CN116070826A - Scheduling method for parallel machine of spraying operation of wagon body - Google Patents
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Abstract
The invention discloses a parallel machine scheduling method for spraying operation of a wagon body, relates to the technical field of spraying operation, establishes a parallel machine scheduling model, establishes a model objective function with a minimum maximum finishing time objective, and designs a model solving method based on a sea squirt swarm algorithm; the goblet sea squirt swarm algorithm has high robustness, the parameters are simple and easy to operate, a new population initialization mode is adopted for incompatible operation families, the initial overall quality is improved, a plurality of neighborhood search strategies are adopted, the quality of solutions is further improved, and the convergence speed of the algorithm is accelerated; when the obtained scheduling method is used for spraying operation, the spraying efficiency and character spraying quality of the automatic spraying machine can be improved, and the intervention of human resources is reduced.
Description
Technical Field
The invention belongs to the technical field of spraying operation, and particularly relates to a scheduling method of a parallel machine for spraying operation of a wagon body.
Background
The parallel machine scheduling problem (Parallel Machine Scheduling Problem, PMSP) belongs to a typical problem with higher complexity in the actual production process. It can be described as n workpieces being processed on m machines, each workpiece only requiring one processing on the machine, and the optimal processing batch is solved to minimize the total processing time. Similar to shop scheduling, once processing begins, jobs in a lot cannot be increased or decreased.
The truck body spraying operation has complex process types and various processes, is a key process for shipping the truck carriage, and the spraying quality and the spraying efficiency of the truck body spraying operation directly influence the productivity of the whole truck industrial chain. A plurality of constraint factors exist in the spraying process of a spraying workshop, such as the number of characters, the types, the roughness of the carriage surface, the number of props and the like; in addition, the spraying parameters of the automatic spraying machine influence the quality of the spraying process, such as the air inflow of a spray head air pump, the distance between the spray head and a carriage and the like, can be automatically adjusted through built-in software; however, due to the limitation of the range of automatic spraying, when the automatic spraying machine sprays characters with different end faces and characters with different character sizes, the automatic spraying machine needs to be moved and the spraying parameters are reset, and the manual intervention is still needed to bring a lot of uncertain factors for scheduling schemes. Therefore, the quality of character spraying is improved while the spraying efficiency of the automatic spraying machine is improved, and the reduction of human resource intervention is important.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a dispatching method of a parallel machine for spraying operation of a wagon body, which aims at minimizing the maximum finishing time target to establish a model objective function and designs a model based on a sea squirt swarm algorithm to solve the model; the goblet sea squirt swarm algorithm has high robustness, simple parameters and easy operation, adopts a new population initialization mode for incompatible operation families, improves the initial overall quality, adopts various neighborhood search strategies, further improves the quality of solutions, and accelerates the convergence speed of the algorithm.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for scheduling a parallel machine for spraying operation of a wagon body comprises the following steps:
s1, a parallel machine scheduling model is established according to the characteristics of a truck spraying procedure, and the scheduling model comprises:
1.1, reasonably supposing a scheduling model;
1.2 setting parameters and decision variables;
1.3, constructing an objective function of a scheduling model;
s2, optimizing and calculating an objective function based on the goblet sea squirt swarm algorithm;
2.1, collecting data to be processed, and regarding each type size with spray characters as a processing task, wherein spray guns of different types are regarded as different spray machines;
2.2, converting the data to be processed by adopting a double-layer coding mode of a procedure coding OS and a machine coding MS, and converting the scheduling model into a mathematical model, namely converting the mathematical model into a mathematical problem which can be calculated;
2.3 setting parameters of the goblet sea squirt swarm algorithm, and initializing the swarm according to the coding mode of the step 2.2;
2.4, calculating the fitness value of the group of the ascidians in the goblet, sequencing, and selecting the leader with the best fitness and the follower as the other members;
2.5, the leader performs neighborhood search, the follower performs follow-up motion, the population is reordered, and updating iteration of the individual is completed;
2.6 repeating the step 2.5 until the maximum iteration times are reached, obtaining a current population optimal scheme, namely an optimal solution of a mathematical model, namely an optimal solution of a scheduling model, and an optimal solution of a scheduling model objective function;
s3, comparing and verifying the effectiveness of the scheduling model and the algorithm. Specifically, by comparison with a scheduling scheme based on a minimum process time principle: machining with the minimum machining time is selected in all working procedures, namely, the MS part of each working procedure is determined, and a machining scheme is obtained by optimizing the working procedure arrangement part of each working procedure; and then comparing with the scheduling method obtained by the invention, and verifying the effectiveness of the scheduling method.
