts of information respectively. A conventional method is as follows: each gene of the first section chromosome is the number of a task, and the number of times of occurrence of a certain task number is equal to the number of processes of the task. The number of times of occurrence of the same task number represents the number of processes of the task. Different processing sequences can be obtained by disordering the arrangement order of the task numbers. The second section chromosome expresses the production resource allocation information. From left to right, each gene represents the production resource used by each process from the first task to the last task.

[0114] Because the flexible job shop scheduling problem model researched in the application has no machine change constraint, multi-path device processes satisfying the no machine change condition must be completed on the same device in sequence to ensure spatial continuity, cannot be changed to other devices within the device resource group, and the device cannot be inserted with other tasks in the middle. If the processing sequence is still encoded according to the process level, a large amount of randomness in the processes such as population initialization, individual crossover, and mutation cannot guarantee that the several device processes that should not change machines are processed continuously in time, and other processes may be inserted in the middle, resulting in a large number of infeasible solutions that do not satisfy the constraint conditions. Repairing solutions that do not meet the constraint conditions is also more complex, and different processing sequences may become the same processing sequence after repair, causing waste of calculation.

[0115] The no machine change condition is that if the resource group numbers of two device processes are the same, and no other processes are inserted between the two processes or only manual processes with a cumulative processing time of not more than 60 minutes are inserted, then the two device processes satisfy the no machine change condition and should be processed on the same device. Correspondingly, the two device processes and the manual processes that may exist between them will form a constraint process group, which will be processed as a whole. The step of decomposing the task into several constraint process groups is shown in Algorithm 1.

[0116]

[0117]

[0118] According to the characteristics of the constraint condition, the encoding of the processing sequence in INSGA-II will no longer be the process level encoding method, but will use the constraint process group encoding method. In the section of the chromosome representing the processing sequence, each gene will represent a constraint process group of a task, and the constraint process group contains one or more processes.

[0119] According to the task decomposition method of Algorithm 1, the constraint process groups obtained can be divided into three categories:

[0120] 1) composed of one manual process or one device process;

[0121] 2) composed of multiple device processes;

[0122] 3) composed of multiple device processes and manual processes, the first and last processes must be device processes.

[0123] For the third case, the constraint process group uses both equipment resources to process the equipment process and needs the manual operator to complete the corresponding manual process, so it is necessary to allocate the corresponding production resources to each process at the process level. Although the production resources used in the other two cases are single, in order to unify the coding method, the corresponding production resources are specified for each process in turn.

[0124] Suppose a production plan contains 3 tasks, a total of 7 processes (for example, O 1,1 represents the first process of task 1), 6 constraint process groups—[O 1,1 ,O 1,2 ], [O 1,3 ], [O 2,1 ], [O 2,2 ], [O 3,1 ], [O 3,2 ], [O 1,1 ,O 1,2 ] represent that the two processes belong to a constraint group, which is the first constraint process group of task 1, denoted as G 1,1 . A possible scheduling scheme of two-chromosome coding method is shown in Figure 5 . Each gene of the first chromosome represents a constraint process group, and its processing order is [O 3,1 ], [O 2,1 ], [O 1,1 ,O 1,2 ], [O 1,3 ], [O 2,2 ], [O 3,2 ], in which the first and second processes of task 1 [O 1,1 ,O 1,2 ] are represented by the third gene “1” in the first chromosome as a constraint process group; the second chromosome from left to right is the production resource allocation of each process of the first, second and third tasks, for example, task 1 has three processes, so the first three genes of the second chromosome represent the production resource allocation of O 1,1 , O 1,2 , O 1,3 , respectively, the fourth gene represents the production resource allocation of the first process of task 2, and so on.

