CN110929930A - Scheduling and scheduling optimization method for marine crankshaft production line - Google Patents
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Abstract
The invention provides a scheduling and scheduling optimization method for a marine crankshaft production line, which comprises the steps of firstly, determining the processing sequence, the processing time and the variable conditions of processing equipment by combining the actual problems of marine crankshaft production enterprises; then reasonably setting some assumed conditions without considering emergencies in the processing production process; reasonably setting constraint conditions and optimization targets of the model according to variables and assumed conditions, and establishing a mathematical model; then designing an improved differential evolution algorithm, namely a simulated annealing mixed differential evolution (SADE) algorithm, introducing a simulated annealing operator, and improving the selection operation in the differential evolution algorithm; and finally, solving the product scheduling sequence problem of the marine crankshaft production line by using the SADE algorithm, and carrying out comparative analysis on the product scheduling sequence problem and the differential evolution algorithm to verify the effectiveness of the SADE algorithm.
Description
Technical Field
The invention relates to the field of large ship manufacturing, in particular to a scheduling and optimizing method for a marine crankshaft production line.
Background
With the progress of society and the development of technology, the national demand for manufacturing industry is increasing. Advanced manufacturing is becoming the strategic industry of our country, and although the manufacturing industry of our country is developing rapidly, there is still a certain distance compared with abroad. Especially, the development of large-scale manufacturing industry, the development direction of manufacturing industry tends to the development direction of intelligent manufacturing in recent years. In addition, along with the acceleration of the update iteration speed of the product, the demands of customers on the product are inconsistent, and under the condition, the production of the product gradually presents the characteristics of diversification and small batch, so that the production of a production line by a manufacturing enterprise is more difficult, and the production cannot be finished by only relying on an experienced manager, so that the production scheduling is used as the basic problem of production management, and the improvement and optimization of the production scheduling are more important in the survival development of the enterprise.
The solution algorithms for the model of the scheduling problem can be roughly classified into three types: an optimal solution algorithm, a backtracking method and an artificial intelligence algorithm. In actual production, the production problem is often an NP-hard problem, and the optimal solution method is too simple, is not suitable for the scheduling problem with higher complexity and cannot be well solved. The backtracking method is easy to fall into the local optimal solution, and cannot ensure the optimal or better scheduling result. The artificial intelligence algorithm is a high-efficiency, practical and strong-robustness searching method, and can effectively solve complex optimization problems such as NP-hard problem and nonlinearity, so the artificial intelligence algorithm is the most suitable method for solving the scheduling problem. The differential evolution algorithm has the advantages of high convergence speed and strong robustness in the optimizing process, has a better and obvious approximation effect compared with the genetic algorithm, has the parameter setting which is much less than that of the genetic algorithm and the particle swarm algorithm, and has the influence on the final result which is much less than that of the genetic algorithm and the particle swarm algorithm due to different parameter settings, so the differential evolution algorithm is the algorithm which is most suitable for solving the scheduling problem in the artificial intelligence algorithm.
Based on the problems, the invention provides a production scheduling and scheduling optimization method for a marine crankshaft production line based on a differential evolution algorithm.
Disclosure of Invention
The invention provides a scheduling and scheduling optimization method for a marine crankshaft production line. The method is characterized in that a mathematical model is established by combining actual problems of crankshaft production enterprises, simulated annealing and a differential evolution algorithm are combined, a simulated annealing operator is introduced in the selection operation process of the differential evolution, the differential evolution algorithm is designed and improved, finally, the SADE algorithm is used for solving the product scheduling sequence problem of the marine crankshaft production line, and the SADE algorithm is compared and analyzed with the differential evolution algorithm to verify the effectiveness of the SADE algorithm.