The shortest machining time means that the machining machine of each process selects the machine with the shortest machining time among the selectable machines, in comparison with the machining scheme based on the shortest machining time.
The reasonable assumption of the scheduling model in step 1.1 includes:
(1) the spraying task of each character size of each character is independent and is not influenced by other spraying tasks;
(2) the spraying operation of the same end face does not exceed the working space of the automatic spraying machine;
(3) each job task can only be processed in one parallel machine at most;
(4) each batch of products can only be processed once at most on a parallel machine;
(5) considering the time of moving the automatic spraying machine when spraying different end face characters;
(6) considering parameter changing time of automatic spraying machine software when spraying different character size working procedures;
(7) in static shop scheduling, assuming that 4 different caliber guns spray 64 different size characters, the machines and workpieces in the shop need to meet the following constraints:
(1) Pre-designating a workpiece machining process;
(2) The machine can only process one workpiece at a time;
(3) If there is no special case, each workpiece has equal process priority;
(4) The processing time and machine specified in advance must not be changed.
The parameters and decision variables in step 1.2 include:
the objective function in step 1.3 is:
minC max ＝min[max(C j )] (1)
the constraint conditions are as follows:
C ijk ≤S ghk +M(1-γ ijghk ) (5)
wherein, the formula (1) represents that the maximum finishing time of the workpiece is minimum, namely the finishing time of the last finishing procedure is minimum; the formula (2) shows that the manual moving trolley in the dispatching has minimum time, namely the use amount of human resources is minimum, and for an automatic spraying process, the manual investment is the variable cost, so that the method is the main direction of enterprise cost control; formula (3) shows that one process can be processed by only one machine; equation (4) represents a next process in which the workpiece can be machined only by the previous process in which the workpiece is machined; equation (5) shows that one machine can be occupied by only one process at a time.
The steps 1.1-1.3 are the steps of the process for establishing the parallel machine scheduling model, and parameters, decision variables, constraint conditions and objective functions jointly form the parallel machine scheduling model.
In step 2.2, the first layer process coding scheme:
the initial individual adopts Logistic chaotic mapping iterative equation to obtain the sequence of process codes, chaos is an unstable phenomenon spontaneously generated by a deterministic system, and the method can not repeatedly go through all states in a certain range, and has more superiority than blind random search by utilizing chaos variables to perform optimal search. Logistic chaotic mapping stack
The substitution equation is: y (k+1) =μy (k) (1-y (k)), k=1, 2..n (6)
x j ＝u j +z nj (v j -u j ) (7)
In the formula (6), y (k) is the value of a chaotic variable in the kth iteration, k is the number of iterations, and mu is a parameter; when the value of the parameter mu is 4, the Logistic mapping is in a complete chaotic state, and a good result can be obtained.
In the formula (7), v j And u j Upper and lower bounds, x, respectively, of the j-th dimensional variable value j Representing the value of the j-dimensional component;
defining individual dimension as m, population scale as N, randomly generating m-dimension initial sequence z 1 ＝(z 11 ,z 12 ,...,z 1m ) Iterating each component in the initial sequence through a formula (6) to obtain an initial chaotic sequence matrix; then transforming the initial chaotic sequence matrix to a variable interval of a target problem through a formula (7) to complete initial chaotic mapping; generating a group of random variables, obtaining a chaotic vector after multiple iterations of a formula (6), and mapping the chaotic vector into a display code through a formula (7) to obtain an individual OS partial code x= (x) 1 ,x 2 ,...,x m )。
The generation rules for population initialization are demonstrated by applying a Logistic chaotic mapping iterative equation to an example of 3 work piece 3 procedures, as shown in the following table.
TABLE 1 Process coding
The processing sequence obtained by decoding the coding sequence shown in Table 1 is O 11 O 12 O 31 O 21 O 32 O 22 O 23 O 33 O 13 . Wherein O is ij I represents a workpiece, and j represents a process. O (O) ij The process j representing the workpiece i is processed in this order.
