CN110619437A - Low-energy-consumption flexible job shop scheduling method - Google Patents

Low-energy-consumption flexible job shop scheduling method Download PDF

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CN110619437A
CN110619437A CN201910893374.3A CN201910893374A CN110619437A CN 110619437 A CN110619437 A CN 110619437A CN 201910893374 A CN201910893374 A CN 201910893374A CN 110619437 A CN110619437 A CN 110619437A
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machine tool
workpiece
workshop
energy
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周琦
朱晓春
解潇晗
梁伟
周志成
朱孟周
丁文政
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Nanjing Institute of Technology
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

A low-energy-consumption flexible job shop scheduling method comprises the following steps: step 1, constructing a workshop scheduling model taking energy consumption and completion time as optimization targets, wherein a workshop comprises workpieces of a machine tool to be processed, the energy consumption and completion time of the workshop are obtained according to the quantity of the workpieces and the machine tool, and the optimization targets are that the energy consumption of the workshop is minimum and the completion time is shortest; and 2, aiming at a workshop scheduling model, providing an improved genetic algorithm, obtaining the optimal conditions of energy consumption and completion time by adopting a multi-layer coding strategy, and finishing flexible workshop operation scheduling. In order to solve the problem of multi-objective optimization, the invention provides a multi-layer coding mode for the production problem of a flexible process route with more processing procedures and more processing equipment; generating an effective solution by using a target weighting method; aiming at MOFJSP, a scheduling model is established, and an optimal solution can be obtained through a multilayer coding genetic algorithm verified through example simulation, so that the optimal scheduling of workshop operation is completed.

Description

Low-energy-consumption flexible job shop scheduling method
Technical Field
The invention relates to the field of workshop scheduling, in particular to a low-energy-consumption flexible job workshop scheduling method.
Background
The manufacturing industry is the main body of national economy and is the basis of the foundries. With the rapid development of manufacturing industry, energy consumption is huge, so that the production cost of a job shop is increased, and the environment is damaged. Therefore, efficient reduction of energy consumption through plant scheduling is an inevitable requirement for enterprises to realize sustainable development [1 ]. The traditional job shop scheduling usually takes the shortest completion time, the lowest cost and the like as optimization targets. And in the step 2, aiming at the job shop scheduling problem of which the minimum maximum completion time is an optimization target, an improved genetic algorithm based on dynamic crossing and variation probability is provided, and the optimization capability and the convergence speed of the algorithm are obviously improved.
In recent years, the problem of energy waste caused by high-speed economic development is becoming more severe, and the problem of energy consumption is widely concerned by scholars at home and abroad, so that the research of multi-objective flexible job shop scheduling problem (MOFJSP) oriented to energy consumption optimization is particularly important. Liu et al [3] propose a non-dominated sorting genetic algorithm to solve the production scheduling problem with minimized power consumption as the optimization objective. Mansouri et al [4] definitely uses energy consumption as one of indexes of workshop scheduling, establishes a multi-target mixed integer linear optimization model, and provides a heuristic algorithm to perform rapid balance analysis between completion time and energy consumption. Mouzon et al [5] developed various algorithms and multi-objective mathematical programming models for the problem of scheduling operations on a single CNC machine with the goal of reducing energy consumption and total completion time, and the study showed that when the machine is started when it is required to process a workpiece, the proportion of the energy saved to the total energy consumption can reach 80%.
[1] Xiaoli (Xiaoli). Production scheduling optimization method research [ M ] based on genetic algorithm. University of science and technology in china, 2006.
[2] And fourthly, tensioning letter and strengthening. An improved genetic algorithm [ J ] for solving job shop scheduling problems. The manufacturing industry is self-organized, 2018, 40(08): 113-.