In order to solve the problems, the technical scheme adopted by the invention is that a scheduling and scheduling optimization method for a marine crankshaft production line is mainly combined with actual problems of crankshaft production enterprises to establish a mathematical model and design and improve a differential evolution algorithm, namely a simulated annealing mixed differential evolution (SADE) algorithm, and mainly comprises the following steps:
step 1: determining a processing sequence, processing time and variable conditions of processing equipment by combining actual problems of crankshaft production enterprises;
step 2: setting an assumed condition related to an actual problem, and not considering emergencies in the process production process, assuming the following conditions:
(1) the production sequence of each type of crankshaft at each station is fixed, namely the production sequence of the crankshafts of different types is consistent;
(2) only one workpiece can be produced at one station, and the same workpiece can be produced at the same station only in a fixed time;
(3) the processing time of the product on the station comprises the preparation time of the product on the station, and is not related to the product putting sequence;
(4) when the shaft machining time is neglected, namely the shaft parts are assembled and machined, the shaft parts are in place by default;
(5) the processing and manufacturing operation time of each product is only related to the type of the product, and the processing and manufacturing operation time of the same product is fixed;
(6) each station continuously works without considering the occurrence of special conditions;
and step 3: reasonably setting constraint conditions of the model and an optimization target thereof according to the steps 1 and 2, and establishing a mathematical model;
and 4, step 4: according to the mathematical model in the step 3, simulated annealing and a differential evolution algorithm are combined, a simulated annealing operator is introduced in the selection operation process of differential evolution, a simulated annealing mixed differential evolution algorithm is designed, the differential evolution algorithm is improved, and the specific operation method is as follows:
step 4.1, setting initial conditions, such as population, mutation operators and crossover operators;
step 4.2, initializing a population, wherein a simulated annealing mixed differential evolution algorithm adopts floating point real number coding and randomly generates an initial population by using a rand () function;
step 4.3, determining population fitness, wherein the SADE algorithm is used as an optimization algorithm, and can optimize an experimental solution through continuous cooperation and competition among individuals so as to continuously approach an optimal solution, wherein generally, a target function of a mathematical model is a fitness function;
minf(x)，x＝[x1，x2…xd]，lk≤xk≤uk，k＝1，2…d (1)
in the formula (1), ukDenotes the upper limit of search,/kRepresents a search lower limit, d represents a dimension;
4.4, performing mutation operation, namely randomly selecting three random variation sources of different individuals from the population, and performing mutation operation by using a mutation operator, wherein the mutation mechanism is as follows:
ti(g)＝xr1(g)+F·[xr2(g)-xr3(g)](2)
in the formula (2), r1, r2 and r3 are different integers, and F is a scale factor;
step 4.5, performing cross operation, wherein after the SADE algorithm is subjected to the mutation operation, the cross operation needs to be performed, and the main idea of the cross operation is as follows: target individual tiWith the current individual xiExchange to generate new individual viThereby enhancing the search capability of the local area, the invention adoptsAnd carrying out cross operation on the binomial cross, wherein for the binomial cross, firstly, uniformly distributed random numbers r need to be generated and are in a (0, 1) interval, when the condition that r is less than or equal to cr is met, corresponding components of the target individual are received, otherwise, the corresponding components are kept unchanged, and the expression is as follows:
in formula (3), rnd is an integer within the interval 1-d;
4.6, selecting operation, combining simulated annealing and differential evolution algorithm in order to improve the capability of searching global optimal solution of the optimization algorithm and accelerate convergence speed, introducing a simulated annealing operator in the algorithm process of differential evolution, improving the selection operation in the differential evolution algorithm, wherein the selection operation after improvement is as follows:
suppose the optimal solution in the current generation is XtThe fitness corresponding to the current optimal solution is ftThen, the simulated annealing operation of the individual X corresponding to the currently executed selection operator is as follows:
when f is less than or equal to ftSelecting X to enter the next generation;
when f is>ftIn time, X is selected to enter the next generation with a certain probability, and the basic differential evolution algorithm does not select X to enter the next generation at this time.
The probability value calculation method is as follows:
the method comprises the following steps that T is annealing temperature, generally, the annealing temperature is gradually reduced along with the increase of iteration times, only the influence of fitness f is generally considered in selection probability in past documents, the influence of an independent variable X is not considered, the influence on the selection probability is introduced, the probability of selection is larger as the distance between the independent variable and a current optimal solution is longer, and therefore an optimization algorithm is helped to jump out a local optimal solution and a global optimal solution is searched;
step 4.7, setting a termination condition, stopping iteration after the iteration times of the SADE algorithm reach the set condition, outputting an experimental result at the moment as an optimal solution, and increasing and reducing the maximum evolution algebra according to requirements, wherein the parameter is debugged for multiple times, and finally selecting gen to be 50;
and 5: and (4) solving the product scheduling sequence problem of the marine crankshaft production line according to the improved SADE algorithm in the step (4), and comparing and analyzing the SADE algorithm with a differential evolution algorithm to verify the effectiveness of the SADE algorithm.
