# Evaluation of the Forms of Education of High School Students Using a Hybrid Model Based on Various Optimization Methods and a Neural Network

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Neural Network to Measure Homework Performance

- Multilayer Perceptron (MLP) neural network trained by the Resilient Propagation method;
- Random Forest Algorithm.

- Number of topics the assignment deals with;
- Number of types of activities students use while doing the assignment;
- Number of questions in the assignment;
- Length of the assignment;
- Complexity in formulating the assignment;
- Age of a student;
- Sex of a student;
- Distance from home to school;
- Average math score;
- Average reading score;
- Learning mode;
- Family income.

- The number of topics covered by the assignment—this value is determined by lexemes specific to a particular topic. For example, the “electric current” lexeme means that the assignment has a topic related to electricity.
- The length of the assignment is the number of words required to formulate the assignment.
- The complexity of the assignment formulation is an expert value determined in scores in the range from 1 (the assignment is formulated clear and unambiguously) to 3 (there are redundant data and ambiguous formulations).
- The age of the school student is in years.
- Sex is a binary value.
- The distance from home to school is indicated in kilometers.
- The average math score is the average score in mathematics for the previous schooling period (transferred to a five-point system). Depending on the school, this is a quarter or trimester grade.
- The average score in reading is calculated for lower grades or in the national language for students of senior grades.
- Learning mode—binary value (distant—0 or in-class—1).
- Family income is a value determined in points from 1 (the family receives subsidies from the state) to 3 (the family can afford expenditures higher than average).

#### 2.2. Optimization Algorithms for Solving Multicriteria Problems

- Generating initial population. Filling the population with individuals in which the array elements (bits) are filled randomly within the boundaries defined by the user.
- Determining algorithm parameters. The parameters are size of the population $N\_pop$, the number of generations $N\_pok$, the probability of crossover ${P}_{skresch}$, and the probability of mutation ${P}_{myt}$, which determine for each population the number of pairs of crossing chromosomes and the number of mutating chromosomes.
- Generating initial population. The initial population can be randomly generated.
- Choosing a parental couple. The selection of the parent pair is carried out using the roulette method, that is, the proportional selection method. Chromosomes are displayed as a segment of lines or roulette sectors in such a way that their size is proportional to the value of the objective function. Next, we randomly generate numbers in the range from 0 to 1, and those individuals in whose segments the random numbers fall are selected as parents. In this case, the chromosome numbers of the parents must be different.
- Crossover. For a crossover, we pick a random point and choose chromosomes. After that, we use the single-point crossover.
- Mutation. The number of mutations is determined, and chromosomes for mutation are selected. A single-point mutation is carried out.
- Checking the condition for completing the evolution process. If the condition for the termination of the algorithm is not met, then go to Step 4; otherwise, go to Step 8. As a condition for the termination of the process, there can be a specified number of generations or a defined number of identical individuals.
- Formation of a Pareto-optimal solution.

## 3. Results

- The average relative time for completing homework, taking into account the difficulty of a particular subject, is as follows:

- 2.
- Average relative efficiency of homework in terms of material assimilation$${K}_{2}=\frac{\overline{Ef}\times {\overline{t}}_{lesson}}{E{f}_{max}}\to max,\phantom{\rule{0ex}{0ex}}\overline{Ef}={a}_{N}*kol,$$

- Has the time you spend on your homework changed when you switched to distance learning?

- If changed, select by how much.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Pareto-optimal set for solving a problem by a method using a backtracking search algorithm.

$\mathit{\xi}$ | ${\mathit{K}}_{1}$ | ${\mathit{K}}_{2}$ | $\mathit{\mu},{\mathrm{min}}^{-1}$ |
---|---|---|---|

0.0 | 0.0682 | 0.0943 | 0.9869 |

0.1 | 0.0688 | 0.0951 | 0.9721 |

0.2 | 0.0670 | 0.0927 | 0.9867 |

0.3 | 0.0680 | 0.0941 | 0.9731 |

0.4 | 0.0676 | 0.0934 | 0.9798 |

0.5 | 0.0679 | 0.0939 | 0.9749 |

0.6 | 0.2570 | 0.3661 | 0.25 |

0.7 | 0.4869 | 0.7573 | 0.1209 |

0.8 | 0.4544 | 0.6933 | 0.1477 |

0.9 | 0.7296 | 1.5957 | 0.0574 |

1.0 | 0.8406 | 3.3763 | 0.0271 |

$\mathit{\xi}$ | ${\mathit{K}}_{1}$ | ${\mathit{K}}_{2}$ | $\mathit{\mu},{\mathrm{min}}^{-1}$ |
---|---|---|---|

