CN110515356B - Optimized scheduling method for cold-rolled and coated steel plate processing process for household appliances - Google Patents
Optimized scheduling method for cold-rolled and coated steel plate processing process for household appliances Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 108
- 230000008569 process Effects 0.000 title claims abstract description 72
- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 43
- 239000010959 steel Substances 0.000 title claims abstract description 43
- 230000006870 function Effects 0.000 claims abstract description 39
- 238000005457 optimization Methods 0.000 claims abstract description 31
- 238000004519 manufacturing process Methods 0.000 claims abstract description 30
- 238000005097 cold rolling Methods 0.000 claims abstract description 13
- 238000004364 calculation method Methods 0.000 claims abstract description 7
- 238000011049 filling Methods 0.000 claims description 21
- 239000000047 product Substances 0.000 claims description 9
- 239000013589 supplement Substances 0.000 claims description 9
- 238000003754 machining Methods 0.000 claims description 8
- 230000009469 supplementation Effects 0.000 claims description 7
- 230000003044 adaptive effect Effects 0.000 claims description 6
- 230000001502 supplementing effect Effects 0.000 claims description 5
- 206010012186 Delayed delivery Diseases 0.000 claims description 3
- 230000007812 deficiency Effects 0.000 claims description 3
- 230000003111 delayed effect Effects 0.000 claims description 3
- 238000012804 iterative process Methods 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 239000000203 mixture Substances 0.000 claims description 3
- 238000006467 substitution reaction Methods 0.000 claims description 3
- 238000007514 turning Methods 0.000 claims description 3
- 238000002156 mixing Methods 0.000 claims description 2
- 239000010960 cold rolled steel Substances 0.000 description 6
- 238000006243 chemical reaction Methods 0.000 description 3
- 238000012423 maintenance Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 238000011112 process operation Methods 0.000 description 2
- 238000000137 annealing Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000011248 coating agent Substances 0.000 description 1
- 238000000576 coating method Methods 0.000 description 1
- 238000005238 degreasing Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000000227 grinding Methods 0.000 description 1
- 238000005554 pickling Methods 0.000 description 1
- 238000007747 plating Methods 0.000 description 1
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Abstract
The invention discloses an optimized scheduling method of a cold-rolled and coated steel plate processing process for household appliances, which belongs to the technical field of intelligent optimized scheduling of a production workshop, and comprises the steps of firstly representing uncertain processing time and delivery date by fuzzy numbers through previous production data of a cold-rolling factory and priori knowledge of processing personnel, then establishing a scheduling model of the cold-rolled and coated steel plate processing process for the household appliances, determining an optimization target of the model, and finally optimizing the optimization target of the scheduling model by using an optimized scheduling method based on a novel teaching and learning optimization algorithm; the invention uses triangle fuzzy number and trapezoid fuzzy number to represent the uncertain steel plate processing time and delivery date, which can describe the actual production condition of cold rolling factory more objectively; the designed objective function calculation method can accurately calculate the customer satisfaction degree; the invention can obtain the high-quality solution of the scheduling problem of the cold rolling and coated steel plate processing process for the household appliances in a short time, improve the customer satisfaction and increase the economic benefit of enterprises.
Description
Technical Field
The invention relates to an optimized scheduling method for a cold-rolled and coated steel plate processing process for household appliances, and belongs to the technical field of intelligent optimized scheduling of production workshops.
Background
Cold rolled and coated steel sheets are widely used in various household electrical appliances as an important processing material, and the types and parts of the household electrical appliances using the material are mainly as follows: the panel for refrigerator, side plate, washing machine box, air conditioner outdoor machine box, computer case, micromotor casing, fax machine, printer, copier and other office equipment inner parts, and the casing of video and audio equipment. At present, the domestic proportion of cold-rolled and coated steel sheets for household appliances is gradually increased, along with the market competition of cold-rolled steel sheet manufacturing industry at home and abroad becoming fierce, how to improve the production efficiency in the cold-rolled steel sheet manufacturing process and deliver the cold-rolled steel sheets within the delivery date required by customers as much as possible becomes the key for improving the economic benefit and the market competition of enterprises.
For the processing technology of cold-rolled and coated steel plates, the whole process generally comprises the following links: pickling, cold rolling, degreasing, annealing, leveling, plating and finishing. However, different household electrical appliances have different requirements on the steel plate in terms of size, plate shape, thickness, surface and other qualities, so that cold rolling enterprises not only need to have the production capacity of large-batch steel plates, but also need to adapt to market demands to produce various types of cold rolled steel plate products. At present, in order to solve the contradiction between the yield and the batch size, cold-rolled steel plate manufacturing enterprises mostly adopt a flexible manufacturing mode, for example, each processing link is provided with one or more sets of units which can be replaced mutually, so that the flexibility of the manufacturing capacity and the flexibility of the production work and rest are ensured. In order to improve the production efficiency, the cold rolling mill usually performs production scheduling in the form of a contract lot, which is a lot of unprocessed product contracts that are combined into one lot and processed in batch units. In summary, the process for processing the cold-rolled and coated steel plate for the household appliance is characterized in that each batch of steel plate is processed according to the requirement of a customer and the corresponding process flow, an available set of machine set is selected for processing in each process in the process of processing, one set of machine set can only process one batch of steel plate at most at the same time, and then the available set is selected for processing in the next process until all processes are finished.
