CN113592319A

CN113592319A - INSGA-II-based flexible job shop scheduling method and device under complex constraint

Info

Publication number: CN113592319A
Application number: CN202110891753.6A
Authority: CN
Inventors: 张林宣; 刘胤; 罗术; 王静; 刘晓东; 包磊
Original assignee: Tsinghua University; Weichai Power Co Ltd
Current assignee: Tsinghua University; Weichai Power Co Ltd
Priority date: 2021-08-04
Filing date: 2021-08-04
Publication date: 2021-11-02

Abstract

The invention discloses a flexible job shop scheduling method and a device under the complex constraint based on INSGA-II, wherein the method comprises the following steps: acquiring basic production information and scheduling constraint 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 constraint comprises a non-change constraint and an elastic shift time constraint; modeling the scheduling problem of the flexible machining workshop under complex constraint by taking the minimization of total weighted pull-out loss and the minimization of total cost as double optimization targets to obtain a scheduling model of the flexible machining workshop; and inputting the production information of the current workshop into the scheduling model to obtain the optimal scheduling scheme of the current workshop. The method combines specific production characteristics to accurately establish the FJSP model, and enables the generated scheduling scheme to be closer to the real situation and have more usability.

Description

INSGA-II-based flexible job shop scheduling method and device under complex constraint

Technical Field

The invention relates to the technical field of workshop scheduling, in particular to a flexible job workshop scheduling method and device based on INSGA-II complex constraint.

Background

The classic flexible job shop scheduling problem model is as follows: according to the FJSP proposed by Brucker, the problem model can be described as follows: with n tasks J to be processed₁,…,J_nAnd M different machines M₁,…,M_mEach task J_iFrom n to_iProcedure O_i,1,…,O_i,niIs composed of, and these n_iThe processes must be processed in this order; each process O_i,jCorresponding to an optional machine set

O_i,jCan be processed on any one machine, and the processing time on each machine is t_i,j(in the partial FJSP model, any one M in the set of optional machines_kWill correspond to a processing time t respectively_i,j,k) (ii) a Machines cannot handle two or more tasks simultaneously. To simplify the problem, the following assumptions are generally made:

(1) all machines are in a usable state at the initial moment when t is 0;

(2) all workpieces are in a state of being capable of being machined at the initial moment when t is 0;

(3) process O_i,jFrom the set M only_i,jSelecting a machine for processing;

(4) different workpieces are not limited by priority, so that the workpieces are independent from one another;

(5) the process that has already begun processing cannot be interrupted;

(6) the transport time of the workpiece between the machines and the machine setup time required for the process have been included in the processing time t_i,j,kAnd (4) the following steps.

The method for solving the flexible job shop scheduling problem mainly comprises an accurate algorithm and an approximate algorithm.

1. Precision algorithm

The precise algorithm mainly comprises a branch-and-bound method, a mixed integer programming model, an enumeration method based on an extraction graph model, a Lagrange relaxation method and the like, can theoretically ensure that a global optimal solution is found, but has large corresponding time overhead, and is particularly difficult to apply to a job shop scheduling problem with large problem scale.

Brucker et al propose FJSP (flexible job shop scheduling) including two workpieces to be processed, and a machine available for each process is a set formed by a series of machines, and propose a polynomial graphic algorithm for solving. Sawik makes a multi-level ILP model for the flexible manufacturing system, which is a hierarchical decision structure and comprises part type selection, machine loading, part processing sequence and process scheduling, and also gives a linear programming formula of each level and an algorithm for solving a part scheduling scheme. Jiang et al propose an FJSP model with an alternative process plan, consider the job scheduling problem and the selection problem of the process plan at the same time, and use 0-1 integer programming to model the problem, and solve the scheduling scheme that makes the absolute value of the completion date deviation minimum or the total completion time minimum. Torabi et al propose a mixed integer nonlinear programming (MINLP) to solve the periodic multi-product batch scheduling problem in a flexible job shop, and an effective enumeration method is adopted to replace the complex mixed integer nonlinear programming problem, so that the optimal solution is determined more simply and conveniently, the method is suitable for small-scale problems, and when the method is applied to large-scale problems, a plurality of mixed 0-1 integer programming problems with huge calculation amount need to be solved, and the method is difficult to use. Roshanaei et al established two mixed integer linear programming models based on position and sequence to describe the processing process in a flexible job shop, and performed numerical solution with maximum completion time as an optimization criterion.

The precise algorithm can solve from a theoretical perspective to obtain an optimal solution, but is usually based on some simplified assumptions, and the scale of the considered problem is not too large; for the MOFJSP (multi-object flexible job scheduling problem), especially for the MOFJSP in the high-dimensional field, because the computational complexity is very high, it is difficult for the precise algorithm to obtain effective application.

2. Approximation algorithm

With the increase of the scale of the problem and the more diversified and complex constraint, the accurate modeling and solving of the problem become more difficult, the huge calculation overhead makes the original accurate algorithm difficult to be continuously and effectively applied, and for the complex problem, an approximate algorithm which does not pursue the optimal solution but seeks the suboptimal solution and the better solution starts to become a new research direction.

The heuristic algorithm is designed according to the intuitive feeling of people or long-term accumulated historical experience aiming at a specific problem, when the heuristic algorithm is used for solving a specific problem, although the optimal solution cannot be obtained, the deviation degree of a feasible solution and the optimal solution cannot be predicted, the feasible solution can be provided within an acceptable time, and therefore, a plurality of heuristic methods are applied to complex FJSP solution.

The scheduling rule is simple to operate, low in calculation complexity and capable of solving a large-scale production scheduling problem in a short time, and therefore the method is widely applied to FJSP. The comprehensive assignment rule comprises two parts, wherein one part is a rule for determining the priority order of workpieces, and a priority index is defined on the basis of the rules of classic S/LPT (short/long processing time), M/LRW (last/last remaining processing time), FCFS (first come first served), and the like, and the large value is preferentially selected for scheduling; another part is the machine allocation rule, which allocates the machine with the earliest process completion time among the selectable set of machines in a greedy manner. Kacem et al first uses different scheduling rules such as S/LPT, FIFO (first in first out), LIFO (last in first out), etc. to allocate resources for the process, converts FJSP into JSP, and then uses genetic algorithm to further optimize. Wang et al propose a heuristic algorithm based on FBS (filtered beam search) for an FJSP model containing maintenance activities and maintenance resource constraints, and design a branching scheme to combine machine availability constraints and maintenance resource constraints. Sobeyko et al discusses FJSP targeting total weighted semester, proposes an efficient iterative local search method, and combines SBH (shifting bottleneck heurostic) with the local search method proposed herein and VNS (variable neighbor search) method.