[3]Liu Y，Dong H，Lohse N，et al。An investigation into minimising total energy consumption and total weighted tardiness in job shops[J]。Journal of Cleaner Production，2014，65:87-96。
[4]Mansouri SA，Aktas E and Besikci U。Green scheduling ofa two machine flow shop:Trade-off between makespan and energy consumption[J]。European Journal of Operational Research，2016，248(3):772–788。
[5]Mouzon G，Yildirim M B，Twomey J。Operational methods for minimization of energy consumption of manufacturing equipment[J]。International Journal of Production Research，2007，45(18-19):4247-4271。
Disclosure of Invention
The invention aims at a manufacturing job shop to construct a scheduling model taking energy consumption and completion time as optimization targets. Aiming at the model, an improved genetic algorithm is provided, a multi-layer coding strategy is adopted, and the flexible workshop operation scheduling problem is effectively solved under the condition of optimal energy consumption and completion time. The feasibility and the effectiveness of the algorithm in solving the scheduling problem of the low-energy-consumption flexible job shop are verified through simulation data.
A low-energy-consumption flexible job shop scheduling method comprises the following steps:
step 1, constructing a workshop scheduling model taking energy consumption and completion time as optimization targets, wherein a workshop comprises workpieces of a machine tool to be processed, the energy consumption and completion time of the workshop are obtained according to the quantity of the workpieces and the machine tool, and the optimization targets are that the energy consumption of the workshop is minimum and the completion time is shortest;
and 2, aiming at a workshop scheduling model, providing an improved genetic algorithm, obtaining the optimal conditions of energy consumption and completion time by adopting a multi-layer coding strategy, and finishing flexible workshop operation scheduling.
Further, in the step 1, J workpieces and M machine tools are arranged in the flexible operation workshop, and the total energy consumption E of the machine tools in the operation modepDivided into four parts, i.e. cutting energy Ec jmEnergy consumption of load Ea jmBasic energy consumption E for maintaining normal operation of systembAnd energy consumption E of auxiliary system of machine toolaExpressed as:
wherein, Xm jnIs an integer variable that has two possible values: 0 or 1, if working procedure O on machine tool mjnThen set to 1; otherwise, setting the value to 0;
the load power consumption of the machine tool is influenced by the actual load, and the load power P is within the allowable load rangea jm(t) and cutting power Pc jmThe relationship between (t) is expressed as:
in the formula, δ is the load dissipation coefficient, so:
basic energy consumption E for maintaining normal operation of machine toolbExpressed as:
substituting the formulas (3) and (4) into the formula (1) to obtain:
when the machine tool is in idle mode of operation, loading or unloading the workpiece, positioning, clamping and changing the tool consumes a great deal of energy EuI.e. the no-load energy consumption, is expressed as:
in actual machining, the machine tool is normally in four states: starting, no-load, processing and stopping states, when the machine tool is in different states, the energy consumption value of the machine tool is different, and the total energy consumption of the workshop manufacturing system can be calculated according to the following formulas (5) and (6):
Etotal＝Es+Eu+Ep (7)
wherein E issAnd energy consumption is reduced for starting the machine tool.
Further, the optimization goal of the plant scheduling model is total energy consumption (f)1) And total completion time (f)2) The specific mathematical model is as follows:
the constraints imposed are:
Tmax≥Cjm,j∈J,m∈M (9)
Cjm≤Sjk,m,k∈M,m≠k,j∈J (12)
Cjm≤S(j+1)m,j∈J,m∈M (13)
constraint (9) defines the total completion time TmaxFinish time C of the last workpiece or morejm；
The constraint (10) indicates that each process of each workpiece can only be allocated to one machine tool;
constraint (11) represents the completion time C of the workpiece j on the machine mjmStarting time S of workpiece j on machine tool mjmAnd a processing time TjmComposition is carried out;
the constraint (12) gives a preferential constraint between the working processes of the workpiece j, i.e. the workpiece can only process the next working process in the next production stage after the workpiece completes a certain working process in the current stage, SjkRepresents a start time of machining a workpiece j on a machine tool k;
constraints (13) ensure that one machine can only process the next workpiece after the current workpiece is completed.
Furthermore, the workshop scheduling model is a multi-objective function with constraints, and an objective weighting method is adopted to normalize time and energy consumption and then carry out weighted summation to find an optimal solution; f. ofi KIs the ith objective function of genetic algorithm evolution to the K generation, and the two objective functions are expressed as follows:
U(K)＝αf1 K+(1-α)f2 K (14)
in the formula, α is an energy consumption weight, a decision maker takes a value of α according to preference of each target, and can evaluate all targets in the same proportion by normalizing different standard values into a comparable unit, so that an optimization objective function of normalized weighted values is as follows:
in the formula: f. of1'K、f2'KIs f1 K、f2 KEach normalized target fi'KIs defined as:
in the formula:as an objective function fi KGiven minimum and maximum values.