The scheduling problem of the processing process of the cold-rolled and coated steel plate for the household appliance belongs to a typical scheduling problem of a flexible job shop, and an efficient scheduling scheme is formulated in the manufacturing process, so that the manufacturing period is shortened, and the economic benefit of an enterprise is improved. However, the following two problems commonly exist in the cold rolling and coating steel plate processing process of cold rolling steel plate manufacturing enterprises at present: firstly, the order demand of cold-rolled and coated steel plates is large, but the manufacturing time is long, and the on-time delivery is difficult to ensure; second, when scheduling production, it is often assumed that the processing time and the delivery date are accurate values, but in actual production, due to uncertain factors such as equipment failure, regular maintenance of the unit, different proficiency of workers, etc., the delivery date proposed by the customer is not an accurate time point (both proper delay and advance delivery can be tolerated), which results in that the scheduling plan is often disconnected from the actual production.
Disclosure of Invention
The invention aims to solve the technical problem of scheduling the processing process of the cold-rolled and coated steel plate for the household appliances, provides a calculation method of customer satisfaction under the condition of considering uncertain processing time and delivery date, and provides an optimized scheduling method based on a novel teaching and learning optimization algorithm on the basis of the calculation method.
The technical scheme adopted by the invention is as follows: an optimized scheduling method for the processing process of a cold-rolled and coated steel plate for household appliances comprises the following steps:
(1) Firstly, uncertain processing time, finishing time and delivery date are represented by fuzzy numbers through previous production data of a cold rolling plant and priori knowledge of processing personnel;
(2) Then establishing a scheduling model of the processing process of the cold-rolled and coated steel plate for the household appliance, and determining an optimization target of the model; the scheduling model is established according to the processing completion time of each batch of cold-rolled and coated steel plates on each unit, in actual production, the scheduling model is influenced by various uncertain factors such as equipment faults, unit regular maintenance, different proficiency of workers and the like, the processing time is difficult to accurately predict, the completion time can only be estimated in a certain interval, and therefore the processing time and the completion time are represented by triangular fuzzy numbers;
(3) And finally, optimizing the optimization target of the scheduling model by using a novel teaching and learning optimization algorithm.
The specific steps of the step (1) are as follows:
step1.1 represents the processing time and completion time by triangular fuzzy numbers, and each operation O is set i,j Shows the jth process of the ith batch of steel sheets in the unit M k The machining time is expressed by triangular fuzzy number
Wherein
The minimum processing time is indicated and is,
the most likely processing time is indicated by the time,
the maximum processing time is shown and the completion time of each operation is shown as
Wherein
Represents the minimum completion time of the jth process for lot i,
indicating the most likely completion time for the jth pass of lot i,
the maximum completion time of the jth process in lot i is expressed by the membership function of formula (1):
wherein,
fuzzy completion time membership function for batch i;
step1.2 in actual production, the delivery date proposed by the customer is not a precise moment (either the proper delay or advance can be tolerated), so the delivery date of each lot is represented by the fuzzy number of trapezoid, and the delivery date of the ith product is represented by D i ＝(d 1 ,d 2 ,d 3 ,d 4 ) Wherein [ d ] 2 ,d 3 ]The time period is the optimal delivery date, the satisfaction degree of the delivery client in the interval is 1, namely 'most satisfactory', if the time period is beyond the interval, the satisfaction degree of the delivery client is linearly reduced if the delivery date is advanced or delayed, and d 1 Critical time point for advance delivery with customer satisfaction of 0, d 4 For the critical time point of 0 customer satisfaction at the delayed delivery, the delivery time membership function expression is as follows:
wherein,
is a batch i fuzzy delivery date membership function;
the specific steps of the step (2) are as follows:
2.1, the machining process meets the following constraint conditions: at any moment, the same batch of steel plates can be processed on one set of machine set at most; at most one process can be processed by the same set of unit at any time; either operation may not be interrupted during processing; the working procedure of the same batch of steel plates needs to be finished in the previous working procedure before the next working procedure can be carried out;
2.2 calculating customer satisfaction AI based on the completion time and scheduled delivery date of each batch of steel sheets i ，
Wherein AI is i Representing customer satisfaction of the ith lot,
a fuzzy completion time membership function for lot i,
is a fuzzy lead time membership function for lot i,
the area of the membership function of the fuzzy completion time of the batch i;
the optimization objective is to maximize average customer satisfaction:
wherein,
indicating maximum average customer satisfaction and n represents the number of batches.
