CN114662765B - Batch scheduling method for discrete manufacturing irrelevant workpieces - Google Patents
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Abstract
The invention discloses a batch scheduling method for discrete manufacturing of irrelevant workpieces. It comprises the following steps: making an assumption on a batch processing scheduling environment of smelting and forming of irrelevant workpieces; establishing a minimum total batch quantity objective function, a minimum average empty rate objective function and a minimum finishing time objective function; constraining parameters in the three functions; constructing a solution form; generating a possible solution and a random solution, and updating the possible solution and the random solution to obtain an updated solution; batch movement optimization is adopted for updating solutions, so that the maximum finishing time at the modeling procedure is reduced; batch merging optimization is adopted for updating solutions, so that the dispatching completion time of a single batch processor is reduced; the optimized optimal solution is the batch scheduling optimal solution for smelting and forming the discrete manufacturing irrelevant workpieces. The invention adopts intelligent scheduling to optimize an optimal scheduling scheme, improves the utilization rate of the sandboxes and the parallel batch processors, and reduces the total batch quantity of scheduling and the finishing time of smelting forming.
Description
Technical Field
The invention relates to the technical field of workshop scheduling, in particular to a batch processing scheduling method for discrete manufacturing of irrelevant workpieces.
Background
The process of producing discrete manufactured products is typically broken down into a number of processing tasks to complete. Each task requires only a small portion of the capabilities and resources of the enterprise. Enterprises generally build functionally similar equipment into production organizations (departments, sections, or groups) in terms of space and administrative management. In each department, workpieces are processed in different types of working procedures from one work center to another work center. Enterprises often arrange the location of production equipment in a primary process flow to minimize the distance of material transport. In addition, the processing process route and the equipment are very flexible, and the product design, the processing requirement and the order quantity are more varied. Products of discrete manufacture are often assembled from multiple parts by a series of processes that are not continuous.
In conventional shop scheduling, one machine can only process one job at a time. For parallel lot scheduling, such as wafer fabrication, semiconductor fabrication, circuit testing, and foundry scheduling, a batch processor (The batch processing machine, BPM) may process job lots consisting of multiple jobs at the same time. Similar to shop scheduling, once processing begins, jobs in a batch cannot be increased or decreased. For parallel machine scheduling problems, jobs are assigned to different lots, and then lots are assigned to parallel BPMs, which may be divided into the same parallel BPM, a unified parallel BPM, and unrelated parallel BPMs.
The production of hot and cold working discrete manufacturing enterprises is generally simplex or small batch. Smelting and forming are the core processes of hot and cold working discrete manufacturing operations that determine the quality of the manufacturing task. There are many constraints in the smelting forming process, such as sandbox size constraints, incompatibility characteristics (i.e., processing technology characteristics of the operation), different materials for different operations, casting characteristics (casting mode, casting temperature, casting speed, etc.), and capacity of the melting furnace. At present, manual scheduling is still adopted for batch processing of discrete manufacturing irrelevant workpieces, and the manual scheduling is usually not comprehensive in consideration, so that a proper scheduling scheme cannot be found, and the scheduling quality cannot be improved.
Disclosure of Invention
The invention aims to provide a batch scheduling method for discrete manufacturing of irrelevant workpieces, which adopts an intelligent scheduling method, improves the utilization rate of sandboxes and parallel batch processors, and reduces the total batch quantity of scheduling and the finishing time of smelting forming.
In order to achieve the above object, the present invention provides a batch scheduling method for discrete manufacturing of unrelated workpieces, comprising the steps of:
step 1), according to the characteristics of different sizes of workpieces and incompatibility of workpiece groups in discrete manufacturing, making an assumption on batch processing scheduling environments of smelting and forming of irrelevant workpieces;
Step 2), respectively establishing a minimum total batch quantity objective function (1), a minimum average empty rate objective function (2) and a minimum finishing time objective function (3) aiming at batch processing scheduling of smelting and forming of irrelevant workpieces;
step 3), constraining parameters in the minimum total batch number objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) according to the actual conditions of the site;
Step 4), solving an objective function (1) for minimizing the total batch number, an objective function (2) for minimizing the average empty rate and an objective function (3) for minimizing the finishing time, wherein one solution is a scheduling scheme, and each solution is set to be in a form of X= [ XB|XD ], wherein XB is a sequence formed by batch numbers, and XD is a sequence formed by batch processor numbers corresponding to the batch numbers in the XB one by one;
step 5), dividing all solutions X of the minimum total batch number objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) into two parts, wherein one part of solutions adopts a heuristic algorithm to generate a feasible solution, and the other part of solutions adopts a random algorithm to generate a random solution;
Step 6), carrying out cross update and mutation update on XB sequences and XD sequences in the feasible solution and the random solution according to a virus gene update mode to obtain an update solution X, thereby enriching the diversity of the solution;
Step 7), moving the batch number with the minimum working time corresponding to the batch processor with the maximum finishing time in the XD sequence corresponding to the updated solution X to the batch processor with the minimum finishing time for processing; or selecting the batch number with the largest working time corresponding to the batch processor with the largest finishing time from the XD sequence, and simultaneously selecting the batch number with the smallest working time corresponding to the batch processor with the smallest finishing time from the XD sequence, and exchanging the batch processors;
Step 8), carrying out batch merging optimization on all batch numbers corresponding to the same batch processor in the XD sequence corresponding to the updated solution X;
and 9), optimizing the optimal solution X= [ XB|XD ], namely the optimal batch scheduling scheme for smelting and forming the discrete manufacturing irrelevant workpieces.
