CN115099612A - Flexible job shop batch scheduling method considering carbon emission - Google Patents
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Abstract
The invention discloses a flexible job shop batch scheduling method considering carbon emission, which solves the problem of flexible job shop batch scheduling by improving an NSGA-II algorithm and taking completion time and carbon emission as targets. Firstly, establishing a mathematical model of batch scheduling of a flexible job workshop; and setting related parameters for improving the NSGA-II algorithm, and coding the population individuals by adopting a four-section coding mode so as to initialize the population. Then, designing crossover and mutation operators, and carrying out crossover mutation operation on the four segments of genes of batch division, sub-batch workpiece quantity division, process sequencing and machine selection respectively. A concept of recessive genes is provided, and a distinguishing method of the recessive genes is designed, so that an individual can be effectively decoded by the method. The remaining good individuals are then selected by non-dominated ranking and crowding. And finally, outputting a Pareto optimal solution set when the iteration times are reached.
Description
Technical Field
The invention relates to the field of workshop scheduling, in particular to a flexible job workshop batch scheduling method considering carbon emission.
Background
Workshop scheduling is the core of enterprise production management, and the production cycle of enterprise's product can be shortened to effectual scheduling scheme, improves production efficiency to improve economic benefits. However, the rapid development of enterprises is accelerated, the problem of environmental pollution and the problem of energy exhaustion are increasingly highlighted, and the workshop scheduling considering environmental factors is a brand-new research direction in the current workshop scheduling problem. In addition, the current enterprise production mode has the characteristics of complexity, small batch and multiple types, most of actual production and processing workshops are mainly flexible workshops, and workpieces are usually produced in a batch cutting mode. Therefore, the invention provides a flexible job shop batch scheduling method considering carbon emission.
Regarding the batch scheduling problem of the flexible job shop, the problem has become a hot topic in the scheduling field at present. As an NSGA-II algorithm for genetic algorithm fusion multi-objective optimization, the method has the advantages of high running speed and good convergence and is widely applied to the workshop scheduling problem. However, the phenomenon of generation of a large number of illegal solutions can occur when the crossing method of the NSGA-II algorithm crosses the chromosome, and the initialization population under batch scheduling can cause different lengths of the chromosome, so that the phenomenon of generation of the illegal solutions is more obvious in the crossing process, and the algorithm search range is greatly reduced; on the other hand, at present, researchers do not deeply consider batch cross variation, and the search range of the algorithm can be enlarged for batch genetic operation, so that the optimal solution can be found out better.
Disclosure of Invention
In view of the deficiencies of the prior art, it is an object of the present invention to provide a flexible job shop batch scheduling method that takes into account carbon emissions.
In order to achieve the purpose, the invention adopts the following scheme:
a flexible job shop batch scheduling method taking into account carbon emissions, said scheduling method comprising the steps of:
And 2, designing a random batching strategy, randomly dividing the workpieces into a plurality of batches, obtaining the quantity of the workpieces under each sub-batch, and preparing for the initial population of the algorithm by the batching method.
the invention further improves that:
the specific method of the step 1 comprises the following steps:
establishing an objective function f of minimum completion time for the model 1 ：
f 1 ＝MinMax(C i )
For the moldModeling an objective function f for minimum carbon emissions 2 ：
The invention takes a numerical control workshop as a research object, and the carbon emission calculation model is established according to the actual production of the numerical control cutting workshop. The carbon emission in the production process of the numerical control workshop can be divided into two parts of electric energy consumption and material consumption according to different carbon discharge modes, wherein the electric energy consumption comprises electric energy consumed by the operation of a processing machine and electric energy consumed by systems such as lighting and temperature control systems in workshop production. The consumption of material includes carbon emissions due to the consumption of raw materials in the plant and carbon emissions due to the consumption of auxiliary materials, mainly the wear of the tools.
According to the classification, the carbon emission of the numerical control cutting workshop can be subdivided into the carbon emission consumed by the electric energy of a machine, the carbon emission consumed by raw materials, the carbon emission worn by a cutter and the carbon emission of systems such as workshop lighting and air exhaust, and then a mathematical model is established for four major factors influencing the carbon emission.
Establishing a mathematical model of carbon emission caused by electric energy loss of a machine, specifically:
f 2 ＝Min(CE m +CE p +CE tw +CE l )
electrical energy consumption under machine load:
electric energy consumption of the machine under no load:
the carbon emission caused by the electric energy loss of the machine is specifically as follows:
establishing a mathematical model of carbon emission caused by consumption of raw materials in a cutting process, which specifically comprises the following steps:
wherein:
SEC means removal of 1cm during processing 3 Calculated value of special energy consumption to be consumed by material, MRR represents material removal rate, C 0 And C 1 Is related to the special coefficient of SEC, is related to factors such as cutter material, processing environment and the like,
is the volume of the raw material cut per unit time.