The specific steps of optimizing the optimization target of the scheduling model based on the novel teaching and learning optimization algorithm in the step (3) are as follows:
step3.1 initialise population: assuming that the population size is popsize, the population includes more than one individual, and assuming that the total number of steps required for processing each individual is
Wherein u i Each of the units is a randomly generated code string with a length of the total process number U, wherein one of the units is represented as (p) 1 ,p 2 ,...,p U ) The total number of steps of the other individuals is the same as that of the individual, but the order of the steps is different, p in the individual w ∈{1,2,...,n}， w∈{1,2,...,U}，p w Is the w-th bit of the code string, n is the number of batches, if p w K, then p w Is u in the total number of processes k If k is the m-th occurrence, it represents p w Corresponding to the mth process step O of the kth batch k,m Then, an adaptive value, i.e., an objective function value Q, for each individual is calculated according to equations (3) and (5),
in order to make scheduling as compact as possible, greedy active decoding is used for decoding each individual coding string, according to operation in a process operation string, greedy strategy is used for performing active decoding on each machine capable of processing the operation in sequence, then the machine with the shortest completion time is selected for processing, summation of triangular fuzzy numbers is needed in the calculation process, subtraction is carried out, large operation is taken, the summation and subtraction operations are used for calculating fuzzy completion time, and two triangular fuzzy numbers X = (X =) are obtained 1 ,x 2 ,x 3 ) And Y = (Y) 1 ,y 2 ,y 3 ) The summation operation is defined as:
X+Y＝(x 1 +y 1 ,x 2 +y 2 ,x 3 +y 3 ) (6)
the subtraction operation is defined as:
X-Y＝(x 1 -y 1 ,x 2 -y 2 ,x 3 -y 3 ) (7)
in calculating the blur start time and the completion time, a sorting operation using the blur number is required, X = (X) for two triangular blur numbers 1 ,x 2 ,x 3 ) And Y = (Y) 1 ,y 2 ,y 3 ) The sorting adopts the following basis:
according to the following steps of 1: calculating Z for X and Y separately 1 Wherein
Will Z 1 As the primary basis for sorting;
according to 2: if Z of two triangular fuzzy numbers 1 Are equal, then Z is defined 2 (X)＝x 2 ，Z 2 (Y)＝y 2 A 1 is formed of 2 As a secondary basis for sorting;
according to 3: if the first two bases of the two triangular fuzzy numbers are equal, Z is defined 3 (X)＝x 3 -x 1 ， Z 3 (Y)＝y 3 -y 1 Is a reaction of Z 3 As a basis for sorting;
the triangular fuzzy number can be sorted and enlarged by using the three bases;
according to the calculated adaptive value Q of each individual, taking the superior individual of the Teacher _ p in percentage in the population as an initial 'Teacher' population, taking the rest individuals as a 'student' population, and simultaneously enabling the iteration number gen =1;
step3.2, updating each student individual in the student population through a teaching stage or an inter-learning stage, when updating each student individual, not simultaneously using the teaching stage and the inter-learning stage when updating each individual, firstly randomly generating a real number delta between 0 and 1, if delta is less than the real number teaching between 0 and 1, updating the student individual through the teaching stage, otherwise updating the student individual through the inter-learning stage;
the individuals are updated using a "teaching" phase by first generating a string sequence Pick of the same length as the code string, while randomly filling each digit of the Pick with {0,1}, and then randomly selecting a teacher X from the teacher population teacher And student X old The interleaving is performed starting with the first bit of Pick, if this bit equals 0, X is then added teacher Filling new individuals X with the same position in the process new In this position, whereas if 1, X is old In the same place process fill in X new And the process is started from X teacher And X old Is deleted, then X is deleted teacher And X old The working procedures after the middle position are shifted to the left by one position in sequence, the vacant positions in the middle are filled, and the steps are repeated until a new individual X new Is filled up; after crossing, if X new The performance of the product is superior to that of X old I.e. X new Has an objective function value Q larger than X old Then use X new Substitution of X old And go to Step4, otherwise go to Step3;
the "learning-by-learning" stage differs from the "teaching" stage only in that the generation of new individuals is randomly selected to divide by X old Another student X outside old_2 And X old Performing intersection, wherein the rest steps are the same as the teaching stage;
finally, according to X new Updating the learning history matrix LHM corresponding to the individual, and in the iterative process, each student X old As long as the update produces a new solution X new The student's LHM is used to X new Recording, wherein each student has a corresponding LHM for recording the position information of each student individual in the updating process, each line in the LHM represents each bit in the individual coding string, each column represents the batch number which possibly appears in each bit in the coding string, the w-th column element which is equal to n represents that the individual has the w-th batch number i of the coding string recorded for n-1 times in the iterative operation process of the algorithm, the subtraction 1 is because the initial value of each element is 1, the LMH recording method is concretely as follows, if X is new W th bit equals lot number i and X new Is superior to X old I.e. X new Has an objective function value Q larger than X old Then add 1 to the element in row w and column i of the LHM if X is new Has an objective function value of less than or equal to X old Then add to the element at line w and column i of the LHM
A penalty factor greater than 1 if X new Is not equal to the batch number i, the w-th row and i-th column elements of the LHM are unchanged;
step3.3, update X by "filling class" phase new Has an objective function value of less than or equal to X old Let the current number of courses supplement tu _ n =0, the current supplement mode g =1,1 represents that the codes are supplemented by sequential filling operation during course supplement, 2 represents that the codes are supplemented by random exchange operation, and each student updates in the stages of teaching and learning, and if X is newly solved new Has an objective function value of less than or equal to X old The individuals of (1) are examined for deficiencies and omissions by 'course filling', firstly, X is found in the LHM of the student in turn new Each bit encodes a corresponding element, constructing a set L = { L = { L = 1 ,L 2 ,L 3 ,...,L U And the L is normalized,the roulette is then used in L to select the larger elements, the probability of each element being selected being calculated using equation (8) below, the number of rows in the LHM corresponding to the code string position w that needs to be changed.
