# Adaptive Curriculum Sequencing and Education Management System via Group-Theoretic Particle Swarm Optimization

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## Abstract

**:**

## 1. Introduction

- A new search paradigm combining symmetric group theory with metaheuristics is proposed for tackling an NP-hard problem;
- Both intrinsic and extrinsic characteristics of users are involved in the learning process as the objective function;
- The balanced relationship between diversification and intensification is maintained during the optimization procedure.

## 2. Materials and Methodology

#### 2.1. Problem Formulation

_{o8}, which generate one of the optimal sequences of a curriculum $s=({s}_{2},{s}_{7},{s}_{8})$ to cover the maximal targets with the minimal paths. Note that each user’s preference is represented by a level, each learning object is represented by a rectangle, and each knowledge concept is represented by a circle. The solid arrow connecting two concepts is the prerequisite relationship and the dash arrow stands for the dependent relationship between knowledge concepts and learning contents.

#### 2.2. Particle Representation

#### 2.3. Landscape Decomposition

#### 2.4. Moving Neighborhood

#### 2.5. Swarm Topology

#### 2.6. Objective Function

_{i}is the expected time for learning the element ${s}_{i}$ in the curriculum sequence, and $\overline{T}$ and $\overline{T}$ are the upper and lower limits of learning time, respectively. The objective function ${f}_{3}$ evaluates the period between the upper and lower limits of total time.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**An example of ACS problem formulation with the inputs of users’ preferences, learning contents, and knowledge concepts, and the output of possible curriculum sequences.

**Figure 3.**An illustration of neighborhood movement with the guidance trends of four-layered hierarchical operations.

**Figure 5.**The fitness curves of the compared methods with different dataset sizes: (

**a**) fitness results obtained by material size 50; (

**b**) fitness results obtained by material size 200; (

**c**) fitness results obtained by material size 500; (

**d**) fitness results obtained by material size 1000.

Method | Parameter | Value |
---|---|---|

GA | Population size | 30 |

Crossover rate | 0.5 | |

Mutation rate | 0.2 | |

ACO | Population size | 30 |

Pheromone factor | 1.0 | |

Heuristic factor | 1.5 | |

Evaporation rate | 0.3 | |

PSO | Population size | 30 |

Inertial weight | 0.8 | |

Acceleration coefficient | 2.0 | |

DE | Population size | 30 |

Crossover rate | 0.5 | |

Low bound | 0.3 | |

High bound | 0.6 | |

ATSA | Population size | 30 |

Initial speed | 1 | |

Subordinate speed | 4 | |

IChOA | Population size | 30 |

Chaotic rate | 0.5 | |

Turbulence factor 1 | 1.5 | |

Turbulence factor 2 | 0.3 | |

GT-PSO | Population size | 30 |

Random 1 and 2 | 0.4 | |

Random 3 and 4 | 0.5 | |

Random 5 and 6 | 0.3 | |

Acceleration coefficient | 2.0 |

**Table 2.**The fitness scores of the compared methods with different dataset sizes and evaluation metrics of mean, standard deviation, best value, and p-value.

Number of Materials | Metric | GA | ACO | PSO | DE | ATSA | IChOA | GT-PSO |
---|---|---|---|---|---|---|---|---|

50 | Mean | 9.642 | 9.607 | 9.424 | 9.285 | 9.280 | 9.323 | 9.266 |

Std | 0.317 | 0.325 | 0.217 | 0.111 | 0.253 | 0.186 | 0.128 | |

Best | 9.307 | 9.254 | 9.241 | 9.042 | 8.904 | 9.006 | 8.953 | |

p-value | 0.000 | 0.000 | 0.000 | 0.006 | 0.024 | 0.017 | / | |

200 | Mean | 16.750 | 16.608 | 16.686 | 16.418 | 16.378 | 16.403 | 16.214 |

Std | 0.371 | 0.377 | 0.248 | 0.166 | 0.305 | 0.234 | 0.174 | |

Best | 16.480 | 16.276 | 16.308 | 16.055 | 15.873 | 15.947 | 15.847 | |

p-value | 0.000 | 0.000 | 0.001 | 0.016 | 0.037 | 0.021 | / | |

500 | Mean | 27.354 | 27.151 | 27.141 | 27.032 | 26.875 | 27.068 | 26.907 |

Std | 0.435 | 0.418 | 0.277 | 0.206 | 0.326 | 0.364 | 0.304 | |

Best | 27.133 | 26.937 | 26.829 | 26.550 | 26.106 | 26.248 | 26.218 | |

p-value | 0.001 | 0.000 | 0.001 | 0.009 | 1.000 | 0.018 | / | |

1000 | Mean | 65.138 | 64.176 | 63.778 | 63.411 | 63.399 | 63.514 | 62.805 |

Std | 0.462 | 0.459 | 0.396 | 0.327 | 0.338 | 0.406 | 0.473 | |

Best | 64.392 | 63.863 | 63.414 | 62.758 | 62.478 | 62.303 | 61.882 | |

p-value | 0.001 | 0.001 | 0.001 | 0.019 | 0.033 | 0.028 | / | |

+/=/- | 4/0/0 | 4/0/0 | 4/0/0 | 4/0/0 | 3/0/1 | 4/0/0 | 4/0/0 |

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**MDPI and ACS Style**

Sheng, X.; Lan, K.; Jiang, X.; Yang, J.
Adaptive Curriculum Sequencing and Education Management System via Group-Theoretic Particle Swarm Optimization. *Systems* **2023**, *11*, 34.
https://doi.org/10.3390/systems11010034

**AMA Style**

Sheng X, Lan K, Jiang X, Yang J.
Adaptive Curriculum Sequencing and Education Management System via Group-Theoretic Particle Swarm Optimization. *Systems*. 2023; 11(1):34.
https://doi.org/10.3390/systems11010034

**Chicago/Turabian Style**

Sheng, Xiaojing, Kun Lan, Xiaoliang Jiang, and Jie Yang.
2023. "Adaptive Curriculum Sequencing and Education Management System via Group-Theoretic Particle Swarm Optimization" *Systems* 11, no. 1: 34.
https://doi.org/10.3390/systems11010034