Furthermore, the encoding mode of the multilayer encoding strategy in the step 2 is integer encoding, the workpiece processing procedure encoding is mainly divided into two layers, and the first layer is the processing sequence of the workpiece procedures; the second layer is a processing machine tool corresponding to each procedure; in the first layer, the same workpiece is denoted by the same numeral and the workpiece processes are determined according to the order in which they appear in the code, and the second layer denotes the code of the machine tool selected for each process.
Further, the fitness function of the genetic algorithm is an optimization objective function of the plant scheduling model, namely, formula (15).
Further, in the step 2, in the genetic algorithm operation stage, an initial population is randomly generated, and new individuals are generated by using basic genetic operations, namely selection, crossover and mutation, which are described in detail as follows:
step 2-1, selecting operation: based on individual fitness, the individual fitness selected by the operator for crossover and mutation operations is generally not the highest; selecting individuals with better adaptability by adopting a roulette method, wherein the probability of the selected individuals is in direct proportion to the fitness of the individuals;
step 2-2, cross operation: the crossover operator simulates the mating recombination process between biological chromosomes, and generates a new individual by carrying out certain crossover probability and crossover method on partial genes in two paired chromosomes, wherein the crossover operator is an important characteristic of a genetic algorithm; the cross probability is usually 0.6-0.9; the integer crossing method is adopted, and the operation flow is as follows:
2-2-1, randomly selecting two chromosomes in a parent from the population, and taking out a first layer code of each chromosome;
step 2-2-2, randomly selecting a crossing position for crossing;
step 2-2-3, comparing individuals before and after crossing, adjusting redundant genes into missing genes, and adjusting second-layer codes to generate a new population;
step 2-3, mutation operation: since the crossover operation cannot generate a solution with new information, in order to obtain a solution with maximum fitness, the population needs to perform mutation operation with a specified mutation probability, which is generally 0.001-0.1.
The invention has the beneficial effects that: aiming at solving the problem of multi-objective optimization, the invention provides a multi-layer coding mode for the production problem of a flexible process route with more processing procedures and more processing equipment; generating an effective solution by using a target weighting method; aiming at MOFJSP, a scheduling model is established, and an optimal solution can be obtained through a multilayer coding genetic algorithm verified through example simulation, so that the optimal scheduling of workshop operation is completed.
Drawings
Fig. 1 is a power distribution curve of a general machine tool in the embodiment of the present invention.
FIG. 2 is a convergence graph of the multilayer coding genetic algorithm of scheme 1 in the example of the present invention.
Fig. 3 is a time-optimal gantt chart of the scheme 1 in the embodiment of the present invention.
Fig. 4 is an optimal gantt chart of energy consumption in scheme 2 in the embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
The MOFJSP problem can be described as: m machine tools are arranged to process J workpieces. The nth process of the jth workpiece is represented as OjnThe number of the working procedures of each workpiece is one or more, and the determined sequence can be realized, and each working procedure can be finished by one or more machine tools. And the machine tool M belongs to M and processes the workpiece J belongs to J, so that corresponding processing time and energy consumption are generated. Between two consecutive machining tasks, the machine tool can be kept idle or switched off. Frequent turning on or off of the machine consumes additional energy and shortens the life of the machine, while the machine is idling and consumes only a small amount of energy, so the machine should be kept idling for a while. The main scheduling objective studied herein is to minimize energy consumption, to satisfy certain constraints, and to determine the processing sequence of the workpieces and the corresponding processing equipment, mostAnd finally, the overall scheduling performance index is optimal. The constraints are as follows:
(1) each process of the workpiece can only be processed on one machine tool;
(2) the workpiece can not be interrupted in the machining process;
(3) at the same time, each machine tool can only process one workpiece, and each workpiece can only process on one machine tool;
(4) the machine tool may have a stopped or no-load operating condition.