The meta-heuristic algorithm combines a random algorithm and a local search algorithm, is not limited to specific application occasions, and has extremely strong universality as a universal framework.

Genetic algorithms are widely applied to scheduling problems as a typical meta-heuristic algorithm. Zhang et al propose an effective genetic algorithm to solve FJSP, combine and use the tactics of global selection, local selection, random selection to generate the high-quality initial population in the initialization stage of the population, use improved chromosome expression mechanism and relevant operator, guarantee the solution produced is feasible solution in order to avoid the repair mechanism to the infeasible solution. There have also been many studies using improved genetic algorithms to solve FJSP, and Rooyani et al proposed a two-stage genetic algorithm that provides a high quality initial population for the second stage at the end of the first stage. Cheng et al propose a dual population mixed genetic algorithm, which is responsible for global search and local search, respectively, and improves performance through co-evolution. Yang et al use minimum maximum completion time, key machine workload and machine total workload as optimization targets, use NSGA-II (Non-dominated Sorting Genetic Algorithm II, Non-dominated Sorting Genetic Algorithm with elite strategy) to solve the multi-target scheduling optimization problem, randomly generate the processing sequence when generating the initial species group, mix different initial species groups in different proportions by using two rules of random generation and shortest processing time in the machine selection part, and compare the experimental results with greedy random self-adaptive search process and other algorithms to prove the effectiveness of the Algorithm performance. Li et al embed a variable neighborhood search algorithm into a genetic algorithm to solve FJSP, and find a proper machine idle time period for a key process to insert by adopting a key process migration strategy based on machine idle time among different machines, thereby reducing the maximum completion time. The simulated annealing algorithm can accept a scheme worse than the current solution with a certain probability in an iterative process, so that local optimality is skipped, the simulated annealing algorithm has strong global search capability, Altoe et al takes the minimized maximum completion time and total delay as optimization targets, a scheduling scheme for generating double-target FJSP based on the simulated annealing algorithm of cluster search is provided, a group of non-dominant solutions is generated to obtain pareto boundaries, and a series of selectable high-quality solutions are provided for a decision maker.

In general, the problem that the precise algorithm can solve is small in scale, the actual problem needs to be simplified quite often, and the calculation amount which is increased sharply along with the increase of the problem scale enables the applicable occasions to be limited; the heuristic algorithm greatly improves the efficiency of the algorithm by using a designed scheduling rule, greatly reduces the calculation amount, and can obtain a scheduling scheme at a higher speed, but the scheduling rules are emphasized, so that the optimization of a certain specific index is prone to, the optimal solution is difficult to find from a global perspective, short-sight and one-side defects may exist, and the optimal solution is easy to fall into a local optimal solution or even a secondary solution. The meta-heuristic algorithm balances the advantages and the defects of the two methods to a certain extent, finds an approximate optimal solution from a global perspective as much as possible within acceptable time and calculation cost, has better performance on larger-scale problems, and is widely applied to FJSP.

But review the past studyIt can be found that most research work focuses on the algorithm performance research under the standard FJSP problem model, the optimization performance of the algorithm is improved through the fusion of different algorithms, the proposal of a new algorithm and the embedding of a new strategy, but the actual production process is often more complicated, factors influencing production and constraints needing to be met are more various, different enterprises have unique production characteristics, and the method has different differences from the standard FJSP problem model, so that the difficulty of directly applying past research results to the actual production process is increased. In actual workshop production, the selectable machine set is often the same type of machine, the time for processing a certain process is approximately the same, the difference is almost negligible, and if the process j (using O) of a certain workpiece i_i,jShown) is processed on machine M1, the next step O_i,j+1The optional machine set of (2) includes M1 (e.g., { M1, M2, M3}), and if a machine other than M1 is used, processes such as workpiece disassembly, transportation, installation and the like are required, which wastes time and human resources; meanwhile, steps of re-tool setting and the like possibly existing in the installation process also influence the machining precision. Obviously, the machine M1 is used to continue processing procedure O_i,j+1The method is a better choice, and most of the previous researches do not pay attention to the point of avoiding unnecessary changing machines in the machining process. Secondly, the shift information is often simplified and ignored, it is difficult to accurately reflect the real production situation over a long period of time (one week, one month), and the optimization of the work schedule according to the actual task amount is not considered.

Disclosure of Invention

The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.

Therefore, one purpose of the invention is to provide a flexible job shop scheduling method under the complex constraint of INSGA-II, aiming at the scheduling problem of a flexible machine and shop which needs to consider the constraint conditions of shift change, flexible extension of shift time, no-change constraint and the like, accurately modeling and solving a reasonable scheduling scheme according to the actual production characteristics, and optimizing the aim to minimize the total weighted pull-out loss and the total cost.

The invention also aims to provide a flexible job shop scheduling device under the complex constraint of INSGA-II.

In order to achieve the above object, an embodiment of the present invention provides a flexible job shop scheduling method based on the complex constraint of INSGA-ii, including the following steps:

acquiring basic production information and scheduling constraint 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 constraint comprises a non-change constraint and an elastic shift time constraint;

modeling the scheduling problem of the flexible machining workshop under complex constraint by taking the minimization of total weighted pull-out loss and the minimization of total cost as double optimization targets to obtain a scheduling model of the flexible machining workshop; and

and inputting the production information of the current workshop to the scheduling model to obtain the optimal scheduling scheme of the current workshop.

In order to achieve the above object, an embodiment of the present invention provides a flexible job shop scheduling apparatus under the complex constraint of INSGA-ii, including:

the system comprises an acquisition module, a scheduling module and a processing module, wherein the acquisition module is used for acquiring basic production information and scheduling constraint of a workshop, the basic production information comprises one or more of order tasks, equipment resources and manual resources, process information and shift information, and the scheduling constraint comprises a non-changing mechanism constraint and an elastic extension shift time constraint;

the modeling module is used for modeling the flexible machining workshop scheduling problem under complex constraint by taking total weighted drag loss minimization and total cost minimization as double optimization targets to obtain a scheduling model of the flexible machining workshop; and

and the scheduling module is used for inputting the production information of the current workshop to the scheduling model to obtain the optimal scheduling scheme of the current workshop.