Further, in step 1), the assumptions made include:
a, when the moment is zero, all workpieces are reached and prepared, different types of sandboxes are prepared, and each batch processor can be used;
b. In each dispatching scheme, each workpiece is distributed to different workpiece groups, each workpiece group is divided into different batches of work according to the modeling procedure of the workpiece, each batch of work is distributed with one type of sandboxes, the total batch number is the sum of the different types of sandboxes, and each batch of work can only be processed once at most on a batch processor;
c, the quantity of different types of sandboxes used in the scheduling process is enough;
d, the weight of all the jobs in the sandbox has no influence on the selection of the sandbox type;
e, the number of the workpieces contained in each batch of operation can be different;
f, once each batch processor starts working, the batch processor cannot be interrupted, the operation is not allowed to be added or deleted in batch processing, and each batch processor can only process one batch of operation at a time;
g, irrespective of the waiting time of each batch processor between the previous batch and the next batch;
h, each batch processor can process all types of sandboxes;
i, the total finishing time of each scheduling scheme is from the first batch job starting time to the last batch job ending time.
Further, in step 2), the minimum total lot number objective function (1), the minimum average empty rate objective function (2) and the minimum completion time objective function (3) are respectively:
min f1＝ng (1)
Wherein,
F 1 is the total lot number in the scheduling scheme,
N g is the total number of lots in the dispatch protocol,
F 2 is the average empty rate of all sandboxed types for batch processing,
Y bv is a decision variable, which is used to determine the decision,
N d is the total number of sandboxed types,
O Dv is the sandbox size for sandbox type Dv,
Dv is the v-th sandbox type,
S Bbt is the sum of all the job sizes of lot B b,
B b is the B-th batch,
X ib is a decision variable that is used to determine,
A it is a decision variable that is used to determine,
S i is the size of the i-th job,
N is the number of jobs to be performed,
F 3 is the total completion time of the scheduling scheme,
M is the total number of batch processors,
C k is the total processing time of the kth batch processor,
Y bv is a decision variable, which is used to determine the decision,
Z bk is a decision variable, and,
T kv is the processing time of the kth batch processor to process the v-th sandbox type Dv.
Still further, in step 3), the constraint includes:
Wi≤Q,i∈[1,n] (9)
Si≤ODv,i∈[1,n],v∈[1,nd] (10)
WBbt≤Q,b∈[1,ng] (12)
SBbt≤ODvYbv,b∈[1,ng] (13)
Wherein,
Equation (4) shows that if workpiece J i is assigned to lot Bb, then X ib =1, otherwise, X ib =0,
Equation (5) shows that if workpiece J i is assigned to the t-th incompatible workpiece family Ut, a it =1, otherwise a it =0,
In equation (6), M k is the kth BPM, BPM is the batch processor, equation (6) indicates that if the batch Bb is assigned to the kth batch processor, Z bk = 1, otherwise, Z bk = 0,
Equation (7) shows that if the lot Bb is assigned to sandbox Dv, then Y bv =1, otherwise Y bv =0,
In equation (8), n l is the total number of incompatible workpiece families Ut, equation (8) indicates that each batch can only be in one workpiece family at most,
In the formula (9), W i is the weight of the job J i, Q is the maximum capacity of the melting furnace, the formula (9) indicates that the weight of each job does not exceed the maximum capacity of the melting furnace,
In equation (10), S i is the size of job J i, equation (10) indicates that the size of each job does not exceed the maximum size of sandboxes provided,
In equation (11), W Bbt is the sum of all the job weights for lot B b,
Equation (12) shows that the sum of all the operating weights of batch B b does not exceed the maximum capacity of the melting furnace,
Equation (13) shows that the sum of all job sizes for lot B b does not exceed the maximum size of the sandboxes provided.
Still further, in step 5), the step of heuristically generating includes:
Step ①, carrying out batch classification on all the operations strictly according to the workpiece family information, wherein the batch number is marked as S j;
Step ②, starting from the first job in the lot number S j, randomly selecting a sandbox capable of boxing the first job, placing the sandbox type at the corresponding position in the XD sequence, and for other jobs in the lot number S j, establishing a new lot number if the following conditions are met:
a. inserting a job into the current lot number violates the constraint of the incompatible workpiece family of equation (8);
b. inserting workpieces into the current lot number violates the sandbox size constraint of equation (10) and equation (13);
c. inserting workpieces into the current lot number violates the furnace capacity constraints of equation (9) and equation (12);
Step ③, repeat step ② until all jobs in the sequence of lot number S j are completed in batches.
Still further, in step 6), the cross update includes respectively performing an order cross, a linear order cross, a position-based cross, a sequence-based cross, and a priority operation cross on the XB sequence, and further includes respectively performing a two-point cross, a multi-point cross, and a uniform two-point cross on the XD sequence; the mutation update includes respectively performing interactive mutation, frame shift mutation, inversion mutation, insertion mutation and displacement mutation on the XB sequence and the XD sequence.
