CN113554216B - Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method - Google Patents
Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method Download PDFInfo
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Abstract
The invention relates to a Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method, which optimizes extrusion efficiency and extrusion quality in the process of polymer hybrid manufacturing. Firstly, based on a long-short-term memory neural network, an extrusion efficiency and extrusion quality model is built by combining a K-fold crossover algorithm and a genetic algorithm, and the problem of insufficient generalization capability of the model is solved. And setting a parameter screening link, eliminating an unreasonable network structure in the optimizing process, and improving the modeling operation speed. And secondly, adopting an improved hybrid variation differential evolution multi-objective optimization algorithm to optimize and solve the technological parameters in the polymer hybrid manufacturing process. And the global searching capability and the local searching capability of the model are balanced by utilizing the mixed mutation strategy, so that the distribution and diversity of the population are improved. The invention improves the LSTM neural network modeling method and the multi-objective optimization differential algorithm. Has a vital function of improving the process optimization control of the polymer mixed manufacturing.
Description
Technical Field
The invention belongs to the technical field of polymer hybrid manufacturing, and particularly relates to a Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method.
Background
The process of polymer mixed manufacture has the characteristics of nonlinearity, time lag, coupling and the like. Meanwhile, the problem that the number of samples is small due to operation data in the production process can be solved, so that modeling of the high polymer mixed manufacturing process parameters becomes more difficult. In addition, the variation of the conventional multi-objective optimized differential evolution algorithm is based on a differential vector, and the algorithm itself contains fewer controllable parameters, so that the controllable parameters have direct influence on the performance of the algorithm. If the controllable parameters are not reasonably selected, a large number of inferior solutions can be formed in the evolution process; in the differential evolution process, the mutation rate F and the crossover rate Cr are often set as fixed parameters or linearly changed along with the algebra of evolution, so that the optimization requirements cannot be well adapted; the differential evolution algorithm has weak local searching capability.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method for solving the problems in the background art.
According to the technical scheme provided by the invention, the Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method comprises the following steps of:
1) Establishing an objective function for a research object according to extrusion efficiency and extrusion quality in the process of polymer mixed manufacturing;
2) Adding constraint conditions, specifically including upper and lower temperature limits, upper and lower pressure limits and heat balance;
3) Taking extrusion speed, melt temperature and pressure as decision variables;
4) Constructing an extrusion efficiency and extrusion quality model by combining a K-fold crossover algorithm and a GA genetic algorithm on the basis of a long and short-time memory neural network;
5) And optimizing and solving the technological parameters in the polymer hybrid manufacturing process by utilizing an improved multi-objective optimization hybrid variation differential evolution algorithm.
In the technical scheme of the invention, the extrusion efficiency and extrusion quality model based on long-short-term memory neural network and combined with the K-fold crossover algorithm and the GA genetic algorithm specifically comprises the following steps:
1) And eliminating flaw Data in the original Data set, carrying out normalization pretreatment on the Data set, and eliminating the influence of dimension and magnitude. The data set is subjected to K-fold intersection through a K-fold intersection algorithm, and two general methods are adopted for selecting the K value: k=10 or k=n, and the calculation amount is extremely large when k=n, so k=10 is set here. I.e. the data set is divided into 10 subsets k1, k2, …, k10 of the same width and dimension, the matrices Team1, team2, …, team10 are established.
Data set＝Team1＝Team2＝…＝Team10 (1)
Data set＝(k1,k2,k3,…,k10) (2)
2) Meanwhile, for better representing the superiority and inferiority of the operation network superparameter selection, the mean value of the MSE is used as an objective function of the GA genetic algorithm. The calculation process is as follows:
when i=10, the model built by each calculation is reasonable in structure, and the average mean square error fed back at this time is:
when i is less than 10, the condition that the structure is unreasonable and the data set is unevenly distributed exists in the modeling process is represented, and at the moment, the average mean square error fed back is as follows:
3) In the modeling process, the change trend of the training set and the test set is judged by using the Loss function so as to judge the rationality of the model, and the Loss function Loss of the model is defined, wherein the formula is as follows:
wherein x is predict Representing the predicted value, x value Representing actual values
4) Generating LSTM neural network superparameter by GA genetic algorithm in constraint range: the initial values of hidden layer neuron number Units, LSTM training round number epochs, hidden layer network layer number Layers and random discard parameter probability dropout determine the initial network structure of the neural network.