[0125] 1) It can be seen that the allocation of production resources for each task and process corresponding to each gene position in the second chromosome is a definite mapping relationship. Using this mapping relationship, a repair mechanism for the second chromosome can be designed to satisfy the no-machine-change constraint. The repair steps are as follows: According to Algorithm 1, the task is decomposed into several constraint process groups. The total number of constraint process groups is equal to the length of the first chromosome segment. Information on which processes (and their positions in the chromosome) will form a constraint group is obtained, and the position information of the equipment processes within the constraint process group is retained (e.g., a constraint process group [pos1, pos2, ... pos...). k ]);

[0126] 2) For each element in the constrained process group, establish the corresponding mapping relationship to constrain the process group [pos1,pos2,…pos]. k For example, this constraint process group represents chromosomes pos1, pos2, ... pos k The processes corresponding to the genes at each position should use the same equipment, therefore pos2,…pos can be processed together. k All are mapped to pos1, i.e., pos2→pos1,…pos k →pos1;

[0127] 3) Using the mapping relationship obtained in the previous step, repair the new individuals generated during the initialization, crossover, and mutation phases, ensuring that the equipment used in each process corresponding to the constrained process group is the same equipment used in the first process within the group. Figure 5 Taking the task information in the example, there exists a mapping relationship like this: 2→1, which means that in the second segment of the chromosome, the value of the second gene should be the same as the value of the first gene.

[0128] 2. Chromosome Decoding

[0129] To meet the process sequence constraints and enable each constrained process group to begin as early as possible, a greedy insertion decoding strategy is employed. The application of this strategy in the decoding process is as follows: Figure 6 As shown.

[0130] When a constrained process group G i,j They were assigned to production resource M k When going up, check in chronological order.

[0131] Check in M k The time interval between the end time of each constrained operation group in the previous process and the start time of the next constrained operation group [t] start ,t end [This refers to the idle time period, where the constraint operation group is attempted to be inserted into that time interval. Assume constraint operation group G...] i,jThe previous constraint operation group G in the process flow i,j-1 The end time is C i,j-1 Constraint process group G i,j In M k The processing time required for the upper processing is t i,j,k Then G i,j To insert the time interval [t] start ,t end The following formula must be satisfied:

[0132] max{t start C i,j-1}+t i,j,k ≤t end (2-11)

[0133] When the inequality in this formula holds, the constraint process group G is... i,j The processing task can be completed within this time interval, and the corresponding start time is max{t}. start C i,j-1}.exist Figure 6 China G 3,2 It was assigned to M3, and its previous constraint process group G 3,1 The end time is 3, and there are already two constraint operation groups G in the task sequence of M3. 1,1 and G 2,2 There exists a time interval [2,5], therefore G can be used. 3,2 Shift left and insert into the time interval, and start processing at t=3.

[0134] In this problem model, since shift information needs to be considered, the working hours of equipment and personnel are a series of discontinuous available time periods. Therefore, when using an insertion-based greedy decoding strategy, corresponding calculations must be performed to account for this characteristic. For example, the start time max{t} obtained from equation (2-11) start C i,j-1} is not necessarily located in M k If, during the work period, the specified time falls between the end of the workday and a break period, then the constraint on process group G is... i,j The earliest true start time t r It should be the start time of the next working period (t) r ≥max{t start C i,j-1}), t r With t end It's not necessarily all working hours between them, t r With t end The cumulative available time after removing rest periods is denoted as a. r,end Then G i,j To insert the time interval [t]start t end ] should satisfy the following formula.

[0135] t i,j,k ≤a r,end ,t r ≥max{t start ,C i,j-1} (2-12)

[0136] The working conditions of each device and manual operator are calculated day by day in the decoding process, and the end time of shift is dynamically adjusted according to the actual completion of each day, and the processing information of each day is saved for calculating the two optimization objectives.

[0137] 3. Selection operator

[0138] The selection operation is performed by using binary tournament, and each time two individuals are randomly selected from the parent population, and the one with lower Pareto level is selected to participate in the subsequent crossover and mutation operation; if the two individuals are in the same Pareto level, the individual with larger crowding distance is selected.