The flexible job shop scheduling method and device based on INSGA-II complex constraint of the embodiment of the invention have the following beneficial effects: the FJSP model is accurately established by combining specific production characteristics, and the generated scheduling scheme is closer to the real situation and has higher usability; by applying the improved non-dominated sorting genetic algorithm with the elite strategy, a high-quality scheduling scheme can be searched, so that limited resources such as energy resources, equipment resources, human resources, time resources and the like can be coordinated and utilized more efficiently and reasonably, enterprises can improve the performance of a production system, save energy, reduce emission, reduce product cost, reduce pull-out and improve the market competitiveness of the enterprises.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a flow diagram of a flexible job shop scheduling method under the complex constraint of INSGA-II according to one embodiment of the present invention;

FIG. 2 is a schematic diagram of a process sequence for an adjacent tool requiring the same tool for processing according to one embodiment of the present invention;

FIG. 3 is a schematic illustration of a spaced one-hand process in accordance with one embodiment of the present invention;

FIG. 4 is a schematic diagram of the sequence of spacing different sets of devices according to one embodiment of the present invention;

FIG. 5 is a schematic illustration of two segment chromosome coding according to one embodiment of the present invention;

FIG. 6 is a block diagram of a greedy insertion decoding strategy according to one embodiment of the present invention

FIG. 7 is a diagram of an example interleaving operation according to one embodiment of the present invention;

FIG. 8 is a flow chart of the INSGA-II algorithm according to one embodiment of the present invention;

FIG. 9 is a flow diagram of dynamic shift adjustment according to one embodiment of the present invention;

FIG. 10 is a schematic structural diagram of a flexible job shop scheduling device under the complex constraint of INSGA-II according to an embodiment of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.

Nowadays, market demands are diversified and personalized, production tasks within a period of time often include a plurality of products with different production characteristics, complex and various production tasks provide a small challenge for enterprises to further improve production efficiency and intelligent manufacturing degree, and therefore production optimization scheduling problems faced by modern manufacturing enterprises usually show the characteristics of multiple targets, multiple constraints, high nonlinearity and the like. The invention aims at the production characteristics of various products and small batch in the machining workshop of an actual manufacturing enterprise, meanwhile, because the product quality requirement is extremely high, the required processing period is also longer, some special constraints set for ensuring the processing quality and the processing stability exist in the processing process, the complex production requirement causes that the manual scheduling task made by field managers becomes extremely complex and fussy, the quality of the scheduling scheme is difficult to be effectively ensured, the response speed cannot be well matched with the complex and changeable production environment and production requirement, and therefore, the automatic generation of the scheduling scheme by designing an efficient algorithm is a better choice than the manual scheduling depending on experience.

The invention defines a constraint process group, designs a constraint process group division algorithm and a suitable unequal length two-segment chromosome coding mode, and can reduce resource waste caused by unnecessary equipment replacement in the processing process;

in the prior art, work shift information is generally simplified, all production resources are considered to be in an available state after the time of zero, and the available time period is continuous and fixed; the production and processing activities carried out according to the work shift considered by the invention are more in line with the actual situation, the available time period of the production resources is a discontinuous time period after the rest time is removed, the work shift is dynamically adjusted according to the task amount, the work shift is not fixed information but belongs to information which can be optimized and adjusted, and the task amount in different periods can be better matched.

The following describes a flexible job shop scheduling method and device under complex constraints based on INSGA-II according to an embodiment of the present invention with reference to the accompanying drawings.

Firstly, a flexible job shop scheduling method under the complex constraint based on INSGA-II provided by the embodiment of the invention will be described with reference to the attached drawings.

FIG. 1 is a flowchart of a flexible job shop scheduling method under the complex constraint of INSGA-II according to an embodiment of the present invention.

As shown in FIG. 1, the flexible job shop scheduling method under the complex constraint of INSGA-II comprises the following steps:

in step S101, basic production information and scheduling constraints of the plant are obtained, where the basic production information includes one or more of order tasks, equipment resources and manual resources, and shift information, and the scheduling constraints include a non-change-machine constraint and an elastic shift time constraint.

First, basic production information is introduced.

1. Order task

The order task contains the following information: order number, order priority, lead time. The order number is a unique number and is used for establishing a corresponding relation with the process to be executed by the product. The priority of the order is divided into 4 grades, which are respectively represented by

numbers

1, 2, 3 and 4 from high to low, and different priorities correspond to different stall penalty weights.

2. Equipment resources and manual resources

Two major types of production resources, namely equipment resources and manual resources, are needed in the processing process of products. Correspondingly, the working procedures can be divided into two types, namely equipment working procedures and manual working procedures, the equipment working procedures need to use corresponding production equipment, each equipment is responsible for by a special equipment operator, and one person and one machine can cooperatively finish the processing tasks of the equipment working procedures; the manual process does not need to use special equipment, and a manual worker with corresponding manual skills can independently complete the processing task. The equipment operator and the manual worker are two different types of workers, and no intersection exists between the equipment operator and the manual worker.

The equipment resources and the manual resources have the concept of resource groups, for example, the equipment resource group is taken as an example, one equipment resource group number comprises a plurality of pieces of equipment, any one equipment process Oi, j can designate one equipment resource group number, any one piece of equipment under the equipment resource group number can be selected to complete the processing of the process, the resource group is similar to an optional machine set in the classic FJSP, and a plurality of workers are under the same manual resource group number.

3. Process information

The process information includes: order number, work order number, resource group number and processing time consumption. The two processes with the same order number represent different processes under the same order task, and the work order number represents that the current process is the number 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, the process is represented as the equipment sequence, and if the resource group number belongs to the manual resource group number, the process is represented as the manual sequence.

4. Information of shift

The shift information is used to describe the work and rest periods of the day, which is also a piece of information that is simplified by most FJSP studies in which the following assumptions are: all machines are in a usable state at the initial moment when t is 0 and are in a usable state or an occupied state at a later time, and there is no unusable time period due to rest. However, in actual production, daily processing and manufacturing work is often performed according to the schedule of the shift, different shifts correspond to different working time periods, and processing tasks cannot be performed at times other than the working time. The shift information in the local processing room is shown in table 1, wherein the ending time 7:00 of the next big shift represents seven morning.

TABLE 1 shift information

Second, scheduling constraints are introduced.

1. Without changing the machine constraint

For any manual process, one manual worker can be arbitrarily selected from a plurality of manual workers under the manual resource group number of the manual process to complete the manual processing task. For the equipment process, the installation and the disassembly of the workpiece on the corresponding equipment bring corresponding time and labor consumption, and simultaneously influence the accuracy and the stability of the processing, in order to avoid frequently changing the equipment used by a certain workpiece, the equipment selected by two or more equipment processes meeting specific conditions is required to be kept consistent according to the processing requirements of the aerospace structure machining workshop, namely, the constraint is not changed, and the specific description is as follows.

(1) If two or more adjacent processes of a product belong to equipment processes and equipment resource group numbers are the same, the same equipment must be selected for production, equipment replacement is not allowed, and other products are not allowed to be inserted in the middle. An example of three sequential apparatus processes is shown in figure 2.

