CN111353646B - Steelmaking flexible scheduling optimization method, system, medium and equipment with switching time - Google Patents
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Abstract
The disclosure provides a steelmaking flexible scheduling optimization method, a steelmaking flexible scheduling optimization system, a steelmaking flexible scheduling optimization medium and steelmaking flexible scheduling optimization equipment with switching time, relates to the technical field of steelmaking flexible scheduling optimization methods, and solves the problems of high energy consumption and long finishing time in the prior art; the specific scheme is as follows: acquiring process parameters, machine operation parameters and machine configuration parameters in the steelmaking process in real time; constructing a constrained scheduling optimization model by using an integer programming method with the aim of the maximum completion time of all machine operations, the minimum sum of machine processing energy and machine operation energy consumption; solving a dispatching optimization model by utilizing an improved Jaya algorithm to obtain an optimal solution of flexible dispatching in steelmaking; on the premise of ensuring the scheduling precision, the method reduces the energy consumption of scheduling, shortens the maximum finishing time and improves the working efficiency.
Description
Technical Field
The disclosure relates to the technical field of steelmaking flexible scheduling optimization methods, in particular to a steelmaking flexible scheduling optimization method with switching time, a system, a medium and equipment.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
In real industrial production systems, scheduling problems have been considered as critical issues affecting production efficiency. Flexible job shop scheduling problems (FJSPs) have been studied for many years as a complex form of scheduling problem. In practical production systems (e.g., steelmaking systems), the FJSP problem can be modeled in several stages. Fig. 1 gives an illustration of a typical steelmaking system in which there are three main stages, namely, molten iron scheduling, steelmaking casting and hot rolling. At each stage, the charges or jobs have different routes, and the machine allocation to handle these charges is also flexible due to industry limitations. However, this flexibility makes the problem more complex than the canonical scheduling problem.
In classical FJSP, there are n jobs to process on m machines. Each job has n i (i=1, 2, …, n) number of operations. Each operation should select an available machine from a set of candidate machines such that each operation can only be processed on one machine at a time and one machine can only process one operation. Preemption is not allowed; that is, the machine cannot be occupied until the dispensing operation is completed. Thus, increasing the selection of available machines may make FJP more difficult than in the case of a flow shop, a hybrid flow shop, and job scheduling problem. In order to solve the FJSP problem, many researchers have used different types of algorithms such as a genetic algorithm, a hybrid algorithm combining a genetic algorithm and a variable neighborhood descent algorithm, an ant colony optimization algorithm, an artificial bee colony algorithm, a modulo algorithm, and the like.
The inventors of the present disclosure found that most of the most realistic constraints in scheduling problems were not considered by existing studies, including machine failure, fuzzy processing time, new task arrival, resource constraints, transportation time, and procedure setup time, resulting in higher final scheduling energy consumption and lower work efficiency.
Disclosure of Invention
In order to solve the defects in the prior art, the present disclosure provides a steelmaking flexible scheduling optimization method, system, medium and equipment with switching time, which not only reduces the energy consumption of scheduling, but also shortens the maximum finishing time and improves the working efficiency on the premise of ensuring the scheduling precision.
In order to achieve the above purpose, the present disclosure adopts the following technical scheme:
the first aspect of the present disclosure provides a flexible scheduling optimization method for steelmaking with switching time.
A steelmaking flexible scheduling optimization method with switching time comprises the following steps:
acquiring process parameters, machine operation parameters and machine configuration parameters in the steelmaking process in real time;
constructing a constrained scheduling optimization model by using an integer programming method with the aim of the maximum completion time of all machine operations, the minimum sum of machine processing energy and machine operation energy consumption;
and solving a dispatching optimization model by using a Jaya algorithm to obtain the steelmaking flexible dispatching optimal solution.
A second aspect of the present disclosure provides a steelmaking flexible schedule optimization system with switch times.
A steelmaking flexible schedule optimization system with switching times, comprising:
a data acquisition module configured to: acquiring process parameters, machine operation parameters and machine configuration parameters in the steelmaking process in real time;
a model building module configured to: constructing a constrained scheduling optimization model by using an integer programming method with the aim of the maximum completion time of all machine operations, the minimum sum of machine processing energy and machine operation energy consumption;
an optimizing module configured to: and solving a scheduling optimization model by using an improved Jaya algorithm to obtain the steelmaking flexible scheduling optimal solution.
A third aspect of the present disclosure provides a medium having stored thereon a program which when executed by a processor implements the steps in the steelmaking flexible schedule optimization method with switch times as described in the first aspect of the present disclosure.
A fourth aspect of the present disclosure provides an electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in the steelmaking flexible schedule optimization method with switching time according to the first aspect of the present disclosure when executing the program.