(5) The operation priority between the processes of the same workpiece does not change.
(6) Regardless of the preparation time before the workpiece is machined, all the workpieces and the machine tool are ready at time t-0.
The energy consumption model of the plant may limit the total energy consumption within the manufacturing system while minimizing the maximum completion time. The associated symbol definitions are shown in the following table.
Assume that there are J workpieces in a flexible job shop, M machine tools. According to the energy balance equation of the manufacturing system, the total energy consumption E of the machine tool in the running modepCan be divided into four parts, i.e. cutting energy Ec jmEnergy consumption of load Ea jmBasic energy consumption E for maintaining normal operation of systembAnd energy consumption E of auxiliary system of machine toolaIt can be expressed as:
the load power consumption of the machine tool is influenced by the actual load, and the load power P is within the allowable load rangea jm(t) and cutting power Pc jmThe relationship between (t) can be expressed as:
in the formula: delta-load dissipation factor. Therefore, the method comprises the following steps:
basic energy consumption E for maintaining normal operation of machine toolbCan be expressed as:
the compounds of formula (3) and (4) can be substituted for formula (1):
when the machine tool is in idle mode of operation, loading or unloading the workpiece, positioning, clamping and changing the tool consumes a great deal of energy Eu(i.e., no load energy consumption), can be expressed as:
in actual machining, the machine tool is normally in four states: start, idle, process and stop conditions. The power distribution curve of a general machine tool in the machining process is shown in figure 1. When the machine tool is in different states, the energy consumption values of the machine tool are different. From equations (5), (6), the total energy consumption of the plant manufacturing system can be calculated as follows:
Etotal＝Es+Eu+Ep (7)
the optimization target of the workshop scheduling model is total energy consumption (f)1) And total completion time (f)2) The specific mathematical model is as follows:
the constraints imposed are:
Tmax≥Cjm,j∈J,m∈M (9)
Cjm≤Sjk,m,k∈M,m≠k,j∈J (12)
Cjm≤S(j+1)m,j∈J,m∈M (13)
the constraint (9) defines that the maximum completion time is equal to the completion time of the last workpiece. The constraint (10) indicates that each process for each workpiece can only be assigned to one machine tool. Constraint (11) represents the completion time C of the workpiece j on the machine mjmStarting time S of workpiece j on machine tool mjmAnd a processing time TjmAnd (4) forming. The constraint (12) gives a preferential constraint between the machining processes of the workpiece j, i.e. the workpiece can not process the next process in the next production stage until the current stage has completed a certain process. Constraints (13) ensure that one machine can only process the next workpiece after the current workpiece is completed.
The mathematical model is a multi-objective function with constraints. Although there is no optimal or near optimal solution in the multi-objective optimization problem (MOP), a set of pareto optimal solutions that trade off between maximum completion time and total energy consumption can be obtained. There are many methods for solving the MOP, the most notable of which is a target weighting method, in which time and energy consumption are normalized and then weighted and summed to find the optimal solution. f. ofi KIs the ith objective function of genetic algorithm evolution to K generation, and the two objective functions are expressed as follows:
U(K)＝αf1 K+(1-α)f2 K (14)
in the formula: and alpha is the energy consumption weight. And the decision maker takes the value of alpha according to the preference of each target. All targets can be evaluated in the same scale by normalizing the different standard values to comparable units. Therefore, the normalized weighted value optimization objective function is:
in the formula: f. of1'K、f2'KIs f1 K、f2 KThe normalized value of (a). Each normalized target fi'KIs defined as:
in the formula:as an objective function fi KGiven minimum and maximum values.
The Genetic Algorithm (GA) is a random search algorithm, the theoretical basis of which is the biological evolution principle of Darwin and the genetic theory of Mendelian, simulates the heredity and evolution of organisms in nature, and has the characteristics of strong parallelism, randomness and self-adaptive probability. The GA uses existing information to guide the search process, and performs other genetic operations such as selection, crossover, mutation, etc., by estimating fitness of the chromosomes, to converge to an optimal or satisfactory solution.