Further, in step 7), the specific steps of the batch movement optimization are as follows:
step ①, selecting a batch processor with the largest finishing time from XD sequences corresponding to a solution X, and marking the batch processor as Mmax and the processing time as Tmax; selecting a batch processor with minimum finishing time, marking the batch processor as Mmin, and marking the processing time as Tmin;
Step ②, selecting a lot number with the minimum processing time from Mmax, and moving the lot number to mman for processing, wherein the formed solution is denoted as X;
step ③, recalculating the time on the batch processors Mmax and Mmin to be T 'max and T' min respectively;
Step ④, if max { T 'max, T' min } -is less than or equal to Tmax, updating X with X, and entering the next round of optimization process;
Step ⑤, if the condition of step ④ is not satisfied, selecting a lot number with the largest processing time on Mmax, and simultaneously selecting a lot number with the smallest processing time on mman, and exchanging batch processors for the largest lot number and the smallest lot number, wherein the formed solution is X;
step ⑥, repeating the steps ③ to ④;
Step ⑦, the condition in step ④ is not satisfied twice in succession, ending the optimization process;
In step ⑧, update solution X is subjected to steps ① through ⑦.
Further, in step 8), the specific steps of the batch merge optimization are as follows:
Step ①, performing all batch numbers corresponding to each sandbox type in the XD sequence corresponding to one solution X Is a combination of (a);
Step ②, traversing the batch numbers combined together in step ①, if the size of the existing sandbox type is not less than the sum of the sizes of all the workpieces in the two batches after the two batch numbers are combined, selecting the sandbox type with the smallest size in preference, and the sum of the masses of all the workpieces in the two batch numbers is not greater than the maximum capacity of the melting furnace, combining the two batches into a new batch, removing the two batch numbers from the combination, returning to step ① until all the combinations are traversed, and entering the next step;
In step ③, the updated solution X goes through steps ① to ②, and the optimization process is ended.
The invention has the advantages that:
1. The method comprises the steps of respectively establishing a minimum total batch quantity objective function, a minimum average empty rate objective function and a minimum finishing time objective function aiming at batch scheduling of smelting and forming of irrelevant workpieces, and providing a specific solving algorithm for the three functions, wherein the optimal solution of the functions is used as a batch scheduling optimal scheme for smelting and forming of the irrelevant workpieces in discrete manufacturing;
2. each solution is set to be in a form of X= [ XB|XD ], wherein XB is a sequence formed by batch numbers, XD is a sequence formed by sandbox type numbers corresponding to the batch numbers in the XB one by one; the specific solution algorithm for the three functions is as follows: firstly, dividing all solutions into two parts, wherein one part of solutions adopts a heuristic algorithm to generate a feasible solution, and the other part of solutions adopts a random algorithm to generate a random solution; then, the XB sequence and the XD sequence in all solutions X are subjected to cross update and mutation update according to a virus gene update mode to obtain an update solution X; finally, two different local better guiding search strategies, namely batch movement optimization and batch merging optimization, are designed aiming at incompatible workpiece family constraint in the modeling process, so that the convergence speed of an algorithm is accelerated, and an optimized optimal solution X= [ XB|XD ] is an optimal batch processing scheduling scheme for smelting and forming of discrete manufacturing irrelevant workpieces.
The batch processing scheduling method for discretely manufacturing irrelevant workpieces adopts intelligent scheduling, optimizes an optimal scheduling scheme, improves the utilization rate of sandboxes and parallel batch processors, and reduces the total batch quantity of scheduling and the finishing time of smelting forming.
Drawings
FIG. 1 is a flow chart of a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 2 is a schematic diagram of the batch information encoding and decoding of the batch information in the batch dispatch method for discrete manufacturing of unrelated workpieces according to the present invention;
FIG. 3 is a Gantt chart of a batch information in a batch dispatch method for discrete manufacturing of unrelated workpieces according to the present invention after genetic decoding;
FIG. 4 is a cross-sequence diagram of a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 5 is a cross-schematic view of a location-based process in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 6 is a sequence-based cross-schematic diagram of a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 7 is a cross-schematic diagram of a preferred operation in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 8 is a schematic representation of the variation of the process variation in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 9 is a schematic diagram of frame shift variation in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 10 is a schematic diagram of reverse variation in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 11 is a schematic illustration of insertion variation in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 12 is a graph illustrating variation in displacement in a batch scheduling method for discrete manufacturing of unrelated workpieces in accordance with the present invention;
FIG. 13 is a comparative Schedule Gantt chart of the embodiment of FIG. 2 after BMS1a optimization;
fig. 14 is a comparative scheduled gater graph of the embodiment of fig. 2 after BMS2 optimization.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention relates to a batch scheduling method for discrete manufacturing irrelevant workpieces, which comprises the following steps (see a flow chart 1 for details):
Step 1), according to the characteristics of different sizes of workpieces and incompatibility of workpiece groups in discrete manufacturing, making an assumption on batch processing scheduling environments of smelting and forming of irrelevant workpieces. The assumptions made include:
a, when the moment is zero, all workpieces are reached and prepared, different types of sandboxes are prepared, and each batch processor can be used;
b. In each dispatching scheme, each workpiece is distributed to different workpiece groups, each workpiece group is divided into different batches of work according to the modeling procedure of the workpiece, each batch of work is distributed with one type of sandboxes, the total batch number is the sum of the different types of sandboxes, and each batch of work can only be processed once at most on a batch processor;
c, the quantity of different types of sandboxes used in the scheduling process is enough;
d, the weight of all the jobs in the sandbox has no influence on the selection of the sandbox type;
e, the number of the workpieces contained in each batch of operation can be different;
f, once each batch processor starts working, the batch processor cannot be interrupted, the operation is not allowed to be added or deleted in batch processing, and each batch processor can only process one batch of operation at a time;
g, irrespective of the waiting time of each batch processor between the previous batch and the next batch;
h, each batch processor can process all types of sandboxes;
i, the total finishing time of each scheduling scheme is from the first batch job starting time to the last batch job ending time.