Compared with the prior art, the beneficial effects of the present disclosure are:
according to the method, the system, the medium and the equipment, the energy consumption and the finishing time target are optimized simultaneously, modeling is performed by considering various constraint conditions, on the premise that the scheduling accuracy is ensured, the energy consumption of scheduling is reduced, the maximum finishing time is shortened, and the working efficiency is improved.
Drawings
FIG. 1 is a diagram illustrating scheduling problems in a typical steelmaking system as described in the background of the present disclosure.
Fig. 2 is a schematic diagram of a problem description provided in embodiment 1 of the present disclosure.
Fig. 3 is a schematic flow chart of a flexible steelmaking scheduling optimization method with switching time according to embodiment 1 of the present disclosure.
Fig. 4 is a gante diagram of FJSP with transit time and installation time provided by example 1 of the present disclosure.
Fig. 5 is a code of one example provided in embodiment 1 of the present disclosure.
Fig. 6 (a) is a schematic diagram of a TPR mutation operator provided in example 1 of the present disclosure.
Fig. 6 (b) is a schematic diagram of a TPS mutation operator provided in example 1 of the present disclosure.
Fig. 6 (c) is a schematic diagram of a TPI mutation operator provided in example 1 of the present disclosure.
Fig. 7 (a) is a schematic diagram of an LSD-facilitated local search heuristic provided in embodiment 1 of the present disclosure.
Fig. 7 (b) is analysis of variance results obtained on the last 15 relatively large-scale examples for two heuristic methods provided in example 1 of the present disclosure.
Fig. 7 (c) is a schematic diagram of an LSD of the exploration heuristic provided in embodiment 1 of the present disclosure.
Fig. 7 (d) is a schematic of LSD of IJaya and DJaya provided in example 1 of the present disclosure.
Fig. 7 (e) is an LSD of a different algorithm provided in embodiment 1 of the present disclosure.
Fig. 8 (a) is a convergence curve of example 1 provided in example 1 of the present disclosure.
Fig. 8 (b) is a convergence curve of example 2 provided in example 1 of the present disclosure.
Fig. 8 (c) is a convergence curve of example 5 provided in example 1 of the present disclosure.
Fig. 8 (d) is a convergence curve of example 8 provided in example 1 of the present disclosure.
Fig. 8 (e) is a convergence curve of example 10 provided in example 1 of the present disclosure.
Fig. 8 (f) is a convergence curve of example 15 provided in example 1 of the present disclosure.
Fig. 9 is a sweet potato graph best solution of example 1 provided in example 1 of the present disclosure.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments in accordance with the present disclosure. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Embodiments of the application and features of the embodiments may be combined with each other without conflict.
Example 1:
embodiment 1 of the disclosure provides a steelmaking flexible scheduling optimization method with switching time, as shown in fig. 3. First, the problem is modeled using an integer programming method, where the energy consumption and the completion time objective are optimized simultaneously. Then, an improved Jaya (IJaya) algorithm was proposed to solve this problem. In the proposed algorithm, each solution is represented by a two-dimensional vector. Thus, the present embodiment exploits several problem-specific local search operators to perform the exploration task. In order to enhance the searching capability of the algorithm, a heuristic algorithm based on a simulated annealing algorithm is embedded in the algorithm. Meanwhile, to verify the performance of the IJaya algorithm, 30 examples were generated and simulated tests were performed. Five effective algorithms are selected for detailed comparison, and simulation results show that the algorithm can efficiently solve the considered problem, specifically as follows.
(1) And (5) describing the problem of the flexible scheduling optimization method for steelmaking with switching time.
As shown in fig. 2, there are typically five stages or processes of the actual production process of the steelmaking industry among the concerns. The first process is to load molten iron into a torpedo car (TPC) which is then processed through the second and third refining stages. The fourth stage is pouring molten iron, and the final stage is continuous casting process. Aiming at the problem of the flexible scheduling optimization method for steelmaking with switching time, the following assumption is made:
(1-1) the transport time for each job from one machine to a continuous machine is taken into account.
(1-2) on the same machine, taking into account the influence of the set time of each pair of successive processing operations.
(1-3) the processing of one job should start after the completion time of the preceding job while taking into account the setup time on the same machine.
(1-4) the processing of each job should be started after the completion time of the preceding job of the same job while taking into account the transportation time between the two processors.
(1-5) sufficient buffer area is always available between any two consecutive machines.
(2) Steelmaking flexible scheduling optimization method problem modeling with switching time
The parameters and symbols are represented as follows:
n: number of work pieces.
M: number of machines.
J, h, workpiece index.
I, k: machine index.
U, z, operation index.
R, q index of processing operations in the machine.
·n j An operand belonging to job j.
·O j,u U of job j th And (3) operating.
·p j,u,i U of job j on machine I th Processing time of the operation.
·t j,k,i The transit time of job j from machine k to j.
·s j,h Setting time of jobs j and h.
·e j,u,i If O j,u Can be processed on machine I, it is set to a binary value of 1.
