**1. Introduction**

Group Teaching Optimization Algorithm (GTOA) is aimed at improving the knowledge of the whole class by simulating the group teaching mechanism.** **Group teaching is a teaching approach widely applied in many educational programmers on an international level [1]. It takes various formats as a teaching method, such as ability grouping, mixed-ability grouping, mixed-age grouping etc. Education aims to enable students not only to acquire knowledge but also to become capable and enthusiastic lifelong learners. Prior research has found that learning is more likely to be effective where a student plays a proactive role in the learning process [2]. Such a proactive process, including learning on students’ own initiative and strategies, these strategies are determined partly on subject matter to be taught and partly by the nature of the learner. It aims to cater for individual differences, develop skills (e.g. communication skills, collaborative skills, and critical thinking skills), generic knowledge and socially acceptable attitudes or to generate conforming standards of behavior and judgment, a “group mind”. To adapt group teaching to be suitable for using as an optimization technique, needs only the essential population size and stopping criterion without extra control parameters, this has great potential to be used widely. GTOA is first examined over unconstrained global optimization problems and the optimization results are compared with other art algorithms [3]. GTOA optimization techniques is very essential for engineering applications, which is direction for researchers optimization techniques have encouraged to develop better optimization methods to solve real-world engineering optimization problems.

**2. Inspiration of GTOA**

The Group teaching optimization algorithm is inspired by group teaching mechanism. The idea of the GTOA is aimed to improving the knowledge of the whole class by simulating the group teaching mechanism. Considering various potential among students, it is rather complicated for group teaching to be implemented in practice. In order to adapt group teaching to be suitable for using as an optimization technique, we first assume population, decision variables and fitness value are corresponds to the best, average and worst groups of students, the subjects offered to students and the knowledge of students, respectively [4]. This GTOA tool incorporates a set of deterministic and stochastic methods and also a set of computational intelligence techniques which offers a friendly interface that allows the students to practice the theory learned, and also to verify and compare the features of the optimization methods.

In China, Confucius is a great well-known educationist and ideologist, who first started private education system [5]. He first time put forward the teaching idea of “teaching students according to their aptitude”. In other words, this teaching idea is that the teacher should formulate appropriate teaching methods for different students based on their different characteristics [6]. More specifically, group teaching is aimed at highlighting students’ subjectivity, which is to adapt the school education to the differences of students by offering various courses and teaching methods. In fact, there are a lot of differences among students, such as intelligence, learning attitude, learning ability and economic conditions [7]. Thus although group teaching is an effect way to improve the overall quality of students, there is no uniform mode of group teaching in practice [8].

**3. Steps of GTOA**

To adapt group teaching to be suitable for using as an optimization technique, without loss of generality, four simple rules are first defined [9]. Then a group teaching model is built under the guide of the four steps as;

- Teacher allocation phase
- Ability grouping phase
- Teacher phase
- Student phase

**3.1 Teacher allocation phase**

A good teacher allocation mechanism is very important for improving the knowledge of students [10]. In order to accelerate the convergence of the proposed GTOA, outstanding group and average group share the same teacher [11]. The best solutions among obtained so far are saved, the teacher allocation in proposed method can be expressed as

For i=1: N, j=1: N

X_{newij} =X_{oldij} + r * (G _{best (j)} – X _{oldij} ) (1)

Where r is a random number, r∼U (0, 1), *Xnew _{ij}* if it gives better function value.

**3.2. Ability grouping phase**

Ability grouping, also known as tracking, is the practice of grouping students together according to their talents Within-class grouping – a teacher’s practice of putting students of similar ability into small groups usually for instruction [12]. One group with strong ability of accepting knowledge can be called outstanding group. Another group with poor ability of accepting knowledge can be called average group [13]. The distribution of knowledge based on ability grouping is expressed with X and Y as outstanding and average groups as;

**3.3. Teacher phase**

In order to achieve this goal, the teacher should make a proper teaching plan for his or her students [14]. More specifically, the teacher can try his or her best to improve the varying student’s knowledge of the whole class as

**3.4. Student phase**

During spare time, one student can gain his or her knowledge by two different ways [15]: one through self-learning and the other through interaction with other students, which can be expressed as

**4. Implementation and Numerical expression of GTOA for optimization**

**Step 1: **Analyzing algorithmic parameters as

GTI- Group Teaching Information, GTP- Group Teaching Population, GTC- Group Teaching Consideration.

**Step 2**. Evaluate the population in random search space as

X^{j} =X^{i}+r (Xn –X^{o}) (6)

**Step 3**. Improvising new groups as follows

X^{new}=X^{1new,} X^{2new}, …..X^{dnew } (7)

For each note X^{i new}= 1, 2, 3……D

In order to accelerate the final tuning of best students and compute outstanding group, average group and the worst group is expressed as,

**Step 4**. Update the current number of population and evaluate the function fitness.

If X^{new} is better than X^{worst}

^{ }X^{new}= X^{worst} (9)

**Step 5**.Checking the stopping criterion.

If stopping criterion is meet (Max Best students) is meet, computation is terminated, otherwise repeat steps 3& 4.

**5. Flowchart of GTOA**

**6. Pseudo code of GTOA**

**7.Advantages & Disadvantages of GTOA **

**8. Applications of GTOA**

- Aerial vehicles navigation [16].
- Wireless sensor [17].
- Data collection system [18].
- Multi-robot path planning [19].
- Engineering design problem [20].

**Reference**

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