And 2) respectively establishing a minimum total batch quantity objective function (1), a minimum average empty rate objective function (2) and a minimum finishing time objective function (3) aiming at batch processing scheduling of irrelevant workpiece smelting and forming. The minimum total batch quantity objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) are respectively as follows:
min f1＝ng (1)
Wherein,
F 1 is the total lot number in the scheduling scheme,
N g is the total number of lots in the dispatch protocol,
F 2 is the average empty rate of all sandboxed types for batch processing,
Y bv is a decision variable, which is used to determine the decision,
N d is the total number of sandboxed types,
O Dv is the sandbox size for sandbox type Dv,
Dv is the v-th sandbox type,
S Bbt is the sum of all the job sizes of lot B b,
B b is the B-th batch,
X ib is a decision variable that is used to determine,
A it is a decision variable that is used to determine,
S i is the size of the i-th job,
N is the number of jobs to be performed,
F 3 is the total completion time of the scheduling scheme,
M is the total number of batch processors,
C k is the total processing time of the kth batch processor,
Y bv is a decision variable, which is used to determine the decision,
Z bk is a decision variable, and,
T kv is the processing time of the kth batch processor to process the v-th sandbox type Dv.
And 3) constraining parameters in the objective function (1) for minimizing the total batch number, the objective function (2) for minimizing the average empty rate and the objective function (3) for minimizing the finishing time according to the actual conditions of the site.
The constraints include:
Wi≤Q,i∈[1,n] (9)
Si≤ODv,i∈[1,n],v∈[1,nd] (10)
WBbt≤Q,b∈[1,ng] (12)
SBbt≤ODvYbv,b∈[1,ng] (13)
Wherein,
Equation (4) shows that if workpiece J i is assigned to lot Bb, then X ib =1, otherwise, X ib =0,
Equation (5) shows that if workpiece J i is assigned to the t-th incompatible workpiece family Ut, a it =1, otherwise a it =0,
In equation (6), M k is the kth BPM, BPM is the batch processor, equation (6) indicates that if the batch Bb is assigned to the kth batch processor, Z bk = 1, otherwise, Z bk = 0,
Equation (7) shows that if the lot Bb is assigned to sandbox Dv, then Y bv =1, otherwise Y bv =0,
In equation (8), n l is the total number of incompatible workpiece families Ut, equation (8) indicates that each batch can only be in one workpiece family at most,
In the formula (9), W i is the weight of the job J i, Q is the maximum capacity of the melting furnace, the formula (9) indicates that the weight of each job does not exceed the maximum capacity of the melting furnace,
In equation (10), S i is the size of job J i, equation (10) indicates that the size of each job does not exceed the maximum size of sandboxes provided,
In equation (11), W Bbt is the sum of all the job weights for lot B b,
Equation (12) shows that the sum of all the operating weights of batch B b does not exceed the maximum capacity of the melting furnace,
Equation (13) shows that the sum of all job sizes for lot B b does not exceed the maximum size of the sandboxes provided.
And 4) solving the objective function (1) for minimizing the total lot number, the objective function (2) for minimizing the average empty rate and the objective function (3) for minimizing the finishing time, wherein one solution is a scheduling scheme, and each solution is set to be in a form of X= [ XB|XD ], wherein XB is a sequence formed by batch numbers, and XD is a sequence formed by sandbox type numbers corresponding to the batch numbers in the XB one by one.
And 5) dividing all solutions X of the minimum total batch number objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) into two parts, wherein one part of solutions adopts a heuristic algorithm to generate a feasible solution, and the other part of solutions adopts a random algorithm to generate a random solution. The heuristic generation steps are as follows:
Step ①, carrying out batch classification on all operations (operations: modeling procedure corresponding to a certain workpiece) strictly according to the workpiece family information, wherein the batch number is marked as S j;
Step ②, starting from the first job in the lot number S j, randomly selecting a sandbox capable of boxing the first job, placing the sandbox type at the corresponding position in the XD sequence, and for other jobs in the lot number S j, establishing a new lot number if the following conditions are met:
a. inserting a job into the current lot number violates the constraint of the incompatible workpiece family of equation (8);
b. inserting workpieces into the current lot number violates the sandbox size constraint of equation (10) and equation (13);
c. inserting workpieces into the current lot number violates the furnace capacity constraints of equation (9) and equation (12);
Step ③, repeat step ② until all jobs in lot number S j are completed in batches.
In the embodiment shown in fig. 2,3 batches, 2 sandboxes, 2 molding batch processors, 1 melting furnace and 2 working procedures of each workpiece are described, wherein a feasible solution x= [1,2,3, 1|1,3, 1,2,1] is obtained by first matching rules of incompatible workpiece groups, the obtained batch information is subjected to gene encoding and decoding as shown in fig. 2, and a Gantt chart after gene decoding is shown in fig. 3. In fig. 3, taking a square at the origin of the coordinate axes as an example, 1 in the upper left corner indicates the lot number, 4 in the upper right corner indicates the processing time of the lot on the apparatus M1, 101 indicates the 1 st process of the workpiece 1 to be processed in the lot, and the background of the color patch indicates the workpiece group to which the workpiece in the lot belongs.
And 6) carrying out cross updating and mutation updating on XB sequences and XD sequences in the feasible solution and the random solution according to a virus gene updating mode to obtain an updated solution X and enrich the diversity of the solution.