After the position w of the change is determined, a process e for determining this position is required, so that the set L' = { L } is constructed using the reciprocal of all the elements in the LHMw line 1 ,L 2 ,L 3 ,...,L n Using a roulette wheel to select smaller elements in L' and fill the elements into positions w, the probability of each element being selected being given by (9);
in addition, in order to ensure that the new solution obtained by course supplementation is a feasible scheduling solution, the encoding string needs to be supplemented completely, and the encoding string is used alternately in the following two supplementing modes to improve the global exploration capability of the algorithm, which specifically comprises the following operations:
filling in sequence: mixing X new All the steps except step e are carried out in accordance with X new Sequentially filling the mixture into positions except the position w to form a new solution X' new ；
Random exchange: at X new Finding the positions of all elements with the same e-batch number, and randomly selecting a position w' from the positions new Element in w bit is put into X' new In the w' position of (2), while adding X new The rest elements are put into X 'according to the original position' new ；
X 'is newly dissolved after each course supplement according to the obtained solution' new Updating the LHM corresponding to the subject, and tu _ n = tu _ n +1, g = g +1, g can only equal 1 or 2, when g =3, let g =1, if X' new Is superior to X new If yes, let tu _ n = tu _ n-1 and g = g-1, and meanwhile, judge whether tu _ n is equal to the maximum number of courses for supplementing 6, if yes, go to Step4, otherwise go to Step3;
step3.4, maintaining excellent and judging whether the termination condition is reached: and (3) preserving the whole population and the Teacher population, selecting the superior individual of the previous percent of the Teacher _ p as a new Teacher population, judging whether an iteration termination condition is met, if so, outputting the best Teacher individual as a final result, and otherwise, turning to Step2.
The beneficial effects of the invention are: the invention establishes a scheduling model for considering the processing process of the cold rolling and the coated steel plate for the household appliances, respectively represents the processing time and the delivery date by using the triangular fuzzy number and the trapezoidal fuzzy number, and more objectively describes the actual production condition of a cold rolling factory; designing a customer satisfaction calculation method which can accurately calculate the target value of the scheduling model; an optimized scheduling method based on a novel teaching and learning optimization algorithm is designed, so that a high-quality solution of the scheduling problem in the processing process of the cold-rolled and coated steel plate for household appliances can be obtained in a short time, the customer satisfaction is improved, and the economic benefit of an enterprise is increased.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic representation of the expression of the present invention;
FIG. 3 is a flow chart of optimization of an optimization target based on an optimization scheduling scheme of a novel teaching and learning optimization algorithm according to the present invention;
FIG. 4 is a schematic diagram of an individual LMH in the optimization process of the optimization target based on the optimization scheduling scheme of the novel teaching and learning optimization algorithm.
Detailed Description
The invention is further illustrated by the following figures and examples.
Example 1: as shown in fig. 1, the optimized scheduling method for the processing process of the cold-rolled and coated steel plate for the household appliance comprises the following specific steps:
(1) Firstly, uncertain processing time and delivery date are represented by fuzzy numbers through previous month production data of a cold rolling mill and priori knowledge of processing personnel, in actual production, the processing time cannot be accurately predicted under the influence of a plurality of uncertain factors such as cutter and grinding tool replacement of a machine, the completion time and the delivery date can only be estimated in a certain interval, and therefore, the processing time and the delivery date are represented by triangular fuzzy numbers; in actual production, due to the influences of various uncertain factors such as equipment faults, regular overhaul of a unit, different proficiency of workers and the like, the machining time is difficult to predict accurately, and the completion time can only be estimated in a certain interval, so that the machining time and the completion time are represented by triangular fuzzy numbers;
step1.1 operations O i,j The jth process of the ith batch of steel sheets is shown in the machine set M k The machining time is expressed by triangular fuzzy number
Wherein
The minimum processing time is indicated and is,
the most likely processing time is indicated by the number of,
represents the maximum processing time; the completion time of each operation is expressed as
Wherein
Represents the minimum completion time of the jth process for lot i,
indicating the most likely completion time for the jth pass of lot i,
the maximum completion time of the jth process in lot i is represented by the membership function:
