# A Solving Algorithm for Nonlinear Bilevel Programing Problems Based on Human Evolutionary Model
## 3 Design of the Proposed Algorithm
### Experimental Results  
We execute the proposed algorithm 20 independent runs on each problem in that the result could show its performance directly. Therefore, the optimal solutions obtained by the proposed algorithm are recorded, as well as the corresponding computing time taken by the algorithm are listed in Table 3. Moreover, the comparison of the solutions by the proposed algorithm with those in related references is demonstrated in Table 4.  
As to the performance of the proposed algorithm, the computing time and iteration show the feasibility and stability of the algorithm to some extent. Obviously, it can be seen from Table 3 that the iteration and computing time with little change illustrate the presented algorithm is generally feasible and steady for all examples. In concrete terms, it is worth noticing that the computing time for Example 1 is less than others due to its small scale which at least shows the feasibility of the proposed algorithm. For Example 4, on the contrary, it is a large-scale problem, so it has the most computing time and iteration. However, it is notable that the computing times in Example 1 and 4 vary in a small interval, which also demonstrates the algorithm is steady during these numerical experiments. Furthermore, as to Example 2 and Example 3, it can be seen that the fluctuation in the iteration is tiny, but the corresponding computing time varies greatly. The reason is that the population is initialized randomly and the population size is adaptively adjusted; what is more, the range of the size is not strictly limited to a small interval so that the amount of the individuals may vary greatly for each run. Finally, as for the small-scale examples (Example 1, 2, and 3), the maximal iterations are much less than the maximum setting value of the corresponding parameter, which also illustrates the efficiency and feasibility of the constructed algorithm is acceptable. Meanwhile, it is undeniable that for Example 4, the iteration parameter is up to the maximum setting value of the related parameter indicating that the presented algorithm should be improved to efficiently solve larger-scale problems. Overall, these results indicate that the proposed algorithm is feasible and stable for all experiments. Next, the optima obtained by the novel algorithm is compared with the existing studies to show its performance in detail. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Recombination**} & \multicolumn{2}{c}{**Mutation**} & \multirow{2}{*}{**Max Age**} & \multicolumn{2}{c}{**Population Size**} & \multicolumn{2}{c}{**Iteration**} \\ \cline{3-8}  & & \(K\) & \(A\) & & **Initial** & **Min** & **Max** & **Max** & **Min** \\ \hline Example 1 & & & 0.1 & 10 & 50 & 20 & 150 & 100 & 30 \\ \hline Example 2 & & & 0.1 & 20 & 50 & 30 & 200 & 150 & 50 \\ \hline Example 3 & & & 0.5 & 5 & 80 & 50 & 150 & 100 & 30 \\ \hline Example 4 & & & 0.5 & 8 & 80 & 50 & 200 & 200 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the algorithm. In Table 4, Column 'Reference [PERSON] et al.' lists the results given by [PERSON] et al. for all examples, and Column 'Reference' sequentially lists the results obtained by [PERSON] for Example 1 [3], [PERSON] and [PERSON] for Example 2 [48], [PERSON] and [PERSON] for Example 3 [49], [PERSON] et al. for Example 4 [30]. According to the comparison of the results in Table 4, it can be observed that the solutions obtained by our algorithm for Example 2 is better than those produced by the compared algorithms in the references. For this situation, we can draw a primary conclusion that the presented algorithm is capable to improve the current algorithm. However, as for Example 1, the upper objective function in this paper are a little worse than these given by the compared algorithms while the results of the lower objective function are better than in the existing researches.