Further, in the step 1, a crankshaft processing stock layout sequence is taken as an optimization variable;
further, in the step 3, the minimum maximum completion time of the crankshaft is set as an optimization target, and a penalty factor is introduced to the constraint to judge whether the machining number of various types of crankshafts meets the requirement of the planned number. If not, inserting a penalty factor;
furthermore, in the step 5, the SADE algorithm is used for solving the product scheduling sequence problem of the marine crankshaft production line, and the SADE algorithm is compared and analyzed with the differential evolution algorithm, so that the feasibility of the SADE algorithm is verified.
Drawings
FIG. 1 is a flowchart of a simulated annealing improved differential evolution algorithm of the scheduling optimization method for marine crankshaft production line
FIG. 2 is a schematic diagram of a three-dimensional model of a crankshaft in an embodiment of a scheduling optimization method for production scheduling of a marine crankshaft production line according to the invention
FIG. 3 is a layout diagram of a marine crankshaft production shop for the scheduling optimization method of the marine crankshaft production line scheduling of the present invention
FIG. 4 is a production flow chart of the marine crankshaft of the scheduling optimization method for the production line of the marine crankshaft of the present invention
FIG. 5 is a comparison chart of the GA, PSO, DE, SADE algorithm optimization process of the scheduling optimization method of the marine crankshaft production line
Detailed Description
For a better understanding of the present invention, reference will now be made in detail to the present embodiments of the invention, examples of which are illustrated in the accompanying drawings. In addition, the embodiments described are only a part of the examples of the present invention, and not all examples.
The invention provides a scheduling and scheduling optimization method for a marine crankshaft production line, which is characterized in that a mathematical model is established by combining actual problems of crankshaft production enterprises, simulated annealing and a differential evolution algorithm are combined, a simulated annealing operator is introduced in the selection operation process of the differential evolution, the differential evolution algorithm is designed and improved, finally, the SADE algorithm is used for solving the problem of the product scheduling sequence of the marine crankshaft production line, and the SADE algorithm is compared and analyzed to verify the effectiveness of the SADE algorithm.
The invention researches the improvement and optimization of the production sequence of the products processed and manufactured in the crankshaft manufacturing link, and mainly researches the production line of the crankshaft manufacturing workshop. The marine crankshaft generally consists of a crank throw, a main journal shaft, a free end and an output end. The produced marine crankshaft, such as A-type marine crankshaft, is formed by splicing 7 crank throws, 6 main journals, 1 free end and 1 output end. The invention relates to other two types of marine crankshafts in production: the model B consists of 6 crank throws, 5 main journal shafts, 1 free end and 1 output end; the C model consists of 5 bell cranks, 4 main journal shafts, 1 free end and 1 output end.
As shown in fig. 2: the invention relates to a three-dimensional model schematic diagram of a crankshaft in an embodiment of a scheduling and optimizing method for production scheduling of a marine crankshaft production line, wherein 1 is a free end, 2 is a crank throw, 3 is a main journal shaft and 4 is an output end.
As shown in fig. 3: the layout of the production shop of the marine crankshaft is the optimized scheduling method for the production scheduling of the marine crankshaft production line.
As shown in fig. 4: the marine crankshaft production flow of the embodiment of the scheduling and scheduling optimization method for the marine crankshaft production line is disclosed by the invention.
