# Coordinated Multi-UAV Reconnaissance Scheme for Multiple Targets
## 4 Proposed Method
### Static Reconnaissance Allocation Scheme  
Static reconnaissance refers to a situation where the positions, value coefficients \(c_{j}\), and minimum reconnaissance revenue \(G_{min}\) of all the task areas are known, as well as the positions, endurance time \(T_{i}\), and reconnaissance ability \(\beta\) of the UAVs. The task of static  
Figure 3: Flow chat of the proposed algorithm. reconnaissance allocation is to plan the task assignment set \(p\), reconnaissance sequence \(q\), and reconnaissance time \(t\) under the constraints defined in Formulas (7) and (8), with the objective of achieving the goals outlined in Formulas (5) and (6). In this paper, the MTCMO algorithm is used to optimize the static reconnaissance problem. The MTCMO algorithm [32] is a relatively advanced constrained multi-objective evolutionary algorithm, characterized by its use of decreasing constraint boundaries, so that auxiliary tasks and master tasks maintain a high correlation during the evolution process. In addition, an improved \(\epsilon\) method is designed for auxiliary tasks, which can retain infeasible solutions with excellent objective values to help the main population cross the infeasible region and provide supplementary directions for infeasible solutions with lower constraint values to help the main population enter the feasible region from the infeasible region. 1. Calculate the Degree of Constraint Violation. In general, multi-objective optimization problems will have various constraints, which are of the form \[ \begin{cases}g_{i}(x)\leq 0,&i=1,...,k\\ h_{i}(x)=0,&i=k+1,...,n,\end{cases} \] (9) where \(g(x)\) and \(h(x)\) are inequality and equality constraints, and the \(k\) and \(n-k\) are the number of inequality and equality constraints, respectively. For convenience, equality constraints are often transformed into inequality constraints by using positive boundary correction parameters: \[|h_{i}(x)|-\sigma\leq 0,i=k+1,...,n.\] (10) According to Formulas (9) and (10), the constraint violation degree of each constraint for the individual is calculated using the following formula: \[cv_{i}(x)= \begin{cases}max(0,g_{i}(x)),&1\leq i\leq k\\ max(0,|h_{i}(x)|-\sigma),&k+1\leq i\leq n.\end{cases} \] (11) Finally, the constraint violation degree of an individual is calculated as follows: \[CV(x)=\sum_{i=1}^{n}cv_{i}(x).\] (12) If the constraint violation degree of an individual is not greater than 0, it is called a feasible solution; otherwise, it is an infeasible solution. According to the Constraint Dominance Criterion (CDP) [53], feasible solutions are considered better than infeasible solutions, and the comparison between infeasible solutions can be carried out using the constraint violation degree. Individuals with a small constraint violation degree are considered better than those with a large constraint violation degree. 2. \(\epsilon\) Method. Set a constraint bound \(\epsilon_{T}\) that shrinks with the number of iterations and satisfies the following formula: \[\epsilon_{T}=\epsilon_{0}\cdot(1-\frac{T}{MaxT})^{(\frac{-\log(\epsilon_{0}) -\epsilon}{\log(1-\eta p)})},\] (13) \(MaxT\) represents the maximum number of iterations, \(pp\) is a parameter that controls the rate of decrease of \(\epsilon_{T}\), and \(\epsilon_{0}\) denotes the initial constraint violation, which is equal to the maximum CV among the initial primary and auxiliary populations. 3. MTCMO Algorithm Flow. The main process of the MTCMO algorithm is illustrated in Figure 4. Firstly, two populations with NP individuals, denoted as \(P_{1}\), and \(P_{2}\), are randomly initialized in the search space. Each individual represents a set of decision variables, that is, an allocation scheme. Next, the two parent populations \(P_{1}\) and \(P_{2}\) use the Multiobjective Evolutionary Algorithm (MOEA) operator to generate offspring populations \(O_{1}\) and \(O_{2}\) with NP/2 individuals, respectively.