Dynamic Optimization of Carbonization Process Parameters Based on Genetic Programming

—The properties of carbon fiber are closely related to the carbonization process, in which high temperature carbonization is the key factor affecting its strength, modulus and other properties. In order to solve the problem that it is difficult to adapt to the complex industrial production environment and the dynamic factors existing in the carbonization process, taking the furnace temperature and heating rate of high temperature furnace as decision variables, energy consumption and yield as optimization objectives, and element temperature as dynamic factors, the dynamic optimization model of carbonization process parameters is established and the validity of the model is verified. Aiming at the parameter optimization problem of carbonization process in uncertain environment, a dynamic multi-objective optimization algorithm of carbonization process parameters based on genetic programming and knowledge transfer is proposed. And compare it with other latest algorithms to prove its efficiency and advantages.


Introduction
At present, the preparation process parameters of carbon fiber usually depend on the experience of the operator, which has great problems in the actual industrial production. If only based on the experience of workers, it is difficult to find the best carbonization process parameters under complex production conditions, resulting in low yield, high energy consumption and other problems [1] . The production of carbonization process is complex, so it is necessary to determine the best production conditions and consider the yield and economic indicators at the same time. At present, there is no research on optimizing the energy of high temperature furnace in carbon fiber carbonization process and maximizing the yield at the same time [2] . The energy consumption management of the carbonization process and the method of maximizing production need to consider many factors, including: high temperature furnace temperature, heating rate, component temperature, driving speed and 2 N flow rate, the best production conditions need to be determined and both yield and economic indicators need to be taken into account [3] [4] .
In this paper, taking the furnace temperature and heating rate of high temperature furnace as decision variables, energy consumption and yield as optimization objectives, and component temperature as dynamic factors, a dynamic multi-objective optimization mathematical model of carbonization process parameters in uncertain environment is constructed and the effectiveness of the model is verified. Aiming at the parameter optimization of carbonization process in uncertain environment, a dynamic optimization algorithm of carbonization process parameters based on genetic programming [5] and knowledge transfer [6] is proposed.

Model description
In view of the problem that it is difficult to adapt to the complex carbonization production environment by setting carbon fiber carbonization process parameters by artificial experience, the uncertainty of carbonization process is considered, that is, the dynamic change of production environment with time in carbonization process. Taking the furnace temperature and heating rate of high temperature furnace as decision variables, energy consumption and yield as optimization objectives, and component temperature as dynamic factors, a multiobjective optimization model of carbonization process parameters under uncertain environment is constructed: x is driving speed, i E P is total energy consumption in process i, Y is yield.
For convenience of description, f is used to express the relationship between decision variables and optimization objectives selected in the multi-objective optimization model of carbonization process parameters described above, as shown in equation (3).
In order to ensure the safety and reliability of the carbonization production process, the parameters in the actual carbonization production process should meet a certain range, as shown in formula (4). Where L represents the lower limit of the variable and H represents the upper limit of the variable. 1 1 1 Through the above analysis, the dynamic multiobjective optimization model of carbon fiber carbonation production process can be expressed as shown in formula (5). Among them, t stands for different carbonized production environment, t=1,2,3…,10.

Model verification
In order to verify the effectiveness of the proposed carbonization process parameter optimization model and the problem in uncertain environment, this section uses LINGO to simulate and analyze the carbonization process parameter optimization problem in uncertain environment. As shown in Table 1, 10 groups of small examples are generated by changing the element temperature and driving speed. The objective function is to minimize energy consumption and maximize yield. Based on the above experimental settings, the smallscale problem is solved by using LINGO software. Table  1 shows the solution of furnace temperature, heating rate, energy consumption and yield of high temperature furnace calculated by LINGO when the original temperature and driving speed are fixed. The simulation results show that the parameter optimization model of carbonization process proposed in this paper is reasonable.

