# Enabling Knowledge Discovery in Multi-Objective Optimizations of Worker Well-Being and Productivity

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## Abstract

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## 1. Introduction

## 2. Method

#### 2.1. Application Study

#### 2.1.1. Model Definition

#### 2.1.2. Well-Being and Productivity Evaluation

#### 2.1.3. Mathematical Modeling of Optimization

#### 2.1.4. Optimization Method

#### 2.2. Knowledge Discovery

#### 2.2.1. FPM

#### 2.2.2. InfS-R

## 3. Results

#### 3.1. Data Filtering

#### 3.2. Data Clustering

#### 3.3. Data Visualization

#### 3.4. Knowledge Discovery

#### 3.5. Knowledge Interpretation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Selected clusters for lowest $CT$ (marked by “+”), compromise between $CT$ and $\stackrel{=}{ER}$ (marked by “x”), and lowest $\stackrel{=}{ER}$ (marked by “-”).

**Figure 8.**InfS-R of ${\overline{ER}}_{13}$ and ${\overline{ER}}_{14}$ for $G{S}_{w}$ and ${X}_{w}$ variables.

Manikin Number | Stature (mm) | Elbow Height (mm) | Sex |
---|---|---|---|

1 | 1629 | 984 | Female |

2 | 1755 | 1091 | Male |

3 | 1656 | 1020 | Female |

4 | 1780 | 1134 | Male |

5 | 1668 | 963 | Female |

6 | 1794 | 1068 | Male |

7 | 1800 | 1094 | Female |

8 | 1936 | 1221 | Male |

9 | 1602 | 949 | Female |

10 | 1731 | 1047 | Male |

11 | 1590 | 1006 | Female |

12 | 1717 | 1114 | Male |

13 | 1457 | 875 | Female |

14 | 1574 | 961 | Male |

Indices | Parameters | ||
---|---|---|---|

$w=1\dots W$ | Welding spots | $TW$ | Welding time (s) |

$g=1\dots G$ | Welding guns | $TG$ | Time to change welding gun (s) |

$s=1\dots S$ | Welding sides | $TS$ | Time to change welding side (s) |

$m=1\dots M$ | Manikins | $TF$ | Time to move to a far position (s) |

$sq=1\dots SQ$ | Welding sequence | $TN$ | Time to move to a near position (s) |

Variables | $P{G}_{sq}$ | Previous gun: 1 if different, 0 if same | |

${X}_{w}$ | Welding spot sequence | $P{S}_{sq}$ | Previous side: 1 if different, 0 if same |

${Y}_{w}$ | Welding gun used at each welding spot | $P{F}_{sq}$ | 1 if previous spot is far, 0 if near |

${Z}_{w}$ | Welding side at each welding spot | $P{N}_{sq}$ | 1 if previous spot is near, 0 if far |

Objectives | $E{R}_{{m}_{{s}_{{g}_{w}}}}$ | RULA score for a manikin on a side with a welding gun at a welding spot | |

$CT$ | Cycle time of welding process (s) | ||

${\overline{ER}}_{m}$ | Average RULA score per manikin in the welding process | ||

$\stackrel{=}{ER}$ | Average RULA score of all manikins in the welding process |

Optimization Algorithm | NSGA-II |
---|---|

Population size | 150 |

Child population size | 150 |

Tournament size | 2 |

Mutation operator | Polynomial |

Mutation probability | 0.2 |

Crossover probability | 0.9 |

Crossover operator | SBX |

Maximum iterations | 25,000 |

Result Selected | $\mathit{C}\mathit{T}\left(\mathbf{s}\right)$ | $\stackrel{\mathit{=}}{\mathit{E}\mathit{R}}$ | Sequence |
---|---|---|---|

$\mathrm{Lowest}CT$ | 47 | 3.09 | Spot sequence: 7-1-3-2-5-4-6 Gun sequence: 3-3-3-3-3-3-3 Side sequence: 1-1-1-1-2-2-2 |

$\mathrm{Compromise}\mathrm{between}CT$$\mathrm{and}\stackrel{=}{ER}$ | 63 | 2.89 | Spot sequence: 4-5-6-7-1-2-3 Gun sequence: 3-3-3-3-2-2-2 Side sequence: 2-2-2-1-1-1-1 |

$\mathrm{Lowest}\stackrel{=}{ER}$ | 85 | 2.86 | Spot sequence: 4-5-6-7-1-2-3 Gun sequence: 4-5-6-7-1-2-3 Side sequence: 2-2-2-1-1-1-1 |

