## 6 Results and Discussion
### Preliminary Observations  
To assess the behaviors in optimizing the three estimation methods, we follow the procedure of tuning the following two parameters of the MUCPSO algorithm: population \(p\) and chaotic maps as described in [63]. Here, for each estimation method, 80 experiments are performed using a combination of 10 values of \(p\) = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and eight chaotic maps = Bernoulli, Chebyshev, Circle, Gauss, Logistic, Sine, Singer, and Sinusoidal, which can be defined as pairs of (10, Bernoulli), (10, Chebyshev),..., (100, Sinusoidal). To reduce the coincidence, 1000 runs were applied to each pair in experiment. The common parameter value of \(p\) is finally selected as a fixed-optimum value for all the estimation methods.  
Figure 2 illustrates the experimental results for the problem of searching a minimum solution for the Use Case Points estimation method. The vertical axis shows all results from eighty experiments. It can be seen that a small population \(p\) (10) means the MUCPSO produces a good solution. In contrast, the bigger the \(p\), the worse the solution. Hence, the combination of small \(p\) and Chebyshev as the chaotic function is recommended. The optimum combination is reached using \(p\) = 10 and chaotic = Chebyshev.  
Next, Figure 3 illustrates the experimental results for the problem of searching for a minimum solution in the Agile estimation method. The vertical axis shows all results from eighty experiments. It can be seen that a small population \(p\) (10) means the MUCPSO produces a good solution. In contrast, the bigger the \(p\), the worse the solution. Hence, the combination of small \(p\) and Sinusoidal as the chaotic function is recommended. The optimum combination is reached using \(p\) = 10 and chaotic = Sinusoidal.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Weight Parameters** & **Range** & **Dimension** \\ \hline \multirow{3}{*}{UCP} & Simple & [5, 7, 49] & \\  & Average & [7.5, 12.49] & \\  & Complex & [12.5, 15] & \\ \hline \multirow{3}{*}{COCOMO} & A & [0, 10] & \\  & B & [0.3, 2] & 2 \\ \hline \multirow{9}{*}{Agile} & Team position & [0.91, 1] & \\  & Process & [0.89, 1] & \\  & Environmental factors & [0.96, 1] & \\  & Team dynamics & [0.85, 1] & \\  & Expected team change & [0.91, 1] & \\  & Introduction to new tools & [0.96, 1] & \\  & Vendor defect & [0.90, 1] & \\  & Team member responsibility & [0.98, 1] & \\  & Personal issue & [0.98, 1] & \\  & Expected delay & [0.96, 1] & \\  & Expected ambiguity & [0.95, 1] & \\  & Expected change & [0.97, 1] & \\  & Expected relocation & [0.98, 1] & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Three software effort estimation as benchmark methods.  
Figure 2: Parameter tuning for Use Case Points estimation model.  
Finally, Figure 4 illustrates the experimental results for the problem of searching for a minimum solution using the COCOMO estimation method. The vertical axis shows all results from eighty experiments. It can be seen that a large population \(p\) (90) means the MUCPSO produces a good solution. In contrast, the smaller the \(p\), the worse the solution. Hence, the combination of large \(p\) and Sinusoidal as the chaotic function is recommended. The optimum combination is reached for \(p=90\) and chaotic = Sinusoidal.