## 3 Proposed Algorithm
### Population Initialization Based on Tent Mapping
From the four figures, it can be seen that the efficiency and optimization effect of CDPIO algorithm is obviously better than that of PIO algorithm, no matter whether it is low-dimensional single peak, low-dimensional multi-peak, high-dimensional single peak, or high-dimensional multi-peak function. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Function** & **Scope** & **Best** \\ \hline f1 & _[PERSON]_ & [\(-\)100,100] & \(-\)1 \\ \hline f2 & _[PERSON]_ & [\(-\)10,10] & 0 \\ \hline f3 & _[PERSON]_ & [\(-d^{2}\),\(d^{2}\)] & \(-\)50 \\ \hline f4 & _[PERSON]_ & [\(-\)10,10] & 0 \\ \hline f5 & _[PERSON]_ & [\(-\)100,100] & 0 \\ \hline f6 & \(\mathit{Schaffer}\) & [\(-\)10,10] & 0 \\ \hline f7 & \(\mathit{Six}\)_Hump_Camel_Back_ & [\(-\)3,3]\&[-\)2,2] & \(-\)1.0316 \\ \hline f8 & _[PERSON]_ & [\(-\)100,100] & 0 \\ \hline f9 & _[PERSON]_ & [\(-\)5.12,5.12] & 0 \\ \hline \hline \end{tabular} Experimental setting parameters are shown in Table 2:

\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of pigeons \(\mathit{N_{p}}\) & Dimension \(D*5\) \\ Compass factor C & 0.3 \\ Parameter of position \(x_{0}\) & 0 \\ Parameter of size \(\gamma\) & 1 \\ Number of iterations of map and compass \(\mathit{N_{C1}max}\) & 6 \\ Number of iterations of landmark \(\mathit{N_{C2}max}\) & 4 \\ The total number of iterations \(\mathit{N_{c}}\) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameters. ### Nonlinear Correlation Performance of CDPIO

The performance of PIO algorithm for finding the optimal value of the function with \(x_{i}\), \(x_{i-1}\) will gradually decline with the increase of the dimension of the search space. In order to test the nonlinear correlation of the CDPIO algorithm and the ability of jumping out of the local optimal solution, we selected three test functions. The three test functions [26] have the same characteristics and all have the form of \(x_{i}\), \(x_{i-1}\). The two algorithms mentioned above are compared and analyzed on the basis of the three test functions. It is concluded that the CDPIO algorithm proposed in this paper has better performance than PIO algorithm. Figure 2 shows the iterative convergence curve of the algorithm. Figure 2a-d respectively represent the convergence curves of 2 algorithms obtained on TRID, DIXON-PRICE and ROSENBROCK function. The abscissa represents the number of iterations, and the ordinate represents the optimal adaptive value. The formula of the three test functions is as follows. (1) TRID:

\[f(x)=\sum\
olimits_{i=1}^{d}(x_{i}-1)^{2}-\sum\
olimits_{i=1}^{d}x_{i}x_{i-1} \tag{14}\]

(2) DIXON-PRICE:

\[f(x)=(x_{1}-1)^{2}+\sum\
olimits_{i=2}^{d}i\left(2{x_{i}}^{2}-x_{i-1}\right)^ {2} \tag{15}\]

(3) ROSENBROCK:

\[f(x)=\sum\
olimits_{i-1}^{d-1}\left[100\left(x_{i+1}-{x_{i}}^{2}\right)^{2}+( x_{i}-1)^{2}\right]x_{i}\in[-5,10] \tag{16}\]

The CDPIO algorithm and PIO algorithm proposed are used for testing on the basis of the three functions, and the result analysis diagram is shown below. Figure 1: Comparison of convergence curves of 2 algorithms obtained on the benchmark functions. (**a**) is the iterative graph of the low-dimensional unimodal function; (**b**) is the iterative graph of low-dimensional multimodal function; (**c**) is the iterative graph of the high-dimensional unimodal function; (**d**) is the iterative graph of high-dimensional multimodal function. It can be concluded from the results of the above three simulation experiments that the convergence accuracy of CDPIO algorithm is significantly improved compared with the PIO algorithm, which is closer to the optimal value and the curve is smoothed. Among them, the closer the optimal fitness value is to 1.0, the higher the optimization precision; the inflection point of the curve appears first, and the convergence speed becomes faster. The smoother the curve is, the stronger the ability of the algorithm to escape the local optimal solution.