in addition, in actual production, the lead time proposed by the customer is not a precise moment (either suitable delay or lead delivery can be tolerated), so that the lead time of each lot of products is represented by a trapezoidal fuzzy number, for example, the lead time of lot i can be represented by D i ＝(d 1 ,d 2 ,d 3 ,d 4 ) Wherein [ d ] 2 ,d 3 ]The time period is the most ideal delivery date, the satisfaction of the delivery client is 1 (namely 'most satisfactory') in the interval, if the interval is exceeded (delivery date is advanced or delayed), the satisfaction of the client is linearly reduced, and d 1 For a critical time point at which customer satisfaction is 0 (i.e. "least satisfied") at lead time, d 4 For the critical time point of 0 customer satisfaction at the delayed delivery, the delivery time membership function expression is as follows:
table 1 shows an example of processing data, assuming three sets of machines, three cold rolled steel sheets, two previous batches with two processes and three third batches with three processes, where "-" in table 1 indicates that the process could not be processed on this machine:
TABLE 1 processing data
(2) Then establishing a scheduling model of the processing process of the cold-rolled and coated steel plate for the household appliance, determining an optimization target of the model, and finally optimizing the optimization target of the scheduling model by using a novel teaching and learning-based optimization algorithm;
the step2.1 processing process needs to meet the following constraint conditions: at any moment, the same batch of steel plates can be processed on one set of machine set at most; at most one process can be processed by the same set of unit at any time; either operation may not be interrupted during processing; the working procedure of the same batch of steel plates is required to be finished in the previous working procedure before the next working procedure is carried out;
step2.2 calculating customer satisfaction AI according to the completion time of each batch of steel plates and the scheduled delivery date i ，
Wherein AI is i Representing customer satisfaction of the ith lot,
a fuzzy completion time membership function for lot i,
is a fuzzy lead time membership function for lot i,
the area of the membership function of the fuzzy completion time of the batch i;
the optimization objective is to maximize average customer satisfaction:
wherein,
representing maximum average customer satisfaction, n represents the number of batches;
(3) And finally, optimizing the optimization target of the scheduling model by using a novel teaching and learning optimization algorithm, as shown in fig. 3, specifically comprising the following steps:
step3.1 initialisation population: assuming that the population size is popsize, the population includes more than one individual, and assuming that the total number of steps required for processing each individual is
Wherein u is i Each of the units is a randomly generated code string with a length of the total process number U, wherein one unit is represented as (p) 1 ,p 2 ,...,p U ) The total number of steps of the other units is the same as that of the other units, but the sequence of the steps is different, and p in the unit w ∈{1,2,...,n}， w∈{1,2,...,U}，p w Is the w-th bit of the code string, n is the number of batches, if p w K, then p w Is u in the total number of processes k If k is the m-th occurrence, it represents p w Corresponding to the mth process step O of the kth batch k,m As shown in fig. 2, 3 batches of 3 sets of units, the first two batches have two processes, the third batch has three processes, then the adaptive value of each individual, i.e. the objective function value Q, is calculated according to the formulas (3) and (5),
in order to make scheduling as compact as possible, greedy active decoding is used for decoding each individual coding string, according to operation in a process operation string, greedy strategy is used for performing active decoding on each machine capable of processing the operation in sequence, then the machine with the shortest completion time is selected for processing, summation of triangular fuzzy numbers is needed in the calculation process, subtraction is carried out, large operation is taken, the summation and subtraction operations are used for calculating fuzzy completion time, and two triangular fuzzy numbers X = (X =) are obtained 1 ,x 2 ,x 3 ) And Y = (Y) 1 ,y 2 ,y 3 ) The summation operation is defined as:
X+Y＝(x 1 +y 1 ,x 2 +y 2 ,x 3 +y 3 ) (6)
the subtraction operation is defined as:
X-Y＝(x 1 -y 1 ,x 2 -y 2 ,x 3 -y 3 ) (7)
in calculating the blur start time and the completion time, a sorting operation using the blur number is required, X = (X) for two triangular blur numbers 1 ,x 2 ,x 3 ) And Y = (Y) 1 ,y 2 ,y 3 ) The sorting adopts the following basis:
according to 1: calculating Z for X and Y separately 1 In which
Will Z 1 As the primary basis for sorting;
according to the following 2: if Z of two triangular fuzzy numbers 1 Are equal, then Z is defined 2 (X)＝x 2 ，Z 2 (Y)＝y 2 Is a reaction of Z 2 As a secondary basis for sorting;
according to the following 3: if the first two bases of the two triangular fuzzy numbers are equal, Z is defined 3 (X)＝x 3 -x 1 ， Z 3 (Y)＝y 3 -y 1 Is a reaction of Z 3 As a basis for sorting;
the triangular fuzzy number can be sorted and enlarged by using the three bases;
according to the calculated adaptive value Q of each individual, taking the superior individual of the Teacher _ p percent in the population as an initial 'Teacher' population, taking the rest individuals as 'student' populations, and simultaneously enabling the iteration number gen =1;
step3.2 updates each student individual in the student population through a teaching stage or a mutual learning stage, firstly randomly generates a real number delta between 0 and 1 when each student individual is updated, if delta is smaller than a real number teaching between 0 and 1, the teaching stage is used for updating the student individual, otherwise, the mutual learning stage is used for updating the student individual;