Solution method
Aiming at the dynamic multi-objective optimization model of carbonization process parameters in uncertain environment, considering the use of knowledge transfer to solve the uncertainty of carbonization process, a dynamic multi-objective optimization algorithm of carbonization process parameters based on genetic programming and knowledge transfer is proposed. The coding ability of genetic programming based on tree is used to solve the problem that it is difficult to code the parameter optimization model of carbonization process. By sharing the common coding subtree among individuals, the knowledge transfer is realized, the search space of the algorithm is expanded, the convergence speed of the algorithm is accelerated, and the uncertainty problem widely existing in the process of carbonization production is solved.
Genetic programming requires the definition of terminal set and function set. The function set includes all functions that will be used in the program. The terminal set includes all the constants and variables that will be used in the program. The terminal set of the algorithm proposed in this paper is shown in Table 2, and the definition of function set is shown in Table 3. As shown in Fig.1, the method of knowledge transfer in GP is as follows: the standard genetic programming operation is carried out in the two source domains, and then the optimal evolutionary individual is selected from each environment in the two runs, then the common subtree between the two individuals is found, and the tree with the lowest depth is obtained as a function. Send it to the function domain of the target domain, and combine the function or the tree to generate the initial population. In the process of evolution, the two tasks can clearly share knowledge so as to solve the dynamic problems of the environment.  Table 4. Table 4. CP-TLGP algorithm.

Algorithm : CP-TLGP
Step1: Set the number of population to N, the maximum number of iterations to Gen, the function set F and the termination set T, the crossover probability to pc and the mutation probability to pm. Step2: The useful knowledge of the last environment (SubTree) is extracted for the initial population generation of the current environment, and a set of initial population PU is randomly generated according to the prescribed function set termination set and the optimal subtree obtained from the previous environment. Step3 The fitness values of individuals in PU population are calculated. Non-dominated quick sorting and crowding degree calculation are carried out according to the obtained fitness values. According to the results obtained above, the competition is selected in the population, and N parents suitable for breeding are obtained. Step4 Randomly select pc* N individuals from the N parents selected in Step3 for pairwise crossover operation to obtain the child population PC.
Step5: Randomly select pm* N individuals from the N parents selected in Step3 for mutation operation, and obtain the child population PM. Step6: The descendant populations PC and PM are merged into the population PU for non-dominated quick sorting and crowding degree calculation, and the truncate operation is performed on PU to keep the population number as N.
Step7: If the number of iterations reaches the set maximum number of iterations Gen, the algorithm terminates and outputs the best solution, otherwise returns to Step3.

Experiment and discussion
In this study, HV [7] and IGD [8] were used as evaluation indexes. The higher the HV value, the better the convergence and diversity of the algorithm. The smaller the IGD value is, the closer the solution set obtained by the algorithm is to the Pareto frontier surface, thus improving the convergence. In this paper, the proposed algorithm is compared with SGEA [9] and Tr-RM-MEDA [10] algorithms. In the execution process of the above algorithms, many common parameters need to be used, such as species evolution algebra, population number, crossover probability, mutation probability and so on. It is extremely important that how to set more appropriate common parameters and when the algorithm can achieve the optimal execution state. At the same time, this paper uses Taguchi method to set 9 different parameters, and the three algorithms carry out 10 experiments on each parameter setting. The results obtained are shown in Table 5 and Table 6. No.
Parameter settings CP-TLGP SGEA [9] Tr-RM-MEDA [10]  No. Parameter settings CP-TLGP SGEA [9] Tr-RM-MEDA [10]  According to the data in Table 5, it can be seen that compared with the comparison algorithm, the average IGD value of CP-TLGP algorithm is lower, indicating that the algorithm has superior performance in solving complex problems. However, under the second and sixth parameter configurations, the SGEA algorithm performs best, while under the ninth parameter configuration, the Tr-RM-MEDA algorithm performs best. This shows that the performance of CP-TLGP algorithm is affected by the configuration of iterations and needs to be properly adjusted and optimized in practice. As can be seen from Table 6, the CP-TLGP algorithm performs well in terms of HV mean, which is better than the other two comparison algorithms in most cases, which shows that the diversity of solutions has been greatly improved after using knowledge transfer.

Conclusion
In order to solve the problem that the carbonization process parameters are difficult to adapt to the complex carbonization production environment and the uncertainty of the production environment, a dynamic multi-objective optimization model of carbonization process parameters is constructed in this paper. Considering the use of knowledge transfer combined with genetic programming to solve the dynamic model of this paper, a dynamic multi-objective optimization algorithm based on genetic programming and knowledge transfer is proposed to optimize the energy consumption and output of the carbonization process. This paper considers the research situation of single task, aiming at the problem that the overall optimization efficiency may be low when there are multiple carbonization process parameter optimization tasks at the same time. Therefore, in the future research, we can consider to build a multi-task optimization model of carbonization process parameters to solve, to further optimize the carbonization process.