The cross updating comprises the steps of respectively performing sequence cross, linear sequence cross, position-based cross, sequence-based cross and priority operation cross on XB sequences, and further comprises the steps of respectively performing two-point cross, multi-point cross and uniform two-point cross on XD sequences; the mutation update includes respectively performing interactive mutation, frame shift mutation, inversion mutation, insertion mutation and displacement mutation on the XB sequence and the XD sequence.
The XB sequences are crossed as follows:
in order to enrich the diversity of the population, global optimization is performed in a mode that the gene segment with excellent parent is inherited to the offspring, and the convergence of an algorithm is accelerated.
(A) Order crossing (Order Crossover, OX)
Step 1: the intersecting fragments p11, p22 of the parent p1, p2 are noted and swapped.
Step 2: and (3) matching and rejecting p11 and p2 non-intersecting gene segments in a left-to-right sequence to obtain a.
Step 3: p22 is sequentially filled from left to right according to the relative position of the p22 from the 2 nd intersection position to obtain NP1; NP2 was obtained in the same manner.
Specifically, the sequence cross-over diagram is shown in fig. 4.
(B) Linear order crossing (Liner Order Crossover, LOX)
The linear order crossover differs from the order crossover in that: p22 in Step 3 is filled in order from left to right according to the index of the relative position.
(C) Position-based crossover (Position Based Crossover, PBX)
Step 1: randomly generating a plurality of crossing points (the same position points in two parents), and copying the gene of the P1 crossing point to obtain a.
Step 2: and (3) matching the non-empty gene fragment in the a with the parent P2 in sequence from left to right, and marking to obtain the b.
Step 3: filling the non-marker genes in the b into the non-empty gene segments of the a in sequence from left to right to obtain NP1; NP2 was obtained in the same manner.
Specifically, a schematic view of the position-based intersection is shown in fig. 5.
(D) Order-based interleaving (Order Based Crossover, OBX)
Step 1. Randomly generating a plurality of crossing points (the same position points in two parents), and copying the gene of the P1 crossing point to obtain a.
Step 2, matching the non-empty gene fragment in the a with the parent P2 in sequence from left to right, and marking to obtain the b.
Step 3, filling the non-empty gene segments in the a in the b marked gene segments in sequence from left to right to obtain NP1; NP2 was obtained in the same manner.
Specifically, a sequence-based cross-over schematic is shown in fig. 6.
(E) Preferential operation cross (PRECEDENCE OPERATION CROSSOVER, POX)
Step 1: the workpiece is randomly divided into two non-empty workpiece sets J1 and J2.
Step 2: all the processes in the workpiece set J1 of the parent P1 are copied to a, all the processes in the workpiece set J2 of the parent P2 are copied, and the relative positions of the processes are reserved and marked as b.
Step 3: filling the genes in the b into the non-empty gene segments of the a in sequence from left to right to obtain NP1; NP2 was obtained in the same manner.
Specifically, a cross-over diagram of the priority operation is shown in fig. 7.
The XD sequences were crossed as follows:
(a) Two-point intersection
Randomly generating 2 crossing positions, and exchanging genes between two crossing positions in the parent.
(B) Multi-point cross
The two points are crossed and diverged to randomly generate a plurality of crossed positions, and genes corresponding to the crossed positions in the parent are exchanged.
(C) Even two-point intersection
Two intersections are randomly generated and the intersection fragments are controlled by randomly generating 3 integers (0, 1, 2). When 0, the front part of the parent is exchanged; if 1, the intermediate part of the parent is exchanged; at 2, the latter part of the parent is swapped.
The manner of mutation of XB sequence and XD sequence is as follows:
the local optimizing capacity of the algorithm is enhanced by fine tuning the genes, and the premature phenomenon of the algorithm is relieved.
(A) Interchangeable variation
Two positions were randomly generated for gene exchange, and specifically, the schematic diagram of the exchange variation is shown in fig. 8.
(B) Code shift variation
Two parameters are randomly generated: the mutation position and the right shift distance r. If the last position is exceeded, then continue from the first position. Specifically, a frame shift variation is shown in fig. 9.
(C) Reverse variation
Two positions were randomly generated, with the genes between the two points in reverse order. Specifically, the reverse mutation diagram is shown in fig. 10.
(D) Insertion variation
Two positions are randomly generated, and the gene at the first position is placed at the second position. Specifically, the schematic diagram of the insertion variation is shown in fig. 11.
(E) Variation of displacement
Three positions are randomly generated, and the whole gene between the first two positions is inserted into the third position. Specifically, a displacement variation schematic diagram is shown in fig. 12.
Step 7), moving the batch number with the minimum working time corresponding to the batch processor with the maximum finishing time in the XD sequence corresponding to the updated solution X to the batch processor with the minimum finishing time for processing; or selecting the batch number with the largest working time corresponding to the batch processor with the largest finishing time in the XD sequence, and selecting the batch number with the smallest working time corresponding to the batch processor with the smallest finishing time in the XD sequence, wherein the batch processor and the batch processor exchange the batch processor, so that the batch processor is prevented from selecting two batch numbers to exchange the batch processor or exchanging the sequence of the two batch numbers under a random strategy through batch movement optimization (BMS 1), the largest finishing time at a modeling process is reduced, and the convergence of an algorithm is improved.
Specifically, the batch movement optimization (BMS 1) includes BMS1a and BMS1b.