(2) If two equipment processes of a product with the same equipment resource group number are not adjacent, but the middle separated process is one or more hand processes, because the hand processes do not need to detach the workpiece from the equipment during processing, an objective condition for realizing no change exists, and whether the two equipment processes before and after need to be forcibly arranged on the same equipment depends on the total processing time of the separated hand processes. If the accumulated processing time (only considering the normal time in the process, and not considering the waiting time caused by the occupation of the manual staff) in the middle of the two equipment sequences does not exceed 60min, the two equipment procedures must be completed on the same equipment, as shown in fig. 3, and when the manual procedure at the middle interval is executed, the equipment waits, and other products are not allowed to be processed in an inserting manner (the operations of disassembling, installing workpieces and the like are brought by processing other products); if the accumulated processing time of the manual sequence exceeds 60min, the two equipment procedures are not required to be arranged on the same equipment.

(3) If two device processes with the same device resource group number of a product are not adjacent and the middle process includes a device process with a different device resource group number, it is not mandatory that two device processes with the same device resource group number are arranged on the same device, and a corresponding example is shown in fig. 4 below.

2. Elastically extending shift time constraints

For the shifts except for the big shift, if the residual processing time required by a certain process is not more than 30 minutes when a given shift is about to end on the same day, the equipment or the manual operator in charge of processing can properly prolong the working time of the shift, so that the task of the process is completed before next shift; and if the residual processing time required by the process exceeds 30 minutes, the processing task is carried out again in the next shift according to the scheduled shift ending time. Because the ending time of the shift of the big class and the starting time of the next shift of the big class are continuous, the time length of the shift can not be prolonged any more, tasks which are not completed in the shift of the day are all left in the next shift for continuous processing, and the constraint does not need to be considered.

In step S102, modeling the flexible machining workshop scheduling problem under the complex constraint with the total weighted drag loss minimization and the total cost minimization as the dual optimization targets to obtain a scheduling model of the flexible machining workshop.

In step S103, the production information of the current plant is input into the scheduling model, so as to obtain the optimal scheduling scheme of the current plant.

The following introduces the dual optimization objectives.

1. Total weighted stall loss minimization

If the completion time of the last process of a certain order task is later than the order delivery time, the stall loss is generated, and the stall loss of a single order is defined as a stall weight value and a stall duration (in hours). The stall weights for different priority tasks are shown in table 2 below.

TABLE 2 task deadline weight information for different priorities

2. Total cost minimization

The cost considered here consists of two parts: energy consumption cost and labor performance cost. Energy consumption costs here refer to the energy consumption by the equipment resources, irrespective of the energy consumption of the part of the tool used by the tradesman. The energy consumption of the device resources consists of two parts:

(1) the processing energy consumption (processing energy) refers to energy consumed by equipment in a processing process for completing a corresponding processing task of a workpiece, and because the time required for starting and shutting down the equipment is short, the energy consumption caused by starting and shutting down the equipment is not considered, so the processing energy consumption is equal to the power of a machine processing state multiplied by the processing time.

(2) The No-load energy consumption (No load energy consumption) refers to the energy consumed by the equipment to maintain the normal operation of the equipment during the time when the next processing task does not arrive immediately after the equipment completes the processing task of a certain workpiece, so that the equipment needs to wait and is in an idle state. The idle consumption is equal to the power of the machine in idle state multiplied by the idle duration.

The state of the device is divided into three types: the power of the equipment in the machining state and the no-load state is related to the serial number of the equipment group, and the equipment in the same equipment group can be considered to be basically consistent in power. The three state switching rules of the device are:

(1) if the equipment does not have the processing task at the same day, the equipment is always in a shutdown state.

(2) If one or more processing tasks exist on the current day, starting the machine when the first processing task is started, starting the machine to enter a processing state, and entering a shutdown state when the last processing task is finished on the current day.

(3) Waiting time among a plurality of processing time periods on the same day is in an unloaded state, and rest time periods including the middle of the shift are also in the unloaded state.

The cost of the manual performance refers to the performance bonus obtained by the equipment operator according to the processing time length of the equipment operator. The bonus per hour is related to the title of the equipment operator and the equipment resource group to which the equipment responsible by the operator belongs, and the bonus of the equipment operator under the same equipment resource group is closer. The job title of the operator can be divided into: senior technicians, assistant technicians, senior workers, intermediate workers, and junior workers. The difference in prizes within a group is due to differences in the job title of different operators.

Optionally, in an embodiment of the present invention, modeling a flexible machining shop scheduling problem under complex constraints includes: modifying the non-dominated sorting genetic algorithm NSGA-II according to the characteristics of the production process and the constraint conditions in the machining workshop, and generating an improved non-dominated sorting genetic algorithm INSGA-II with the elite strategy; an INSGA-II problem solving model based on an improved non-dominated sorting genetic algorithm with an elite strategy.

And after the optimization target is determined, modeling the scheduling problem of the flexible machining workshop under complex constraint to obtain a scheduling model of the flexible machining workshop. First, the symbols and meanings used in the model will be described as shown in table 3.

TABLE 3 notation and description in scheduling problem model

In this model the following assumptions are made: the model is a static scheduling model, the information of production tasks to be processed is known and processing is not started, the information of all production equipment and operators is determined and is in an available state at the scheduling starting time, and the existing random events such as order change, emergency order insertion, equipment failure, unqualified workpiece quality and the like are not considered; the raw materials required in the processing process are sufficient, and the waiting time caused by insufficient raw materials does not exist; information such as device calendars, handcrafter calendars, etc., although initially known, may be appropriately adjusted for off-hours based on the flexible extension of the end-of-shift time constraint. Based on these assumptions, based on the analysis of the production characteristics and special constraints, requirements of the machined plant, the production scheduling problem can be modeled as follows:

the problem model is a dual-target optimization problem taking the minimum total weighted lag loss and the total cost as targets, and the formula (2-1) and the formula (2-2) are defined formulas of the two targets; the expression (2-3) represents that the total processing time of a certain device is the sum of the processing time of the device every day according to the date; the expression (2-4) indicates that the total idle time of the equipment is also the sum of the idle time of each day according to the date, and the starting time ts of the equipment is one day_i,dAnd the time te of shutdown_i,dAfter the processing time length is eliminated in the time period, the time length of the no-load equipment in the same day is remained; the expression (2-5) shows that at the scheduling starting time, all tasks are in a state to be processed, and all processing can be started after the scheduling starting time; the formula (2-6) represents that the finishing time of the workpiece is the finishing time of the last procedure; the formula (2-7) shows that a certain process can only select one resource from the selectable production resources to complete the processing; the formula (2-8) represents the process constraint of the task, and a series of processes must be finished in sequence according to the process flow; the expression (2-9) represents the capacity constraint of production resources, and only one workpiece can be processed at most at any time; the expression (2-10) indicates that the extension time of the shift in a certain day should not exceed the preset upper limit of the elastic time.