The scheduling and scheduling optimization method for the marine crankshaft production line comprises the following steps:
step 1: determining a processing sequence, processing time and variable conditions of processing equipment by combining actual problems of crankshaft production enterprises;
step 2: setting a hypothesis condition related to the practical problem, not considering the emergency in the process production,
and step 3: reasonably setting constraint conditions and optimization targets of the model according to the step 1 and the step 2, and establishing a mathematical model;
and 4, step 4: according to the mathematical model in the step 3, simulated annealing and a differential evolution algorithm are combined, a simulated annealing operator is introduced in the selection operation process of differential evolution, a simulated annealing mixed differential evolution algorithm is designed, and the differential evolution algorithm is improved;
and 5: and (4) solving the product scheduling sequence problem of the marine crankshaft production line according to the SADE algorithm in the step (4), and comparing and analyzing the SADE algorithm with a differential evolution algorithm to verify the effectiveness of the SADE algorithm.
In the step 1, according to the workshop layout and the production line, the processing sequence and the processing time of the A, B, C type crankshaft are determined, and the crankshaft processing layout sequence is taken as an optimization variable.
In the step 2, the multi-product scheduling optimization of the marine crankshaft production line is assumed as follows:
(1) the production sequence of each type of crankshaft at each station is fixed, namely the production sequence of the crankshafts of different types is consistent;
(2) only one workpiece can be produced at one station, and the same workpiece can be produced at the same station only in a fixed time;
(3) the processing time of the product on the station comprises the preparation time of the product on the station, and is not related to the product putting sequence;
(4) when the shaft machining time is neglected, namely the shaft parts are assembled and machined, the shaft parts are in place by default;
(5) the processing and manufacturing operation time of each product is only related to the type of the product, and the processing and manufacturing operation time of the same product is fixed;
(6) each station continuously works without considering the occurrence of special conditions;
in the step 3, the maximum completion time is set as the minimum optimization target, and a penalty factor is introduced to the constraint to judge whether the machining number of various types of crankshafts meets the requirement of the planned number. If not, a penalty factor intervenes. And establishing a general production line scheduling mathematical model.
The optimization model can be simplified as follows:
minf(x)＝S2(n，m)
s.t.x∈N*
x≥1
x≤Nshaft
(∑x＝i)＝NCrank(i)，i＝1,2,3
explained for the above optimization model: the first row is the optimization variable, i.e., the layout sequence of the crankshaft machining, and the objective function is the minimum time for the last crankshaft to finish the last process. The total number of the crankshafts is n, and the number of the stations is m. s.t are constraints, the first of which means that the argument takes the positive integer N*Corresponding to the crankshaft number in the stock layout sequence. The second constraint is that the number of the crank shaft is more than or equal to 1, and the third constraint is that the number of the crank shaft is less than or equal to the type N of the crank shaftshaftEach type of crankshaft is numbered one. The last one is the constraint of the number of crankshafts, each number in the stock layout sequence represents a type of shaft, the number of each number is calculated and should be equal to the planned number N of shafts of the typeCrank。
In the step 4, the parameters of the simulated annealing mixed differential evolution (SADE) algorithm are set as follows:
(1) encoding and decoding
This is the first and critical issue to apply SADE to solve the scheduling problem. For the production scheduling problem of m machines of n products, the invention expands n products into v workpieces, using operation-based coding, i.e. representing an individual with a sequence of workpiece numbers of length v × m, where each workpiece number is repeated m times. The maximum time-out is a regular performance indicator, and the optimal schedule must be an active schedule. Therefore, it needs to be converted into a workpiece number and distinguished before decoding.
(2) Initial population setting
Reasonable population numbers should be within the (5D,10D) interval, D being the dimension. In addition, to ensure sufficient mutation vectors, NP.gtoreq.4 is generally required. Specifically, the population number represents diversity, and NP is large, increasing the probability of finding an optimal solution, but relatively speaking, the amount of computation increases. Generally for problems with relatively low dimensionality, the population number is chosen to be within 15-30. The population number of the present invention was selected to be 20.
(3) Mutation operator F setting
Too small or too large F changes little the probability density function of the population in the search space, making it difficult to achieve a good mutation effect. It determines the magnification ratio of the deviation vector. F-0.5 is usually a good initial choice, increasing either F or NP appropriately if the population converges prematurely. In general, the larger the F, the larger the perturbation, but the more the solution can be found. The invention takes 0.8.