The technical scheme of the invention is as follows: the objective function, decision variable and constraint conditions are as follows: when solving the multi-objective optimization problem, the objective function, decision variables and related constraints are required to be explicitly optimized; the specific mathematical expression is as follows:
wherein F (X) is an objective function, and F (X) is an objective vector composed of m objective functions; x is a decision variable, and is a decision vector composed of n decision variables;and->Is the kth decision variable x k Lower and upper bounds of (2); h i (X) is the ith inequality constraint; g j (X) is the jth equality constraint.
The technical scheme of the invention is as follows: the multi-objective optimization hybrid variation differential evolution algorithm comprises four processes of population generation, crossing, variation and selection; generating an initialized population in a constraint range, performing mutation operation on the population according to different base vector selection modes and different differential vector calculation modes, and performing cross operation on the mutated population to increase the diversity of the population; and selecting a feasible solution based on a Pareto selection dominance mechanism, and stopping program operation to output an optimal result after a termination condition is reached.
In some specific technical schemes, the population initialization generation process is as follows:
NP n-dimensional individuals are randomly generated within the solution space.
X i (0)＝(x i,1 (0),x i,2 (0),...,x i,n (0)) (8)
i＝1,2,...,NP
The j-th population of the i-th individual is valued as follows:
i＝1,2,...,NP
j＝1,2,...,n
wherein X is i (t) represents the ith individual in the t generation population, t=0 represents the population algebra as the first generation; x is x i，j (t) is the value of the j-th dimension of the i-th individual in the t-generation population;a minimum value representing the j-th dimensional value of the i-th individual; />Representing the maximum value of the ith individual jth dimensional value; rand (0, 1) means that a random number is taken in (0, 1).
In some specific embodiments, the population variation process is as follows:
performing mutation operation on the generated initial population, wherein the individuals of the initial population are formed by X i (t) represents that, in order to reasonably distinguish between the initial population and individuals of the variant population, the individuals of the variant population are represented by V i (t) the mutation strategy is as follows;
(1) DE/rand/1 variant strategy
V s (g)＝X r1 (g)+F·(X r2 (g)-X r3 (g)) (10)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X r1 (g)，X r2 (g)，X r3 (g) R1, r2 and r3 individuals selected randomly from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(2) DE/best/1 variant strategy
V s (g)＝X best (g)+F·(X r1 (g)-X r2 (g)) (11)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population; x is X r1 (g)，X r2 (g) R1, r2 individuals selected randomly from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(3) DE/rand/2 variant strategy
V s (g)＝X r1 (g)+F·(X r2 (g)-X r3 (g)+F·(X r4 (g)-X r5 (g)) (12)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X r1 (g)，X r2 (g)，X r3 (g)，X r4 (g)，X r5 (g is the r1, r2, r3, r4 and r5 individuals selected randomly from g generation population, F is the scaling factor, is [0,2 ]]Random numbers obeying uniform distribution;
(4) DE/best/2 variant strategy
V s (g)＝X best (g)+F·(X r1 (g)-X r2 (g)+F·(X r3 (g)-X r4 (g)) (13)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population;
X r1 (g)，X r2 (g)，X r3 (g)，X r4 (g) Randomly selecting the r1, r2, r3 and r4 individuals from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(5) DE/target-to-best/2 variant strategy
V s (g)＝X s (g)+F·(X best (g)-X s (g)+F·(X r1 (g)-X r2 (g)) (14)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population;
X r1 (g)，X r2 (g) R1, r2 individuals selected randomly from the g generation population; x is X s (g) Is the following in g generation populationMechanically selecting an s-th individual; f is a scaling factor of [0,2 ]]And random numbers subjected to uniform distribution.
The DE/rand/1 variant strategy and the DE/rand/2 variant strategy can improve the exploration capacity of the search algorithm; the DE/best/1 variant strategy and the DE/best/2 variant strategy can improve the development capability of a search algorithm; namely, different mutation strategies have different capacities in global searching and local searching and have emphasis on each;
in order to expand the population searching range, different mutation strategies are adopted for the same multi-objective optimization problem, and the optimal individual in the operation is entered into the next iteration operation in the mixed mutation process.
In some specific embodiments, the population crossover process is as follows:
the diversity of the population determines the optimizing effect to a certain extent, and the purpose of the cross operation is to enhance the diversity of the population; the specific operation mode is that g generation population individuals X are selected according to the population crossing rate Cr s (g) And variant individual V s (g) Thereby generating a test individual W s (g) The method comprises the steps of carrying out a first treatment on the surface of the Binomial interleaving is the most common way of interleaving at present.