the individuals are updated using a "teaching" phase by first generating a string sequence Pick of the same length as the code string, while randomly filling each digit of the Pick with {0,1}, and then randomly selecting a teacher X from the teacher population teacher To student X old The interleaving is performed starting with the first bit of Pick, if this bit equals 0, X is then added teacher Filling new individuals X with the same position in the process new In this position, whereas if 1, X is old In the same place process fill in X new And the process is started from X teacher And X old Is deleted, then X is deleted teacher And X old The working procedures after the middle position are shifted to the left by one position in sequence, the vacant positions in the middle are filled, and the steps are repeated until a new individual X new Is filled up; after crossing, if X new The performance of the product is superior to that of X old I.e. X new Has an objective function value Q larger than X old Then use X new Substitution of X old And go to Step4, otherwise go to Step3;
the "learning-by-learning" stage differs from the "teaching" stage only in that the generation of new individuals is randomly selected to divide by X old Another student X outside old_2 And X old Performing intersection, wherein the rest steps are the same as the teaching stage;
finally, according to X new Updating the learning history matrix LHM corresponding to the individual, and in the iterative process, each student X old As long as the update produces a new solution X new The student's LHM is used to X new Recording, each student has a corresponding LHM for recording the position information of each student individual in the updating process, each line in the LHM represents each bit in an individual code string, each column represents a batch number which may appear in each bit in the code string, the w-th row and i-th column element which are equal to n represent that the individual has the w-th batch number i recorded for n-1 times in the iterative operation process of the algorithm, 1 is subtracted because the initial value of each element is 1, the LMH recording method is concretely as follows, if X is new W th bit equals lot number i and X new Is superior to X old I.e. X new Has an objective function value Q larger than X old Adding 1 to the w-th row/i-th column element of the LHM if X new Has an objective function value of less than or equal to X old Then add to the element at line w, column i of the LHM
A penalty factor greater than 1, if X new Is not equal to the batch number i, the w-th row and i-th column elements of the LHM are not changed;
step3.3, update X by "filling class" phase new Has an objective function value of less than or equal to X old Let the current number of courses supplement tu _ n =0, the current supplement mode g =1,1 represents that the codes are supplemented by sequential filling operation during course supplement, 2 represents that the codes are supplemented by random exchange operation, and each student updates in the stages of teaching and learning, and if X is newly solved new Has an objective function value of less than or equal to X old The individuals of (1) are examined for deficiencies and omissions by 'course filling', firstly, X is found in the LHM of the student in turn new Each bit encodes a corresponding element, constructing a set L = { L = { L = 1 ,L 2 ,L 3 ,...,L U And normalizing L and then selecting larger elements in L using roulette, the probability of each element being selected being calculated using equation (8) below, the number of rows in the LHM corresponding to the code string position w that needs to be changed.
After the position w of the change is determined, the process e of determining this position is required, and therefore the set L' = { L is constructed using the reciprocal of all the elements in the LHMw line 1 ,L 2 ,L 3 ,...,L n Using roulette to select a smaller element in L' to fill it into position w, the probability of each element being selected being given by equation (9) below;
in addition, in order to ensure that the new solution obtained by the course supplementation is a feasible scheduling solution, the encoding string needs to be supplemented completely, and the encoding string is alternately used in the following two supplementing modes, so that the global exploration capability of the algorithm is improved, and the specific operations are as follows:
filling in sequence: x is to be new Removing processe all other steps, according to X new Sequentially filling the mixture into positions except the position w to form a new solution X' new ；
Random exchange: at X new Finding the positions of all elements with the same e-batch number, and randomly selecting a position w' from the positions new Elements in w bits of Medium X' new In the w' position of (2), while adding X new The rest elements in the formula are placed into X 'according to the original position' new ；
X 'is newly dissolved after each course supplement according to the obtained solution' new Updating the LHM corresponding to the subject, and tu _ n = tu _ n +1, g = g +1, g can only equal 1 or 2, when g =3, let g =1, if X' new Is superior to X new If yes, let tu _ n = tu _ n-1 and g = g-1, and meanwhile, judge whether tu _ n is equal to the maximum number of courses for supplementing 6, if yes, go to Step4, otherwise go to Step3;
step3.4, guarantee excellent and judge whether the termination condition is reached: and (3) keeping the whole population and the Teacher population, selecting the better individuals of the previous percent of Teacher _ p as a new Teacher population, judging whether an iteration termination condition is met, if so, outputting the best Teacher individual as a final result, and otherwise, turning to Step2.