BMS1a: for the non-related batch processor scheduling of inconsistent smelting tasks and simultaneous arrival of tasks, moving a minimum work time batch B b in the batch processor M i with the maximum finishing time in the scheduling scheme to the batch processor M j for processing, and if the condition is met: the minimum lot B b at M j has a processing time less than the total processing time difference between M i and M j, and the maximum completion time of the new schedule generated by the exchange is less than the original schedule.
The demonstration process of BMS1a is as follows: the two independent batch processors M 1、M2 are arranged in the dispatching scheme, the finishing time is C max1、Cmax2, and the batch processor M 1 has the maximum finishing time, namely: c max1>Cmax2, setting a lot B b as a lot with the shortest processing time on M 1, wherein the processing time on M 1、M2 is t 1、t2 respectively, and the relation t 2<Cmax1-Cmax2 is t 2+Cmax2<Cmax1, and max { C max1-t1,Cmax2+t2}<Cmax1, so that the maximum finishing time of new dispatching is smaller than that of the original dispatching scheme.
In the embodiment shown in fig. 2, one possible solution for the modeling procedure is x 1 = [2,1,3|1,1,2], and the optimized schedule of BMS1a is shown in fig. 13, which shows that the optimized schedule is shortened by 1 unit time.
Specifically, BMS1b: for irrelevant batch processor scheduling where tasks are not consistently melted and arrive at the same time, one of the batch processors M i with the largest finishing time in the scheduling scheme, batch B b, is exchanged with batch B b' with the smallest batch time of batch processor M j, if the conditions are met: processing time B b at M i is greater than B b', and the absolute value of the difference between processing times B b and B b' at M j is less than the total processing time difference between M i and M j, then the maximum completion time of the new schedule resulting from the exchange is less than the original schedule.
The demonstration process of BMS1b is as follows: assuming that there are two independent batch processors M 1、M2 and C max1、Cmax2 for the completion time in the scheduling scheme, wherein batch processor M 1 has the maximum completion time, set batch B b as the batch with the maximum processing time on M 1, the processing time on M 1、M2 is t 1、t2 respectively, batch B b' as the batch with the minimum processing time on M 2, and the processing time on M 1、M2 is t 1、t2 respectively, the following relationship t 1>t1,|t2-t2|<Cmax1-Cmax2 is satisfied, then C max1-t1+t1<Cmax1 and C max2+|t2-t2|<Cmax1, so the maximum completion time of the new scheduling is smaller than the original scheduling scheme.
By combining BMS1a and BMS1b and borrowing the concept of recursion, a strategy that new scheduling is absolutely better than old scheduling at the modeling procedure is provided as long as BMS1a or BMS1b is satisfied. The invention designs a batch movement optimization (BMS 1) which is absolutely optimized after meeting theorem conditions by BMS1a and BMS1b, wherein the batch movement optimization (BMS 1) comprises the following specific steps:
step ①, selecting a batch processor with the largest finishing time from XD sequences corresponding to a solution X, and marking the batch processor as Mmax and the processing time as Tmax; selecting a batch processor with minimum finishing time, marking the batch processor as Mmin, and marking the processing time as Tmin;
Step ②, selecting a lot number with the minimum processing time from Mmax, and moving the lot number to mman for processing, wherein the formed solution is denoted as X;
step ③, recalculating the time on the batch processors Mmax and Mmin to be T 'max and T' min respectively;
step ④, if max { T 'max, T' min } -is less than or equal to Tmax, updating X with X, and entering the next round of optimization process;
Step ⑤, if the condition of step ④ is not satisfied, selecting a lot number with the largest processing time on Mmax, and simultaneously selecting a lot number with the smallest processing time on mman, and exchanging batch processors for the largest lot number and the smallest lot number, wherein the formed solution is X;
step ⑥, repeating the steps ③ to ④;
Step ⑦, the condition in step ④ is not satisfied twice in succession, ending the optimization process;
In step ⑧, update solution X is subjected to steps ① through ⑦.
The application of the batch movement optimization (BMS 1) avoids the optional two batch exchange batch processors or the batch sequence exchange under a random strategy, so that the search space of the algorithm is greatly reduced, the running time of the algorithm is saved, and the convergence performance of the algorithm is improved. Both steps ③ and ⑤ are considered, in a recursive fashion, again with the aim of reducing the search space.
Step 8), all batch numbers corresponding to the same batch processor in the XD sequence corresponding to the update solution X are subjected to batch merging optimization (BMS 2), and the dispatching completion time of the single batch processor is reduced by reducing the number of batches on the single batch processor.
On a single batch dispatch, the smaller the number of batches means the shorter the dispatch completion time. The specific steps of the batch merge optimization (BMS 2) are as follows:
Step ①, combining all batch numbers corresponding to each sandbox type in the XD sequence corresponding to one solution X in C i 2;
Step ②, traversing the batch numbers combined together in step ①, if the size of the existing sandbox type is not less than the sum of the sizes of all the workpieces in the two batches after the two batch numbers are combined, selecting the sandbox type with the smallest size in preference, and the sum of the masses of all the workpieces in the two batch numbers is not greater than the maximum capacity of the melting furnace, combining the two batches into a new batch, removing the two batch numbers from the combination, returning to step ① until all the combinations are traversed, and entering the next step;
In step ③, the updated solution X goes through steps ① to ②, and the optimization process is ended.