In which W is i，j (g) The value V of the j-th dimension of the ith experimental individual after g generation population variation i，j (g) The value of the j dimension of the ith individual after g generation population variation; x is x i，j (g) Randomly selecting a value of a j-th dimension of an i-th individual in the g-generation population; cr epsilon [0,1 ]]For cross probability, rand (0, 1) is [0,1]And random numbers subjected to uniform distribution.
In some specific technical schemes: the population selection process is as follows:
the selection operation is based on the selection mechanism of Pareto and based on the evaluation function pair W i (g) And X i (g) Non-dominant sorting and selecting dominant individual X i (g+1) entering the next iteration; through the above cyclic operation, when the evolution algebra reaches the evolution algebraWhen the maximum value is reached, the evolution process is finished, and a non-dominant solution set of the pareto optimal front edge is output;
wherein W is i (g) The ith experimental individual after g generation population variation; x is X i (g) Randomly selecting an ith individual from the g generation population; x is X i (g+1) is the randomly selected ith individual in the g+1 generation population.
The technical scheme of the invention is as follows: the mixing and mutation process is specifically as follows:
1) In order to obtain variant population individuals generated by different variant strategies, 4 variant population sets V_rand/1 (t), V_best/1 (t), V_rand/2 (t), and V_best/2 (t) are set, variant individuals are generated by carrying out variant operation by using different variant strategies, and the variant individuals are respectively stored in corresponding populations X (t). Meanwhile, an external archive set V (t) is additionally arranged for storing the optimal solution.
2) And calculating the fitness value of each individual in the variant population, and distributing the fitness value to the individuals with the conflict of the optimization targets by using a non-dominant sorting method. After assigning fitness values, the diversity of the population cannot be fully guaranteed if individuals of the population are ranked for fitness values and individuals of high fitness values are selected. Thus, to ensure population diversity, 2 individuals within each variant population are randomly selected to compare the magnitude of their fitness value, and the individual with the greatest fitness value is stored in the external archive set V (t).
The invention provides an improved LSTM neural network modeling method. The data set is divided through a K-fold intersection algorithm, and the mean value of the mean square error of the model is set as an optimization objective function, so that the problem that the generalization capability of the model is reduced due to unreasonable division of the data set is solved. And optimizing the neural network super-parameters by adopting a genetic algorithm to obtain an optimal network structure and improve modeling accuracy. And judging the curve trend of the loss function by setting a parameter screening link, eliminating an unreasonable network structure in the optimizing process, and improving the modeling operation speed.
The invention adopts an improved differential optimization algorithm of multi-objective mixed variation, and improves the distribution and diversity of the population by setting a method of combining multi-variation population with an external archive set and utilizing the global searching capability and the local searching capability of a mixed variation strategy balance model. And optimizing the parameters of the polymer hybrid manufacturing process through an optimization algorithm to obtain an optimal Pareto solution set.
Compared with the prior art, the invention has the beneficial effects that: the invention has novel structural design and can realize the optimal control of polymer hybrid manufacturing.
Drawings
FIG. 1 is a flow chart of modeling polymer hybrid fabrication.
FIG. 2 is a flow chart of multi-objective optimized differential evolution.
FIG. 3 is a flow chart of the mixed variation.
Detailed Description
The present invention will be further described with reference to the drawings and examples in order to make the objects, technical solutions and advantages of the present invention more apparent.
The invention provides a Kfold-LSTM hybrid variation optimizing macromolecule hybrid manufacturing multi-objective optimizing method, which specifically comprises the following steps:
1) Establishing an objective function for a research object according to extrusion efficiency and extrusion quality in the polymer mixing manufacturing process;
2) Adding constraint conditions, specifically including upper and lower temperature limits, upper and lower pressure limits and heat balance;
3) Taking extrusion speed, melt temperature and pressure as decision variables;
4) Constructing an extrusion efficiency and extrusion quality model by combining a K-fold crossover algorithm and a GA genetic algorithm on the basis of a long and short-time memory neural network;
5) And optimizing and solving the technological parameters in the polymer hybrid manufacturing process by utilizing an improved multi-objective optimization hybrid variation differential evolution algorithm.