In the scheduling problem of the flexible job shop, along with the increase of production equipment, production tasks and corresponding process numbers, the feasible solution space of the problem is increased sharply, and the problem belongs to an NP difficult problem. Other constraint conditions exist in the machined workshop researched by the invention, the available time of equipment and personnel is more complicated by considering actual conditions such as shift change, rest time period and the like, more calculation cost is increased by switching the daily processing, no-load and shutdown states of the equipment, and calculation cost which is hard to bear is brought if an accurate algorithm is adopted to solve the problem, so that a large amount of time is consumed, and the method is difficult to apply in actual production scheduling. The approximation algorithm under the problem model can search for an approximate optimal solution with relatively low calculation cost, and is a better choice. On the basis of a meta-heuristic algorithm, namely a non-dominated sorting genetic algorithm (NSGA-II) with an elite strategy, the invention correspondingly modifies the characteristics of the production process and constraint conditions in a machining workshop, and solves a problem model by using an improved non-dominated sorting genetic algorithm (INSGA-II) with the elite strategy, thereby finding a better scheduling scheme within acceptable calculation time.

Optionally, in an embodiment of the present invention, modifying the non-dominated sorting genetic algorithm NSGA-ii according to characteristics of production processes and constraints in a machining plant comprises: in a chromosome representing a processing sequence, each gene represents a constraint process group including one or more processes for any task.

An improved non-dominated sorting genetic algorithm with elite strategy is introduced.

1. Non-isometric two-segment chromosome coding

The flexible job-shop scheduling problem consists of two sub-problems, one is the process sequence problem and the other is the production resource (equipment or personnel) allocation problem, so that two chromosomes can be used to express the two pieces of information respectively, and a conventional method is as follows: each gene of the first segment of chromosome is the serial number of the task, the occurrence frequency of a certain task serial number is equal to the process number of the task, the occurrence frequency of the same task serial number represents the process of the task, and different processing sequences can be obtained by disordering the arrangement sequence of the task serial numbers; the second chromosome segment expresses production resource allocation information, and each gene from left to right sequentially represents production resources used in each process from the first task to the last task.

Because the flexible machining workshop scheduling problem model researched by the invention has the constraint of not changing machines, a plurality of equipment processes meeting the condition of not changing machines must finish machining on the same equipment in sequence, the spatial continuity is ensured, other equipment in the equipment resource group cannot be changed, and the equipment cannot interpenetrate other tasks for machining in the midway. If the processing sequence is still represented by the encoding according to the process level, a large amount of randomness cannot guarantee that a plurality of equipment processes which should not be changed are continuously processed in time in the processes of population initialization, individual crossing, variation and the like, other tasks may be interspersed in the process, a large amount of infeasible solutions which do not meet the constraint condition can be generated, the repair of the solutions which do not meet the constraint condition is complex, originally different processing sequences may become the same processing sequence after the repair, and calculation waste is caused.

The conditions of not changing the machine are as follows: if the number of the required resource groups between the two equipment procedures is the same, and other procedures are not separated between the two procedures or only manual procedures with accumulated processing time not exceeding 60 minutes are separated, the two equipment procedures meet the condition of not changing machines and should be processed on the same equipment. Accordingly, the two device processes and the hand process possibly existing between the two device processes form a constraint process group, the constraint process group is used for processing as a whole, and the step of dividing the task into a plurality of constraint process groups is shown as an algorithm 1.

According to the characteristics of the constraint conditions, the coding of the processing sequence in INSGA-II is not a coding mode at the process level, but a coding mode for a constraint process group is adopted, each gene represents a constraint process group of a certain task in the chromosome representing the processing sequence, and the constraint process group comprises one or more processes.

According to the task decomposition mode of the algorithm 1, the obtained constraint process groups can be divided into three categories:

1) comprises a manual process or an equipment process;

2) the method comprises a plurality of equipment processes;

3) the method consists of a plurality of equipment processes and a manual process, wherein the first process and the last process are necessarily equipment processes.

For the third kind of situations with both equipment procedures and hand procedures, the constraint procedure group uses both equipment resource processing equipment procedures and needs manual operators to complete the processing of the corresponding hand procedures, so that corresponding production resources need to be allocated to each procedure at the procedure level, and although the production resources used in the other two kinds of situations are single, the corresponding production resources are sequentially assigned to each procedure by taking the procedure as a unit for the unification of the coding mode.

Assuming that a certain production plan includes 3 tasks, 7 processes are shared (e.g., O)_1,11 st step showing 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]The first constraint process group, denoted G, representing that these two processes belong to a constraint group and is task 1_1,1. Then a possible two-segment chromosome coding scheme is shown in FIG. 5, where each gene of the first segment represents a constraint process set representing a process sequence [ O ]_3,1]、[O_2,1]、[O_1,1,O_1,2]、[O_1,3]、[O_2,2]、[O_3,2]Wherein the 1 st and 2 nd processes [ O ] of task 1_1,1,O_1,2]Represented by gene "1" at the third position in the first chromosome as a restriction set; the second chromosome segment sequentially represents the production resource allocation of each process of the first, second and third tasks from left to right, for example, task 1 has three processes, so the first three genes of the second chromosome segment sequentially represent O_1,1、O_1,2、O_1,3The fourth gene represents the production resource allocation of the first process of task 2, and so on.

1) It can be seen that the production resource allocation of which process of which task corresponds to the gene at each position in the second chromosome segment is a definite mapping relation, and the repair mechanism for the second chromosome segment can be designed by using the mapping relation to satisfy the constraint condition of no change, and the repair steps are as follows: according to the algorithm 1, the task is sequentially decomposed into a plurality of constraint process groups, the total number of the constraint process groups is the length of the first segment of chromosome, information of which processes (and positions in the chromosome) form a constraint group is obtained, and position information of equipment processes (such as a certain constraint process group [ pos ]) is reserved₁,pos₂,…pos_k])；

2) Establishing corresponding mapping relation for elements in each constraint process group to constrain the process group [ pos₁,pos₂,…pos_k]For example, the constraint program set represents chromosome pos₁,pos₂,…pos_kThe process corresponding to the gene can be carried out using the same apparatus, and pos can be processed₂,…pos_kAre all mapped to pos₁I.e. pos₂→pos₁,…pos_k→pos₁；

3) And repairing new individuals generated in the processes of an initialization stage, a cross stage, a mutation stage and the like by using the mapping relation obtained in the previous step, so that the equipment used by each process corresponding to the constraint process group is the equipment used by the first process in the group. Taking the task information in fig. 5 as an example, there is a set of such mapping relationships: 2 → 1, indicating that in the second chromosome, the value of the second gene should be the same as the value of the first gene.

