# Multi-Objective Task Scheduling Optimization in Spatial Crowdsourcing
## 4 Performance Evaluation
### Performance of the MOTSO Model
#### 4.2.3 Minimizing the Standard Deviation of the Workload Balance  
In our model, the workload for each worker was the traveled distance plus the duration of the execution time for the tasks done by the same worker, as calculated in [19].  
We considered the standard deviation as a metric to quantify the workload between all workers because the decreased standard deviation of the worker's workload helps to prevent overloading between the workers. Table 12 shows the standard deviation of the workload balance results using the MOTSO model.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Using Gowalla**} \\ \hline
**Name of algorithm** & **ATC value** \\
**A\&S** & 8.30 \\
**GALS** & 5.87 \\
**NLALA-L** & 6.02 \\
**NLALS-T** & 5.80 \\
**BLALS-K** & 5.86 \\
**BLAS-T** & 5.86 \\
**BLA** & 7.8 \\
**LBA** & 5.5 \\
**DCA** & 6.1 \\
**MOTSO (our model)** & 0.5527457 \\ \hline \hline \end{tabular}
\end{table}
Table 11: The results of the average travel cost (_ATC_) using different algorithms.  
Figure 8: The average total travel cost using different algorithms.  
The baseline in our work was the approach introduced in [2]. We compared the MOTSO using the BLA to evaluate the effectiveness of our model according to the workload balance objective under the same experimental settings. Moreover, we computed the standard deviations of workload balance for the two algorithms, i.e., the BLA and our MOTSO model. Furthermore, we conducted a statistical test to compare the two different standard deviation values; for this, we selected \(t\) (independent-samples \(t\)-test).  
Regarding the synthetic dataset (case 1), there was a significant difference in the scores for the BLA (M = 184.1136, SD = 47.17132) and our MOTSO model (M = 44.32074, SD = 55.58566); where the value of \(t\) (1198) = 46.9692 and \(p\) = 0.0001. These results show that our MOTSO model is able to reduce the workload of a worker compared to the BLA. In case 2, the score of the BLA was M = 185.4424 and SD = 45.72034, while the score of our BLA was M = 44.411495 and SD = 56.424235; based on the \(t\)-value (2398) being 67.2718 (\(p=0.0001\)), there was a significant difference in the scores for the BLA and MOTSO in case 2. These results indicate that our model can improve the workload of workers.  
According to the results of the real dataset (Gowalla), the BLA score was M = 182.2911 and SD = 48.25323 and that of our MOTSO was M = 44.339762 and SD = 58.016085, where \(t\)-value (4798) = 89.5599 and \(p=0.0001\). There was a significant difference between the results of the two algorithms, where the workload of the worker decreased more with our MOTSO model.  
Based on the previously mentioned results of an independent-samples \(t\)-test, \(p\) > 0.05 in both the synthetic dataset and the Gowalla dataset, so there was a significant difference between the two algorithms in terms of minimizing the standard deviation of the workload balance, which is in favor of our model. In other words, our model improves the workload balance between all workers compared to the BLA. Thus, our MOTSO model is effective in regard to the load balancing objective.