# Multi-Objective Task Scheduling Optimization in Spatial Crowdsourcing
## 4 Performance Evaluation
### The Performance of the Ranking Strategy Algorithm  
The primary purpose of employing the ranking strategy stage in our model was to enhance the performance of the MOPSO based on the primary objectives of our research. We examined the performance of our model and the impact of the ranking strategy stage on the fitness value by varying the three initialization mechanisms of the positions of the particles in the first iteration under the same parameters, and by randomly initializing the velocity of all particles. The following are the initialization mechanisms of the particles' positions:  
1. Initializing the position of a particle randomly (the percentage of randomness is 100%);
2. Initializing the position of a hybrid particle, both randomly and from the ranked table (the percentage of randomness is 50%);
3. Initializing the positions of all particles from the ranked table (the percentage of randomness is 0%). The fitness function value was computed using Equation (4), as mentioned in our study [19]:  
\[f=NTTC+NWLB+(1-NV) \tag{4}\]  
where \(NTTC\) is the normalized TTCs, \(NWLB\) is the normalized WLB, and \(NV\) is the normalized \(\mid V\mid\). Meanwhile, \((1-NV)\) is the reverse of \(NV\), meaning that we converted the objective of maximizing the number of completed tasks into another form--that is, minimizing the number of uncompleted tasks--in order to unify the direction of the optimization of our objectives. The results of the fitness function values are presented in Table 8.  
In more detail, we investigated the variation of the three initialization mechanisms on each objective (i.e., the number of completed tasks, the total travel costs, and the balance of workers' workload). It should be noted that in the fitness function, we reversed the maximizing the number of completed tasks objective to a new form, i.e., minimizing the number of uncompleted tasks objective. In order to unify the direction of all objectives in terms of \"minimizing\", in Table 9 we display the results of \(1-NV\), which is the number of uncompleted tasks, as well as the normalized TTCs (NTTCs) and the normalized workload balance (\(NWLB\)). Tables 8 and 9 show the evaluation of using the ranking strategy and its impact on the performance of our proposed model. Figure 5 illustrates that there are no essential \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & \multicolumn{3}{c}{**Fitness Function Value**} \\ \hline  & 100\% & 50\% & 0\% \\  & (Randomly) & (Hybrid) & (**Ranked table**) \\ \hline Case 1 & 0.540143 & 0.092286 & **0.096544** \\ \hline Case 2 & 0.537479 & 0.073181 & **0.071633** \\ \hline Gowalla & 0.535224 & 0.060976 & **0.056781** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The results of the fitness function values when varying the initialization mechanisms. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Normalization Values for Each Objective in Terms of Minimization**} \\ \cline{2-9}  & & \(1-NV\) & & \multicolumn{3}{c}{_NWLB_} & \multicolumn{3}{c}{_NTTC_} \\ \cline{2-9}  & **100\%** & **50\%** & **0\%** & **100\%** & **50\%** & **0\%** & **100\%** & **50\%** & **0\%** \\ \hline
**Case 1** & 0.34853 & 0.026923 & 0.034188 & 0.039943 & 0.048828 & 0.051251 & 0.15167 & 0.016535 & 0.011105 \\ \hline
**Case 2** & 0.35715 & 0.026961 & 0.027024 & 0.028998 & 0.034157 & 0.036681 & 0.151331 & 0.012063 & 0.007929 \\ \hline
**Gowalla** & 0.365401 & 0.026474 & 0.024522 & 0.020456 & 0.024455 & 0.026705 & 0.149367 & 0.010047 & 0.005554 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Normalization values of the objectives in terms of minimization when varying the initialization mechanisms. differences between the performance of the proposed MOTSO model when setting the percentage of randomness to 0% or 50%. Thus, we focused on only two of initialization mechanisms:  
1. Initializing the positions of all particles randomly;
2. Initializing the positions of all particles using the output of the ranking strategy stage.