[0139] 4. EPPX crossover operator based on dynamic selection probability

[0140] In INSGA2, EPPX (extended precedence preservative crossover) is used as a crossover operator, and a probability selection rule is introduced on this basis to improve the search effect.

[0141] The two parent chromosomes selected in the crossover process are denoted as Parent1 and Parent2, and each gene on the offspring chromosome needs to be determined whether it will be inherited from Parent1 or Parent2. The probabilities of selecting Parent1 and Parent2 are denoted as P1 and P2, respectively. Since there are only two options of Parent1 and Parent2, the sum of P1 and P2 is 1. P e is defined as the probability of selecting a better parent individual. According to the natural law of survival of the fittest, a better individual should have a higher probability of passing its genetic information to the offspring, so P e should satisfy P e ≥ 0.5. When P e is close to 1, it means that the better parent individual can pass most of its information to the offspring chromosome, and the offspring chromosome has a high similarity to the better parent individual, which is beneficial to accelerating the convergence speed of the algorithm search process; when P eWhen the value is close to 0.5, it means that the better parent and the worse parent pass on about the same amount of chromosomal information to the offspring. This is beneficial for the algorithm to explore new regions and avoid getting stuck in local optima.

[0142] Based on the above analysis, different sizes of P are set at different stages of population iteration. e A higher value for P is more conducive to balancing the algorithm's ability to explore near-optimal solutions with its convergence speed. Setting a larger P value in the early stages of iteration is beneficial. e A higher P value can accelerate convergence; in later stages, a P value close to 0.5 should be set. e A value that is more conducive to escaping local optima, therefore P e The update rule that changes with the iteration algebra is defined as shown in the following equation.

[0143] P e =P max -(P max -P min )·gen cur / gen max (2-13)

[0144] Where gen cur and gen max Represent the current iteration number and the maximum iteration number preset by the algorithm, respectively. cur P is 0 at the very beginning of the algorithm. e The maximum value P max In the last iteration, P e Minimum value P min P min The value can be set to 0.5, P max The values ​​of P1 and P2 will be determined in the experimental section later. The formulas for calculating P1 and P2 are shown below.

[0145]

[0146] P2 = 1 - P1 (2-15)

[0147] The phrase "Parent2 p Parent1" indicates that in the Pareto dominance relationship, Parent1 dominates Parent2. Therefore, Parent1 is the better individual, and the probability of choosing Parent1 is equal to P. e When Parent2 dominates Parent1, the better individual is Parent2, and the probability of choosing Parent1 should be less than 0.5. In this case, P1 is 1-P e The third scenario involves two parent individuals that do not dominate each other; in this case, both have a 0.5 probability of being selected. An example of a crossover operation with P1 = 0.5 and P2 = 0.5 is shown below. Figure 7 As shown.

[0148] The operation steps of the crossover operator can be described as follows:

[0149] 1) Select two parent chromosomes Parent1 and Parent2, generate a random sequence R with the same length as the parent chromosomes, each element in R is uniformly distributed between 0 and 1, and the offspring chromosome obtained by crossover is denoted as Offspring;

[0150] 2) For the first segment of the chromosome, which represents the constraint process group and the processing sequence of the chromosome, the kth gene Offspring(k) of Offspring is calculated as follows:

[0151]

[0152] In formula (2-16), "fa" represents the first available gene, and at the beginning, all genes in the two parent chromosomes are in the available state; assuming that the condition R(k)≤P1 is met when Offspring(k) is calculated, the first available gene X of Parent1 will be assigned to Offspring(k), and then the gene of Parent1 is marked as unavailable, and the first available state X in Parent2 is also marked as unavailable, so as to ensure that the same constraint process group will not be repeatedly inherited into the offspring chromosome, thereby correctly encoding the task information.