As shown in fig. 1, the method for constructing the extrusion efficiency and extrusion quality model based on the long-short-term memory neural network and combining the K-fold crossover algorithm and the GA genetic algorithm in the embodiment of the present invention specifically includes:
1) And eliminating flaw Data in the original Data set, carrying out normalization pretreatment on the Data set, and eliminating the influence of dimension and magnitude. The data set is subjected to K-fold intersection through a K-fold intersection algorithm, and two general methods are adopted for selecting the K value: k=10 or k=n, and the calculation amount is extremely large when k=n, so k=10 is set here. I.e. the data set is divided into 10 subsets k1, k2, …, k10 of the same width and dimension, the matrices Team1, team2, …, team10 are established.
Data set＝Team1＝Team2＝...＝Team10 (1)
Data set＝(k1,k2,k3,...,k10) (2)
2) Meanwhile, for better representing the superiority and inferiority of the operation network superparameter selection, the mean value of the MSE is used as an objective function of the GA genetic algorithm. The calculation process is as follows:
when i=10, the model built by each calculation is reasonable in structure, and the average mean square error fed back at this time is:
when i is less than 10, the condition that the structure is unreasonable and the data set is unevenly distributed exists in the modeling process is represented, and the average mean square error fed back at the moment is as follows:
3) In the modeling process, the change trend of the training set and the test set is judged by using the Loss function so as to judge the rationality of the model, and the Loss function Loss of the model is defined, wherein the formula is as follows:
wherein x is predict Representing the predicted value, x value Representing actual values
4) Generating LSTM neural network superparameter by GA genetic algorithm in constraint range: the initial values of hidden layer neuron number Units, LSTM training round number epochs, hidden layer network layer number Layers and random discard parameter probability dropout determine the initial network structure of the neural network.
As shown in fig. 2, the specific steps of the multi-objective optimized differential evolution algorithm flow in the embodiment of the invention are as follows:
when solving the multi-objective optimization problem, the objective function, decision variables and related constraints need to be explicitly optimized. The specific mathematical expression is as follows:
wherein F (X) is an objective function, and F (X) is an objective vector composed of m objective functions; x is a decision variable, and is a decision vector composed of n decision variables;and->Is the kth decision variable x k Lower and upper bounds of (2); h i (X) is the ith inequality constraint; g j (X) is the jth equality constraint.
The technical scheme of the invention comprises the following steps: the multi-objective optimization hybrid variation differential evolution algorithm comprises four processes of population generation, crossing, variation and selection; generating an initialized population in a constraint range, performing mutation operation on the population according to different base vector selection modes and different differential vector calculation modes, and performing cross operation on the mutated population to increase the diversity of the population; and selecting a feasible solution based on a Pareto selection dominance mechanism, and stopping program operation to output an optimal result after a termination condition is reached.
The population initialization generation process is as follows:
randomly generating NP n-dimensional individuals in a solution space;
(8) X i (0)＝(x i,1 (0),x i,2 (0),...,x i,n (0))
i＝1,2,…,NP
the j-th population of the i-th individual is valued as follows:
(9)
i＝1,2,...,NP
j＝1,2,...,n
wherein X is i (t) represents the ith individual in the t generation population, t=0 represents the population algebra as the first generation; x is x i，j (t) is the value of the j-th dimension of the i-th individual in the t-generation population;a minimum value representing the j-th dimensional value of the i-th individual; />Representing the maximum value of the ith individual jth dimensional value; rand (0, 1) means that a random number is taken in (0, 1).
The technical scheme of the invention is as follows: the improved mutation process is specifically as follows: performing mutation operation on the generated initial population, wherein the individuals of the initial population are formed by X i (t) represents that, in order to reasonably distinguish between the initial population and individuals of the variant population, the individuals of the variant population are represented by V i (t) the mutation strategy is as follows
(1) DE/rand/1 variant strategy
V s (g)＝X r1 (g)+F·(X r2 (g)-X r3 (g)) (10)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X r1 (g)，X r2 (g)，X r3 (g) R1, r2 and r3 individuals selected randomly from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(2) DE/best/1 variant strategy
V s (g)＝X best (g)+F·(X r1 (g)-X r2 (g)) (11)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population; x is X r1 (g)，X r2 (g) R1, r2 individuals selected randomly from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(3) DE/rand/2 variant strategy
V s (g)＝X r1 (g)+F·(X r2 (g)-X r3 (g)+F·(X r4 (g)-X r5 (g)) (12)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X r1 (g)，X r2 (g)，X r3 (g)，X r4 (g)，X r5 (g is the r1, r2, r3, r4 and r5 individuals selected randomly from g generation population, F is the scaling factor, is [0,2 ]]Random numbers obeying uniform distribution;
(4) DE/best/2 variant strategy
V s (g)＝X best (g)+F·(X r1 (g)-X r2 (g)+F·(X r3 (g)-X r4 (g)) (13)
Wherein Vs s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population;
X r1 (g)，X r2 (g)，X r3 (g)，X r4 (g) Randomly selecting the r1, r2, r3 and r4 individuals from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(5) DE/target-to-best/2 variant strategy
V s (g)＝X s (g)+F·(X best (g)-X s (g)+F·(X r1 (g)-X r2 (g)) (14)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population;
X r1 (g)，X r2 (g) R1, r2 individuals selected randomly from the g generation population; x is X s (g) Is thatRandomly selecting an s-th individual in the g generation population; f is a scaling factor of [0,2 ]]And random numbers subjected to uniform distribution.