After the feasible solution x 1 is optimized by the BMS2, the first matching rule of the incompatible workpiece group is analyzed to be x 1 = [2,3,1|2,2,1], and the comparison of the glycerin bit diagrams before and after the optimization is shown in fig. 14, so that the scheduling is shortened by 2.5 unit time after the optimization.
Since batch merge optimization (BMS 2) only merges batches of the same type of workpiece family batches that meet the sandbox size constraint and the melting furnace maximum capacity constraint, no optimization process is performed for the batch processor selection. After the batch merge optimization (BMS 2) is performed on solution X, the total processing time of the batch processor is reduced based on the specificity of the batch processing time in the invention (the batch processing time is only related to the sandbox type corresponding to the batch and the batch processor processing the batch), but there is a high possibility that a batch with a large sandbox size on a certain batch processor is concentrated, and the total completion time of dispatching at the modeling process may not be optimized. Therefore, the batch merge optimization (BMS 2) and the batch move optimization (BMS 1) need to be combined, and the genes optimized by the batch merge optimization (BMS 2) are optimized again by the batch move optimization (BMS 1), so that the batch in the solution X is more reasonable in the process of distributing the batch processor, and the maximum finishing time at the process is optimized.
And 9), optimizing the optimal solution X= [ XB|XD ], namely the optimal batch scheduling scheme for smelting and forming the discrete manufacturing irrelevant workpieces.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (8)
1. A batch scheduling method for discrete manufacturing of unrelated workpieces, comprising the steps of:
step 1), according to the characteristics of different sizes of workpieces and incompatibility of workpiece groups in discrete manufacturing, making an assumption on batch processing scheduling environments of smelting and forming of irrelevant workpieces;
Step 2), respectively establishing a minimum total batch quantity objective function (1), a minimum average empty rate objective function (2) and a minimum finishing time objective function (3) aiming at batch processing scheduling of smelting and forming of irrelevant workpieces;
step 3), constraining parameters in the minimum total batch number objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) according to the actual conditions of the site;
Step 4), solving the objective function (1) for minimizing the total lot number, the objective function (2) for minimizing the average empty rate and the objective function (3) for minimizing the finishing time, wherein one solution is a scheduling scheme, and each solution is set to be in a form of X= [ XB|XD ], wherein XB is a sequence formed by batch numbers, and XD is a sequence formed by sandbox type numbers corresponding to the batch numbers in the XB one by one;
Step 5), dividing all solutions X of the minimum total batch quantity objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) into two parts, wherein one part of solutions adopts a heuristic algorithm to generate a feasible solution, and the other part of solutions adopts a random algorithm to generate a random solution;
Step 6), carrying out cross update and mutation update on the XB sequence and the XD sequence in the feasible solution and the random solution according to a virus gene update mode to obtain an update solution X, and enriching the diversity of the solution;
Step 7), moving the batch number with the minimum working time corresponding to the batch processor with the maximum finishing time in the XD sequence corresponding to the updated solution X to the batch processor with the minimum finishing time for processing; or selecting the batch number with the largest working time corresponding to the batch processor with the largest finishing time from the XD sequence, and simultaneously selecting the batch number with the smallest working time corresponding to the batch processor with the smallest finishing time from the XD sequence, and exchanging the batch processors;
step 8), carrying out batch merging optimization on all batch numbers corresponding to the same batch processor in the XD sequence corresponding to the updated solution X;
and 9), optimizing the optimal solution X= [ XB|XD ], namely the optimal batch scheduling scheme for smelting and forming the discrete manufacturing irrelevant workpieces.
2. The batch scheduling method for discrete manufacturing unrelated workpieces as claimed in claim 1, wherein in step 1), the assumption made comprises:
a, when the moment is zero, all workpieces are reached and prepared, different types of sandboxes are prepared, and each batch processor can be used;
b. In each dispatching scheme, each workpiece is distributed to different workpiece groups, each workpiece group is divided into different batches of work according to the modeling procedure of the workpiece, each batch of work is distributed with one type of sandboxes, the total batch number is the sum of the different types of sandboxes, and each batch of work can only be processed once at most on a batch processor;
c, the quantity of different types of sandboxes used in the scheduling process is enough;
d, the weight of all the jobs in the sandbox has no influence on the selection of the sandbox type;
e, the number of the workpieces contained in each batch of operation can be different;
f, once each batch processor starts working, the batch processor cannot be interrupted, the operation is not allowed to be added or deleted in batch processing, and each batch processor can only process one batch of operation at a time;
g, irrespective of the waiting time of each batch processor between the previous batch and the next batch;
h, each batch processor can process all types of sandboxes;
i, the total finishing time of each scheduling scheme is from the first batch job starting time to the last batch job ending time.
3. Batch scheduling method for discrete manufacturing unrelated workpieces according to claim 2, characterized in that in step 2) the minimum total lot number objective function (1), the minimum average empty rate objective function (2) and the minimum finishing time objective function (3) are respectively:
min f1＝ng (1)
Wherein,
F 1 is the total lot number in the scheduling scheme,
N g is the total number of lots in the dispatch protocol,
F 2 is the average empty rate of all sandboxed types for batch processing,
Y bv is a decision variable, which is used to determine the decision,
N d is the total number of sandboxed types,
O Dv is the sandbox size for sandbox type Dv,
Dv is the v-th sandbox type,
S Bbt is the sum of all the job sizes of lot B b,
B b is the B-th batch,
X ib is a decision variable that is used to determine,
A it is a decision variable that is used to determine,
S i is the size of the i-th job,
N is the number of jobs to be performed,
F 3 is the total completion time of the scheduling scheme,
M is the total number of batch processors,
C k is the total processing time of the kth batch processor,
Y bv is a decision variable, which is used to determine the decision,
Z bk is a decision variable, and,
T kv is the processing time of the kth batch processor to process the v-th sandbox type Dv.