[0153] 3) For the second segment of the chromosome, which represents the production resource allocation, the kth gene Offspring(k) of Offspring is calculated as follows:

[0154]

[0155] According to the size relationship between R(k) and P1, which parent chromosome is selected to inherit the kth gene from.

[0156] 5. Mutation operator

[0157] The two mutation operations designed for the genes in the two segments of the chromosome can be described as follows:

[0158] Step 1: Select an individual, and copy the chromosome S of the individual to S'.

[0159] Step 2: Randomly select a gene G on the chromosome S'.

[0160] Step 3: If the gene G belongs to the chromosome expressing the constraint process group processing sequence on S', go to Step 4, otherwise go to Step 5.

[0161] Step4: Randomly select another gene from the chromosome of S' expressing the processing sequence of constraint process group and exchange it with gene G.

[0162] Step5: Randomly replace the production resource corresponding to gene G with another resource under the same resource group number.

[0163] Step 6: Use the chromosome repair mechanism on S' to ensure that the no-change constraint is met.

[0164] Step7: Obtain a new chromosome S' after the mutation operation of chromosome S, and the mutation operation ends.

[0165] It should be noted that the mutation operation of randomly replacing the production resource corresponding to gene G with another resource under the same resource group number in Step5 may cause the devices used by the original device processes belonging to the same constraint process group to become inconsistent, so the chromosome repair mechanism needs to be used in Step6.

[0166] 6. Improved elitist strategy

[0167] In the basic NSGA-II, the parent population is mixed with the offspring population obtained through crossover and mutation. After fast non-dominated sorting, individuals with low Pareto levels are added to the new population in order from low to high. If the size of the new population exceeds the preset population size after all individuals of a certain Pareto level are put into the new population, only the individuals with larger crowding distance in the critical level are selected to enter the new population to ensure that the population size remains unchanged. The new population is used as the parent population for the next iteration.

[0168] In the later stages of algorithm iteration, since the individuals in the non-critical level are not selected using the crowding distance, there may be a large number of duplicate individuals, which reduces the diversity of the population. To solve this problem, an improved elitist strategy combined with a neighborhood search algorithm is proposed: individuals in the non-critical level are also sorted by crowding distance from large to small, and only the top 90% of individuals are directly selected into the new population. The remaining 10% of individuals will be generated through a neighborhood search algorithm, and three neighborhood structures are designed as follows.

[0169] N1 neighborhood structure: Perturb the chromosome of the constraint process group processing sequence, randomly select two constraint process groups and exchange the sequence.

[0170] N2 neighborhood structure: Perturb the chromosome of the production resource allocation, randomly select a process, and replace the production resource used with the one with the lowest load rate among the available production resources.

[0171] N3 neighborhood structure: from the perspective of artificial performance cost in the optimization of total cost, a device process is randomly selected, and the device used is replaced by the device with the lowest artificial performance cost in the same device resource group.

[0172] The neighborhood search algorithm process can be briefly described as follows:

[0173] (1) randomly select an initial solution in the level to perform neighborhood search, and randomly generate a permutation order of the neighborhood structure

[0174] (2) select the first neighborhood structure in the permutation to generate the corresponding neighborhood solution, if it is better than the initial solution, add it to the new population, and the neighborhood search algorithm ends; otherwise, use the next neighborhood structure;

[0175] (3) if all neighborhood solutions generated by the neighborhood structure are not better than the initial solution, randomly generate a solution to add to the new population, and the algorithm ends.

[0176] 7. Algorithm process

[0177] Based on the above contents, the INSGA-II algorithm process proposed by the application can be described as follows.

[0178]

[0179]

[0180] The algorithm flowchart is shown in Figure 8 .

[0181] Optionally, in an embodiment of the application, the non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and the constraint conditions in the machine shop, including: dynamically adjusting the work shift according to the daily load rate of the device or personnel, wherein the calculation formula of the daily load rate is:

[0182] DLF=t p / t s ,

[0183] Where t p is the processing time of the day, and t s is the shift length of the day.