The DE/rand/1 variant strategy and the DE/rand/2 variant strategy can improve the exploration capacity of the search algorithm; the DE/best/1 variant strategy and the DE/best/2 variant strategy can improve the development capability of a search algorithm; namely, different mutation strategies have different capacities in global searching and local searching and have emphasis on each;
in order to expand the population searching range, different mutation strategies are adopted for the same multi-objective optimization problem, and the optimal individual in the operation is entered into the next iteration operation in the mixed mutation process.
The technical scheme of the invention is as follows: the population crossover process is as follows:
the diversity of the population determines the optimizing effect to a certain extent, and the purpose of the cross operation is to enhance the diversity of the population; the specific operation mode is that g generation population individuals X are selected according to the population crossing rate Cr s (g) And variant individual V s (g) Thereby generating a test individual W s (g) The method comprises the steps of carrying out a first treatment on the surface of the Binomial interleaving is the most commonly used interleaving method at present;
in which W is i，j (g) The value V of the j-th dimension of the ith experimental individual after g generation population variation i，j (g) The value of the j dimension of the ith individual after g generation population variation; x is x i，j (g) Randomly selecting a value of a j-th dimension of an i-th individual in the g-generation population; cr epsilon [0,1 ]]For cross probability, rand (0, 1) is [0,1]And random numbers subjected to uniform distribution. The population selection process is as follows:
the selection operation is based on the selection mechanism of Pareto and based on the evaluation function pair W i (g) And X i (g) Non-dominant sorting and selecting dominant individual X i (g+1) entering the next iteration; through the cyclic operation, when the evolution algebra reaches the maximum value of the evolution algebra, the evolution process is finished, and the pareto optimal front edge is outputNon-dominant solution sets;
wherein W is i (g) The ith experimental individual after g generation population variation; x is X i (g) Randomly selecting an ith individual from the g generation population; x is X i (g+1) is the randomly selected ith individual in the g+1 generation population. As shown in fig. 3, the process of the hybrid mutation in the embodiment of the present invention is specifically as follows:
1) In order to obtain variant population individuals generated by different variant strategies, 4 variant population sets V_rand/1 (t), V_best/1 (t), V_rand/2 (t), and V_best/2 (t) are set, variant individuals are generated by carrying out variant operation by using different variant strategies, and the variant individuals are respectively stored in corresponding populations X (t). Meanwhile, an external archive set V (t) is additionally arranged for storing the optimal solution.
2) And calculating the fitness value of each individual in the variant population, and distributing the fitness value to the individuals with the conflict of the optimization targets by using a non-dominant sorting method. After assigning fitness values, the diversity of the population cannot be fully guaranteed if individuals of the population are ranked for fitness values and individuals of high fitness values are selected. Thus, to ensure population diversity, 2 individuals within each variant population are randomly selected to compare the magnitude of their fitness value, and the individual with the greatest fitness value is stored in the external archive set V (t).
The invention is further described in connection with specific experiments.
According to the invention, an extrusion efficiency model and an extrusion quality prediction model are respectively established through the improved LSTM neural network, and a relation between extrusion efficiency and extrusion quality is established, so that a data base is provided for subsequent multi-objective optimization. The objective function and decision variables of the experiment were set.
minF(x)＝{f Extrusion efficiency (x),f Extrusion quality (x)} (16)
Wherein X= [ S ] Extrusion speed ，S Melt temperature ，S Pressure of ]X is a decision variable l ，X u Take value for optimizing variableUpper and lower limits.