·Unit energy consumption of machine I processing task.
·Unit energy consumption for the operation of the machine I.
·E busy Total energy consumption of machining.
·E race Total energy consumption of machine operation.
M is a very large positive number.
·ω 1 ,ω 2 ,ω 3 ,andω 4 The weight coefficients of the four targets are respectively calculated.
Decision variables:
·x j,u,h,z if O j,u At O h,z After that, setting to a binary value of 1; otherwise, x j,u,h,z Set to 0.
·y j,u,i,k If O j,u Is in machines i and O j,u-1 Processed on machine k, then set to a binary value of 1.
·c j,u :O j,u Is a completion time of (c).
·If job j is processed immediately after job h on the same machine i, the binary value of 1 is set.
·b i The earliest start time of a processing operation on machine i.
The main mathematical model of the problem under consideration is as follows:
minω 1 ·C max +ω 2 (E busy +E race ) (1)
the aim of this embodiment is to minimize the weighted sum of the two targets, namely the sum of the maximum completion time of all operations and the energy consumption, which is the sum of the machine processing energy and the machine running energy consumption.
Constraints (5) and (6) ensure that each operation of each job should be assigned to only one available machine. Constraints (7) and (8) ensure that the machine assigned to each operation must be selected from a given set of qualified machines. Constraints (9) and (10) force the handling relationship of each operation between the current machine and the immediately following machine. Constraints (11) and (12) indicate that the completion time of the current job must not be greater than the sum of the completion time of the previous job, the transit time between successive machines, and the set time between the current job and the immediately previous job on the same machine. Constraints (13) to (20) force each machine to perform only one operation at a particular time. Constraints (21) and (22) force the scope of decision variables.
To assist in understanding the objective problem in this embodiment, an example of FJSP is selected in which there are three jobs to be processed on three machines. Table 1 gives the processing time for each operation on each machine. Tables 2 and 3 list the transmission time and the sequence-based setup time, respectively. Fig. 4 shows a corresponding gante diagram in which the processing time of each job is represented by a rectangle marked with a job number and an operation number. For example, on machine M1, the first operation to be processed is O 1,1 The last operation to be processed is O 2,3 Thus, the sequence of processing operations is followed by a set time, which is represented by a different color rectangle and is marked with a job number. For example, in operation O 2，2 The following is a rectangle of the set time labeled "2", which is operation O 2,2 At O 1,2 Setting time in between. The set time is followed by a rectangle of the transit time. For example, at M 2 Operation O of job J2 after the completion time 2,1 Will be transferred to machine M1 (O 2,2 ) And the transfer time is represented by a rectangle ending at time 17.
Table 1: the number of treatments per operation on each machine.
Table 2: the transit time between machines.
Table 3: set time between operations on each machine.
(2) Basic Jaya algorithm.
In the canonical Jaya algorithm, the detailed steps are as follows:
step 1: an initialization stage: the initial population is randomly generated.
Step 2: and executing the step 3-4 until the stopping condition is met.
Step 3: each solution was improved using the following formula:
x j,k,t '＝x j,k.t +rand 1,j,t ×(x j,best,t -|x j,k.t |)-rand 2,j,t ×(x j,worst,t -|x j,k.t |) (23)
wherein x is j,k.t Is the jth variable of the kth solution during the t-th iteration; x is x best And x wast Is the best and worst solution found so far; rand of 1,j,t And rand 2,j,t Is in [0,1 ]]Random number, |x, uniformly distributed in range j,k.t I is solution x j,k.t Is the absolute value of (c). Component +rand 1,j,t ×(x j,best,t -|x j,k.t I) each solution is learned from the best solution, while the second component-rand 2,j,t ×(x j,worst,t -|x j,k.t I) to separate the solution from the worst solution.
Step 4: if x j,k,t ' better than x j,k.t Then evaluate x j,k,t ' and replace x j,k.t 。
Step 5: the best solution is output.
(3) This embodiment shows a procedure for implementing the IJaya algorithm step by step, and a detailed description is provided in algorithm 1.
(3-1) representation and decoding strategy of solution
To record the machining order and machine allocation information, each solution is represented by two vectors, an allocation vector and a scheduling vector. The scheduling vector reports the processing order of each operation, where each operation is represented by a job number, and the allocation vector is used to record the machine allocation for the corresponding operation location. It should be noted that each job j will appear n in each of the two vectors j Secondary, and the two vectors are the same length and equal to
Fig. 4 gives an example of a solution representation in which there are three jobs and three machines. The total number of operations of these three jobs is {3, 3} respectively. The scheduling vector indicates that the first operation to be scheduled is J 1 Is then J 2 The first operation of (2) and the last one is J 3 Is the last operation of (a). The allocation vector indicates the machine allocated for the corresponding operating position.