The genetic algorithm plays an important role in solving the nonlinear optimization problem, the chromosome represents a potential optimal solution in the problem, and when a complex problem is solved, a single chromosome cannot accurately express the solution of the problem. The invention improves the genetic algorithm under MOFJSP environment, adopts a multilayer coding strategy, divides the individual codes into a plurality of layers, and the codes of each layer represent different meanings, so that the multilayer codes interact with each other to solve the solution of the whole problem, thereby realizing the purpose of expressing the solution of the complex problem by using a single chromosome.
The coding mode provided by the invention is integer coding, and the work piece processing procedure coding is shown in the following table.
The coding of the chromosome is mainly divided into two layers, wherein the first layer is the processing sequence of the work piece working procedure; the second layer is a processing machine tool corresponding to each procedure. In the first layer, the same workpieces are denoted by the same numerals, and the workpiece processes are determined according to the order in which they appear in the code. If the 1 st appearance "1" indicates the 1 st process "1-1" of the 1 st workpiece, the 2 nd appearance "1" indicates the 2 nd process "1-2" of the 1 st workpiece, and so on. The second level indicates the code of the processing machine selected in each step, and as shown by machine codes 1, 3, 2, 3, and 1 in table 2, the "1-1" step is performed on machine 1, and the "3-1" step is performed on machine 3.
The genetic algorithm follows the principle of 'survival of suitable persons and elimination of inferior persons' in the nature. The higher the individual adaptation degree, the higher the probability of being selected in the next generation. Generally, fitness is related to the objective function. In the present invention, the above objective function (i.e., equation (15)) is a fitness function.
During the GA operation phase, an initial population was randomly generated. Using basic genetic manipulation (i.e., selection, crossover and mutation), new individuals are generated. These three operations are described in detail as follows:
(1) selecting operation: the individual fitness selected by the operator for crossover and mutation operations is typically not the highest based on the individual fitness. The invention adopts a roulette method to select individuals with better adaptability, and the probability of the selected individuals is in direct proportion to the fitness of the individuals.
(2) And (3) cross operation: the crossover operator simulates the mating recombination process between biological chromosomes, and generates a new individual by carrying out certain crossover probability and crossover method on partial genes in two paired chromosomes, wherein the crossover operator is an important characteristic of a genetic algorithm. The cross probability is usually 0.6-0.9. The invention adopts an integer crossing method, and the operation flow is as follows:
randomly selecting two chromosomes in a parent from a population, and taking out a first layer code of each chromosome;
and selecting crossing positions randomly for crossing.
Comparing the individuals before and after the crossing, adjusting the redundant gene into the missing gene, and adjusting the second layer code to generate a new population.
(3) Mutation operation: since the crossover operation cannot produce a solution with new information, the population needs to perform mutation operations with a specified mutation probability in order to be able to obtain a solution with maximum fitness. The probability of mutation is generally 0.001 to 0.1.
The multilayer coding genetic algorithm provided by the invention is realized in a Matlab R2016a environment, and runs on a computer with a processor of Intel i787003.2GHz and a memory of 16 GB. The parameters of the improved genetic algorithm are shown in the following table.
Parameter name Value of
Number of populations 40
Maximum number of iterations 100
Probability of crossing 0.8
Probability of variation 0.05
The experimental data are derived from actual production data in the literature, where the number of workpieces J is 6 and the number of machines M is 6. Example data of machining energy consumption, machining time, process-selectable machine tools, and the like are shown in the following table.
Due to the relationship between energy consumption and completion time, the energy consumption weight α is determined by the preference of the decision maker. When the decision maker wants to minimize the maximum completion time, the power consumption weight is set to α -0. Under the condition, the effective solution set obtained by the algorithm of the invention through 15 times of simulation is shown in the following table.