4. A batch scheduling method for discrete manufacturing unrelated workpieces as claimed in claim 3, wherein in step 3), said constraints comprise:
Wi≤Q,i∈[1,n] (9)
Si≤ODv,i∈[1,n],v∈[1,nd] (10)
WBbt≤Q,b∈[1,ng] (12)
SBbt≤ODvYbv,b∈[1,ng] (13)
Wherein,
Equation (4) shows that if workpiece J i is assigned to lot Bb, then X ib =1, otherwise, X ib =0,
Equation (5) shows that if workpiece J i is assigned to the t-th incompatible workpiece family Ut, a it =1, otherwise a it =0,
In equation (6), M k is the kth BPM, BPM is the batch processor, equation (6) indicates that if the batch Bb is assigned to the kth batch processor, Z bk = 1, otherwise, Z bk = 0,
Equation (7) shows that if the lot Bb is assigned to sandbox Dv, then Y bv =1, otherwise Y bv =0,
In equation (8), n l is the total number of incompatible workpiece families Ut, equation (8) indicates that each batch can only be in one workpiece family at most,
In the formula (9), W i is the weight of the job J i, Q is the maximum capacity of the melting furnace, the formula (9) indicates that the weight of each job does not exceed the maximum capacity of the melting furnace,
In equation (10), S i is the size of job J i, equation (10) indicates that the size of each job does not exceed the maximum size of sandboxes provided,
In equation (11), W Bbt is the sum of all the job weights for lot B b,
Equation (12) shows that the sum of all the operating weights of batch B b does not exceed the maximum capacity of the melting furnace,
Equation (13) shows that the sum of all job sizes for lot B b does not exceed the maximum size of the sandboxes provided.
5. The batch scheduling method for discrete manufacturing unrelated workpieces as claimed in claim 4, wherein in step 5), the step of heuristically generating is:
Step ①, carrying out batch classification on all the operations strictly according to the workpiece family information, wherein the batch number is marked as S j;
Step ②, starting from the first job in the lot number S j, randomly selecting a sandbox capable of boxing the first job, placing the sandbox type at the corresponding position in the XD sequence, and for other jobs in the lot number S j, establishing a new lot number if the following conditions are met:
a. inserting a job into the current lot number violates the constraint of the incompatible workpiece family of equation (8);
b. inserting workpieces into the current lot number violates the sandbox size constraint of equation (10) and equation (13);
c. inserting workpieces into the current lot number violates the furnace capacity constraints of equation (9) and equation (12);
Step ③, repeat step ② until all jobs in lot number S j are completed in batches.
6. The batch scheduling method for discrete manufacturing unrelated workpieces as claimed in claim 5, wherein: in the step 6), the cross updating comprises the steps of respectively adopting an order cross, a linear order cross, a position-based cross, a sequence-based cross and a priority operation cross to the XB sequence, and further comprises the steps of respectively adopting a two-point cross, a multi-point cross and a uniform two-point cross to the XD sequence; the mutation update includes respectively performing interactive mutation, frame shift mutation, inversion mutation, insertion mutation and displacement mutation on the XB sequence and the XD sequence.
7. The batch dispatch method of discrete manufacturing independent workpieces of claim 6, wherein in step 7), the specific steps of batch movement optimization are as follows:
step ①, selecting a batch processor with the largest finishing time from XD sequences corresponding to a solution X, and marking the batch processor as Mmax and the processing time as Tmax; selecting a batch processor with minimum finishing time, marking the batch processor as Mmin, and marking the processing time as Tmin;
Step ②, selecting a lot number with the minimum processing time from Mmax, and moving the lot number to mman for processing, wherein the formed solution is denoted as X;
step ③, recalculating the time on the batch processors Mmax and Mmin to be T 'max and T' min respectively;
step ④, if max { T 'max, T' min } -is less than or equal to Tmax, updating X with X, and entering the next round of optimization process;
Step ⑤, if the condition of step ④ is not satisfied, selecting a lot number with the largest processing time on Mmax, and simultaneously selecting a lot number with the smallest processing time on mman, and exchanging batch processors for the largest lot number and the smallest lot number, wherein the formed solution is X;
step ⑥, repeating the steps ③ to ④;
Step ⑦, the condition in step ④ is not satisfied twice in succession, ending the optimization process;
In step ⑧, update solution X is subjected to steps ① through ⑦.
8. The batch dispatch method of discrete manufacturing independent workpieces of claim 7, wherein in step 8), the specific steps of batch merge optimization are as follows:
Step ①, performing all batch numbers corresponding to each sandbox type in the XD sequence corresponding to one solution X Is a combination of (a);
Step ②, traversing the batch numbers combined together in step ①, if the size of the existing sandbox type is not less than the sum of the sizes of all the workpieces in the two batches after the two batch numbers are combined, selecting the sandbox type with the smallest size in preference, and the sum of the masses of all the workpieces in the two batch numbers is not greater than the maximum capacity of the melting furnace, combining the two batches into a new batch, removing the two batch numbers from the combination, returning to step ① until all the combinations are traversed, and entering the next step;
In step ③, the updated solution X goes through steps ① to ②, and the optimization process is ended.
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