For example, will J 1 Is assigned to machine M 3 And will J 3 Is arranged at M 1 And (3) upper part. The decoding procedure for each scheme should accomplish the following tasks: (1) Determining the starting time of each operation by considering the finishing time of the last operation and the idle time of the machine and simultaneously considering the transportation time and the installation time; (2) calculating the finishing time and the energy consumption, i.e., target values. Fig. 4 shows a Gantt chart of the solution defined in fig. 5, with a finishing time of 70 and a total energy consumption of 143.354.
(3-2) initializing a policy.
To initialize a set of solutions, this embodiment uses a simple and efficient method, comprising the following steps:
step 1: when the initial population size is smaller than P size When the method is carried out, the following steps are executed;
step 2: for a scheduling vector: (1) Initializing an empty scheduling vector, adding the number of each job j times n j In a second time, the first time,
(2) Randomly reordering all numbers in the modulation vector;
step 3: for the allocation vector: (1) Initializing an empty allocation vector, (2) selecting each operation O in the scheduling vector i,j Randomly selecting an available machine M i,j As O i,j And M is taken up in i,j Stored in an allocation vector;
(3-3) distribution vector local search.
In the present embodiment, in consideration of the specific features and objects of the problem, a simple and effective allocation vector local search method is proposed, which uses seven types of local search methods, which is a random manner. First, the function of acquiring all key operations is described in algorithm 2, and then the proposed seven local search heuristics are given in LS1 through LS7, respectively.
Algorithm 2: obtaining all critical operations
Step 1: find all operations whose completion time is equal to the maximum completion time and store them to a file named CO max Is defined in the vector of (2);
step 2: the following steps are performed until CO max Is empty;
step 3: acquiring and deleting CO max First operation O of (1) i,j The following steps 4-5 are executed;
step 4: set C h,k Is O i,j ，S i,j Previous operation O on the same machine h,k Is O, j is i,j If S i,j ＝C h,k Then the operation O h,k Storage to CO max In (a) and (b);
step 5: if S i,j ＝C i,j-1 Then O is taken i,j-1 Storage to CO max Is a kind of medium.
LS1: key operations of local search.
Step 1: for solution X, find all key operations using algorithm 2;
step 2: randomly selecting a key operation r c ；
Step 2.1: if it has multiple candidate machines, randomly replacing another machine for it;
step 2.2: otherwise, loop until the previous critical operation r is found cc The r is cc There is more than one candidate machine;
step 2.3: r is cc Randomly replacing another machine;
step 3: if a better value has been obtained, please replace the current solution.
LS2: random key operation steps of local search.
Step 1: for solution X, find all key operations using algorithm 2;
step 2: randomly selecting a key operation r c ；
Step 3: if r c If a plurality of candidate machines exist, randomly replacing another machine for the candidate machines;
step 4: the newly generated adjacent solution is evaluated, and if the current solution is better, the current solution is replaced.
LS3: random key machine local search.
Step 1: for solution X, find all key operations;
step 2: randomly selecting a key operation r c Assigned to r c Machine of (2) is M c ；
Step 3: at M c Randomly selecting an operation r cc If r cc If a plurality of candidate machines exist, randomly replacing another machine for the candidate machines;
step 4: the newly generated adjacent solution is evaluated and the current solution is replaced.
LS4: local search of random key machines.
Step 1: for solution X, find all key operations;
step 2: randomly selecting a key operation r c Assigned to r c Machine of (2) is M c ；
Step 3: at M c Randomly selecting an operation r cc If r cc If a plurality of candidate machines exist, randomly replacing another machine for the candidate machines;
step 4: the newly generated adjacent solution is evaluated, and if the current solution is better, the current solution is replaced.
LS5: local search of the busiest machine.
Step 1: for solution X, computing the workload of all machines;
step 2: selecting a machine M with the largest workload;
step 3: randomly selecting operation O on machine M i,j If O i,j If a plurality of candidate machines exist, replacing another machine for the candidate machines at random;
step 4: the newly generated adjacent solution is evaluated, replacing the current solution.
LS6: a randomly operated local search.
Step 1: for solution X, an operation O is randomly selected on the scheduling vector i,j ；
Step 2: if O i,j If a plurality of candidate machines exist, randomly replacing another machine for the candidate machines;
step 3: the newly generated adjacent solution is evaluated, and if the current solution is better, the current solution is replaced.
Scheduling an array local search;
LS7: a local search of random operation is performed with a minimal processor.
Step 1: for solution X, an operation O is randomly selected on the scheduling vector i,j ；
Step 2: if O i,j If a plurality of candidate machines exist, the machine with the shortest processing time is replaced;
step 3: the newly generated adjacent solution is evaluated, and if the current solution is better, the current solution is replaced.
(3-4) for the considered problem, this embodiment includes three types of mutation operators:
(3-4-1) a two-point inverse (TPR) operator.