In step 2.2, the second layer machine coding scheme: the machine selection portion of the initial individual employs a hybrid mechanism wherein 50% of the individuals are generated by means of formulas (6) and (7), and 50% of the individuals are selected by the shortest processing time principle according to the mechanism of the least processing time within the machine table, and the MS portion of the machine selection is encoded. The proportion can be arbitrary, and an orthogonal test can be added to verify the influence of different parameters on the convergence speed of the algorithm so as to find the optimal proportion.
For example, with a 3×3 scale shop scheduling problem, the following diagram is shown: the OS portion is the order in which the workpieces appear, the j-th occurrence of workpiece i represents the process, and the position of the corresponding MS portion is the machine order within its selectable range. The coding mode can ensure all constraints of the model and is widely applied to solving FJSP problems.
OS part
MS part
3 x 3 Scale problem encoding examples
In step 2.3, the parameters of the sea squirt swarm algorithm include a maximum number of iterations T max Maximum iteration number and population size of the variable neighborhood search, etc.
In the step 2.4, taking the minimum maximum finishing time and the maximum human resources as optimization targets, judging the end face conditions of the front and back processing procedures on the same machine when calculating the individual fitness value of the sea squirt, and calculating the required human interference; the multi-objective problem is processed using the Parto ordering method, resulting in a set of near optimal solutions, with all non-dominant solutions in the Pareto solution set as the leader and other solutions as the follow-up. The Pareto-based multi-objective processing method can provide a group of approximate optimal solution sets for a decision maker, and can effectively improve the optimization efficiency.
In the step 2.5, POX crossing and four neighborhood search operators are introduced to complete iterative updating of the goblet sea squirt population; the POX crossing method comprises the following steps:
(1) Randomly generating a proper subset omega of the workpiece coding types for the crossed two father individuals and the crossed father individuals;
(2) Removing elements belonging to omega in one parent to form new offspring, sequentially inserting elements belonging to the set in the other parent into the new offspring according to the arrangement sequence of the parent to form crossed individuals;
(3) Performing the same operation on the other parent according to the method in (2) above; specifically, removing elements belonging to omega in another parent to form another new child, and sequentially inserting elements belonging to the set in one parent in the step (2) into the other new child according to the arrangement sequence of the parent to form crossed individuals;
the MS part moves along with the OS part in position;
the four domain search structures are as follows:
(1) Domain structure N1: two points are turned over, two points are arbitrarily selected, and elements between the two points are turned over;
(2) Domain structure N2: two-point exchange, namely arbitrarily selecting two points and exchanging elements of the two points;
(3) Domain structure N3: a single point insert, arbitrarily selecting a point, inserts the point and subsequent elements before the first element.
(4) Domain structure N4: critical path movement, which refers to the machining process on the machine with the greatest finishing time, optimizes the target value by modifying the machining machine for these processes or by interchanging the process positions on other machines.
Finishing the four search strategies for leaders in the goblet sea squirt population, reserving the best individuals and putting the best individuals into the population; and (3) performing POX cross selection on other followers and the goblet sea squirts arranged in the previous Pareto grade respectively, selecting the remained individuals, performing one of the four neighborhood search strategies on the individuals, selecting the best individuals as the next generation, obtaining the iterated goblet sea squirt group, and sorting the iterated goblet sea squirt group to select a new leader and the goblet sea squirt arrangement sequence.
Firstly, a parallel machine scheduling model is established, the characteristics of the problem are described through simple parameters and formulas, the problem cannot be directly solved, then the model is converted into a mathematical model through the coding and decoding method, the mathematical model becomes a mathematical problem which can be calculated, and the mathematical problem is solved through a goblet sea squirt algorithm.