2. Chromosome decoding

On the premise of meeting the process sequence constraint, in order to start each constraint process group as early as possible, a greedy plug-in decoding strategy is adopted to complete the decoding work, and the application of the strategy in the decoding process is shown in fig. 6.

When a constraint process group G_i,jIs arranged to a production resource M_kWhen the above-mentioned two kinds of medicines are used, they are sequentially checked according to time sequence

Is found in M_kTime interval [ t ] between the end time of each constraint process group of the upper process and the start time of the next constraint process group_start,t_end]I.e., idle period, attempts to insert the constraint procedure group into the time interval. Hypothesis constraint process group G_i,jLast constraint process group G on the process flow_i,j-1Has an end time of C_i,j-1Constraint process group G_i,jAt M_kThe processing time required for the upper processing is t_i,j,kThen G is_i,jTo insert a time interval t_start,t_end]The following equation needs to be satisfied:

max{t_start,C_i,j-1}+t_i,j,k≤t_end (2-11)

when the inequality in the formula is satisfied, the process group G is constrained_i,jThe machining task can be completed using this time interval, corresponding to a start time max t_start,C_i,j-1}. In FIG. 6G_3,2Is allocated to M₃Above and above it a constraint process group G_3,1Has an end time of 3, M₃Has two constrained process groups G in the task sequence_1,1And G_2,2Existence of a time interval [2,5 ]]Thus can be G_3,2Shifted to the left and inserted into the time interval, machining is started when t is 3.

In this problem model, the working time of equipment and personnel is a series of discontinuous available time periods due to the shift information that needs to be considered, and corresponding calculations must be made for this characteristic when using the plug-in greedy decoding strategy. Than the start time max { t obtained as equation (2-11)_start,C_i,j-1Is not necessarily located at M_kIf the time is just one of the next shift time or the rest time, the constraint process group G_i,jTrue earliest start time t_rShould be the start time (t) of the next operating period_r≥max{t_start,C_i,j-1})，t_rAnd t_endNot necessarily all the working time, t_rAnd t_endIs removed from the rootThe cumulative useful time after the rest period is recorded as a_r,endThen G is_i,jTo insert a time interval t_start,t_end]The following equation should be satisfied.

t_i,j,k≤a_r,end,t_r≥max{t_start,C_i,j-1} (2-12)

In the decoding process, the working conditions of each device and each manual operator are calculated day by taking the day as a unit, the end time of the shift is dynamically adjusted according to the actual completion condition of each day, and meanwhile, the daily processing information is stored and used for calculating two optimization targets.

3. Selection operator

Selecting a binary tournament, randomly picking out two individuals from a parent population each time, and selecting one of the individuals with a lower Pareto grade to participate in subsequent crossing and mutation operations; if the two are in the same Pareto hierarchy, then the individual with the greater crowding distance is selected.

4. EPPX crossover operator based on dynamic selection probability

In the INSGA2, eppx (extended preceding predictive cross) is used as a crossover operator, and a probability selection rule is introduced on the basis of the crossover operator to improve the search effect.

Marking two Parent chromosomes selected in the crossing process as Parent₁And Parent₂When generating each gene on the chromosome of the offspring, it is necessary to determine that the gene will be divided into Parent₁Or Parent₂Inherit and select Parent₁And Parent₂Respectively, is denoted as P₁And P₂Due to the presence of only Parent₁And Parent₂Two options, so P₁And P₂The sum is 1; definition P_eTo select the probability of a better parent individual, the better individual should have a higher probability of transferring its genetic information to the offspring, according to the laws of nature of survival of the fittest, so P_eShould satisfy P_eNot less than 0.5, when P is_eWhen the number of the parents is close to 1, the method means that better parents can transmit most of information of the parents to offspring chromosomes, and the offspring chromosomes and better parentsThe volume similarity is high, and the convergence speed is accelerated for the algorithm searching process; when P is present_eWhen the number of the chromosomes is close to 0.5, the information which is inherited to the chromosomes of the offspring by the better parent individuals and the poorer parent individuals is close to the same number, so that the algorithm is favorable for exploring a new area, and the phenomenon that the algorithm falls into a local optimal solution is avoided.

According to the above analysis, different sizes of P are set at different stages of population iteration_eThe value is more favorable for balancing the capability of the algorithm to search for an approximate optimal solution and the convergence speed of the algorithm. Setting larger P at the initial stage of iteration_eThe value can accelerate convergence speed, and P close to 0.5 is set at the later stage_eThe value is more favorable for jumping out of the local optimal solution, so P_eThe update rule that varies with the iteration algebra is defined as follows.

P_e＝P_max-(P_max-P_min)·gen_cur/gen_max (2-13)

Wherein gen_curAnd gen_maxRespectively representing the current iteration algebra and the maximum iteration algebra preset by the algorithm, when gen_curIs 0, i.e. P at the beginning of the algorithm_eIs a maximum value P_maxAnd P in the last iteration_eIs a minimum value P_min。P_minMay be set to a value of 0.5, P_maxWill be determined in the experimental part below. P₁、P₂The formula (2) is shown in the following formula.

P₂＝1-P₁ (2-15)

Among them,' Parent₂ p Parent₁"indicates Parent in Pareto dominance relationship₁Dominating Parent₂Thus, Parent₁Is a better individual, and selects Parent at the moment₁Is equal to P_e(ii) a When Parent is present₂Dominating Parent₁The better individual is Parent₂Selecting Parent₁Probability of (2)Should be less than 0.5, where P₁Is 1-P_e(ii) a In the third case, the two parents do not mutually dominate, and the probability of selecting both parents is 0.5. A P₁＝0.5，P₂An example of a 0.5 interleaving operation is shown in fig. 7.

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

1) selection of two Parent chromosomes Parent₁And Parent₂Generating a random sequence R with the same length as the parent chromosome, uniformly distributing each element in R from 0 to 1, and recording the crossed child chromosome as offset;

2) for the first chromosome, i.e. the chromosome representing the processing sequence of the constraint process, the k-th gene offset (k) of offset is calculated as follows:

"fa" in the formula (2-16) represents the first available gene, all of which are in the available state in the chromosomes of the two parents at the very beginning; suppose that the condition R (k) is not more than P is satisfied when calculating Offsprinting (k)₁At this time, Parent₁Will be assigned to offset printing (k) and then will have Parent₁The gene of (1) is marked as unavailable state, and meanwhile, Parent is marked₂X of the first available state in the set is also marked as an unavailable state to ensure that the same constraint process set is not repeatedly inherited into child chromosomes, thereby correctly encoding task information.