(4) Crossover operator CR settings
The basic idea is to continuously adjust the weights of the historical information and the current information so as to control the trial vectors generated by random selection. The method has the advantages that the larger cross probability is set, the search of the seed group to the space is favorably enhanced, and the optimal solution is more conveniently found. The value is generally between 0.6 and 1. The invention takes 0.9.
In the step 5, according to the product type and the station production time setting condition, the DE algorithm and the SADE algorithm are respectively used for solving, and the final production scheduling sequence result is as follows:
scheduling sequence after optimization of DE algorithm: BCCBBABCABACACACACCCC.
The optimal production time is as follows: 1039.6 hours.
The scheduling sequence after the SADE algorithm is optimized is as follows: CAACCCABACACBBBCCBC.
The optimal production time is as follows: 1039.2 hours.
As shown in fig. 5, it is a comparison graph of the optimization process of GA, PSO, DE, SADE algorithms, reflecting the good convergence of SADE. In order to better reflect the performance comparison of the four algorithms on data, the invention performs a plurality of times of operation for testing, counts the iteration times and then analyzes the statistical result.
TABLE 1 statistical comparison
According to the table, for the scheduling problem with relatively small calculation scale in the invention, the convergence rates of the four algorithms are different, the GA algorithm is relatively most mature and stable, the variance of the iteration times is the smallest and is 2.8, but the average iteration time is 11.5, and the convergence rate is the slowest. The basic PSO algorithm and the DE algorithm are equivalent in convergence speed and stability, the convergence speed is higher than that of the GA algorithm, and the stability, namely the variance of the iteration times is slightly larger than that of the GA algorithm. The improved SADE algorithm has the fastest convergence speed among the four algorithms, the optimal solution can be obtained for at least 3 times, and the average iteration number is 4.2, but relatively speaking, the stability is not as good as that of other basic intelligent optimization algorithms, and the optimal result can be obtained by trying to run for many times. Therefore, the improved SADE algorithm effectively improves the searching speed in the optimization process.
Claims (2)
1. A production scheduling and scheduling optimization method for a marine crankshaft production line is characterized by comprising the following steps:
step 1: determining variable conditions including a processing sequence, processing time and processing equipment by combining actual problems of crankshaft production enterprises;
step 2: setting an assumed condition related to an actual problem, and not considering emergencies in the process production process, assuming the following conditions:
(1) the production sequence of each type of crankshaft at each station is fixed, namely the production sequence of the crankshafts of different types is consistent;
(2) only one workpiece can be produced at one station, and the same workpiece can be produced at the same station only in a fixed time;
(3) the processing time of the product on the station comprises the preparation time of the product on the station, and is not related to the product putting sequence;
(4) when the shaft machining time is neglected, namely the shaft parts are assembled and machined, the shaft parts are in place by default;
(5) the processing and manufacturing operation time of each product is only related to the type of the product, and the processing and manufacturing operation time of the same product is fixed;
(6) each station continuously works without considering the occurrence of special conditions;
and step 3: reasonably setting constraint conditions and optimization targets of the model according to the step 1 and the step 2, and establishing a mathematical model;
and 4, step 4: according to the mathematical model in the step 3, simulated annealing and a differential evolution algorithm are combined, a simulated annealing operator is introduced in the selection operation process of differential evolution, a simulated annealing mixed differential evolution algorithm is designed, the differential evolution algorithm is improved, and the specific operation method is as follows:
step 4.1, setting initial conditions, such as population, mutation operators and crossover operators;
step 4.2, initializing a population, wherein a simulated annealing mixed differential evolution algorithm adopts floating point real number coding and randomly generates an initial population by using a rand () function;
step 4.3, determining population fitness, wherein the SADE algorithm is used as an optimization algorithm, and can optimize an experimental solution through continuous cooperation and competition among individuals so as to continuously approach an optimal solution, wherein generally, a target function of a mathematical model is a fitness function;
minf(x)，x＝[x1，x2…xd]，lk≤xk≤uk，k＝1，2…d (1)