Wherein, the sea squirt is a marine invertebrate organism, the whole body is transparent, and the sea plankton is eaten, and the sea squirt is quite similar to jellyfish, and water is pumped into the body as the forward moving propelling force. In the ocean depths, the sea-goblet moves forward in a chain-like action, connecting individuals end to form a "chain", with half of the sea-goblet's number in the chain acting as a leader and the other half as followers. The leader guides the follower to move forward, and gradually searches for the food source with increasing iteration times. Because the followers move strictly according to a 'level system', the followers are only influenced by the behavior of the former sea squirt, so that the sea squirt has strong global searching capability and local development capability. The content of the standard ecteinascidial group algorithm is as follows:
(1) Population initialization
X D×N ＝lb+rand(D,N)×(ub-lb) (1-1)
Let the search space be the euclidean space of D x N, D representing the spatial dimension and N representing the population size. In the formula (1-1), ub= [ ub ] 1 ,ub 2 ,...ub D ]Representing the upper limit of the search space, lb= [ lb 1 ,lb 2 ,...lb D ]Representing the lower limit of the search space, rand (D, N) represents random numbers uniformly distributed between 0 and 1 for D rows and N columns, and a matrix such as that represented by equation (1-2) is generated during population initialization. Wherein the jth ecteinascidiphyllum unit can be represented as
(1) Leader location update
During the movement and food finding process of the goblet sea squirt chain, the leader position update formula is as follows:
wherein c 1 、c 2 、c 3 To control parameters F d Indicating the current food position in d-dimensional space. As can be seen from formulas (1-3), the position change of the leader is only related to the position of the food, c 2 、c 3 Is in [0,1 ]]A random number acquired in the interval c 2 Determining step length, c 3 Determining the leader's direction of progress, and c 1 Is the most important parameter, which directly determines the searching capability and the developing capability of the optimization algorithm of the sea squirt group in the whole iteration process, c 1 The calculation formula of (2) is as follows:
where T represents the current algebra and T represents the maximum number of iterations.
(3) Follower position update
In the movement process of the sea squirt chain, the follower moves forwards in a chain shape under the influence of the front and back individuals and moves forwards along with the position of the leader, and according to the structural feature analysis of the sea squirt, the position update of the follower accords with Newton's law of movement, namely the position of the sea squirt only matches with the initial speed (v 0 ) Acceleration (a), movement time (t * ) Related to the following. The follower position formula is thus as follows:
the standard goblet-sea squirt algorithm aims at solving the discrete problem, wherein the iterative moving process is applicable to the structure of the discrete problem, cannot directly process the scheduling problem of a workshop and needs to be improved on the basis of the original method.
Compared with the prior art, the invention has the beneficial effects that: establishing a model objective function with a minimum maximum finishing time target, and designing a model based on a goblet-sea squirt swarm algorithm; the goblet sea squirt swarm algorithm has high robustness, simple parameters and easy operation, adopts a new population initialization mode for incompatible operation families, improves the initial overall quality, adopts various neighborhood search strategies, further improves the quality of solutions, and accelerates the convergence speed of the algorithm. When the obtained scheduling method is used for spraying operation, the spraying efficiency and character spraying quality of the automatic spraying machine can be improved, and the intervention of human resources is reduced.
Drawings
FIG. 1 is a diagram of a complete optimal schedule Gantt chart in a preferred embodiment of the present invention;
FIG. 2 is a graph of a scheduled Gantt chart implemented according to a process time minimization principle;
FIG. 3 is a graph showing the comparison of processing time in a preferred embodiment of the present invention;
FIG. 4 is a Pareto solution set in the last iteration in a preferred embodiment of the present invention;
FIG. 5 is a flowchart of GWO drawn according to the steps of the operation of the ascidian algorithm in accordance with the preferred embodiment of the present invention;
FIG. 6 is an analysis flow of dynamic spraying in a preferred embodiment of the invention;
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments. 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.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention will be further illustrated, but is not limited, by the following examples.
A method for scheduling a parallel machine for spraying operation of a wagon body comprises the following steps:
s1, a parallel machine scheduling model is established according to the characteristics of a truck spraying procedure, and the scheduling model comprises:
1.1, reasonably supposing a scheduling model;
1.2 setting parameters and decision variables;
1.3, constructing an objective function of a scheduling model;
the steps 1.1-1.3 are the steps of the process for establishing the parallel machine scheduling model, and parameters, decision variables, constraint conditions and objective functions jointly form the parallel machine scheduling model.