Establishing a mathematical model of carbon emission caused by tool abrasion, specifically comprising the following steps:
wherein:
a mathematical model is established for carbon discharge caused by electric energy consumption of systems such as workshop lighting, air exhaust and the like, and the mathematical model specifically comprises the following steps:
CE l ＝F e ·P a ·T
wherein: max (C) k )
The specific constraints are as follows:
P i ≤N i ∧N iz >0；
S iz(j+1)k ≥E izjk ；
E izjk ＝S izjk +PT izjk +ST ijk ×N iz ；
S izjk ＝E ifjk ；
C i ＝max(E izjk ),z＝1,2,...,P i ；
wherein the specific mathematical symbols are defined as follows:
i: a workpiece number;
n: number of kinds of work pieces, work set J ═ { J ═ J } 1 ，J 2 ，...,J n }；
J i : a workpiece set of workpiece i;
j i : total number of steps for workpiece i;
N i : the processing number of the workpieces i;
P i : the number of the sub-batches of the workpiece i;
N iz : the batch number of the z th sub-batch of the workpiece i;
m: the total number of machines;
k: serial number of machine, machine set M ═ { M ═ M 1 ，M 2 ，...,M m }；
C i : finishing time of a workpiece i;
S izjk : starting the processing time of the jth procedure of the z th sub batch of the workpiece i on the machine k;
E izjk : the completion time of the jth procedure of the z th sub-batch of the workpiece i on the machine k;
T izjk : the processing time of the jth procedure of the z th sub batch of the workpiece i on the machine k;
ST ijk : the processing time of the j-th procedure of the unit workpiece i on the machine k;
F e : a discharge factor of electrical energy;
CE m : carbon emissions from machine losses of electrical energy;
CE p : carbon emission caused by non-electric energy loss in the cutting process;
CE tw : carbon emissions due to tool wear;
CE l : the carbon emission caused by the consumption of electric energy by systems such as workshop lighting, air exhaust and the like;
the specific batch method of the step 2 comprises the following specific steps:
step 2.1, initializing parameter i to 1, m to 0, j to 1, p max 。
Step 2.2, selecting the current workpiece model J i The number N of workpieces of the type is processed in batches i 。
Step 2.3, randomly generating the current workpiece model J i Number of batches p i And satisfies 0 < p i ≤p max (p i E.g. Z) if p i If 1, go to step 2.7, and directly output the current workpiece model J i Number of batches p i And number of workpieces N i (ii) a If p is i Not equal to 1, go to step 2.4.
And 2. step 2.4. Randomly generating the number N of first sub-batch workpieces j And satisfies 0 < N j ≤N i -m。
Step 2.5, making m equal to m + N j If m + p i -j>N i Then m is equal to m-N j Returning to step 2.4; if m + p i -j≤N i Step 2.6 is entered.
Step 2.6, outputting the current workpiece model J i Number of sub-batches of workpieces N j If j is equal to p i 1, outputting the number of workpieces of the last sublot of the type of workpiece
And entering step 2.7; otherwise, let j equal to j +1, return to step 2.4 to continue outputting the next sub-batch of workpieces.
Step 2.7, if the batch numbers of all types of workpieces and the number of workpieces in each sublot are not output, making i equal to i +1, initializing m equal to 0, and returning j equal to 1 to the step 2.2; otherwise, outputting the batch result and ending.
The specific parameters of the step 3 are as follows:
N＝100，P n ＝0.8，P m ＝0.02，t max ＝200。
the specific method for initializing the population by adopting a real number coding mode in the step 4 comprises the following steps:
four sections of coding modes are designed to express individual information, wherein the first section represents batch division genes, the second section represents sub-batch workpiece quantity genes, the third section represents procedure sequencing genes, and the fourth section represents machine selection genes. And each type of workpiece is coded in the largest batch in the process sequencing gene segment, so that the process coding segment length of each chromosome is equal, and the coding mode can effectively solve the generation of illegal solutions in the cross variation process.
The cross mutation in the step 5 is implemented by the following steps:
step 5.1, two empty sets are created and are recorded as a set S 1 And set S 2 Randomly in the parent population P 1 Two individuals are selected and stored in a set F in a coding mode respectively 1 And set F 2 In (1).