3) For the second chromosome, i.e., the chromosome representing the allocation of production resources, offset (k), the k-th gene of offset, is calculated as follows:

according to R (k) and P₁The size relationship of (1), which father was selected when generating the kth gene of offsetThe generation chromosome inherits the kth gene from which parent chromosome.

5. Mutation operator

Two variation manipulations designed for genes in two chromosomes can be described as follows:

step 1: an individual is selected and chromosome S of the individual is replicated to S'.

Step 2: one gene of S' on the chromosome was randomly selected and designated G.

Step 3: if the gene G belongs to the chromosome expressing the processing sequence of the restriction engineering group on S', then Step4 is switched, otherwise, Step5 is switched.

Step 4: and randomly selecting a gene from the chromosome expressing the processing sequence of the constraint engineering group on the S', and exchanging the position of the gene with the gene G.

Step 5: and randomly replacing the production resource corresponding to the gene G with another resource under the same resource group number.

Step 6: chromosome repair mechanisms are used for S' to ensure that the invariant constraints are met.

Step 7: obtaining a new chromosome S' after the mutation operation of the chromosome S, and finishing the mutation operation.

It should be noted that the mutation operation of randomly replacing the production resource corresponding to the gene G with another resource under the same resource group number in Step5 may make the facilities used in the facility process originally belonging to the same constraint process group inconsistent, and therefore, a chromosome repair mechanism needs to be used in Step 6.

6. Improved elite retention strategy

In basic NSGA-II, a parent population and a child population obtained through crossing and mutation are mixed, individuals with low Pareto grades are added to a new population layer by layer from low to high after rapid non-dominated sorting, if the scale of the new population exceeds a preset population scale after all the individuals with a certain Pareto grade are placed into the new population, only a part of the individuals with larger crowding distance in a critical level are selected to enter the new population to ensure that the population scale is unchanged, and the new population is used as a parent population of the next iteration.

In the later iteration stage of the algorithm, because individuals of non-critical levels do not use crowding distances for screening, a large number of repeated individuals may exist so as to reduce the diversity of the population, and an improved elite retention strategy combined with a neighborhood search algorithm is provided for the problem: and (3) sequencing the individuals of the non-critical level from large to small according to the crowding distance, only selecting the first 90% of the individuals to directly enter a new population, and generating the remaining 10% of the individuals through a neighborhood search algorithm, wherein three neighborhood structures are designed as follows.

N1 neighborhood structure: and (4) disturbing the chromosomes of the processing sequence of the constraint process group, randomly selecting two constraint process groups and exchanging the sequence.

N2 neighborhood structure: and (3) disturbing the chromosomes distributed by the production resources, randomly selecting a process, and replacing the production resources used by the process with the production resources with the selectable production resources with the lowest load rate.

N3 neighborhood structure: and from the perspective of optimizing the artificial performance cost in the total cost, randomly selecting one equipment process, and replacing the equipment used by the equipment process with the equipment with the lowest artificial performance cost under the same equipment resource group.

The neighborhood search algorithm flow can be briefly described as follows:

(1) randomly selecting an initial solution in the hierarchy to perform neighborhood search, and randomly generating an arrangement order of neighborhood structures

(2) Selecting a first neighborhood structure in the arrangement to generate a corresponding neighborhood solution, if the first neighborhood structure is superior to the initial solution, adding a new population, and ending the neighborhood search algorithm; otherwise, using the next neighborhood structure;

(3) and if the neighborhood solutions generated by all the neighborhood structures are not better than the initial solution, randomly generating a solution to add into the new population, and ending the algorithm.

7. Algorithm flow

The INSGA-II algorithm flow proposed by the invention can be described as follows by combining the contents of the above parts.

The algorithm flow chart is shown in fig. 8.

Optionally, in an embodiment of the present invention, modifying the non-dominated sorting genetic algorithm NSGA-ii according to characteristics of production processes and constraints in a machining plant comprises: and dynamically adjusting the work shift according to the daily load rate of the equipment or personnel, wherein the daily load rate has the calculation formula as follows:

DLF＝t_p/t_s，

wherein, t_pFor the working time of the day, t_sThe time length of the shift of the day.

Dynamic shift adjustment

Due to uncertainty of task volumes in different periods (such as typical off-season and high-season), the scheduling scheme solved according to the current work shift schedule may have a long period of time and is difficult to accept, which is caused by objective reasons that the current production capacity (the number of devices and the working time) is not matched with the task volumes. The other solution is to dynamically adjust the recent work shift according to the obtained scheduling scheme so that the recent work shift is matched with the current task amount as much as possible. When the amount of tasks is too large, the working time needs to be properly prolonged, and the overtime alternative shift of part of the working shift is shown in table 4.

TABLE 4 Shift information and alternate shifts

The daily load rate DLF of a device or person may be defined as:

DLF＝t_p/t_s (2-18)

t in the formula_pAnd t_sThe processing time and the shift time of the day are respectively. Setting a daily load rate threshold value, if the daily load rate of the equipment or personnel in the scheduling scheme exceeds the daily load rate of the equipment or personnel in a certain dayAfter the threshold value is exceeded, and the corresponding shift has an overtime alternative shift, in order to increase the working time length to match a larger task amount, the working shift of the resource (equipment or manual personnel) can be changed into the corresponding overtime alternative shift, that is, the working shift is changed from a single shift to a single shift for overtime for 2 hours and a single shift for 4 hours, or the day of partial weekend rest is adjusted to weekend overtime.

The unchanged work shift easily causes resource waste or great delay loss, the scheduling scheme is obtained by solving according to the algorithm provided in the foregoing, the work shift is dynamically adjusted according to the actual scheduling requirement, and a new scheduling scheme is formulated again by using the adjusted work shift, so that a more reasonable work shift and a corresponding production and processing plan can be formulated in the iterative process, and a corresponding flow chart is shown in fig. 9.

According to the flexible job shop scheduling method based on INSGA-II complex constraint provided by the embodiment of the invention, the FJSP model is accurately established by combining specific production characteristics, and the generated scheduling scheme is closer to the real situation and has higher usability; by applying the improved non-dominated sorting genetic algorithm with the elite strategy, a high-quality scheduling scheme can be searched, so that limited resources such as energy resources, equipment resources, human resources, time resources and the like can be coordinated and utilized more efficiently and reasonably, enterprises can improve the performance of a production system, save energy, reduce emission, reduce product cost, reduce pull-out and improve the market competitiveness of the enterprises.

Next, a flexible job shop scheduling apparatus under the complex constraint based on INSGA-ii proposed in accordance with an embodiment of the present invention will be described with reference to the accompanying drawings.

