( ) Mean T X rand X X F teacher old new  +  + = new X old X teacher X F T F T ( ) ( ) ( ) ( )    −  +  −  + = otherwise X X rand X X f X f X X rand X X r r old r r r r old new : ) : ) 1 2 2 1 2 1 1 r X 2 r X sk N sb N   i i i i i i i sb N i i   j gr i i pr 0    j gr i i sc 0    j gr i i gd 0    j gr i i rp 0    j gr i i ld       =  − = sb j gr N j sum max J 1 0   1 ... 0 − = = st N i i st X st N M N st  T N M M st s s diag V U X   = − − ] 0 ... 0 ... [ 1 1 0 U st st N N  V M M    diag M N st  1 1 0 ... −    M s s s X   1 ... 0 − = = M i i w w ] [w X X diag w  = ( ) T w diag s diag V w U X    = ] [ ] [ V M M st  st M   1 ... 0 − = = st M i i C C st M j v V   1 ... 0 − = = st M i i C C ) / ( st st M N int j j k k M k i k i i C i v w st argmax i    =  − =  max , 1 0 : max ; C j C 1 ,..., 0 − st M C j C , ) ( ) ( ; 0 ) ( 0 ) ( ; ) 0 ( ; 2 / ) ( ) ( ; ) ) ( ( ) 1 ( 1 ) ) ( ( )(k i k i k i k i k i k i k i k i k i k i k i k =  =  =  −         +          − − +  + + +              − +  + − =       i t k h , 1 , , 1 , 0 − = N t  ) (t h i k ) ( ) ( ) ( i k i k i k sb t r sb t h −  + =     maxgr rand t r = ) (     ( ) ( ) G j i j i j i j k i k k sc sc T t r pr pr T t r maxgr t h t h t r t A            +   + −   = , , ) ( , ) ( ) ( ) ( ) ( ) (       () T , ) ( ) ( ; 0 ) ( 0 ) ( ; 2 / ) 1 ( ) ( ; ) ( ) 1 ( ) ( ) 1 ( ) ( ) ( , , maxgr t g maxgr t g if t g t g if maxgr t g t g t h ld t a ld t h round t g i k i k i k i k i k i k j k j k j i i j G j i i k i k =  =   − −           +    − + =      ) (t g i k ) ( , t a k j i ) (t A k 1 = j ld 0 = j ld  1 0    ) 1 ( i ld  + ) 1 ( i ld  −              , , , , , , , , =  ;        ,   ,  ) (  0 : ) ( ) | (    +         t sb t g G j j k G j j k ( )   − = − = − − = 1 1 1 0 ) 1 ( ) (

(an appropriate trend): the variation of the parameter on the previous step gave a positive trend increase and it does not exceed the limit value, then this parameter can be changed in the same direction of variation. If it reached the limit value, then another parameter is varied. If is not reached by the parameters changing then it should be analyzed the influence of parameters ( 16) and the associated with them weight values of the student classification parameters in Table 1 should be changed. The students clusters should be rearranged with using ( 11) and the new composition of the groups should be made. . As can be seen from Fig. 2, learning brought students' grades closer together, with the exception of one student with the lowest level of interest in the subject, his grades are unstable. This was achieved through strengthening the influence of teachers and mentors. According to the model ( 12), teachers pay more attention to weak students, which raises their grades up to the level of average students. This impact outweighed the negative impact of weak students on group grades through the elements of the matrix ( 14).

The example of grades simulation with optimization is shown in

The methodology of creating group of people to work as a team is essential in recruiting in many areas of manufacturing. The gaming form of learning by creating games with the distribution of roles in the group simulates teamwork and can be used for both teaching and training.

This paper considers the problem of optimizing the composition of groups by weighted setting parameters depending on their priority. Clustering of students is proposed based on given parameters and their weights by the method ICA, which is implemented using SVD. By changing the weights of the parameters, clustering can be carried out both for general education and for specialized training. In the case of general education under consideration, the formation of groups is carried out by mixing students from different clusters. This makes it possible to obtain groups approximately equal in learning ability, behavioral characteristics, gender and in social activity.

Also, the problem of finding optimal interaction between students and teachers in such a way that the learning process is progressive is considered. By varying the parameters of the model and its simulation for each group of students, a multidimensional surface can be obtained that displays the dependence of the trend of learning assessments, the local maxima of which can be selected as options for the required learning parameters that set the requirements for teachers, mentors and group leaders. School management can take this into account when distributing teachers and teaching loads among student groups. The simulation results indicate problematic issues that can be eliminated if attention is paid to them in time.

The grades obtained through the simulation can be compared with the actual assessments of the students and thus evaluate the expected learning outcomes with those actually achieved. This will allow objectively to assess the work of teachers and the teamwork of students.

In order for the learning process to be completed successfully, it is necessary to select group members in such a way that their interaction is effective and predictable. This problem is very complex and can be solved by simulation with multi-criteria optimization. Significant ideas for the development of this scientific direction were laid in the last quarter of the 20th century by the rector of VNTU, Professor I.V. Kuzmin, to whose centenary of birth this work is dedicated.