0.0 | 0.0673 | 0.0932 | 0.9979 |

0.1 | 0.0678 | 0.0935 | 0.9979 |

0.2 | 0.0678 | 0.0935 | 0.9979 |

0.3 | 0.0682 | 0.0946 | 0.9912 |

0.4 | 0.0685 | 0.0998 | 0.9785 |

0.5 | 0.0809 | 0.0940 | 0.9749 |

0.6 | 0.2620 | 0.3719 | 0.2468 |

0.7 | 0.4950 | 0.8591 | 0.1209 |

0.8 | 0.5896 | 1.0150 | 0.1002 |

0.9 | 0.7498 | 1.7080 | 0.0536 |

1.0 | 0.8900 | 3.5012 | 0.0105 |

$\mathit{\xi}$ | ${\mathit{K}}_{1}$ | ${\mathit{K}}_{2}$ | $\mathit{\mu},{\mathrm{min}}^{-1}$ |
---|---|---|---|

0.0 | 0.0663 | 0.0917 | 0.9988 |

0.1 | 0.0663 | 0.0917 | 0.9988 |

0.2 | 0.0663 | 0.0917 | 0.9988 |

0.3 | 0.0663 | 0.0917 | 0.9988 |

0.4 | 0.0668 | 0.1020 | 0.8975 |

0.5 | 0.0679 | 0.1070 | 0.8790 |

0.6 | 0.2600 | 0.3709 | 0.2468 |

0.7 | 0.5550 | 0.9103 | 0.1005 |

0.8 | 0.6866 | 1.3500 | 0.0677 |

0.9 | 0.7578 | 1.8140 | 0.0504 |

1.0 | 0.9030 | 3.5776 | 0.0255 |

Function | Indicators | PSO | BSA | GA |
---|---|---|---|---|

efficiency | 100% | 100% | 100% | |

${F}_{1}(x)$ | number of iterations | 523.4 | 492.1 | 483.1 |

solution time | 0.311 | 0.707 | 0.309 | |

efficiency | 100% | 100% | 100% | |

${F}_{2}(x)$ | number of iterations | 591.2 | 527.7 | 497.8 |

solution time | 0.408 | 0.785 | 0.3906 | |

efficiency | 90.1% | 100% | 100% | |

${F}_{3}(x)$ | number of iterations | 754.5 | 692.7 | 684.4 |

solution time | 0.634 | 0.867 | 0.631 | |

efficiency | 92.5% | 100% | 100% | |

${F}_{4}(x)$ | number of iterations | 712.9 | 647.0 | 640.0 |

solution time | 0.612 | 0.823 | 0.5906 | |

efficiency | 95.7% | 100% | 100% | |

Average value | number of iterations | 645.4 | 589.8 | 576.3 |

solution time | 0.491 | 0.795 | 0.481 |

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**MDPI and ACS Style**

Dogadina, E.P.; Smirnov, M.V.; Osipov, A.V.; Suvorov, S.V. Evaluation of the Forms of Education of High School Students Using a Hybrid Model Based on Various Optimization Methods and a Neural Network. *Informatics* **2021**, *8*, 46.
https://doi.org/10.3390/informatics8030046

**AMA Style**

Dogadina EP, Smirnov MV, Osipov AV, Suvorov SV. Evaluation of the Forms of Education of High School Students Using a Hybrid Model Based on Various Optimization Methods and a Neural Network. *Informatics*. 2021; 8(3):46.
https://doi.org/10.3390/informatics8030046

**Chicago/Turabian Style**

Dogadina, Elena Petrovna, Michael Viktorovich Smirnov, Aleksey Viktorovich Osipov, and Stanislav Vadimovich Suvorov. 2021. "Evaluation of the Forms of Education of High School Students Using a Hybrid Model Based on Various Optimization Methods and a Neural Network" *Informatics* 8, no. 3: 46.
https://doi.org/10.3390/informatics8030046