[0184] Dynamic shift adjustment

[0185] Since the task amount in different periods has uncertainty (e.g. typical off-season, peak season), the scheduling scheme obtained according to the current work shift arrangement may have a large delay that is unacceptable, which is caused by the mismatch between the current production capacity (number of devices, working time) and the task amount. The cost of adding devices is large and they will be idle in the off-season. Another solution is to dynamically adjust the recent work shift according to the obtained scheduling scheme, so that it can match the current task amount as much as possible. When the task amount is too large, the working time needs to be appropriately extended, and the overtime shift of part of the work shift is shown in Table 4.

[0186] Table 4 Shift information and alternative shift

[0187]

[0188] The daily load factor DLF of a device or personnel can be defined as:

[0189] DLF = t p / t s (2-18)

[0190] In the formula, t p and t s are the processing time and shift length of the day, respectively. Set a daily load factor threshold. If the daily load factor of a device or personnel in the scheduling scheme exceeds the threshold on a certain day, and the corresponding shift has an overtime shift, in order to increase the working time to match the larger task amount, the work shift of the resource (device or manual personnel) can be changed to the corresponding overtime shift, that is, from single shift to single shift with 2 hours of overtime, single shift with 4 hours of overtime, or adjust part of the weekend rest date to weekend overtime.

[0191] A fixed work shift can easily cause resource waste or large delay loss. According to the algorithm proposed in the above, the scheduling scheme is solved, the work shift is dynamically adjusted according to the actual scheduling demand, and the adjusted work shift is used to develop a new scheduling scheme again. Such an iterative process can develop a more reasonable work shift and the corresponding production and processing plan, and the corresponding flow chart is shown in Figure 9 .

[0192] The flexible job shop scheduling method under complex constraints based on INSGA-II according to the embodiment of the present application can accurately establish the FJSP model in combination with specific production characteristics, and make the generated scheduling scheme closer to the real situation and more applicable; through application of the improved non-dominated sorting genetic algorithm with elitist strategy proposed in the present application, a high-quality scheduling scheme can be searched, so that the limited resources such as energy resources, equipment resources, human resources and time resources can be more efficiently and reasonably coordinated and utilized, and the enterprise can improve the production system performance, save energy and reduce emissions, reduce product cost, reduce delay, and improve its market competitiveness.

[0193] Secondly, the flexible job shop scheduling device under complex constraints based on INSGA-II according to the embodiment of the present application is described with reference to the accompanying drawings.

[0194] Figure 10 The flexible job shop scheduling device under complex constraints based on INSGA-II according to the embodiment of the present application is a structural schematic diagram.

[0195] As shown in the figure, the flexible job shop scheduling device 10 under complex constraints based on INSGA-II includes an acquisition module 100, a modeling module 200 and a scheduling module 300. Figure 10

[0196] The acquisition module 100 is configured to acquire the basic production information and scheduling constraints of the workshop, wherein the basic production information includes one or more of order tasks, equipment resources and manual resources, process information and shift information, and the scheduling constraints include non-replacement constraints and elastic extended shift time constraints.The modeling module 200 is configured to model the flexible machine shop scheduling problem under complex constraints with total weighted delay loss minimization and total cost minimization as dual optimization objectives, to obtain a scheduling model of the flexible machine shop. The scheduling module 300 is configured to input the production information of the current workshop into the scheduling model to obtain the optimal scheduling scheme of the current workshop.

[0197] Optionally, in an embodiment of the present application, modeling the flexible machine shop scheduling problem under complex constraints includes:

[0198] The non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and constraint conditions in the machine shop to generate an improved non-dominated sorting genetic algorithm with elitist strategy INSGA-II; and the problem model is solved based on the improved non-dominated sorting genetic algorithm with elitist strategy INSGA-II.