Serial number Time of completion Total energy consumption Energy consumption of processing
1 55 507.77 468.40
2 57 469.90 435.70
3 54 530.27 500.80
4 51 458.56 430.80
5 54 472.46 447.00
6 56 531.64 496.50
7 55 513.27 487.40
8 51 492.96 460.80
9 55 514.01 485.70
10 58 517.21 491.00
11 55 507.71 474.20
12 55 503.90 475.70
13 51 546.88 522.20
14 53 435.19 408.60
15 55 506.04 472.20
As can be seen from the above table, there is a contradictory relationship between completion time and energy consumption. When the time-out reaches the minimum 51, the corresponding energy consumption minimum is 458.56, and when the total energy consumption reaches the optimum 435.19, the time-out is increased to 53. A shorter maximum completion time will consume more energy and a higher energy consumption will shorten the maximum completion time. When the decision maker wants to minimize the energy consumption, the energy consumption weight is set to be 1, and after 15 times of simulation, the minimum energy consumption is 331.86, which is reduced by about 127 compared with the energy consumption 458.56 corresponding to the shortest completion time. The optimization results of the dual-target weighted values are shown in the following table.
Scheme(s) Energy consumption weight alpha Total energy consumption Energy consumption of processing Time of completion
1 0 458.56 430.80 51
2 1 331.86 304.80 61
The convergence graph of the multilayer encoding genetic algorithm of scheme 1 is shown in fig. 2.
As can be seen from FIG. 2, when the iteration number is 7, the optimal solution is quickly converged, the dominant individuals are inherited in a large quantity, the population mean value changes smoothly and continuously tends to the optimal solution, and the search is effective and stable. The time optimal gantt chart for scenario 1 is shown in fig. 3.
As can be seen from fig. 3, the processes are uniformly distributed on 6 machine tools, wherein the machine tool with higher average energy consumption for machining also participates in the machining of the workpiece, resulting in higher energy consumption for machining, which is 430.80. Scheme 2 energy consumption optimal gantt chart is shown in figure 4.
As can be seen from fig. 4, since the average processing energy consumption of M2 and M3 is low, the processes are concentrated on the two machines, and the processing energy consumption is 304.80, which is 126 less than that in case 1. Taking the "1-3" process as an example, the machinable machine tools are M2, M5, and M6, and as can be seen from table 4, since the machining energy consumption of M2 is the smallest, when the workpiece reaches the third process, the workpiece flows to the machine tool M2 to be machined.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (7)

1. A low-energy-consumption flexible job shop scheduling method is characterized by comprising the following steps:
the method comprises the following steps:
step 1, constructing a workshop scheduling model taking energy consumption and completion time as optimization targets,
the workshop comprises workpieces of a machine tool to be processed, energy consumption and completion time of the workshop are obtained according to the number of the workpieces and the machine tool, and the optimization targets are that the energy consumption of the workshop is minimum and the completion time is minimum;
and 2, aiming at a workshop scheduling model, providing an improved genetic algorithm, obtaining the optimal conditions of energy consumption and completion time by adopting a multi-layer coding strategy, and finishing flexible workshop operation scheduling.
2. The low-energy-consumption flexible job shop scheduling method according to claim 1, characterized in that: in the step 1, J workpieces are arranged in a flexible operation workshop, M machine tools are arranged, and the total energy consumption E of the machine tools in the operation modepDivided into four parts, i.e. cutting energy Ec jmEnergy consumption of load Ea jmBasic energy consumption E for maintaining normal operation of systembAnd energy consumption E of auxiliary system of machine toolaExpressed as:
wherein, Xm jnIs an integer variable that has two possible values: 0 or 1, if working procedure O on machine tool mjnThen set to 1; otherwise, setting the value to 0;
the load power consumption of the machine tool is influenced by the actual loadWithin an allowable load range, the load power Pa jm(t) and cutting power Pc jmThe relationship between (t) is expressed as:
in the formula, δ is the load dissipation coefficient, so:
basic energy consumption E for maintaining normal operation of machine toolbExpressed as:
substituting the formulas (3) and (4) into the formula (1) to obtain:
when the machine tool is in idle mode of operation, loading or unloading the workpiece, positioning, clamping and changing the tool consumes a great deal of energy EuI.e. the no-load energy consumption, is expressed as:
in actual machining, the machine tool is normally in four states: starting, no-load, processing and stopping states, when the machine tool is in different states, the energy consumption value of the machine tool is different, and the total energy consumption of the workshop manufacturing system can be calculated according to the following formulas (5) and (6):
Etotal＝Es+Eu+Ep (7)
wherein E issAnd energy consumption is reduced for starting the machine tool.