**Table 5.**Corresponding value for every $G{S}_{w}$ depending on the gun and side availability at each spot.

$\mathit{g}\mathbf{=}\mathbf{1}$ | $\mathit{g}\mathbf{=}\mathbf{2}$ | $\mathit{g}\mathbf{=}\mathbf{3}$ | ||||
---|---|---|---|---|---|---|

$\mathit{s}\mathbf{=}\mathbf{1}$ | $\mathit{s}\mathbf{=}\mathbf{2}$ | $\mathit{s}\mathbf{=}\mathbf{1}$ | $\mathit{s}\mathbf{=}\mathbf{2}$ | $\mathit{s}\mathbf{=}\mathbf{1}$ | $\mathit{s}\mathbf{=}\mathbf{2}$ | |

$w=1$ | $G{S}_{1}=1$ | X | $G{S}_{1}=2$ | X | $G{S}_{1}=3$ | $G{S}_{1}=4$ |

$w=2$ | $G{S}_{2}=1$ | X | $G{S}_{2}=2$ | X | $G{S}_{2}=3$ | $G{S}_{2}=4$ |

$w=3$ | $G{S}_{3}=1$ | X | $G{S}_{3}=2$ | X | $G{S}_{3}=3$ | $G{S}_{3}=4$ |

$w=4$ | X | X | X | X | $G{S}_{4}=1$ | $G{S}_{4}=2$ |

$w=5$ | X | X | X | X | $G{S}_{5}=1$ | $G{S}_{5}=2$ |

$w=6$ | X | X | X | X | $G{S}_{6}=1$ | $G{S}_{6}=2$ |

$w=7$ | $G{S}_{7}=1$ | X | $G{S}_{7}=2$ | X | $G{S}_{7}=3$ | X |

FPM | ||||
---|---|---|---|---|

Case | Filtered Rules | Sig. (%) | Unsig. (%) | Ratio |

$\mathrm{Lowest}CT$ | $G{S}_{1}$ == 4 | 91.53 | 27.07 | 3.38 |

$G{S}_{2}$ > 2 | 100 | 40.85 | 2.45 | |

$G{S}_{3}$== 3 | 79.1 | 28.86 | 2.74 | |

$G{S}_{1}$$==4G{S}_{2}$$2G{S}_{3}$== 3 | 75.14 | 7.58 | 9.91 | |

$\mathrm{Compromise}\mathrm{between}CT$$\mathrm{and}\stackrel{=}{ER}$ | $G{S}_{1}$ < 4 | 71.29 | 68.59 | 1.03 |

$G{S}_{3}$ > 2 | 64.36 | 45.51 | 1.41 | |

${X}_{5}$ > 2 | 82.18 | 69.4 | 1.18 | |

$G{S}_{1}$$<4G{S}_{3}$$>2{X}_{5}$ > 2 | 52.48 | 17.38 | 3.02 | |

$\mathrm{Lowest}\stackrel{=}{ER}$ | $G{S}_{1}$ == 2 | 100 | 41.86 | 2.39 |

$G{S}_{2}$ == 2 | 100 | 31.93 | 3.13 | |

$G{S}_{3}$ == 1 | 100 | 23.45 | 4.26 | |

$G{S}_{1}$$==2G{S}_{2}$$==2G{S}_{3}$ == 1 | 100 | 0.73 | 136.99 | |

Worker diversity inclusion | $G{S}_{1}$ == 2 | 93.84 | 38.17 | 2.46 |

$G{S}_{2}$ == 2 | 93.84 | 26.94 | 3.48 | |

$G{S}_{3}$ == 1 | 82.35 | 22.73 | 3.62 | |

$G{S}_{1}$$==2G{S}_{2}$$==2G{S}_{3}$ == 1 | 75.95 | 0.32 | 237.34 |

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**MDPI and ACS Style**

Iriondo Pascual, A.; Smedberg, H.; Högberg, D.; Syberfeldt, A.; Lämkull, D.
Enabling Knowledge Discovery in Multi-Objective Optimizations of Worker Well-Being and Productivity. *Sustainability* **2022**, *14*, 4894.
https://doi.org/10.3390/su14094894

**AMA Style**

Iriondo Pascual A, Smedberg H, Högberg D, Syberfeldt A, Lämkull D.
Enabling Knowledge Discovery in Multi-Objective Optimizations of Worker Well-Being and Productivity. *Sustainability*. 2022; 14(9):4894.
https://doi.org/10.3390/su14094894

**Chicago/Turabian Style**

Iriondo Pascual, Aitor, Henrik Smedberg, Dan Högberg, Anna Syberfeldt, and Dan Lämkull.
2022. "Enabling Knowledge Discovery in Multi-Objective Optimizations of Worker Well-Being and Productivity" *Sustainability* 14, no. 9: 4894.
https://doi.org/10.3390/su14094894