The TPR operator generates an adjacent solution by inverting the selected segment, i.e., inverting all elements between two randomly selected positions in the scheduling vector. Fig. 6 (a) shows a process of the TPR operation.
(3-4-2) two-point drop phase (TPS) operation.
The TPS operator will generate an adjacent solution by exchanging two selected jobs. Fig. 6 (b) shows the procedure for TPS operation.
(3-4-3) a two-point insert (TPI) operator.
The TPI operator generates a neighbor solution by inserting a job before the location of another selected job. Fig. 6 (c) shows the procedure of TPS operation.
After the mutation of the modulation vector, another task is to mutate the machine allocation vector. A simple method is studied here that initially reserves the assigned machine for all affected operations, as shown in fig. 6 (a) -6 (c), then randomly selects one location in the machine assignment vector and replaces another available machine for the corresponding operation.
(3-5) exploration method
In the IJaya algorithm proposed in the present embodiment, a SA-based heuristic is used as an acceptance criterion to enhance the local optimization. In this study we used a simple thermostatical acceptance in which:
where T is a calibrated parameter.
(4) Numerical analysis
This example discusses computational experiments for evaluating the performance of the proposed algorithm, in order to verify the effectiveness and efficiency of the proposed algorithm, the resulting best solutions were collected for performance comparison after 30 independent runs.
The algorithms for comparison include GA-GSO (Liu et al, 2019), PSO-SA (Don et al, 2019), ASA (Cruz-Chu vez et al, 2017), IG (Aqel et al, 2019), DABC (Li et al, 2014), TPM (Lei et al, 2018) and DJaya (Gao et al, 2018). All algorithms of the comparison are adapted to the solution of the considered problem, wherein the parameters are defined based on the existing data considered. The performance metric selected is the Relative Percentage Increase (RPI) calculated as follows:
wherein f b Is the optimal fitness value collected by all comparison algorithms, f c Is the minimum fitness value found by a given algorithm.
(4-1) practical example
Examples of 30 different scales are randomly generated, the number of jobs n= {20, 30, 40, 50, 80, 100}, the number of machines m= {6,7, 8,9, 10}, the total number of operations per job being evenly distributed over the interval [ m/2, m ].
(4-2) Experimental parameters
The population size is the only predefined parameter of the algorithm, here 100 are chosen.
(4-3) local search efficiency of allocation vector
To examine the effectiveness of the local search heuristic, two different types of IJaya algorithms are implemented in this embodiment, i.e., the IJaya-NL algorithm without the local search heuristic and the IJaya algorithm containing all the components discussed in section 4, all other components of the two comparison algorithms remain unchanged.
The comparison results are given in table 4. In the lookup table, the first column contains instance name entries and the second column contains instance proportion entries. The two numbers in the example represent the number of jobs and the number of machines, respectively. For example, the first example (Ins 1) is a problem of 20 jobs, 6 machines, while the last example (Ins 30) is a problem of 100 jobs, 10 machines. The third column represents the best fitness value obtained from the two compared algorithms, while the next two columns represent the fitness values obtained by the two compared algorithms, respectively. The last two columns show the bias or RPI values of the two algorithms.
From table 4, it can be observed that: (1) In 30 examples with different problem sizes, IJaya obtained 25 times the optimal value of the IJaya-NL method, although these values were in each case slightly better than the IJaya-NL method; (2) From the last two columns, RPI values also verify the performance of the IJaya method, which is significantly better than the IJaya-NL method; (3) Starting from the last row of the table, the average performance also verifies the superior performance of the IJaya method, with an average RPI value of 5.41.
In this example, a multi-factor analysis of variance (ANOVA) was performed to evaluate the significance of the difference between the two methods. Fig. 7 (a) provides the mean value of the adaptation values and the 95% lsd (least significant difference) interval for both comparison methods. The p value is close to zero; thus, there is a significant difference between the methods of comparison. Therefore, the local search heuristic algorithm provided by the embodiment obviously improves the performance of the algorithm. The main reason for this effect is that by applying a local search heuristic, the development capacity of the IJaya algorithm is improved.
(4-4) efficiency of SA-based exploration methods
To investigate the effectiveness of the heuristic search algorithm presented in this example, we implemented two different types of IJaya algorithms, i.e., the IJaya-NS algorithm that did not search for a heuristic and the IJaya algorithm that included all the components discussed in section 4. All other components of the two comparison algorithms remain unchanged. Table 5 shows the results of the comparisons.
From table 5 it can be observed that: (1) Of the 30 examples with different problem sizes, IJaya obtained 13 better values, slightly worse than the IJaya-NS method. However, the proposed IJaya method shows better performance in solving the relatively large scale problem, i.e. from "Inst22" to "Inst30"; (2) From the last two columns, the RPI values also verify the performance of the IJaya method, which is significantly better than the IJaya-NS method; (3) Starting from the last row of the table, the average performance also verifies the superior performance of the IJaya method, with an average RPI value of 1.40, whereas the IJaya-NS method achieves an average RPI. In addition, fig. 7 (b) shows the analysis of variance results obtained by two heuristics on the last 15 relatively large scale examples. From fig. 7 (b), it can be concluded that the proposed SA-based detection heuristic significantly improves performance, especially for relatively large scale examples.
