Improvement of Teaching-Learning-Based-Optimization

—Teaching-Learning-Based-Optimization is an optimization algorithm that simulates the teaching process. In the standard Teaching-Learning-Based-Optimization there are some problems such as precocity and low optimization accuracy. Through daily discovery, students' learning effect is better when there are exercise lessons than when there are no exercise lessons. Students who study toward teacher on one’s own learn better than students who do not. Therefore, this paper proposes a teaching mode that combines exercise lessons and one-to-one to improve the Teaching-Learning-Based-Optimization.


Introduction
Many phenomena in nature are closely related to human life and social progress, the survival of the fittest is the process of finding the best, such as Ant Colony Optimization Algorithm, Particle Swarm Optimization and other bionic population optimization algorithms. Not only the animals in nature have survival of the fittest, but also in human life, the first place in each class is also the "optimal solution" in a class. This is the Teaching-Learning-Based-Optimization (TLBO) proposed by Indian scholar Rao in 2011. At the beginning of a collective, an optimal solution is selected as a "teacher", and the optimal solution is sought in the subsequent stages of teacher teaching and student learning.
. The maximum number of iterations is max it . The optimal solution sought is the minimum. This paper assumes that the adaptability of all students in the class at the -th i iteration is: When 0 t  , it is the adaptability of the classmates at the beginning of the class, from which the best individual is selected as the teacher, and initialization is completed at the same time:

Teaching phase
mean Gra is the average adaptability of all students in the class, During the teaching phase, students learn from the difference between mean Gra and the teacher tea Gra . If student j X (this student is not the teacher) learns well in the teaching phase, that is, the adaptability after learning phase is better than the original adaptability. Otherwise, the original adaptability j Grai is retained as the adaptability of the student. The process is as follows: =round(1+rand(1)) TF (3) rand(1) is a random number on the interval(0,1).
TF is a teaching factor, and round is a round to the nearest integer (if it is 0.5, it is rounded to the larger integer). Since rand(1) is in the range of (0,1), the teaching factor TF can only be 1 or 2.

Learning phase
This phase is learning and communication between students without teacher. In this phase, two students M X and N X are randomly selected, their adaptability are M Grai and N Grai , and t X learns from the better in M Grai and N Grai , the adaptability after learning is assumed as Grai is retained.

Improvement of TLBO
In daily teaching, teaching phase and learning phase are traditional teaching methods, but the teaching effect is relatively insufficient. In our learning process, both teachers and students will try some new learning methods. Teachers will learn by themselves to improve teaching level, students will join cram school, learn from each other, etc. Similar to our usual exercise lessons, teachers will arrange some homework after the teaching phase, students will learn and complete the homework after class, and the teacher will explain the homework in the next lessons. After such a cycle, the students' knowledge will be more consolidated and reward better results.
At the same time, in some university teachings, some teachers teach more than a hundred students (we call them large classes), and some classes can only accommodate about 30 people (we call them small classes) because of the small classroom. From the perspective of the final learning effect, the learning effect of the small class is significantly better than that of the large class. Through observation, it is found that in the small class, students will ask the teacher more frequently about the aspects they do not understand. Because of the small number of students, teachers can also basically take into account each student. In the large class, the proportion of students who ask the teacher about the aspects they do not understand is relatively small. Therefore, on the basis of the standard TLBO, the consolidation of the exercise lesson and the one-to-one teaching phase are added: after the teaching phase and the learning phase, this paper adds the teacher's double teaching and one-to-one teaching phase to improve TLBO, one-to-one is mean that all students learn from the teacher individually. In this algorithm, it is not considered that the teacher cannot take full account of all students.
The entire improved TLBO process is as follows:

Teaching phase
In the standard TLBO, the value of the teaching factor (1 (0,1)) TF round rand   is only 1 or 2, and each student has a different ability of learning from the teaching phase. Therefore, this paper modified the generation function of teaching factor TF , which is called CFTLBO (Change TF Teaching-Learning-Based-Optimization). In this paper, the generation function of the teaching factor is set to , the value of TF is randomly selected between (1,2). The test results are shown in Table 1. Each data in Table 1 is an average of 50 experiments( =50 N ).

Learning phase
In this phase, students still learn from each other. Two students are randomly selected for learning. If the adaptability after learning is better, the new adaptability is used to replace the original one, otherwise the original adaptability is maintained.

Exercise lesson phase
In this phase, the teacher arranges homework during the teaching phase, so he needs to take class again. This process is similar to the teaching phase, which is called as DTTLBO (Double Teaching Teaching-Learning-Based-Optimization) in this paper. It also calculates the average adaptability of all students in the class '   orders of magnitude multiple of e. Therefore, the optimization effect of DTTLBO is more significant.

One-To-One Teaching
In the first three phase, the teacher will change as the number of iterations increases. Therefore, in this phase, Student i X learns one-to-one from the optimal solution at the exercise lesson phase, the survival of the fittest is the same as before, this paper calls this phase as OTOTLBO (one-to-one Teaching-Learning-Based-Optimization). Table 1 shows the results obtained by retaining the standard teaching factor TF and adding one-to-one teaching without the exercise lesson phase, and the optimization results obtained by the CDOTLBO (Change TF and Double teaching and One to one Teaching-Learning-Based-Optimization), which is a combination of the three improvement methods.
From Table 1, it can be seen that the value of the optimal solution sought by OTOTLBO at 500 iterations is e , It can be seen from this effect that after adding one-to-one teaching phase, the effect of optimizing is more significant.
From the data in Table 1, it is found that the optimization effect of CDOTLBO after combination has improved very much compared to the standard TLBO.

Simulation results
This paper improves on the standard TLBO, and obtains three improvements: CFTLBO, DTTLBO, OTOTLBO, and comprehensively obtains CDOTLBO.
The test method in this paper is to use MATLAB to write code for simulation. The relationship between the optimal solution and the number of iterations in various improvements is shown in Figures 1 to 5 respectively.
The effect of changing the TF is not obvious in the simulation diagram. Therefore, Figure.        It can be seen from Figures 1 and 2 that the optimization accuracy of CFTLBO after 1000 iterations is slightly better than that of standard TLBO. The optimization results are not yet become 0 when the number of iterations is 1000. In Figure 3, When the number of iterations is 1000, the optimization results is near -250 10 . In Figure 4, when the number of iterations is 600-700, the optimization result is 0, indicating that the optimization effect of OTOTLBO has a greater advantage than the previous two. Figure 5 is the final result, when the number of iterations is 450 , The optimization result has been less than -300 10 , and in the course of the experiment, it was found that when the number of iterations is about 470, the optimization result has become 0.

Conclusion
This paper has proposed an improved teaching optimization algorithm called CDOTLBO, which is improved on the basis of TLBO. It is experimentally obtained that CDOTLBO has a higher optimization accuracy. After the TLBO was created, some scholars found some better method based on it. This algorithm has also been widely used in general [11][12][13][14][15], such as multishop collaborative comprehensive scheduling based on hybrid teaching optimization algorithm proposed by Liao Bufan [15].