In the embodiment, the population size popsize =100, the Teacher ratio Teacher _ p =20, the ratio teaching in the teaching stage and the mutual learning stage =0.7, and the penalty coefficient of LHM
TABLE 2 values of objective function determined for different problem scales
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (3)
1. An optimized scheduling method for the processing process of a cold-rolled and coated steel plate for household appliances is characterized by comprising the following steps:
(1) Firstly, uncertain processing time, finishing time and delivery date are represented by fuzzy numbers through previous production data of a cold rolling plant and priori knowledge of processing personnel;
(2) Then establishing a scheduling model of the processing process of the cold-rolled and coated steel plate for the household appliance, and determining an optimization target of the model;
(3) Optimizing the optimization target of the scheduling model by using a novel teaching and learning optimization algorithm;
the specific steps of optimizing the optimization target of the scheduling model based on the novel teaching and learning optimization algorithm in the step (3) are as follows:
step3.1 initialise population: assuming that the population size is popsize, the population includes more than one individual, assuming that the total number of steps each individual requires processing is
Wherein u i Each of the units is a randomly generated code string with a length of the total process number U, wherein one unit is represented as (p) 1 ,p 2 ,...,p U ) The total number of steps of the other individuals is the same as that of the individual, but the order of the steps is different, p in the individual w ∈{1,2,...,n}，w∈{1,2,...,U}，p w Is the w-th bit of the code string, n is the number of batches, if p w K, then p w Is u in the total number of processes k If k is the m-th occurrence, it represents p w Corresponding to the mth process step O of the kth batch k,m Then, an adaptive value, i.e., an objective function value Q, for each individual is calculated according to equations (3) and (5),
wherein, to make the toneThe method comprises the steps of enabling the degree to be as compact as possible, decoding each individual coding string by greedy active decoding, sequentially performing active decoding on each machine capable of processing the operation by a greedy strategy according to the operation in a working procedure operation string, selecting the machine with the shortest completion time for processing, summing triangular fuzzy numbers in the calculation process, subtracting and taking a large operation, wherein the summing and subtracting operations are used for calculating fuzzy completion time, and for two triangular fuzzy numbers X = (X is X =) 1 ,x 2 ,x 3 ) And Y = (Y) 1 ,y 2 ,y 3 ) The summation operation is defined as:
X+Y＝(x 1 +y 1 ,x 2 +y 2 ,x 3 +y 3 ) (6)
the subtraction operation is defined as:
X-Y＝(x 1 -y 1 ,x 2 -y 2 ,x 3 -y 3 ) (7)
in calculating the blur start time and the completion time, a sorting operation using the blur number is required, X = (X) for two triangular blur numbers 1 ,x 2 ,x 3 ) And Y = (Y) 1 ,y 2 ,y 3 ) The sorting adopts the following basis:
according to the following steps of 1: calculating Z for X and Y separately 1 Wherein
Will Z 1 As the primary basis for sorting;
according to 2: if Z of two triangular fuzzy numbers 1 Equal, then define Z 2 (X)＝x 2 ，Z 2 (Y)＝y 2 A 1 is formed of 2 As a secondary basis for sorting;
according to the following 3: if the first two bases of the two triangular fuzzy numbers are equal, defining Z 3 (X)＝x 3 -x 1 ，Z 3 (Y)＝y 3 -y 1 A 1 is formed of 3 As a basis for sorting;
the triangular fuzzy number can be sorted and enlarged by using the three bases;
according to the calculated adaptive value Q of each individual, taking the superior individual of the Teacher _ p in percentage in the population as an initial 'Teacher' population, taking the rest individuals as a 'student' population, and simultaneously enabling the iteration number gen =1;
step3.2 updates each student individual in the student group through a teaching stage or an inter-learning stage, when each student individual is updated, a real number delta between 0 and 1 is randomly generated at first, if delta is smaller than a real number teaching between 0 and 1, the teaching stage is used for updating the student individual, otherwise, the inter-learning stage is used for updating the student individual;
the individuals are updated using a "teaching" phase by first generating a string sequence Pick of the same length as the code string, while randomly filling each bit of Pick with {0,1}, and then randomly selecting a teacher X from the teacher population teacher And student X old The interleaving is performed starting with the first bit of Pick, if this bit equals 0, X is then added teacher Filling new individuals X with the same-position procedures new In this position, whereas if 1, X is old In the same place process fill in X new And the process is started from X teacher And X old Is deleted, then X is deleted teacher And X old The working procedures after the middle position are shifted to the left by one position in sequence, the vacant positions in the middle are filled, and the steps are repeated until a new individual X new Is filled up; after crossing, if X new The performance of the product is superior to that of X old I.e. X new Has an objective function value Q larger than X old Then use X new Substitution of X old And go to Step4, otherwise go to Step3;
the "learning-by-learning" stage differs from the "teaching" stage only in that the generation of new individuals is randomly selected to divide by X old Another student X outside old_2 And X old Performing intersection, wherein the rest steps are the same as the teaching stage;
finally, according to X new Updating the learning history matrix LHM corresponding to the individual, and in the iterative process, each student X old As long as the update produces a new solution X new The student's LHM is used to X new Recording, each student has a corresponding LHM for recording the position information of each student individual in the updating process, each line in the LHM represents each bit in an individual code string, each column represents a batch number which may appear in each bit in the code string, the w-th row and i-th column element which are equal to n represent that the individual has the w-th batch number i recorded for n-1 times in the iterative operation process of the algorithm, 1 is subtracted because the initial value of each element is 1, the LMH recording method is concretely as follows, if X is new W th bit equal to lot number i and X new Is superior to X old I.e. X new Has an objective function value Q larger than X old Then add 1 to the element in row w and column i of the LHM if X is new Has an objective function value of less than or equal to X old Then add to the element at line w and column i of the LHM