Step 5.2, the parent population P 1 The four segments of code in the individual of (2) perform the interleaving operation, respectively:
step 5.2.1, batch crossing:
randomly generating a real number a less than 1 if a is less than the crossover probability P n Then the parent individual F 1 The nth gene and the parent individual F 2 Exchanging the nth gene, and respectively storing the exchanged batch division genes into an offspring individual set S 1 And set S 2 In (1).
Step 5.2.2, crossing the number of the sub-batch workpieces:
the crossing of the sub-batch workpiece number has strict constraint requirements, and the practical significance is not to randomly change the sub-batch workpiece number but to change the batch number according to the crossing of the batch, so that the sub-batch number and the workpiece number of the chromosome individual need to be adjusted, and the sum of the sub-batch workpiece number must be ensured to be equal to the total number of the workpieces of the type. Therefore, whether the batch cross causes different batch times is judged before the sub-batch workpiece quantity cross is carried out, and if the batch cross causes the different batch times P from the original gene, the batch cross is judged a Then P is added according to the specific batch method of step 2 i Is set to P a Randomly generating the number of the sub-batches of workpieces; if the same number of batches P as the original gene appears after batch crossing a Exchanging the genes of the sub-batch workpiece quantity according to a batch crossing method, and respectively storing the exchanged sub-batch workpiece quantity genes into the filial generation individual set S 1 And set S 2 In (1).
Step 5.2.3, the working procedures are crossed:
(1) randomly generating a real number a less than 1 if a is less than the crossover probability P n Then the parent individual F 1 S in the sequence section of (1) wherein the nth gene is copied to the same position 1 In (3), the initialization value of n is 1.
(2)n＝n+1。
(3) Repeating the operations (2) and (3) until the number of n is equal to that of the parent individual F 1 The process (2) ranks the number of genes.
(4) Then selecting a parent individual F 2 A 1 to F 2 Neutralizing offspring S 1 Genes with different middle sequences are supplemented to S according to position priority 1 The vacant gene positions are used for forming a complete gene individual.
(5) In the same manner as above for S 2 And operating to generate new filial generation individuals.
Step 5.2.4, machine crossing:
the machine selective crossover is the same as batch crossover.
Step 5.3, similar to the crossover operation, the mutation operation is also a four-part operation. The specific mutation operation is as follows:
step 5.3.1, batch variation:
randomly selecting a gene segment at a position in the batch segmentation genes, and setting the maximum batch number p max And randomly generating an integer a larger than 0 to replace the current batch number.
Step 5.3.2, variation of the number of the sub-batch workpieces:
the variation of the sublot workpiece quantity segment gene is varied according to the variation result of the batch, when the batch number is changed from one number to another number, the corresponding sublot workpiece quantity needs to be generated again by the sublot workpiece quantity, and the quantity of the sublot workpieces is ensured to be equal to the total quantity of the workpieces of the type.
Step 5.3.3, process variation:
the process sequencing segment gene mutation is realized by adopting an inverse mutation mode, randomly selecting genes at any position of an individual chromosome, and mutually exchanging the genes at the selected gene position.
Step 5.3.4, machine mutation:
machine selection segment gene mutation is performed on the machine selection gene by adopting a machine distribution mutation method. Randomly selecting a gene at a position in the machine selection segment genes, determining a processing procedure corresponding to the single gene machine selection, reselecting one machine device which can meet the processing task of the procedure, and replacing the gene with a machine selection gene for executing mutation operation.
Step 5.4, carrying out cross variation on a plurality of pairs of chromosomes to generate new filial generation individuals, and fusing the father generation individuals and the filial generation individuals to generate a new population R 1 。
The step 6 is implemented by the following steps:
step 6.1, decoding: in pair population R 1 Before the individual in (b) performs the fast non-dominated sorting and the calculation of congestion degree, each individual in the population needs to be decoded. Since the process sequencing segment setting in step 4 encodes each type of workpiece in the largest batch, the process sequencing segment gene and the machine selection segment gene of each chromosome have a part of the invalid gene interfering with the expression of individual information, and therefore, the valid gene can be set as the dominant gene and the invalid gene can be set as the recessive gene according to the batch division segment gene. The specific formula of the distinguishing method of the dominant and recessive genes is as follows:
wherein cList [ i ] is a batch dividing segment gene, and pList [ j ] is a process sorting segment gene.
In the decoding process, the scheduling solution can be obtained by only reading the dominant genes according to the arrangement sequence.
Step 6.2, fast non-dominated sorting: obtaining corresponding value of each individual according to the objective function, mapping the corresponding value to a two-dimensional coordinate, and setting two objective functions f at each position of a horizontal coordinate and a vertical coordinate 1 And f 2 Different non-dominated grades are obtained according to Pareto domination, and the fitness of the individual in different grades can be judged according to each grade.