S2, optimizing and calculating an objective function based on the goblet sea squirt swarm algorithm;
2.1, collecting data to be processed, and regarding each type size with spray characters as a processing task, wherein spray guns of different types are regarded as different spray machines;
2.2 adopting double-layer coding of procedure coding OS and machine coding MS to convert the scheduling model into a mathematical model, namely converting the mathematical model into a mathematical problem which can be calculated;
2.3 setting parameters of the goblet sea squirt swarm algorithm, and initializing the swarm according to the rules of the step 2.2;
2.4, calculating the fitness value of the group of the ascidians in the goblet, sequencing, and selecting the leader with the best fitness and the follower as the other members;
2.5, finishing updating iteration of the individual;
2.6 repeating the step 2.5 until the maximum iteration times are reached, obtaining the current population optimal scheme as an optimal solution, namely an optimal solution of a mathematical model, namely an optimal solution of a scheduling model, and an optimal solution of a scheduling model objective function.
The parallel machine scheduling model describes the characteristics of the problem through simple parameters and formulas, and can not be directly solved, then the model is converted into a mathematical problem which can be calculated through the encoding and decoding method, and the mathematical problem is solved through the goblet sea squirt algorithm.
Wherein the specific parameters and decision variables include:
the objective function is:
minC max ＝min[max(C j )] (1)
wherein, the formula (1) represents that the maximum finishing time of the workpiece is minimum, namely the finishing time of the last finishing procedure is minimum; equation (2) represents that the manual movement of the trolley in the dispatching has minimum time, that is, the use amount of human resources is minimum, and for the automatic spraying process, the manual input is the variable cost, which is the main direction of enterprise cost control.
The constraint conditions are as follows:
C ijk ≤S ghk +M(1-γ ijghk ) (5)
wherein, the formula (3) represents that one working procedure can be processed by only one machine; equation (4) represents a next process in which the workpiece can be machined only by the previous process in which the workpiece is machined; equation (5) shows that one machine can be occupied by only one process at a time.
Taking a certain truck spraying factory batch spraying operation as an example, fig. 1-6:
step 1: the original machining schedule and the corresponding machining schedule were obtained from data obtained from a truck spray factory investigation, as shown in tables 2 and 3.
Table 2 processing machine table
Table 3 processing schedule
Step 2: the data from step 1 can be used to obtain 69 spraying tasks, that is, each individual is double-layer coded according to the description of the double-layer coding, and is respectively sequence and machine selection, the sequence part coding rules are shown in the table 1, the codes 1-69 are sequence, the codes 70-138 are machine selections, the machine selection part coding means the sequence number of the optional machine of the sequence, for example, a certain optional machine set [ 13 ] 4, and if the corresponding machine selection part coding is 2, the process is processed by the machine 3 when decoding. That is, the individual length of one goblet sea squirt in the algorithm is 138, wherein the first 69 codes represent the processing sequence of 39 workpieces, the last 69 codes represent the machine selection of 69 processing tasks, 50% of the individual machines have the shortest processing time in the task selection machines according to the machine selection part generation rule, and the other 50% of the individual machines have the random selection machines according to the chaos vector in the selection machine set, so that the following code example table is obtained. The above ratio may be arbitrary, and an orthogonal test may be added to verify the influence of different parameters on the convergence speed of the algorithm to find the optimal ratio.
Coding example table
The coding meaning is according to the above table that O ij I represents a workpiece, and j represents a process. O (O) ij The process j representing the workpiece i is processed in this order. For example O 11 M 4 : the first bit 1 of the OS portion is representative of workpiece 1, the second bit 1 is representative of process 1, i.e., the 1 st process of workpiece 1, the corresponding 70 th bit MS portion is 4, representative of the process selecting the 4 th process in its machine set, and so on.
Step 3: setting parameters of the goblet sea squirt algorithm, setting a population scale to be 100, namely, an initial population comprises 100 individuals with the length of 138, obtaining an initial processing sequence according to the decoding mode, calculating the maximum processing time of each individual, updating the target value of each individual in the goblet sea squirt group, selecting non-dominant solutions in Pareto solutions as leaders of the population, and selecting the rest of individuals as followers.
Step 4: obtaining 4 neighborhood individuals from a leader in a neighborhood searching mode, and selecting the best one to put back to the population; obtaining a new individual by using a POX crossing mode for the follower and the previous individual, and randomly selecting one of 4 field structures for the individual after POX crossing selection to perform mutation operation; when all individuals in the population are updated, the individuals are reordered according to the target value, and a new leader is selected.
