## 3 Proposed Algorithm
### Population Initialization Based on Tent Mapping
To sum up, CDPIO algorithm has good ability to resist local extreme values for most functions, especially for simple low-dimensional functions, wherein it has good robustness, efficiency, and global search ability. Figure 2: Comparison of convergence curves of 2 algorithms obtained on the three test functions. (**a**) is the convergence curves of 2 algorithms obtained on TRID function; (**b**) is the convergence curves of 2 algorithms obtained on DIXON-PRICE function; (**c**) is the convergence curves of 2 algorithms obtained on ROSENBROCK function. ## 5 Application in Coordinated Target Search of UAVs

UAVs play a key role in search missions, as they can find targets in complex environments. The searching problem of UAVs is a relatively complex multi-objective optimization problem under multiple constraints. Most search algorithms cannot meet the requirements of high efficiency and low power consumption in the search process. In order to further verify the superiority of CDPIO algorithm, not only in reference function optimization but also in the process of solving practical problems, this paper used the CDPIO algorithm to solve the cooperative search problem of UAVs. ### Environment Initialization

The search area was divided into discrete areas of \(D_{x}\times D_{y}\) to construct a relatively real environment map. The grid \((a,b)\) is numbered as \(v=a+(b-1)\times D_{y}\), \(v\in\left\{1,2,3,\cdots D_{x}\times D_{y}\right\}\); \(D_{x}\) and \(D_{y}\) represent the number of grids in two dimensions of length and width. For each network \(v\in\left\{1,2,3,\cdots D_{x}\times D_{y}\right\}\), a certain value \(Z_{v}(l)\) is given, where \(Z_{v}(l)\) is the information structure, which comprehensively describes the environment and target information in the current grid, as shown below: \(Z_{v}(l)=\left(z_{v}(l),x_{v}(l),v\in\left\{1,2,3,\cdots D_{x}\times D_{y} \right\}\right)\), including \(z_{v}(l)\in[0,1]\), as the target probability exists, and describing the moment \(l\) the \(vth\) grid has the possibility of searching for the target. The value of \(x_{v}(l)\) is 0 or 1, indicating whether the UAV fully understands the environmental information at the place; \(\omega_{v}(l)\) is the function of UAV position and time. When the UAV moves to the current grid, the signal of pheromone information will be generated at the corresponding position, and the information will be transmitted to the nearby UAVs through network communication. ### Cost Function

The cooperative target search problem of UAV is a very complex multi-objective optimization problem. It is very important to select the relevant multi-objective cost function. The cost function set is introduced as follows:

\(F_{1}\): describes the probability of finding a target;

\(F_{2}\): describes the environmental certainty of UAV;

\(F_{3}\): describes the time cost and fuel cost between two consecutive way points;

\(F_{4}\): used to estimate whether the UAV's trajectory is within the search area. A better search task requires a larger cost function: \(F_{1},\ F_{2},\ F_{3}\) and a lower cost function \(F_{4}\). Therefore, the inverse values of the cost functions \(F_{1},\ F_{2},\) and \(F_{3}\) are used for unified optimization. ### Experimental Result

In this paper, CDPIO and PIO algorithms were used to solve the problem. It was stipulated that 10 UAVs should be used to search for targets, among which 10 UAVs should successfully avoid two obstacle threat areas and successfully search for three targets. The experimental results are shown in Figure 3.

As shown in Figure 3a, CDPIO was used for the simulation experiment. Figure 3b shows an experimental study using PIO. In the figure above, no matter whether PIO or improved CDPIO was used, 10 UAVs can successfully avoid the threat areas and find the target together. However, when CDPIO algorithm was used for target search, the UAV was more sensitive to the threat area and its average distance from the threat area was larger.