A penalty factor greater than 1 if X new Is not equal to the batch number i, the w-th row and i-th column elements of the LHM are not changed;
step3.3, update X by "filling class" phase new Has an objective function value of less than or equal to X old Let the current number of courses supplementation tu _ n =0, the current supplementation mode g =1,1 represents that the codes are supplemented by sequential filling operation during course supplementation, 2 represents that the codes are supplemented by random exchange operation, and each student updates in the "teaching" and "inter-learning" stages and then solves X if the students newly solve new Has an objective function value of less than or equal to X old The individuals of (1) are examined for deficiencies and omissions by 'course filling', firstly, X is found in the LHM of the student in turn new Each bit encodes a corresponding element, and a set L = { L is constructed 1 ,L 2 ,L 3 ,...,L U H, and normalize L, then select the larger element in L using roulette, the probability of each element being selected being calculated using equation (8) below, the elementThe line number of the element in the LHM corresponds to the position w of the code string needing to be changed;
after the position w of the change is determined, the process e of determining this position is required, and therefore the set L' = { L is constructed using the reciprocal of all the elements in the LHMw line 1 ,L 2 ,L 3 ,...,L n Using a roulette wheel to select smaller elements in L' and fill the elements into positions w, the probability of each element being selected being given by (9);
in addition, in order to ensure that the new solution obtained by the course supplementation is a feasible scheduling solution, the encoding string needs to be supplemented completely, and the encoding string is alternately used in the following two supplementing modes, so that the global exploration capability of the algorithm is improved, and the specific operations are as follows:
filling in sequence: mixing X new In all the steps except step e according to X new Sequentially filling the mixture into positions except the position w to form a new solution X' new ；
Random exchange: at X new Finding the positions of all elements with the same e-batch number, and randomly selecting a position w' from the positions new Element in w bit is put into X' new In the w' position of (A), while X is simultaneously substituted new The rest elements in the formula are placed into X 'according to the original position' new ；
According to the obtained new solution X 'after each class supplementation' new Updating the LHM corresponding to the individual, and tu _ n = tu _ n +1, g = g +1, g can only be equal to 1 or 2, when g =3, let g =1, if X' new Is superior to X new If yes, let tu _ n = tu _ n-1, g = g-1, and at the same time, judge tu _ n whether equal to the maximum number of courses for supplement 6, if equal, go to Step4, otherwise go to Step3;
step3.4, maintaining excellent and judging whether the termination condition is reached: and (3) preserving the whole population and the Teacher population, selecting the superior individual of the previous percent of the Teacher _ p as a new Teacher population, judging whether an iteration termination condition is met, if so, outputting the best Teacher individual as a final result, and otherwise, turning to Step2.
2. The method for optimizing and scheduling a machining process of a cold-rolled and coated steel plate for household appliances according to claim 1, wherein the method comprises the following steps: the specific steps of the step (1) are as follows:
step1.1 represents the processing time and completion time by triangular fuzzy numbers, and each operation O is set i,j The jth process of the ith batch of steel sheets is shown in the machine set M k The machining time is expressed by triangular fuzzy number
Wherein
The minimum processing time is indicated and is,
the most likely processing time is indicated by the number of,
the maximum processing time is shown and the completion time of each operation is shown as
Wherein
Represents the minimum completion time of the jth process of lot i,
indicating the most likely completion time for the jth pass of lot i,
the maximum completion time of the jth process in lot i is represented by the membership function of formula (1):
wherein,
a membership function of fuzzy completion time of the batch i;
step1.2 uses a trapezoidal fuzzy number to indicate the delivery date of each lot of products, and the delivery date of the ith lot of products is indicated as D i ＝(d 1 ,d 2 ,d 3 ,d 4 ) Wherein [ d ] 2 ,d 3 ]The time period is the optimal delivery date, the satisfaction degree of the delivery client in the interval is 1, namely 'most satisfactory', if the time period is beyond the interval, the satisfaction degree of the delivery client is linearly reduced if the delivery date is advanced or delayed, and d 1 Critical time point for customer satisfaction of 0 at lead time, d 4 For the critical time point of 0 customer satisfaction at the delayed delivery, the delivery date membership function expression is as follows:
wherein,
is a fuzzy lead time membership function for lot i.
3. The method for optimizing and scheduling a machining process of a cold-rolled and coated steel plate for household appliances according to claim 1, wherein the method comprises the following steps: the specific steps of the step (2) are as follows:
step2.1 makes the processing process meet the following constraint conditions: at any moment, the same batch of steel plates can be processed on one set of machine set at most; at most one process can be processed by the same set of unit at any time; either operation may not be interrupted during processing; the working procedure of the same batch of steel plates is required to be finished in the previous working procedure before the next working procedure is carried out;
step2.2 calculating customer satisfaction AI based on the completion time and scheduled delivery date of each batch of steel sheets i ，
Wherein AI is i Representing customer satisfaction of the ith lot,
a fuzzy completion time membership function for lot i,
is a fuzzy lead time membership function for lot i,
the area of the membership function of the fuzzy completion time of the batch i;
the optimization objective is to maximize average customer satisfaction:
wherein,
representing maximum average customer satisfaction, and n represents the number of batches.
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