Step 6.3, congestion degree calculation: the crowdedness is the distance between two nearest individuals adjacent to each other in a two-dimensional coordinate, and the specific crowdedness distance formula is as follows:
drawings
FIG. 1 is a flow chart of a flexible job shop batch scheduling method that accounts for carbon emissions.
FIG. 2 is a carbon emission profile for a flexible job shop.
Fig. 3 is a diagram illustrating a four-segment encoding scheme.
FIG. 4 is a schematic diagram of a method for crossing the number of sub-batches of workpieces based on batch crossing.
FIG. 5 is a schematic diagram of a process crossover method based on batch crossover.
FIG. 6 is a schematic diagram of a variation method of the number of sub-batches of workpieces based on batch variation.
FIG. 7 is a schematic diagram of a decoding scheme based on a dominant recessive gene.
Detailed Description
The invention will be further described with reference to the accompanying drawings and the detailed description below:
as shown in fig. 1, the flexible job shop batch scheduling method considering carbon displacement of the present invention specifically includes the following steps:
first, the examples are set forth with one specific processing schedule as in the following table.
establishing an objective function f of minimum completion time for the model 1 ：
f 1 ＝MinMax(C i )
Establishing an objective function f of minimum carbon emission for the model 2 ：
The invention takes a numerical control workshop as a research object, and the carbon emission calculation model is established according to the actual production of the numerical control cutting workshop. The carbon emission in the production process of the numerical control workshop can be divided into two parts of electric energy consumption and material consumption according to different carbon emission modes, wherein the electric energy consumption comprises electric energy consumed by the operation of a processing machine and electric energy consumed by systems for illumination, temperature control and the like in workshop production. The consumption of materials includes carbon emission due to consumption of raw materials of a workshop and carbon emission due to consumption of auxiliary materials, and the consumption of the auxiliary materials is mainly abrasion of a cutter.
According to the classification, the carbon emission of the numerical control cutting workshop can be subdivided into carbon emission consumed by machine electric energy, carbon emission consumed by raw materials, carbon emission consumed by cutters, and carbon emission of systems for workshop illumination, air exhaust and the like, a carbon emission distribution diagram of the whole flexible operation workshop is shown in fig. 2, and then a mathematical model is established for four major factors influencing the carbon emission.
Establishing a mathematical model of carbon emission caused by electric energy loss of a machine, specifically:
f 2 ＝Min(CE m +CE p +CE tw +CE l )
electrical energy consumption under machine load:
electric energy consumption of the machine under no load:
the carbon emission caused by the electric energy loss of the machine is specifically as follows:
establishing a mathematical model of carbon emission caused by consumption of raw materials in a cutting process, which specifically comprises the following steps:
wherein:
SEC means removal of 1cm during processing 3 Calculated value of special energy consumption to be consumed by material, MRR represents material removal rate, C 0 And C 1 Is related to the special coefficient of SEC, is related to factors such as cutter material, processing environment and the like,
is the volume of the raw material cut per unit time.
Establishing a mathematical model of carbon emission caused by tool abrasion, specifically:
wherein:
a mathematical model is established for carbon discharge caused by electric energy consumption of systems such as workshop lighting, air exhaust and the like, and the mathematical model specifically comprises the following steps:
CE l ＝F e ·P a ·T
wherein: max (C) k )
The specific constraints are as follows:
P i ≤N i ∧N iz >0；
S iz(j+1)k ≥E izjk ；
E izjk ＝S izjk +PT izjk +ST ijk ×N iz ；
S izjk ＝E ifjk ；
C i ＝max(E izjk ),z＝1,2,...,P i ；
wherein the specific mathematical symbols are defined as follows:
i: a workpiece number;
n: number of kinds of work pieces, work set J ═ { J ═ J } 1 ，J 2 ，...,J n }；
J i : a workpiece set of workpieces i;
j i : total number of steps for workpiece i;
N i : the processing number of the workpieces i;
P i : the number of the sub-batches of the workpiece i;
N iz : the batch number of the z th sub-batch of the workpiece i;
m: the total number of machines;
k: serial number of machine, machine set M ═ { M ═ M 1 ，M 2 ，...,M m }；
C i : finishing time of the workpiece i;
S izjk : starting processing time of the jth procedure of the z th sub batch of the workpiece i on a machine k;
E izjk : the completion time of the jth procedure of the z th sub-batch of the workpiece i on the machine k;
T izjk : the processing time of the jth procedure of the z th sub batch of the workpiece i on the machine k;
ST ijk : the processing time of the j-th procedure of the unit workpiece i on the machine k;
F e : a discharge factor of electrical energy;
CE m : carbon emissions from machine losses of electrical energy;
CE p : carbon emission caused by non-electric energy loss in the cutting process;
CE tw : carbon emission caused by tool wear;
CE l : the carbon emission caused by the consumption of electric energy by systems such as workshop lighting, air exhaust and the like;
and 2, designing a random batching strategy, dividing the workpieces into a plurality of batches at random, obtaining the quantity of the workpieces under each sub-batch, and preparing for an initialization population of the algorithm by the batching method. The method comprises the following specific steps:
step 2.1, initializing parameter i to 1, m to 0, j to 1, p max ＝3；
Step 2.2, selecting the current workpiece model J i The number N of workpieces of the type is processed in batches i 。
Step 2.3, randomly generating the current workpiece model J i Number of lots p i And satisfies 0 < p i ≤p max (p i E.g. Z) if p i If 1, if p i If it is 1, go to step 2.7, and directly output the current workpiece modelJ i Number of batches p i And number of workpieces N i (ii) a If p is i Not equal to 1, go to step 2.4.