As shown in fig. 10, the flexible job shop scheduling device 10 under the complex constraint of INSGA-ii includes: an acquisition module 100, a modeling module 200, and a scheduling module 300.

The obtaining module 100 is configured to obtain basic production information and scheduling constraints of a workshop, where the basic production information includes one or more of an order task, an equipment resource, a manual resource, process information, and shift information, and the scheduling constraints include a non-change constraint and an elastic shift time constraint. And the modeling module 200 is used for modeling the flexible machining workshop scheduling problem under complex constraint by taking the total weighted drag loss minimization and the total cost minimization as double optimization targets to obtain a scheduling model of the flexible machining workshop. And the scheduling module 300 is configured to input the production information of the current workshop to the scheduling model, so as to obtain an optimal scheduling scheme of the current workshop.

Optionally, in an embodiment of the present invention, modeling a flexible machining shop scheduling problem under complex constraints includes:

modifying the non-dominated sorting genetic algorithm NSGA-II according to the characteristics of the production process and the constraint conditions in the machining workshop, and generating an improved non-dominated sorting genetic algorithm INSGA-II with the elite strategy; an INSGA-II problem solving model based on an improved non-dominated sorting genetic algorithm with an elite strategy.

Optionally, in one embodiment of the invention, the flexible machining shop scheduling problem under complex constraints is modeled with the following constraints:

wherein, T_WTFor total weighted lag loss, W_iTo be C_iFor completion time of production task i, D_iPreset lead time for production task i, T_CFor the total cost, P_iFor the energy consumption cost of the plant i in the processing state, PB_iPerformance bonus per unit time for operator of device i, h_iIs the total processing time of the equipment i, P_iIs the energy consumption cost of the device i in the unloaded state,

is the total idle time length of the device i, h_i,dThe total processing time of the equipment i on the d day te_i,dFor device i to work on the day after day d, ts_i,dFor the moment when the device i starts to enter the machining state on day d, C_i,0For production task i, procedure O0_i,0Time of completion of t_startFor scheduling the start time, C_i,jFor production task i j process O_i,jN is the total number of production tasks, n_iFor the number of steps of production task i, X_i,j,kFor decision variables, if the j process O of the production task i_i,jFrom production resources k, then X_i,j,kIs 1, otherwise is 0, M_i,jIs O_i,jM is the total number of devices, X_u,v,kAs decision variables, A_s,e,iFor the cumulative time of availability of a production resource i between times s and e, Y_i,j,u,v,kIn order to make a decision on a variable,

for production of resources i at the actual off-duty time of day d, CT_i,dScheduled off-hours, f scheduled according to a predetermined shift on day d for production resource i_tThe upper limit of the time length of the shift ending time is flexibly prolonged.

Optionally, in an embodiment of the present invention, modifying the non-dominated sorting genetic algorithm NSGA-ii according to characteristics of production processes and constraints in a machining plant comprises:

in a chromosome representing a processing sequence, each gene represents a constraint process group including one or more processes for any task.

and dynamically adjusting the work shift according to the daily load rate of the equipment or personnel, wherein the daily load rate has the calculation formula as follows:

DLF＝t_p/t_s，

It should be noted that the foregoing explanation of the method embodiment is also applicable to the apparatus of this embodiment, and is not repeated herein.

According to the flexible job shop scheduling device based on the INSGA-II complex constraint, provided by the embodiment of the invention, the FJSP model is accurately established by combining specific production characteristics, and the generated scheduling scheme is closer to the real situation and has higher usability; by applying the improved non-dominated sorting genetic algorithm with the elite strategy, a high-quality scheduling scheme can be searched, so that limited resources such as energy resources, equipment resources, human resources, time resources and the like can be coordinated and utilized more efficiently and reasonably, enterprises can improve the performance of a production system, save energy, reduce emission, reduce product cost, reduce pull-out and improve the market competitiveness of the enterprises.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims

1. A flexible job shop scheduling method based on INSGA-II complex constraint is characterized by comprising the following steps:

2. The method of claim 1, wherein modeling the flexible machining shop scheduling problem under complex constraints comprises:

modifying the non-dominated sorting genetic algorithm NSGA-II according to the characteristics of the production process and the constraint conditions in the machining workshop, and generating an improved non-dominated sorting genetic algorithm INSGA-II with the elite strategy;

and solving a problem model based on the improved non-dominated sorting genetic algorithm INSGA-II with the elite strategy.

3. The method of claim 2, wherein the flexible machining shop scheduling problem under the complex constraint is modeled with a constraint:

wherein, T_WTTo total weighted lag loss, C_iFor completion time of production task i, D_iPreset lead time for production task i, T_CFor the total cost, P_iFor the energy consumption cost of the plant i in the processing state, PB_iPerformance bonus per unit time for operator of device i, h_iIs a devicei Total processing time, P_i ^*For the energy consumption cost of the device i in the idle state,

4. The method according to claim 2, wherein the modifying of the non-dominated ranking genetic algorithm NSGA-ii according to the characteristics of the production process and the constraints in the machining shop comprises:

5. The method according to claim 2, wherein the modifying of the non-dominated ranking genetic algorithm NSGA-ii according to the characteristics of the production process and the constraints in the machining shop comprises:

dynamically adjusting work shift according to the daily load rate of equipment or personnel, wherein the daily load rate has a calculation formula as follows:

DLF＝t_p/t_s，

6. A flexible job shop scheduling device based on INSGA-II complex constraint is characterized by comprising:

7. The apparatus of claim 6, wherein modeling the flexible machining shop scheduling problem under complex constraints comprises:

modifying the non-dominated sorting genetic algorithm NSGA-II according to the characteristics of the production process and the constraint conditions in the machining workshop, and generating an improved non-dominated sorting genetic algorithm INSGA-II with the elite strategy; and solving a problem model based on the improved non-dominated sorting genetic algorithm INSGA-II with the elite strategy.

8. The apparatus of claim 6, wherein the flexible machining shop scheduling problem under the complex constraint is modeled with a constraint:

wherein, T_WTTo total weighted lag loss, C_iFor completion time of production task i, D_iPreset lead time for production task i, T_CFor the total cost, P_iFor the energy consumption cost of the plant i in the processing state, PB_iPerformance bonus per unit time for operator of device i, h_iIs the total processing time of the equipment i, P_i ^*For the energy consumption cost of the device i in the idle state,

9. The apparatus of claim 6, wherein the modifying of the NSGA-II algorithm according to the characteristics of the production process and the constraint conditions in the machining shop comprises:

10. The apparatus of claim 6, wherein the modifying of the NSGA-II algorithm according to the characteristics of the production process and the constraint conditions in the machining shop comprises:

DLF＝t_p/t_s，