[0199] Optionally, in an embodiment of the present application, the flexible machine shop scheduling problem under complex constraints is modeled with the following constraints:

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] where T WT is the total weighted tardiness loss, W i is the total cost, C i is the completion time of production task i, D i is the preset delivery time of production task i, T C is the total cost, P i is the energy cost of equipment i in the processing state, PB i is the unit time performance bonus of the operator of equipment i, h i is the total processing time of equipment i, P i is the energy cost of equipment i in the idle state, is the total idle time of equipment i, h i,d is the total processing time of equipment i on day d, te i,d is the total working time of equipment i on day d, ts i,d is the time when equipment i starts to enter the processing state on day d, C i,0 is the completion time of production task i on the 0th operation O i,0 , t start is the start time of scheduling, C i,j is the completion time of production task i on the jth operation O i,j , n is the total number of production tasks, n i is the number of operations of production task i, X i,j,k is a decision variable, if the jth operation O i,j of production task i is processed on production resource k, the value of X i,j,k is 1, otherwise 0, Mi,j is O i,j is a resource group, m is the total number of devices, X u,v,k is a decision variable, A s,e,i is the cumulative available duration of the production resource i between time s and e, Y i,j,u,v,k is a decision variable, is the actual off-duty time of the production resource i on the dth day, CT i,d is the planned off-duty time of the production resource i on the dth day according to the predetermined shift arrangement, f t is the upper limit of the duration of the flexible extension of the end time of the shift.

[0212] Optionally, in an embodiment of the present application, the non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and the constraint conditions in the machine shop, including:

[0213] In the chromosome representing the processing sequence, each gene represents a constraint process group for any task, and the constraint process group contains one or more processes.

[0214] Optionally, in an embodiment of the present application, the non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and the constraint conditions in the machine shop, including:

[0215] The work shift is dynamically adjusted according to the daily load rate of the equipment or personnel, wherein the calculation formula of the daily load rate is:

[0216] DLF=t p / t s ,

[0217] wherein t p is the processing duration of the day, and t s is the shift duration of the day.

[0218] It should be noted that the foregoing explanation and description of the method embodiment also apply to the device of this embodiment, which will not be described here again.

[0219] The flexible job shop scheduling device under complex constraints based on INSGA-II proposed in the embodiment of the present application accurately establishes the FJSP model combined with specific production characteristics, and makes the generated scheduling scheme more close to the real situation and more usable; through the application of the improved non-dominated sorting genetic algorithm with an elite strategy proposed in the present application, a high-quality scheduling scheme can be searched, so that the limited resources such as energy resources, equipment resources, human resources, and time resources can be more efficiently and reasonably coordinated and utilized, so that the enterprise can improve the production system performance, save energy and reduce emissions, reduce product cost, reduce delay, and improve its market competitiveness.

[0220] In addition, the terms "first", "second", etc. are used only for the purpose of description, and should not be understood as indicating or implying relative importance or a specific number of the technical features indicated. Therefore, the features defined as "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless otherwise explicitly and specifically limited.

[0221] In the description of the present application, the description referring to the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Also, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples, without contradiction.

[0222] Although the embodiments of the present application have been shown and described above, it is understood that the above-described embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-described embodiments within the scope of the present application.