Step 2.4, randomly generating the number N of the first sub-batch workpieces iz And satisfies 0 < N j ≤N i -m。
Step 2.5, making m equal to m + N j If m + p i -j>N i When m is equal to m-N j Returning to step 2.4; if m + p i -j≤N i Step 2.6 is entered.
Step 2.6, outputting the current workpiece model J i Number of sub-batches of workpieces N j If j is equal to p i 1, outputting the number of workpieces of the last sublot of the type of workpiece
And entering step 2.7; otherwise, let j equal to j +1, return to step 2.4 to continue outputting the next sub-batch of workpieces.
Step 2.7, if the batch numbers of all types of workpieces and the number of workpieces in each sub-batch are not output, making i equal to i +1, initializing m equal to 0, and returning j equal to 1 to the step 2.2; otherwise, outputting the batch result and ending.
N＝100，P n ＝0.8，P m ＝0.02，t max ＝200。
four sections of coding modes are designed to express individual information, wherein the first section represents batch division genes, the second section represents sub-batch workpiece quantity genes, the third section represents procedure sequencing genes, and the fourth section represents machine selection genes. And a maximum lot (in p) is set for sequencing this gene segment in the process max Is 3 isFor example), each type of workpiece is encoded, so that the length of the process encoding segment of each chromosome is equal, and the encoding mode can effectively solve the generation of illegal solutions in the cross mutation process, and is shown in fig. 3.
step 5.1, two empty sets are created and are recorded as a set S 1 And set S 2 Randomly in the parent population P 1 Two individuals are selected and stored in a set F in a coded form 1 And set F 2 In (1).
Step 5.2, the parent population P 1 The four segments of code in the individual of (2) perform the interleaving operation, respectively:
step 5.2.1, batch crossing:
randomly generating a real number a less than 1 if a is less than the crossover probability P n Then the parent individual F 1 The nth gene and the parent individual F 2 Exchanging the nth gene, and respectively storing the exchanged batch division genes into an offspring individual set S 1 And set S 2 In (1).
Step 5.2.2, crossing the number of the sub-batch workpieces (the method for crossing the number of the sub-batch workpieces based on the crossing of the batch is shown in fig. 4):
the crossing of the sub-batch workpiece number has strict constraint requirements, and the practical significance is not to randomly change the sub-batch workpiece number but to change the batch number according to the crossing of the batch, so that the sub-batch number and the workpiece number of the chromosome individual need to be adjusted, and the sum of the sub-batch workpiece number must be ensured to be equal to the total number of the workpieces of the type. Therefore, before the crossing of the number of the sub-batch workpieces, whether the crossing of the batch leads to the appearance of different batch times is judged, if the crossing of the batch leads to the appearance of different batch times Pa from the original gene, the P is divided according to the specific batch method of the step 2 i Is set to P a Randomly generating the number of the sub-batches of workpieces; if the batches are crossed with the original onesNumber of batches P with identical appearance of genes a Exchanging the genes of the sub-batch workpiece quantity according to a batch crossing method, and respectively storing the exchanged sub-batch workpiece quantity genes into the filial generation individual set S 1 And set S 2 In (1).
Step 5.2.3, process crossover (process crossover method based on batch crossover is shown in fig. 5):
(1) randomly generating a real number a less than 1 if a is less than the crossover probability P n Then the parent individual F 1 S in the sequence section of (1) wherein the nth gene is copied to the same position 1 In (3), the initialization value of n is 1.
(2)n＝n+1。
(3) Repeating the operations (2) and (3) until the number of n is equal to that of the parent individual F 1 The process in (1) sorts the number of genes.