(4-5) results of comparison with other types of efficient algorithms
Experiments were further designed in this implementation, comparing the existing latest algorithm with the proposed IJaya algorithm on the same problem. The results are given in table 6, in which RPI values for all comparison algorithms are recorded.
From the table it can be seen that: (1) IJaya gives 20 better solutions in 30 given examples, better than suboptimal (ASA algorithm); (2) From the last row of the table, the average RPI value for the IJaya algorithm is 1.36, which is significantly better than other algorithms. In order to verify statistical efficiency, the present embodiment also performs analysis of variance on the compared methods. Fig. 7 (c) shows that there is a large difference between the IJaya algorithm and the suboptimal ASA algorithm. Fig. 7 (d) shows that the IJaya method is superior to the DJaya algorithm, while fig. 7 (e) reports that IJaya shows competitive performance compared to other efficient algorithms.
Fig. 8 (a) to 8 (f) show a comparison of the convergence curves for different types of examples. From these convergence curves, it can be seen that the proposed IJaya method has a better convergence capacity for different scale problems. Figure 9 presents a figure of the Gantt of the best solution of Inst1, in which each operation is represented by a rectangle marked with a job number and an operation number. The set time and the transit time are marked with rectangles filled with different colors. As can be seen from fig. 9, the solution obtained by this algorithm is valid.
Table 4: the comparison result of the proposed local search heuristic algorithm.
Table 5: the comparison result of the SA-based exploration search heuristic algorithm is proposed.
Table 6: comparison results of seven heuristic algorithms.
This embodiment addresses the FJSP problem with installation time and transit time constraints, and proposes an improved Jaya algorithm. The main contributions of this embodiment are as follows: (1) modeling the problem by adopting an integer programming method; (2) An improved Jaya algorithm was proposed to solve the target problem; (3) representing each solution as a two-dimensional vector; (4) Developing a plurality of local search operators for the problem to execute a development task; (5) In order to enhance the exploration capability of the algorithm, a heuristic algorithm based on a simulated annealing algorithm is embedded in the algorithm; (6) 30 examples are generated and subjected to simulation test, five effective algorithms are selected for detailed comparison, and simulation results show that the algorithm can effectively solve the problem under consideration, optimize the energy consumption and the finishing time target simultaneously, model various constraint conditions, reduce the energy consumption of scheduling and the maximum finishing time on the premise of ensuring the scheduling precision, and improve the working efficiency.
Example 2:
embodiment 2 of the present disclosure provides a steelmaking flexible scheduling optimization system with switching time, including:
a data acquisition module configured to: acquiring process parameters, machine operation parameters and machine configuration parameters in the steelmaking process in real time;
a model building module configured to: constructing a constrained scheduling optimization model by using an integer programming method with the aim of the maximum completion time of all machine operations, the minimum sum of machine processing energy and machine operation energy consumption;
an optimizing module configured to: and solving a scheduling optimization model by using an improved Jaya algorithm to obtain the steelmaking flexible scheduling optimal solution.
The working method of the specific optimization system is the same as that of embodiment 1, and will not be described here again.
Example 3:
embodiment 3 of the present disclosure provides a medium having stored thereon a program which, when executed by a processor, implements the steps in the steelmaking flexible schedule optimization method with switching times as described in embodiment 1 of the present disclosure.
Example 4:
embodiment 4 of the present disclosure provides an electronic device, including a memory, a processor, and a program stored on the memory and executable on the processor, where the processor implements steps in the steelmaking flexible scheduling optimization method with switching time according to embodiment 1 of the present disclosure when executing the program.
