# Some Algorithms to Solve a Bi-Objectives Problem for Team Selection
## 5 Result
### Result  
We compared DCA, Genetic Algorithm, and CPLEX-MIQP [27] algorithms in terms of the value of objective function and processing time. It is different from the results of the experiment on random generation data with standard distribution and on very little previous experimental data [1; 2]. DCA produced excellent results. The above results did not recur in our experiments. After we redesigned another version of the Genetic algorithm, it produced results that outperformed other algorithms. In the first experiment, when we searched for the best team among 3738 contestants. CPLEX only finds the optimal solution in the absence of all business constraints. The CPLEX and GA found an optimal solution better than the DCA result, but CPLEX needed more time to search. When we add 37 and 38 constraints to the model, CPLEX cannot solve the problem, while other cases have out of memory errors. The results of running all three algorithms to find a team of three members from 3728 candidates displayed in Figures 11 and 12. The new design of the genetic algorithm yielded the best objective value and the most optimal processing time. It is dozens of times faster than DCA. The result of DCA depends a lot on starting points. These points may fall into the valley that does not contain the optimal global solution. Genetic algorithms created mutations of interest very quickly after some generations by the creation of a large population of individuals. We execute the proposed scheme of the Genetic Algorithm several times with different initial solutions. The objective values and execution times of different execution shown in Figure 13. Twenty times of executions return the same resolution, and the average execution time is about 3.8 s. It shows that the set of selected parameters balanced the two expected factors: execution time and optimum solution. \begin{table}
\begin{tabular}{c c c c c} \hline
**ID** & _dom_ & _rec_ & _mut_ & **Observation Results** \\ \hline
1 & 0.7 & 0.2 & 0.1 & Fast convergence, good, and stable fitness values. \\ \hline
2 & 0.6 & 0.3 & 0.1 & Fast convergence, good and stable fitness values. More stable than pair 1. \\ \hline
3 & 0.4 & 0.4 & 0.2 & Slow convergence, good, and stable fitness values. \\ \hline
4 & 0.2 & 0.7 & 0.1 & Slow convergence, worse, and unstable fitness values. \\ \hline \end{tabular}
\end{table} 
Table 1: Different pair values of the rates of the selection of recessive, dominant, and mutant genes during the crossover. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Parameter** & \(G\) & \(D\) & \(\gamma\) & \(\omega\) & _mut_ & _dom_ & _rec_ \\ \hline
**Value** & 5 & 0.9 & 0.1 & 0.5 & 0.1 & 0.6 & 0.3 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameter to execute Genetic Algorithm for solving MDSB. Figure 11: The objective value of three tested algorithms to find a team of three members from 3728 candidates. Figure 12: The time execution of three tested algorithms to find a team of three members from 3728 candidates. Figure 13: (**A**) the objective values of genetic algorithm corresponding to different initial points. (**B**) the execution times of genetic algorithm corresponding to different initial points. We conduct a comparison of the algorithms we have designed with CPLEX once again. We realize that CPLEX will consume many resources corresponding to the number of decision variables that it must handle. We, therefore, reduced the remaining set of candidates to 2000--these are the top candidates. Other parameters remain the same. Figure 14 illustrates the returned objective values of the algorithms to find a team of three members from the top 2000 candidates in the dataset. The genetic algorithm not only gives optimal results better than DCA and CPLEX, but also the processing time is much lower. It is ten times faster than DCA and hundreds of times more than CPLEX (see Figure 15). CPLEX can only provide solutions for models with up to 32 business constraints. It is futile for the remaining cases.