(4) Then selecting a parent individual F 2 Will F 2 Neutralizing offspring S 1 Genes with different middle sequences are supplemented to S according to position priority 1 The vacant gene positions are used for forming a complete gene individual.
(5) In the same manner as above for S 2 And operating to generate new filial generation individuals.
Step 5.2.4, machine crossing:
the machine selective crossover is the same as the batch crossover.
Step 5.3, similar to the crossover operation, the mutation operation is also a four-part operation. The specific mutation operation is as follows:
step 5.3.1, batch variation:
randomly selecting a gene segment at a position in the batch segmentation genes, and setting the maximum batch number p max An integer a larger than 0 is randomly generated in 3 to replace the current batch number.
Step 5.3.2, variation of the number of sub-batch workpieces (the variation method of the number of sub-batch workpieces based on batch variation is shown in fig. 6):
the variation of the sublot workpiece quantity segment gene is varied according to the variation result of the batch, when the batch number is changed from one number to another number, the corresponding sublot workpiece quantity needs to be generated again by the sublot workpiece quantity, and the quantity of the sublot workpieces is ensured to be equal to the total quantity of the workpieces of the type.
Step 5.3.3, process variation:
the process sequencing segment gene mutation is realized by adopting an inverse mutation mode, randomly selecting genes at any position of an individual chromosome, and mutually exchanging the genes at the selected gene position.
Step 5.3.4, machine mutation:
machine selection segment gene mutation is performed on a machine selection gene by using a machine-distributed mutation method. Randomly selecting a gene at a position in the machine selection segment genes, determining a processing procedure corresponding to the single gene machine selection, reselecting one of available machine equipment which can meet the processing task of the procedure, and replacing the gene with a machine selection gene for performing mutation operation.
Step 5.4, carrying out cross variation on a plurality of pairs of chromosomes to generate new filial generation individuals, and fusing the father generation individuals and the filial generation individuals to generate a new population R 1 。
step 6.1, decoding: in the pair population R 1 Before the individual in (b) performs the fast non-dominated sorting and the calculation of congestion degree, each individual in the population needs to be decoded. Since the process sequencing segment setting in step 4 encodes each type of work in the largest batch, resulting in the process sequencing segment gene and the machine selection segment gene of each chromosome having a part of the null gene interfering with the expression of individual information, the valid gene can be set as the dominant gene and the null gene as the recessive gene according to the batch division segment gene. The specific formula of the distinguishing method of the dominant and recessive genes is as follows:
wherein cList [ i ] is a batch dividing segment gene, and pList [ j ] is a process sorting segment gene.
In the decoding process, the scheduling solution can be obtained by only reading the dominant genes according to the arrangement sequence. The specific decoding process is shown in fig. 7.
Step 6.2, fast non-dominated sorting: obtaining corresponding value of each individual according to the objective function, mapping the corresponding value to a two-dimensional coordinate, and setting two objective functions f at each position of a horizontal coordinate and a vertical coordinate 1 And f 2 Different non-dominated grades are obtained according to Pareto domination, and the fitness of the individual in different grades can be judged according to each grade.
Step 6.3, congestion degree calculation: the crowding degree is the distance between two adjacent nearest individuals in a two-dimensional coordinate through each individual, and the specific crowding degree distance formula is as follows:
Claims (5)
1. A flexible job shop batch scheduling method taking into account carbon emissions, characterized in that the scheduling method comprises the steps of:
step 1, establishing a mathematical model for batch scheduling of a flexible job workshop, wherein carbon emission and completion time are set as objective functions in the model, and corresponding constraint conditions are established;
step 2, designing a random batching strategy, randomly dividing the workpieces into a plurality of batches, obtaining the quantity of the workpieces under each sub-batch, and preparing for an initialization population of the algorithm by the batching method;
step 3, setting algorithm parameters of the improved NSGA-II algorithm: initializing population number N and cross probability P n Probability of mutation P m And the maximum number of iterations t max ；
Step 4, initializing population R by adopting real number coding 0 Selecting high-quality individuals according to non-dominated sorting, and performing cross variation on the high-quality individuals to obtain a parent population P 1 ；
Step 5, the parent population P is treated 1 The individuals in (1) are selected, crossed and mutated to generate a filial generation population Q 1 The population P 1 And Q 1 Combining to obtain a new population R 1 ；
Step 6, for population R 1 Decoding the individuals in the step (1), selecting the individuals with high fitness through rapid non-dominated sorting and congestion degree calculation, and storing the individuals in the next generation parent population P 2 ；
Step 7, judging whether the maximum iteration times t is reached max If not, executing step 5; and if so, outputting all solutions in the optimal Pareto solution set.