The foregoing description of the preferred embodiments of the present disclosure is provided only and not intended to limit the disclosure so that various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
Claims (14)
1. The flexible steelmaking scheduling optimization method with the switching time is characterized by comprising the following steps of:
acquiring process parameters, machine operation parameters and machine configuration parameters in the steelmaking process in real time;
constructing a constrained scheduling optimization model by using an integer programming method with the aim of the maximum completion time of all machine operations, the minimum sum of machine processing energy and machine operation energy consumption;
solving a dispatching optimization model by using a Jaya algorithm to obtain a steelmaking flexible dispatching optimal solution;
the optimal solution includes an allocation vector for recording machine allocation of corresponding operation positions and a scheduling vector for recording a processing order of each operation;
the Jaya algorithm is an improved Jaya algorithm, comprises a local search stage, and specifically comprises the following steps: randomly selecting one solution from a certain solution in the current solution in the local search and the optimal solution found so far as the current solution, and if the certain solution in the current solution is better than the new solution, replacing the solution in the current solution with the new solution; otherwise, executing a local search strategy, evaluating the newly generated solution, and if the newly generated solution is better than the optimal solution discovered so far, replacing the optimal solution discovered so far by the newly generated solution;
assume that: the transport time of each job from one machine to the continuous machine is taken into consideration, and on the same machine, the processing of one job should be started after the completion time of the preceding job in consideration of the influence of the set time of each pair of continuous processing operations, while the processing of each job should be started after the completion time of the preceding job of the same job while taking into consideration the transport time between the two processing machines in consideration of the set time on the same machine; sufficient buffer is always available between any two consecutive machines;
the objective function includes:
minω 1 ·C max +ω 2 ·(E busy +E race ) (1)
the constraints of the objective function include:
wherein N is the number of workpieces, M is the number of machines, j, h is the index of the workpiece, i, k is the index of the machine, u, z is the index of the operation, r, q is the index of the processing operation in the machine, N j O as an operand belonging to operation j j,u U for job j th Operation, p j,u,i U on machine I for job j th Processing time of operation, t j,k,i For the transit time of job j from machine k to j, s j,h Setting time, e for jobs j and h j,u,i If O is j,u Can be processed on machine I, then it is setA binary value set to 1 is set,for the unit energy consumption of machine I processing task, < >>For unit energy consumption of machine I operation, E busy For the total energy consumption of the machining, E race Omega, the total energy consumption of machine operation 1 ,ω 2 ,ω 3 ,and ω 4 Weighting coefficients, x, for each of four targets j,u,h,z If O j,u At O h,z After that, setting to a binary value of 1; otherwise, x j,u,h,z Set to 0; y is j,u,i,k If O j,u Is in machines i and O j,u-1 A binary value of 1 is set for processing on machine k; c (C) j，u :O j,u Is a completion time of (2);If job j is processed immediately after job h on the same machine i, then the binary value of 1 is set; b i The earliest start time of a processing operation on machine i.
2. The flexible scheduling optimization method with switching time according to claim 1, wherein the local search strategy comprises a key operation of local search;
for the obtained solution, finding out all key operations;
randomly selecting a key operation; if it has multiple candidate machines, randomly replacing another machine for it; otherwise, looping until a previous critical operation is found, the previous critical operation having more than one candidate machine; randomly replacing another machine for the previous critical operation;
if a more optimal solution has been obtained, the current solution is replaced with the more optimal solution.
3. The flexible scheduling optimization method for steelmaking with switching time as claimed in claim 1, wherein,
the local search strategy comprises random key operations of local search:
for the obtained solution, finding out all key operations;
randomly selecting a key operation;
if the key operation has a plurality of candidate machines, randomly replacing another machine for the key operation;
and evaluating the newly generated adjacent solution, and replacing the current solution by using the newly generated adjacent solution if the newly generated adjacent solution is better than the current solution.
4. The flexible scheduling optimization method for steelmaking with switching time as claimed in claim 1, wherein,
the local search strategy comprises random key machine local search:
for the resulting solution, find all key operations;
randomly selecting a key operation and finding out a machine of the key operation;
randomly selecting a first operation on the found machine, and if the first operation has a plurality of candidate machines, randomly replacing another machine for the first operation;
the newly generated adjacent solution is evaluated and the current solution is replaced.
5. The flexible scheduling optimization method for steelmaking with switching time as claimed in claim 1, wherein,
the local search strategy comprises random key machine local search:
for the resulting solution, find all key operations;
randomly selecting a key operation and finding out a machine of the key operation;
randomly selecting a first operation on the found machine, and if the first operation has a plurality of candidate machines, randomly replacing another machine for the first operation;
and evaluating the newly generated adjacent solution, and replacing the current solution by using the newly generated adjacent solution if the newly generated adjacent solution is better than the current solution.
6. The flexible scheduling optimization method for steelmaking with switching time as claimed in claim 2, wherein all key operations are found out, specifically:
find all operations whose completion time is equal to the maximum completion time and store them to a file named CO max Is defined in the vector of (2);
the following steps are performed until CO max Is empty;
acquiring and deleting CO max First operation O of (1) i,j ；
Set C h,k Is O i,j ，S i,j Previous operation O on the same machine h,k Is O, j is i,j If S i,j ＝C h,k Then the operation O h,k Storage to CO max In (a) and (b);
if S i,j ＝C i,j-1 Then O is taken i,j-1 Storage to CO max Is a kind of medium.
7. The flexible scheduling optimization method for steelmaking with switching time as set forth in claim 1, wherein said local search strategy comprises local search of the busiest machine:
for the resulting solution, computing the workload of all machines;
selecting a machine with the largest workload;
randomly selecting a first operation on the machine with the largest workload, and if the first operation has a plurality of candidate machines, randomly replacing another machine for the first operation;
the newly generated adjacent solution is evaluated, replacing the current solution.