Claims

1. A flexible job shop scheduling method under complex constraints based on INSGA-II, characterized in that, The method comprises the following steps: acquiring basic production information and scheduling constraints of a workshop, wherein the basic production information comprises one or more of order tasks, equipment resources and manual resources, process information and shift information, and the scheduling constraints comprise no-machine-changing constraints and flexible extended shift time constraints, wherein the no-machine-changing constraints are that, according to the machining requirements of a space structure machining workshop, the selected equipment of two or more equipment processes that meet preset conditions needs to be consistent; the flexible extended shift time constraints are that, except for the large shift, if the remaining machining time required by a process is not more than 30 minutes when the scheduled shift of the day is about to end, the equipment or manual operator responsible for the machining extends the shift working time to complete the process task before the shift ends, otherwise if the remaining machining time required by the process is more than 30 minutes, the equipment or manual operator responsible for the machining goes off work according to the scheduled shift end time and continues to perform the machining task in the next shift; total weighted delay loss minimization and total cost minimization are taken as double optimization objectives to model a flexible machining workshop scheduling problem under complex constraints, to obtain a scheduling model of the flexible machining workshop, wherein the modeling of the flexible machining workshop scheduling problem under complex constraints comprises: an improved non-dominated sorting genetic algorithm II (INSGA-II) with an elitist strategy is generated by modifying a non-dominated sorting genetic algorithm II (NSGA-II) according to the characteristics of the production process and constraint conditions in the machining workshop; the problem model is solved based on the improved INSGA-II with an elitist strategy; and the production information of the current workshop is input into the scheduling model to obtain an optimal scheduling scheme of the current workshop.

2. The method of claim 1, wherein, The flexible machining workshop scheduling problem under complex constraints is modeled with the following constraints: C i,0 = t start ,C i,j t start , where T WT is the total weighted tardiness loss, W i is the weight of tardiness of production task i, C i is the completion time of production task i, D i is the preset delivery time of production task i, T C is the total cost, P i is the energy cost of equipment i in processing state, PB i is the performance bonus of operator of equipment i per unit time, h i is the total processing time of equipment i, P i * is the energy cost of equipment i in idle state, is the total idle time of equipment i, h i,d is the total processing time of equipment i on day d, te i,d is the time when equipment i enters shutdown state at the end of day d, ts i,d is the time when equipment i enters processing state on day d, C i,0 is the completion time of production task i on operation O i,0 , t start is the start time of scheduling, C i,j is the completion time of production task i on operation O i,j , n is the total number of production tasks, n i is the number of operations of production task i, X i,j,k is a decision variable, if operation O i,j of production task i is processed on production resource k, then the value of X i,j,k is 1, otherwise 0, M i,j is the resource group of O i,j , m is the total number of equipment, Y i,j,u,v,k is a decision variable, if O i,j and O u,v are both processed on production resource k, then the value of Y i,j is 1, if O u,v is completed before O i,j , then the value of Y u,v is -1, if O i,j and O u,v are not both processed on production resource k, then the value of Y is 0, i,d is the actual off-duty time of production resource i on day d, CT t is the planned off-duty time of production resource i on day d according to the preset shift arrangement, f is the upper limit of the length of the extended flexible shift end time.

3. The method of claim 1, wherein, the modified NSGA-II according to the characteristics of the production process and constraint conditions in the machining workshop comprises: in a chromosome representing a machining sequence, each gene represents a constraint process group of any task, and the constraint process group contains one or more processes.

4. The method of claim 1, wherein, The modified NSGA-II according to the characteristics of the production process and constraint conditions in the machining workshop comprises: the working shift is dynamically adjusted according to the daily load rate of the equipment or personnel, wherein the calculation formula of the daily load rate is: DLF = t p / t s , Wherein, t p is the processing time of the day, t s is the shift length of the day.