2. A method of flexible job shop batch scheduling that accounts for carbon emissions, wherein the carbon emission targeted flexible job shop batch scheduling mathematical model comprises:
the carbon emission in the production process of the numerical control machine workshop can be divided into the consumption sum of electric energy according to the properties, wherein the consumption of the electric energy comprises the electric energy consumed by the operation of a processing machine and the electric energy consumed by systems for illumination, temperature control and the like in the production of the workshop; the consumption of materials comprises carbon emission caused by consumption of raw materials of a workshop and carbon emission caused by consumption of auxiliary materials, and the consumption of the auxiliary materials comprises abrasion of a cutter;
according to the classification, the carbon emission of the numerical control cutting workshop can be subdivided into the carbon emission consumed by the electric energy of a machine, the carbon emission consumed by raw materials, the carbon emission of cutter abrasion, the carbon emission of systems for workshop illumination, air exhaust and the like, and then a mathematical model is established for four factors influencing the carbon emission;
establishing a mathematical model of carbon emission caused by electric energy loss of a machine, specifically:
f＝Min(CE m +CE p +CE tw +CE l )
electrical energy consumption under machine load:
electric energy consumption of the machine under no load:
the carbon emission caused by the electric energy loss of the machine is specifically as follows:
establishing a mathematical model of carbon emission caused by consumption of raw materials in a cutting process, which specifically comprises the following steps:
wherein:
SEC means removal of 1cm during processing 3 Calculated value of special energy consumption to be consumed by material, MRR represents material removal rate, C 0 And C 1 Is related to the special coefficient of SEC, is related to factors such as cutter material, processing environment and the like,
is the volume of the raw material cut per unit time.
Establishing a mathematical model of carbon emission caused by tool abrasion, specifically:
wherein:
a mathematical model is established for carbon emission caused by electric energy consumption of systems such as workshop lighting and air exhaust, and specifically comprises the following steps:
CE l ＝F e ·P a ·T
wherein: max (C) k )
Wherein the specific mathematical symbols are defined as follows:
i: a workpiece number;
n: number of kinds of work pieces, work set J ═ { J ═ J } 1 ，J 2 ，...,J n }；
J i : a workpiece set of workpieces i;
j i : total number of steps for workpiece i;
N i : the processing number of the workpieces i;
P i : the number of the sub-batches of the workpiece i;
N iz : the batch number of the z th sub-batch of the workpiece i;
m: the total number of machines;
k: serial number of machine, machine set M ═ { M ═ M 1 ，M 2 ，...，M m }；
C i : finishing time of a workpiece i;
S izjk : starting the processing time of the jth procedure of the z th sub batch of the workpiece i on the machine k;
E izjk : the completion time of the jth procedure of the z th sub-batch of the workpiece i on the machine k;
T izjk : the processing time of the jth procedure of the z th sub batch of the workpiece i on the machine k;
ST ijk : the processing time of the j-th procedure of the unit workpiece i on the machine k;
F e : a factor of discharge of electrical energy;
CE m : carbon emissions from machine losses of electrical energy;
CE p : carbon emission caused by non-electric energy loss in the cutting process;
CE tw : carbon emissions due to tool wear;
CE I : the systems of workshop illumination, air exhaust and the like consume electric energy to cause carbon emission.
3. A flexible job shop batch scheduling method considering carbon emissions, wherein the real number encoded initialization population comprises:
designing four sections of coding modes to express individual information, wherein the first section represents batch division genes, the second section represents sub-batch workpiece quantity genes, the third section represents process sequencing genes, and the fourth section represents machine selection genes; and each type of workpiece is coded in the largest batch in the process sequencing gene segment, so that the process coding segment length of each chromosome is equal, and the coding mode can effectively solve the generation of illegal solutions in the cross variation process.