The optimization process adopts a mixed variation MODE algorithm to carry out multi-objective optimization on extrusion efficiency and extrusion quality, and a decision variable is set as a rotation speed S Extrusion speed Solution temperature S Melt temperature Pressure S Pressure of . Considering the upper and lower temperature limits, the upper and lower pressure limits, the heat balance is used as a constraint condition. Setting a decision variable extrusion speed range [1 x 10 ] -6 m 3 /s,6*10 -6 m 3 /s]Melt temperature [270 ℃,320 DEG C]The pressure is [1mpa,5mpa ]]。
The performance evaluation indexes of the multi-target differential evolution algorithm have three kinds of convergence, uniformity and distribution. The convergence represents the convergence degree of the final result of the algorithm, and the closer the optimizing result is to the pareto optimal solution, the better the convergence degree is represented. The better the distribution, the best results will cover the pareto best boundary as much as possible. As an evaluation index of convergence and distribution, an inverse generation distance index (Inversed Generational Distance, IGD) is often used. Uniformity, representing the optimizing performance of the algorithm, the optimizing result should be uniformly distributed along the pareto optimal solution. The uniformity is often measured using Spacing indicators (SPs). For randomness, the functions ZDT1, ZDT2, ZDT3, DTLZ1, DTLZ2 are chosen as test functions. And each algorithm was run 20 times with the average as the final result.
Table 1 lists IGD indices for a solution set of 5 different algorithms in the example, from which it can be seen that the IGD mean values for the mixed variation MODE algorithm are 3.8981 ×10 when optimizing the double objective optimization problem ZDT1, ZDT2, ZDT3, respectively -3 ，3.8168×10 -3 ，6.3401×10 -3 The average value is smaller than the IGD average value when the four algorithms of NSGA-II, NSGA-III, MOPSO and MOEDA are used for optimizing ZDT1, ZDT2 and ZDT 3. IGD means of the mixed variation MODE algorithm are 2.5900 multiplied by 10 respectively in the process of optimizing three target optimization problems DTLZ1 and DTLZ2 -2 ，5.4568×10 -2 The mean value is larger than the IGD mean value when the MOEAD algorithm optimizes the DTLZ1 and the DTLZ 2. From the above analysis, the mixed variation MODE algorithm has better convergence and diversity.
Table 2 lists SP criteria for a solution set of 5 different algorithms in an example fromAs can be seen in Table 2, the SP mean values of the mixed variation MODE algorithm are 5.3073 ×10 when optimizing ZDT1, ZDT3, and DTLZ2, respectively -3 ，8.6509×10 -3 ，4.8488×10 -3 The average value of SP is smaller than that of the four algorithms of NSGA-II, NSGA-III, MOPSO and MOEDA when the algorithm is optimized to ZDT1, ZDT3 and DTLZ 2. The SP average value of the mixed variation MODE algorithm in the process of optimizing the ZDT2 is larger than the SP average value of NSGA-III in the process of optimizing the ZDT 2. The SP average value of the mixed variation MODE algorithm in the DTLZ1 optimizing process is larger than that of the SP average value in the MOEAD to the DTLZ1 optimizing process. From the above analysis, the mixed variant MODE algorithm has better uniformity.
TABLE 1 reverse generation distance Index (IGD) comparison for different optimization algorithms
TABLE 2 comparison of different optimization Algorithm spacing index (SP)
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Claims (9)
1. The Kfold-LSTM hybrid variation optimizing polymer hybrid manufacturing multi-objective optimizing method is characterized by comprising the following steps:
1) Establishing an objective function by taking extrusion efficiency and extrusion quality in a polymer mixing manufacturing process as a research object;
2) Adding constraint conditions, specifically including upper and lower temperature limits, upper and lower pressure limits and heat balance;
3) Taking extrusion speed, melt temperature and pressure as decision variables;
4) Constructing an extrusion efficiency and extrusion quality model by combining a K-fold crossover algorithm and a GA genetic algorithm on the basis of a long and short-time memory neural network LSTM;
wherein, the LSTM neural network hyper-parameters are generated by the GA genetic algorithm within the constraint range: determining initial network structure of the neural network by using the number Units of the hidden layer neurons, the number epochs of LSTM training rounds, the number Layers of the hidden layer network and the initial value of random discarding parameter probability dropout;
5) And optimizing and solving the technological parameters in the polymer hybrid manufacturing process by utilizing an improved multi-objective optimization hybrid variation differential evolution algorithm.