in the formula (1), ukDenotes the upper limit of search,/kRepresents a search lower limit, d represents a dimension;
4.4, performing mutation operation, namely randomly selecting three random variation sources of different individuals from the population, and performing mutation operation by using a mutation operator, wherein the mutation mechanism is as follows:
ti(g)＝xr1(g)+F·[xr2(g)-xr3(g)](2)
in the formula (2), r1, r2 and r3 are different integers, and F is a scale factor;
step 4.5, performing cross operation, wherein after the SADE algorithm is subjected to the mutation operation, the cross operation needs to be performed, and the main idea of the cross operation is as follows: target individual tiWith the current individual xiExchange to generate new individual viTo thereby enhance the local areaThe invention adopts binomial crossing to carry out crossing operation, for the binomial crossing, firstly, a uniformly distributed random number r needs to be generated and is in a (0, 1) interval, when the condition that r is less than or equal to cr is met, a corresponding component of a target individual is received, otherwise, the component is kept unchanged, and the expression is as follows:
in formula (3), rnd is an integer within the interval 1-d;
4.6, selecting operation, combining simulated annealing and differential evolution algorithm in order to improve the capability of searching global optimal solution of the optimization algorithm and accelerate convergence speed, introducing a simulated annealing operator in the algorithm process of differential evolution, improving the selection operation in the differential evolution algorithm, wherein the selection operation after improvement is as follows:
suppose the optimal solution in the current generation is XtThe fitness corresponding to the current optimal solution is ftThen, the simulated annealing operation of the individual X corresponding to the currently executed selection operator is as follows:
when f is less than or equal to ftSelecting X to enter the next generation;
when f > ftSelecting X to enter the next generation according to a certain probability, and the basic differential evolution algorithm does not select X to enter the next generation at the moment;
the probability value calculation method is as follows:
the method comprises the following steps that T is annealing temperature, generally, the annealing temperature is gradually reduced along with the increase of iteration times, only the influence of fitness f is generally considered in selection probability in past documents, the influence of an independent variable X is not considered, the influence on the selection probability is introduced, the probability of selection is larger as the distance between the independent variable and a current optimal solution is longer, and therefore an optimization algorithm is helped to jump out a local optimal solution and a global optimal solution is searched;
step 4.7, setting a termination condition, stopping iteration after the iteration times of the SADE algorithm reach the set condition, outputting an experimental result at the moment as an optimal solution, and increasing and reducing the maximum evolution algebra according to requirements, wherein the value of the maximum evolution algebra is positioned in a [50, 500] interval;
and 5: and (4) solving the product scheduling sequence problem of the marine crankshaft production line according to the improved SADE algorithm in the step (4), and comparing and analyzing the SADE algorithm with a differential evolution algorithm to verify the effectiveness of the SADE algorithm.
2. The method of claim 1, wherein the maximum evolutionary algebra is 50.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113408818A (en) * | 2021-07-07 | 2021-09-17 | 广东工业大学 | Production scheduling optimization method based on ALNS improved simulated annealing |
| CN114217580A (en) * | 2021-12-06 | 2022-03-22 | 东华大学 | Functional fiber production scheduling method based on improved differential evolution algorithm |
| CN114548735A (en) * | 2022-02-17 | 2022-05-27 | 武汉重工铸锻有限责任公司 | Intelligent production scheduling method for batch manufacturing of marine diesel engine crankshafts |
-
2019
- 2019-11-20 CN CN201911139676.8A patent/CN110929930A/en not_active Withdrawn
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113408818A (en) * | 2021-07-07 | 2021-09-17 | 广东工业大学 | Production scheduling optimization method based on ALNS improved simulated annealing |
| CN113408818B (en) * | 2021-07-07 | 2022-02-01 | 广东工业大学 | Production scheduling optimization method based on ALNS improved simulated annealing |
| CN114217580A (en) * | 2021-12-06 | 2022-03-22 | 东华大学 | Functional fiber production scheduling method based on improved differential evolution algorithm |
| CN114217580B (en) * | 2021-12-06 | 2024-04-19 | 东华大学 | Functional fiber production scheduling method based on improved differential evolution algorithm |
| CN114548735A (en) * | 2022-02-17 | 2022-05-27 | 武汉重工铸锻有限责任公司 | Intelligent production scheduling method for batch manufacturing of marine diesel engine crankshafts |
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