Step 5: and (4) repeating the iteration step, wherein when the maximum precision or the maximum iteration times are reached, the iteration is completed, the output result is the optimal solution, and otherwise, the loop execution is continued.
Wherein, FIG. 1 is a complete optimal scheduling Gantt chart of the embodiment, and the ordinate represents automatic spraying machines with calibers of 0.5mm, 0.6mm, 0.8mm and 1.0mm respectively; time units of the Gantt chart are represented on the abscissa. The project completion time was 147 and the mobile machine time was 66.
Fig. 2 is a gante diagram of a scheduling scheme decoded on the basis of minimum processing time, with a scheme completion time of 166.7 and a mobile machine time of 116. Compared with the prior art, the scheduling method has higher efficiency and can save more manpower resources.
Fig. 3 records the optimal solution for each iteration in the iteration process, the abscissa represents the iteration number of the algorithm, and the ordinate represents the values of the two target values of the target function formula (1) and the target function formula (2) in each iteration process. Taking one solution in the Pareto solution set as the optimal result of the generation, it can be seen that the optimal scheme in the initial population takes more than 200 seconds, and the optimal processing path can be found by only overlapping for more than 50 generations after calculation through the algorithm, and the time is only 147 seconds; the mobile machine time is also optimized from the first 100 to the last 60, which greatly saves processing time and scheduling time.
Fig. 4 records all non-dominant solutions of the Pareto solution set in the last iteration, which are mutually non-dominant on both targets for the manager to choose according to the actual needs.
The foregoing is merely illustrative of the preferred embodiments of the present invention and is not intended to limit the embodiments and scope of the present invention, and it should be appreciated by those skilled in the art that equivalent substitutions and obvious variations may be made using the teachings of the present invention, which are intended to be included within the scope of the present invention.
Claims (10)
1. A method for scheduling a parallel machine for spraying operation of a wagon body is characterized by comprising the following steps:
s1, a parallel machine scheduling model is established according to the characteristics of a truck spraying procedure, and the scheduling model comprises:
1.1, reasonably supposing a scheduling model;
1.2 setting parameters and decision variables;
1.3, constructing an objective function of a scheduling model;
s2, optimizing and calculating an objective function based on the goblet sea squirt swarm algorithm;
2.1, collecting data to be processed, and regarding each type size with spray characters as a processing task, wherein spray guns of different types are regarded as different spray machines;
2.2, converting the data to be processed by adopting a double-layer coding mode of a procedure coding OS and a machine coding MS, and converting the scheduling model into a mathematical model;
2.3 setting parameters of the goblet sea squirt swarm algorithm, and initializing the swarm according to the coding mode of the step 2.2;
2.4, calculating the fitness value of the group of the ascidians in the goblet, sequencing, and selecting the leader with the best fitness and the follower as the other members;
2.5, the leader performs neighborhood search, the follower performs follow-up motion, the population is reordered, and updating iteration of the individual is completed;
2.6 repeating the step 2.5 until the maximum iteration times are reached, obtaining the current population optimal scheme, namely, the optimal solution of the mathematical model, namely, the optimal solution of the scheduling model objective function;
s3, comparing and verifying the effectiveness of the scheduling model and the algorithm.
2. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 1, wherein the method comprises the following steps: the reasonable assumption of the scheduling model in step 1.1 includes:
(1) the spraying task of each character size of each character is independent and is not influenced by other spraying tasks;
(2) the spraying operation of the same end face does not exceed the working space of the automatic spraying machine;
(3) each job task can only be processed in one parallel machine at most;
(4) each batch of products can only be processed once at most on a parallel machine;
(5) considering the time of moving the automatic spraying machine when spraying different end face characters;
(6) considering parameter changing time of automatic spraying machine software when spraying different character size working procedures;
(7) in static shop scheduling, the machines and workpieces in the shop floor need to meet the following constraints:
(1) Pre-designating a workpiece machining process;
(2) The machine can only process one workpiece at a time;
(3) Each workpiece has equal process priority;
(4) The processing time and machine specified in advance must not be changed.
3. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 1, wherein the method comprises the following steps: the parameters and decision variables in step 1.2 include:
4. a method of scheduling a parallel machine for rail wagon body painting operations according to claim 3, characterized in that: the objective function in step 1.3 is:
minC max ＝min[max(C j )] (1)
wherein, the constraint condition is:
C ijk ≤S ghk +M(1-γ ijghk )。 (5)
5. the method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 4, wherein the method comprises the following steps: in step 2.2, the first layer process coding scheme:
the initial individual adopts a Logistic chaotic mapping iterative equation to obtain the sequence of the procedure codes, and the Logistic chaotic mapping iterative equation is as follows: y (k+1) =μy (k) (1-y (k)), k=1, 2..n (6)
x j ＝u j +z nj (v j -u j ) (7)
In the formula (6), y (k) is the value of a chaotic variable in the kth iteration, k is the number of iterations, and mu is a parameter;
in the formula (7), v j And u j Upper and lower bounds, x, respectively, of the j-th dimensional variable value j Representing the value of the j-dimensional component;
defining individual dimension as m, population scale as N, randomly generating m-dimension initial sequence z 1 ＝(z 11 ,z 12 ,...,z 1m ) Iterating each component in the initial sequence through a formula (6) to obtain an initial chaotic sequence matrix; then transforming the initial chaotic sequence matrix to a variable interval of a target problem through a formula (7) to complete initial chaotic mapping; generating a group of random variables, obtaining a chaotic vector after multiple iterations of a formula (6), and mapping the chaotic vector into a display code through a formula (7) to obtain an individual OS partial code x= (x) 1 ,x 2 ,...,x m )。
6. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 5, wherein the method comprises the following steps: in step 2.2, the second layer machine coding scheme: the machine selection part of the initial individual adopts a mixed mechanism, part of the individuals are generated according to the modes of formulas (6) and (7), the rest of the individuals are selected according to the mechanism with the minimum processing time in the machine table according to the principle of the shortest processing time, and the MS part selected by the machine is coded.
7. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 6, wherein the method comprises the following steps: in step 2.3, the parameters of the sea squirt swarm algorithm include a maximum number of iterations T max Maximum iteration number and population size of the variable neighborhood search.
8. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 7, wherein: in the step 2.4, taking the minimum maximum finishing time and the maximum human resources as optimization targets, judging the end face conditions of the front and back processing procedures on the same machine when calculating the individual fitness value of the sea squirt, and calculating the required human interference; the multi-objective problem is processed using a Pareto ordering method, resulting in a set of near optimal solutions, all non-dominant solutions in the Pareto solution set as the leader, and other solutions as the follow-up.
9. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 8, wherein: in the step 2.5, POX crossing and four neighborhood search operators are introduced to complete iterative updating of the goblet sea squirt population; the POX crossing method comprises the following steps:
(1) Randomly generating a proper subset omega of the workpiece coding types for the crossed two father individuals and the crossed father individuals;
(2) Removing elements belonging to omega in one parent to form new offspring, and sequentially inserting the elements belonging to omega in the other parent into the new offspring according to the arrangement sequence of the elements in the parent to form crossed individuals;
(3) Performing the same operation on the other parent according to the method in (2) above;
wherein the MS part performs position movement along with the OS part;
the four domain search structures are as follows:
(1) Domain structure N1: two points are turned over, two points are arbitrarily selected, and elements between the two points are turned over;
(2) Domain structure N2: two-point exchange, namely arbitrarily selecting two points and exchanging elements of the two points;
(3) Domain structure N3: a single point insert, arbitrarily selecting a point, inserts the point and subsequent elements before the first element.
(4) Domain structure N4: critical path movement, which refers to the machining process on the machine with the greatest finishing time, optimizes the target value by modifying the machining machine for these processes or by interchanging the process positions on other machines.
10. The method for scheduling the parallel machine for spraying operations on the body of the railway wagon according to claim 9, wherein: in step 2.5, the four search strategies are completed for the leader in the goblet sea squirt population, the best individual is reserved, and the goblet sea squirt population is put into the population; and (3) performing POX cross selection on other followers and the goblet sea squirts arranged in the previous Pareto grade respectively, selecting the remained individuals, performing one of the four neighborhood search strategies on the individuals, selecting the best individuals as the next generation, obtaining the iterated goblet sea squirt group, and sorting the iterated goblet sea squirt group to select a new leader and the goblet sea squirt arrangement sequence.
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