2. The method for optimizing the hybrid manufacturing of a plurality of objects by using a kfield-LSTM hybrid variation optimizing polymer according to claim 1, wherein the specific process of step (4) further comprises:
1) Eliminating flaw Data in an original Data set, carrying out normalization pretreatment on the Data set, and eliminating the influence of dimension and magnitude;
performing K-fold intersection on the data set by a K-fold intersection algorithm, wherein K=10; dividing the data set into 10 subsets k1, k2, …, k10 with the same width and dimension, and establishing matrixes Team1, team2, … and Team10;
Data set＝Team1＝Team2＝...＝Team10 (1)
Data set＝(k1,k2,k3,...,k10) (2)
2) Meanwhile, for better representing the superiority and inferiority of the operation network hyper-parameter selection, the mean value of the MSE is used as an objective function of the GA genetic algorithm; the calculation process is as follows:
when i=10, the model built by each calculation is reasonable in structure, and the average mean square error fed back at this time is:
when i is less than 10, the condition that the structure is unreasonable and the data set is unevenly distributed exists in the modeling process is represented, and the average mean square error fed back at the moment is as follows:
3) In the modeling process, the change trend of the training set and the test set is judged by using the Loss function so as to judge the rationality of the model, and the Loss function Loss of the model is defined, wherein the formula is as follows:
wherein x is predict Representing the predicted value, x value Representing the actual value.
3. The method for producing multi-objective hybrid manufacturing by using Kfold-LSTM hybrid variation optimizing polymers according to claim 1, wherein the objective function, decision variables and related constraints are explicitly optimized when solving the multi-objective optimization problem in step (5); the specific mathematical expression is as follows:
wherein F (X) is an objective function, and F (X) is an objective vector composed of m objective functions; x is a decision variable, and is a decision vector composed of n decision variables;and->Is the kth decision variable x k Lower and upper bounds of (2); h i (X) is the ith inequality constraint; g j (X) is the jth equality constraint.
4. The method for producing multi-objective hybrid optimization by using Kfold-LSTM hybrid variation optimizing polymers according to claim 1, wherein the multi-objective hybrid variation differential evolution algorithm in the step (5) comprises four processes of population generation, crossover, variation and selection; generating an initialized population in a constraint range, performing mutation operation on the population according to different base vector selection modes and different differential vector calculation modes, and performing cross operation on the mutated population to increase the diversity of the population; and selecting a feasible solution based on a Pareto selection dominance mechanism, and stopping program operation to output an optimal result after a termination condition is reached.
5. The method for optimizing the mixed manufacturing of a plurality of targets by using the kfield-LSTM hybrid variation optimizing polymer according to claim 4, wherein the population initialization generating process comprises the following steps:
randomly generating NP n-dimensional individuals in a solution space;
X i (0)＝(x i,1 (0),x i,2 (0),...,x i,n (0)) (8)
i＝1,2,...,NP
the j-th population of the i-th individual is valued as follows:
wherein X is i (t) represents the ith individual in the t generation population, t=0 represents the population algebra as the first generation; x is x i，j (t) is the value of the j-th dimension of the i-th individual in the t-generation population;a minimum value representing the j-th dimensional value of the i-th individual; />Representing the maximum value of the ith individual jth dimensional value; rand (0, 1) means that a random number is taken in (0, 1).