4. A flexible job shop batch scheduling method considering carbon emission is characterized in that the concrete step 5 comprises the following steps:
step 5.1, two empty sets are created and are recorded as a set S 1 And set S 2 Randomly in the parent population P 1 Two individuals are selected and stored in a set F in a coded form 1 And set F 2 Performing the following steps;
step 5.2, the parent population P 1 The four segments of code in the individual of (2) respectively perform the interleaving operation:
step 5.2.1, batch crossing:
randomly generating a real number a less than 1 if a is less than the crossover probability P n Then the parent individual F 1 The nth gene and the parent individual F 2 Exchanging the nth gene, and respectively storing the exchanged batch division genes into an offspring individual set S 1 And set S 2 The preparation method comprises the following steps of (1) performing;
step 5.2.2, crossing the quantity of the sub-batches of workpieces:
the crossing of the sub-batch workpiece quantity has strict constraint requirements, and the practical significance is not to randomly change the sub-batch workpiece quantity but to change the batch number according to the crossing of the batch, so that the sub-batch quantity and the workpiece quantity of the chromosome individual need to be adjusted, and the sum of the sub-batch workpiece quantity and the total quantity of the workpieces of the type must be ensured to be equal; therefore, whether the batch cross causes different batch times is judged before the sub-batch workpiece quantity cross is carried out, and if the batch cross causes the different batch times P from the original gene, the batch cross is judged a Then P is added according to the specific batch method of step 2 i Is set to P a Randomly generating the number of the sub-batches of workpieces; if the same number of batches P appears as the original gene after the batch cross a Exchanging the genes of the sub-batch workpiece quantity according to a batch crossing method, and respectively storing the exchanged sub-batch workpiece quantity genes into the filial generation individual set S 1 And set S 2 Performing the following steps;
step 5.2.3, the working procedures are crossed:
(1) randomly generating a real number a less than 1 if a is less than the crossover probability P n Then the parent individual F 1 S in which the nth gene in the process sequence segment in (1) is copied to the same position 1 In (1), the initialization value of nIs 1;
(2)n＝n+1；
(3) repeating the operations (2) and (3) until the number of n is equal to that of the parent individual F 1 The process in (1) sorts the number of genes;
(4) then selecting a parent individual F 2 Will F 2 Neutralizing offspring S 1 Genes with different middle sequences are supplemented to S according to position priority 1 The vacant gene positions are used for forming complete gene individuals;
(5) in the same manner as above for S 2 Operating to generate new filial generation individuals;
step 5.2.4, machine crossing:
the machine selection crossing mode is the same as batch crossing;
step 5.3, similar to the crossover operation, the mutation operation is also four-part operation; the specific mutation operation is as follows:
step 5.3.1, batch variation:
randomly selecting a gene segment at a position in the batch segmentation genes, and setting the maximum batch number p max Randomly generating an integer a larger than 0 to replace the current batch number;
step 5.3.2, variation of the number of the sub-batch workpieces:
the variation of the sublot workpiece quantity segment gene is varied according to the variation result of the batch, when the batch number is changed from one number to another number, the corresponding sublot workpiece quantity needs to be generated again by the sublot workpiece quantity, and the quantity of the sublot workpieces is ensured to be equal to the total quantity of the workpieces of the type;
step 5.3.3, process variation:
the process sequencing segment gene mutation adopts an inverse mutation mode, randomly selects any position of an individual chromosome, and exchanges genes of the selected gene position;
step 5.3.4, machine mutation:
performing machine selection segment gene mutation by adopting a machine distribution mutation method to perform mutation operation on a machine selection gene; randomly selecting a gene at a position in a machine selection segment gene, determining a processing procedure corresponding to the single gene machine selection, reselecting one machine device which can meet the processing task of the procedure, and replacing the gene with a machine selection gene for executing mutation operation;
step 5.4, carrying out cross variation on a plurality of pairs of chromosomes to generate new filial generation individuals, and fusing the father generation individuals and the filial generation individuals to generate a new population R 1 。
5. A flexible job shop batch scheduling method considering carbon emission is characterized in that in the step 6, a population R is subjected to batch scheduling 1 The individual decoding specific process in (1) comprises:
since the process sequencing gene segment is set to encode each type of workpiece in the largest batch in step 4, which causes that the process sequencing segment gene and the machine selection segment gene of each chromosome have partial invalid genes to interfere with the expression of individual information, the expressed individual information is screened out from the valid genes according to the sequencing sequence under the condition of ensuring the integrity of the chromosome genes; on the basis, the invention provides a concept of a dominant gene, wherein an effective gene is set as a dominant gene and an ineffective gene is set as a recessive gene according to batch segmentation genes; and designing a distinguishing method of the dominant and recessive genes, wherein the specific formula is as follows:
wherein cList [ i ] is a batch dividing segment gene, and pList [ j ] is a process sequencing segment gene;
in the decoding process, the scheduling solution can be obtained by only reading the dominant genes according to the arrangement sequence.
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| CN117555305A (en) * | 2024-01-11 | 2024-02-13 | 吉林大学 | NSGAII-based multi-target variable sub-batch flexible workshop job scheduling method |
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| CN117555305A (en) * | 2024-01-11 | 2024-02-13 | 吉林大学 | NSGAII-based multi-target variable sub-batch flexible workshop job scheduling method |
| CN117555305B (en) * | 2024-01-11 | 2024-03-29 | 吉林大学 | NSGAII-based multi-target variable sub-batch flexible workshop job scheduling method |
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