3. A method according to claims 1-2The low-energy-consumption flexible job shop scheduling method is characterized by comprising the following steps: the optimization target of the workshop scheduling model is total energy consumption (f)1) And total completion time (f)2) The specific mathematical model is as follows:
the constraints imposed are:
Tmax≥Cjm,j∈J,m∈M (9)
Cjm≤Sjk,m,k∈M,m≠k,j∈J (12)
Cjm≤S(j+1)m,j∈J,m∈M (13)
constraint (9) defines the total completion time TmaxFinish time C of the last workpiece or morejm；
The constraint (10) indicates that each process of each workpiece can only be allocated to one machine tool;
constraint (11) represents the completion time C of the workpiece j on the machine mjmStarting time S of workpiece j on machine tool mjmAnd a processing time TjmComposition is carried out;
the constraint (12) gives a preferential constraint between the working processes of the workpiece j, i.e. the workpiece can only process the next working process in the next production stage after the workpiece completes a certain working process in the current stage, SjkRepresents a start time of machining a workpiece j on a machine tool k;
constraints (13) ensure that one machine can only process the next workpiece after the current workpiece is completed.
4. Low energy consumption flexible shop assistant according to claims 1-3The method is characterized in that: the workshop scheduling model is a multi-target function with constraints, and an optimal solution is found by adopting a target weighting method to normalize time and energy consumption and then carry out weighted summation; f. ofi KIs the ith objective function of genetic algorithm evolution to the K generation, and the two objective functions are expressed as follows:
in the formula, α is an energy consumption weight, a decision maker takes a value of α according to preference of each target, and can evaluate all targets in the same proportion by normalizing different standard values into a comparable unit, so that an optimization objective function of normalized weighted values is as follows:
in the formula: f. of1'K、f2'KIs f1 K、f2 KEach normalized target fi'KIs defined as:
in the formula:as an objective function fi KGiven minimum and maximum values.
5. The low-energy-consumption flexible job shop scheduling method according to claim 1, characterized in that: the coding mode of the multilayer coding strategy in the step 2 is integer coding, the workpiece processing procedure coding is mainly divided into two layers, and the first layer is the processing sequence of the workpiece procedures; the second layer is a processing machine tool corresponding to each procedure; in the first layer, the same workpiece is denoted by the same numeral and the workpiece processes are determined according to the order in which they appear in the code, and the second layer denotes the code of the machine tool selected for each process.
6. A low energy consumption flexible job shop scheduling method according to claims 1-5, characterized by: the fitness function of the genetic algorithm is an optimized objective function of the plant scheduling model, namely formula (15).
7. The low-energy-consumption flexible job shop scheduling method according to claim 1, characterized in that: in the step 2, in the genetic algorithm operation stage, an initial population is randomly generated, and new individuals are generated by using basic genetic operations, namely selection, crossover and mutation, which are described in detail as follows:
step 2-1, selecting operation: based on individual fitness, the individual fitness selected by the operator for crossover and mutation operations is generally not the highest; selecting individuals with better adaptability by adopting a roulette method, wherein the probability of the selected individuals is in direct proportion to the fitness of the individuals;
step 2-2, cross operation: the crossover operator simulates the mating recombination process between biological chromosomes, and generates a new individual by carrying out certain crossover probability and crossover method on partial genes in two paired chromosomes, wherein the crossover operator is an important characteristic of a genetic algorithm; the cross probability is usually 0.6-0.9; the integer crossing method is adopted, and the operation flow is as follows:
2-2-1, randomly selecting two chromosomes in a parent from the population, and taking out a first layer code of each chromosome;
step 2-2-2, randomly selecting a crossing position for crossing;
step 2-2-3, comparing individuals before and after crossing, adjusting redundant genes into missing genes, and adjusting second-layer codes to generate a new population;
step 2-3, mutation operation: since the crossover operation cannot generate a solution with new information, in order to obtain a solution with maximum fitness, the population needs to perform mutation operation with a specified mutation probability, which is generally 0.001-0.1.
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