6. The method for optimizing a polymer blend of Kfold-LSTM blend variation as set forth in claim 4, wherein said population variation process is as followsThe following steps: performing mutation operation on the generated initial population, wherein the individuals of the initial population are formed by X i (t) represents that, in order to reasonably distinguish between the initial population and individuals of the variant population, the individuals of the variant population are represented by V i (t) the mutation strategy is as follows;
(1) DE/rand/1 variant strategy
V s (g)＝X r1 (g)+F·(X r2 (g)-X r3 (g)) (10)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X r1 (g)，X r2 (g)，X r3 (g) R1, r2 and r3 individuals selected randomly from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(2) DE/best/1 variant strategy
V s (g)＝X best (g)+F·(X r1 (g)-X r2 (g)) (11)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population; x is X r1 (g)，X r2 (g) R1, r2 individuals selected randomly from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(3) DE/rand/2 variant strategy
V s (g)＝X r1 (g)+F·(X r2 (g)-X r3 (g)+F·(X r4 (g)-X r5 (g)) (12)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X r1 (g)，X r2 (g)，X r3 (g)，X r4 (g)，X r5 (g) Randomly selecting the (r 1, r2, r3, r4, r 5) individuals in the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(4) DE/best/2 variant strategy
V s (g)＝X best (g)+F·(X r1 (g)-X r2 (g)+F·(X r3 (g)-X r4 (g)) (13)
Wherein V is s (g) After variation of g generation populationAn s-th individual; x is X best (g) Is the optimal individual in g generation population; x is X r1 (g)，X r2 (g)，X r3 (g)，X r4 (g) Randomly selecting the r1, r2, r3 and r4 individuals from the g generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
(5) DE/target-to-best/2 variant strategy
V s (g)＝X s (g)+F·(X best (g)-X s (g)+F·(X r1 (g)-X r2 (g)) (14)
Wherein V is s (g) Is the s-th individual after g generation population variation; x is X best (g) Is the optimal individual in g generation population; x is X r1 (g)，X r2 (g) R1, r2 individuals selected randomly from the g generation population; x is X s (g) Randomly selecting an s-th individual from the g-generation population; f is a scaling factor of [0,2 ]]Random numbers obeying uniform distribution;
the DE/rand/1 variant strategy and the DE/rand/2 variant strategy can improve the exploration capacity of the search algorithm; the DE/best/1 variant strategy and the DE/best/2 variant strategy can improve the development capability of a search algorithm; namely, different mutation strategies have different capacities in global searching and local searching and have emphasis on each;
in order to expand the population searching range, different mutation strategies are adopted for the same multi-objective optimization problem, and the optimal individual in the operation is entered into the next iteration operation in the mixed mutation process.
7. The method for optimizing the mixed manufacturing of Kfold-LSTM hybrid variation optimizing polymers according to claim 4, wherein the population crossover process is as follows:
the diversity of the population determines the optimizing effect to a certain extent, and the purpose of the cross operation is to enhance the diversity of the population; the specific operation mode is that g generation population individuals X are selected according to the population crossing rate Cr s (g) And variant individual V s (g) Thereby generating a test individual W s (g) The method comprises the steps of carrying out a first treatment on the surface of the Binomial interleaving is the most commonly used interleaving method at present;
in which W is i，j (g) The value V of the j-th dimension of the ith experimental individual after g generation population variation i，j (g) The value of the j dimension of the ith individual after g generation population variation; x is x i，j (g) Randomly selecting a value of a j-th dimension of an i-th individual in the g-generation population; cr epsilon [0,1 ]]For cross probability, rand (0, 1) is [0,1]And random numbers subjected to uniform distribution.
8. The method for optimizing the mixed manufacturing of Kfold-LSTM hybrid variation optimizing polymers according to claim 4, wherein the population selection process is as follows:
the selection operation is based on the selection mechanism of Pareto and based on the evaluation function pair W i (g) And X i (g) Non-dominant sorting and selecting dominant individual X i (g+1) entering the next iteration; through the cyclic operation, when the evolution algebra reaches the maximum value of the evolution algebra, ending the evolution process and outputting a non-dominant solution set of the pareto optimal front;
wherein W is i (g) The ith experimental individual after g generation population variation; x is X i (g) Randomly selecting an ith individual from the g generation population; x is X i (g+1) is the randomly selected ith individual in the g+1 generation population.
9. The method for optimizing the hybrid manufacturing of a multi-objective polymer by using the kfield-LSTM hybrid variation according to claim 6, wherein the hybrid variation process is as follows:
(1) Setting 4 variant population sets, V_rand/1 (t), V_best/1 (t), V_rand/2 (t) and V_best/2 (t), carrying out variant operation by utilizing different variant strategies to generate variant individuals, and storing the variant individuals into corresponding populations X (t) respectively; meanwhile, an external archiving set V (t) is additionally arranged and used for storing the optimal solution;
(2) Calculating the fitness value of each individual in the variant population, and distributing the fitness value to the individuals with the conflict of the optimization targets by using a non-dominant sorting method; after assigning fitness values, if individuals of the population are ranked for fitness values and individuals with high fitness values are selected, the diversity of the population cannot be fully guaranteed; thus, to ensure population diversity, 2 individuals within each variant population are randomly selected to compare the magnitude of their fitness value, and the individual with the greatest fitness value is stored in the external archive set V (t).
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