## Author Contributions

T.S.N.: Conceptualization, Data curation, Formal analysis, Investigation; Methodology, Software, Writing–original draft, Writing–review & editing; N.A.B.: Conceptualization, Formal analysis, Methodology, Supervision; T.T.T.: Conceptualization; Formal analysis, Methodology, Software, Validation; P.C.L.: Investigation, Methodology, Project administration, Resources; D.C.B.: Formal analysis, Methodology; T.D.N.: Investigation, Software; L.D.P.: Investigation, Software; Q.T.K.: Software, Visualization; B.S.N.: Software; S.N.T.: Formal analysis; Investigation; Methodology; Validation; Supervision. All authors have read and agreed to the published version of the manuscript.

**Figure 1.**
Illustration of the team selection problem. The table at the left of the figure describes the aggregated data through the competitions and training of the candidates. The goal is to select the team with the highest potential for achievement.

**Figure 1.**
Illustration of the team selection problem. The table at the left of the figure describes the aggregated data through the competitions and training of the candidates. The goal is to select the team with the highest potential for achievement.

**Figure 2.**
Basic workflow of the genetic algorithm.

**Figure 2.**
Basic workflow of the genetic algorithm.

**Figure 3.**
The number of users of codeforces.com in Southeast Asian countries.

**Figure 3.**
The number of users of codeforces.com in Southeast Asian countries.

**Figure 4.**
The scores of 8 skills of the top 10 users in Vietnam.

**Figure 4.**
The scores of 8 skills of the top 10 users in Vietnam.

**Figure 5.**
The total number of scores the user has achieved by solving exercises for each skill.

**Figure 5.**
The total number of scores the user has achieved by solving exercises for each skill.

**Figure 6.**
The minimum, maximum, and average scores that the users gained for their skills.

**Figure 6.**
The minimum, maximum, and average scores that the users gained for their skills.

**Figure 7.**
Probability density graphs on corresponding skills: (**A**) math, implementation, brute force, dp, greedy; (**B**) binary search, sortings, constructive algorithms, data structures, strings; (**C**) geometry, bitmasks, trees, combinatorics, two pointers; (**D**) divide and conquer, games, shortest paths, hashing; (**E**) meet-in-the-middle, graph matchings, expression parsing, schedules; (**F**) number theory, dfs and similar, graphs; (**G**) *special; (**H**) probabilities, interactive, dsu; (**I**) matrices, flows, string suffix structures, ternary search; (**J**) Chinese remainder theorem, fft, 2-sat.

**Figure 7.**
Probability density graphs on corresponding skills: (**A**) math, implementation, brute force, dp, greedy; (**B**) binary search, sortings, constructive algorithms, data structures, strings; (**C**) geometry, bitmasks, trees, combinatorics, two pointers; (**D**) divide and conquer, games, shortest paths, hashing; (**E**) meet-in-the-middle, graph matchings, expression parsing, schedules; (**F**) number theory, dfs and similar, graphs; (**G**) *special; (**H**) probabilities, interactive, dsu; (**I**) matrices, flows, string suffix structures, ternary search; (**J**) Chinese remainder theorem, fft, 2-sat.

**Figure 8.**
The procedure of the experiment.

**Figure 8.**
The procedure of the experiment.

**Figure 9.**
(**A**) the time execution of DCA with different values of τ; (**B**) the objective value of DCA with different values of τ; (**C**) average errors of the decision variables with different values of τ.

**Figure 9.**
(**A**) the time execution of DCA with different values of τ; (**B**) the objective value of DCA with different values of τ; (**C**) average errors of the decision variables with different values of τ.

**Figure 10.**
(**A**) the fitness values over generations; (**B**) the execution times over generations.

**Figure 10.**
(**A**) the fitness values over generations; (**B**) the execution times over generations.

**Figure 11.**
The objective value of three tested algorithms to find a team of three members from 3728 candidates.

**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 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.

**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.

**Figure 14.**
The objective values of the algorithms to find a team of three members from the top 2000 candidates.

**Figure 14.**
The objective values of the algorithms to find a team of three members from the top 2000 candidates.

**Figure 15.**
The time execution of the algorithms to find a team of three members from the top 2000 candidates.

**Figure 15.**
The time execution of the algorithms to find a team of three members from the top 2000 candidates.

**Figure 16.**
(**A**) the objective values of the algorithms with different team size; (**B**) the execution time of the algorithms with different team size.

**Figure 16.**
(**A**) the objective values of the algorithms with different team size; (**B**) the execution time of the algorithms with different team size.

**Table 1.**
Different pair values of the rates of the selection of recessive, dominant, and mutant genes during the crossover.

**Table 1.**
Different pair values of the rates of the selection of recessive, dominant, and mutant genes during the crossover.

ID | dom | rec | mut | Observation Results |
---|

1 | 0.7 | 0.2 | 0.1 | Fast convergence, good, and stable fitness values. |

2 | 0.6 | 0.3 | 0.1 | Fast convergence, good and stable fitness values. More stable than pair 1. |

3 | 0.4 | 0.4 | 0.2 | Slow convergence, good, and stable fitness values. |

4 | 0.2 | 0.7 | 0.1 | Slow convergence, worse, and unstable fitness values. |

**Table 2.**
Parameter to execute Genetic Algorithm for solving MDSB.

**Table 2.**
Parameter to execute Genetic Algorithm for solving MDSB.

Parameter | G | D | γ | ω | mut | dom | rec |
---|

**Value** | 5 | 0.9 | 0.1 | 0.5 | 0.1 | 0.6 | 0.3 |