5. A flexible job shop scheduling device based on INSGA-II under complex constraints, characterized in that, comprises: an acquisition module configured to acquire basic production information and scheduling constraints of a workshop, wherein the basic production information comprises one or more of order tasks, equipment resources and manual resources, process information and shift information, and the scheduling constraints comprise no-machine-changing constraints and flexible extended shift time constraints, wherein the no-machine-changing constraints are that, according to the machining requirements of a space structure machining workshop, the selected equipment of two or more equipment processes that meet preset conditions needs to be consistent; the flexible extended shift time constraints are that, except for the large shift, if the remaining machining time required by a process is not more than 30 minutes when the scheduled shift of the day is about to end, the equipment or manual operator responsible for the machining extends the shift working time to complete the process task before the shift ends, otherwise if the remaining machining time required by the process is more than 30 minutes, the equipment or manual operator responsible for the machining goes off work according to the scheduled shift end time and continues to perform the machining task in the next shift; The elastic extension shift time constraint is that, except for the large shift, if the remaining processing time required by a process is less than 30 minutes when the scheduled shift of the day is about to end, the equipment or manual operator responsible for processing extends the shift working time to complete the process task before the shift ends, otherwise, if the remaining processing time required by the process is more than 30 minutes, the equipment or manual operator responsible for processing leaves work on time according to the scheduled shift end time and continues to process the task in the next shift; The modeling module is configured to model a flexible machine shop scheduling problem under complex constraints with total weighted tardiness loss minimization and total cost minimization as dual optimization objectives to obtain a scheduling model of the flexible machine shop, wherein modeling the flexible machine shop scheduling problem under complex constraints comprises: According to the characteristics of the production process and constraint conditions in the machine shop, a non-dominated sorting genetic algorithm NSGA-II is modified to generate an improved non-dominated sorting genetic algorithm with elitist strategy INSGA-II; the problem model is solved based on the improved non-dominated sorting genetic algorithm with elitist strategy INSGA-II; and The scheduling module is configured to input production information of a current machine shop into the scheduling model to obtain an optimal scheduling scheme of the current machine shop.

6. The apparatus of claim 5, wherein, The flexible machine shop scheduling problem under complex constraints is modeled with the following constraints: C i,0 = t start ,C i,j t start , Among them, T WT W is the total weighted average delay loss. i Let C be the drag option value for production task i. i D is the completion time of production task i. i T is the preset delivery time for production task i. C For the total cost, P i PB represents the energy consumption cost of device i during processing. i h is the unit-time performance bonus for the operator of equipment i. i Let P be the total processing time of device i. i * Let i be the energy consumption cost of device i under no-load conditions. h is the total idle time of device i. i,d Let te be the total processing time of equipment i on day d. i,d Let ts be the time when device i enters the shutdown state at the end of day d. i,d Let C be the moment when device i begins processing on day d. i,0 For production task i, the 0th process O i,0 The completion time, t start For the start time of scheduling, C i,j For production task i, the j-th process O i,j The completion time, where n is the total number of production tasks. i Let X be the number of operations for production task i. i,j,k Let O be the decision variable, and let O be the j-th process of production task i. i,j If X is processed from production resource k, then i,j,k The value of M is 1 if it is not 1, otherwise it is 0. i,j For O i,j The resource group, where m is the total number of devices, Y i,j,u,v,k For decision variables, if O i,j and O u,v All are processed from production resource k, when O i,j Prior to O u,v When processing is complete, the value of this variable is 1; when O... i,j Later than O u,v If processing is complete, the value of this variable is -1; if O i,j and O u,v If the processing is not entirely done by production resource k, then the variable value is 0. For production resource i, CT is the actual time it leaves work on day d. i,d For production resource i, according to the scheduled off-duty time on day d, f t The maximum duration for flexibly extending the end time of service shifts.

7. The apparatus of claim 5, wherein, The non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and constraint conditions in the machine shop, comprising: In the chromosome representing the processing sequence, each gene represents a constraint process group of any task, and the constraint process group contains one or more processes.

8. The apparatus of claim 5, wherein, The non-dominated sorting genetic algorithm NSGA-II is modified according to the characteristics of the production process and constraint conditions in the machine shop, comprising: The working shift is dynamically adjusted according to the daily load rate of the equipment or personnel, wherein the calculation formula of the daily load rate is: The working shift is dynamically adjusted according to the daily load rate of the equipment or personnel, wherein the calculation formula of the daily load rate is: DLF = t p / t s , Wherein, t p is the processing time of the day, t s is the shift length of the day.

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