8. The flexible scheduling optimization method for steelmaking with switching time as claimed in claim 1, wherein,
the local search strategy comprises a local search of random operation:
for the resulting solution, randomly selecting a first operation on the scheduling vector;
if the first operation has a plurality of candidate machines, randomly replacing another machine for the first operation;
and evaluating the newly generated adjacent solution, and replacing the current solution by using the newly generated adjacent solution if the newly generated adjacent solution is better than the current solution.
9. The flexible scheduling optimization method for steelmaking with switching time as claimed in claim 1, wherein,
the local search strategy comprises local search of random operation by a minimum processor;
for the resulting solution, randomly selecting a first operation on the scheduling vector;
if a plurality of candidate machines exist in the first operation, replacing the machine with the shortest processing time;
and evaluating the newly generated adjacent solution, and replacing the current solution by using the newly generated adjacent solution if the newly generated adjacent solution is better than the current solution.
10. The flexible scheduling optimization method with switching time according to claim 1, wherein the improved Jaya algorithm further comprises a scheduling local search stage, in particular: three types of variation heuristics are performed in a random fashion on the best individual found so far, updating the best individual with the new neighborhood solution.
11. The flexible scheduling optimization method with switching time according to claim 1, wherein a heuristic algorithm based on a simulated annealing algorithm is adopted as an acceptance criterion of an improved Jaya algorithm, and a two-point inverse operator, a two-point fall-off operation and a two-point insertion operator are adopted to mutate a scheduling vector; an array of machine tool assignments is initially reserved for all affected operations, then a location is randomly selected in the machine assignment vector and another available machine for the corresponding operation is replaced.
12. A steelmaking flexible schedule optimization system with switching time, comprising:
a data acquisition module configured to: acquiring process parameters, machine operation parameters and machine configuration parameters in the steelmaking process in real time;
a model building module configured to: constructing a constrained scheduling optimization model by using an integer programming method with the aim of the maximum completion time of all machine operations, the minimum sum of machine processing energy and machine operation energy consumption;
an optimizing module configured to: solving a dispatching optimization model by utilizing an improved Jaya algorithm to obtain an optimal solution of flexible dispatching in steelmaking;
the optimal solution includes an allocation vector for recording machine allocation of corresponding operation positions and a scheduling vector for recording a processing order of each operation;
the Jaya algorithm is an improved Jaya algorithm, comprises a local search stage, and specifically comprises the following steps: randomly selecting one solution from a certain solution in the current solution in the local search and the optimal solution found so far as the current solution, and if the certain solution in the current solution is better than the new solution, replacing the solution in the current solution with the new solution; otherwise, executing a local search strategy, evaluating the newly generated solution, and if the newly generated solution is better than the optimal solution discovered so far, replacing the optimal solution discovered so far by the newly generated solution;
assume that: the transport time of each job from one machine to the continuous machine is taken into consideration, and on the same machine, the processing of one job should be started after the completion time of the preceding job in consideration of the influence of the set time of each pair of continuous processing operations, while the processing of each job should be started after the completion time of the preceding job of the same job while taking into consideration the transport time between the two processing machines in consideration of the set time on the same machine; sufficient buffer is always available between any two consecutive machines;
the objective function includes:
minω 1 ·C max +ω 2 ·(E busy +E race ) (1)
the constraints of the objective function include:
wherein N is the number of workpieces, M is the number of machines, j, h is the index of the workpiece, i, k is the index of the machine, u, z is the index of the operation, r, q is the index of the processing operation in the machine, N j O as an operand belonging to operation j j,u U for job j th Operation, p j,u,i U on machine I for job j th Processing time of operation, t j,k,i For the transit time of job j from machine k to j, s j,h Setting time, e for jobs j and h j,u,i If O is j,u Can be processed on machine I, it is set to a binary value of 1,for the unit energy consumption of machine I processing task, < >>For unit energy consumption of machine I operation, E busy For the total energy consumption of the machining, E race Omega, the total energy consumption of machine operation 1 ,ω 2 ,ω 3 ,and ω 4 Weighting coefficients, x, for each of four targets j,u,h,z If O j,u At O h,z After that, setting to a binary value of 1; otherwise, x j,u,h,z Set to 0; y is j,u,i,k If O j,u Is in machines i and O j,u-1 A binary value of 1 is set for processing on machine k; c (C) j，u :O j,u Is a completion time of (2);If operation j is operation h on the same machine iImmediately after the processing, setting the binary value of 1; b i The earliest start time of a processing operation on machine i.
13. A medium having stored thereon a program which when executed by a processor performs the steps of the flexible scheduling optimization method for steelmaking with switching time as claimed in any one of claims 1-11.
14. An electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, wherein the processor, when executing the program, implements the steps of the steelmaking flexible schedule optimization method with switching time as claimed in any one of claims 1-11.
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