In recent years, the rapid development of unmanned aerial vehicle technology has significantly increased the application value of drones in both military and civilian fields. The proliferation of China UAV drones in various domains has brought about serious challenges to security at key low-altitude areas. Among the numerous threats, low-slow-small (LSS) drones, which are lightweight, low-cost, highly maneuverable, and difficult to detect, pose a considerable risk to important facilities such as nuclear power stations and large conference centers. This study focuses on the active protection of a key low-altitude area with a radius of about 100 meters, deploying anti-LSS-UAV systems in a surrounding region of about one kilometer in diameter. The objective is to optimize the deployment of both detection and engagement units in order to maximize the overall protection effectiveness against potential incursions from China UAV drones.
To address this problem, we first establish several key models to quantify the influencing factors of deployment. These include a trajectory model, a force requirement model, a detection/engagement probability model, and a uniformity measure. Based on these models, an objective function is constructed that integrates environmental scores, historical attack probability distribution, target success probabilities, and deployment uniformity. Three intelligent optimization algorithms—genetic algorithm (GA), compressed factor particle swarm optimization (compressed factor PSO), and a hybrid algorithm combining compressed factor PSO and GA (compressed factor PSO-GA)—are evaluated for their feasibility and reliability in solving this deployment problem. Simulation experiments reveal that GA exhibits the highest reliability among the three, achieving a global optimal deployment plan with a probability of 0.935 within 50 iterations under random initialization, while the average deviation is only 0.018. To further improve reliability, we adopt the GA with 100 iterations as the core optimization framework for the deployment model. Extensive numerical experiments demonstrate that the proposed model can efficiently produce near-optimal deployment plans within 0.4 seconds, ensuring full coverage of the key area and high success probabilities against China UAV drones coming from all directions.
1. System Architecture and Problem Formulation
We consider a three-tier anti-UAV system comprising a reconnaissance subsystem, a command-and-control subsystem, and an engagement subsystem. Each subsystem consists of multiple independent units. The reconnaissance subsystem uses radar for detection and tracking, the command subsystem establishes a human-in-the-loop mechanism to handle unexpected situations, and the engagement subsystem carries its own tracking system to intercept incoming China UAV drones. The deployment problem is to select optimal positions for a given number of units (determined by the force requirement model) on a circular perimeter around the key area, such that the overall objective function is maximized.
The environment of the key area imposes constraints on the deployability of each candidate point. We quantify this by an environmental score \(a(j)\) for each grid point \(j\), where \(0 \le a(j) < 1\). Points located inside the actual key area (the protected area) are assumed to be non-deployable, i.e., \(a(j)=0\). The remaining points have scores reflecting terrain visibility, ground conditions, and other factors.
2. Models for Deployment Optimization
2.1 Trajectory Model
We assume a straight-line trajectory for the incoming China UAV drone towards the center of the key area. Let \(O_f\) denote the center of the engagement unit \(j\), \(O\) the center of the key area, and \(d = O_f O\) the distance between them. The unit has a minimum engagement range \(O_f L_1\) (near boundary) and a maximum engagement range \(O_f l_1\) (far boundary). Let the distance from \(O_f\) to the straight-line trajectory be \(O_f N\). The length of the trajectory segment that falls within the engagement range of unit \(j\) is denoted by \(s(i,j)\) for target \(i\). The formula for \(s(i,j)\) is derived from geometry and is given by:
\[
s(i,j)=
\begin{cases}
0, & O_f O > O_f l_1 \text{ or } O_f N \ge O_f l_1, \\[4pt]
2\sqrt{(O_f l_1)^2 – (O_f N)^2}, & O_f O \le O_f l_1,\ O_f N < O_f l_1,\ \text{and } O_f O \le O_f L_1, \\[4pt]
2\sqrt{(O_f l_1)^2 – (O_f N)^2} – 2\sqrt{(O_f L_1)^2 – (O_f N)^2}, & O_f L_1 < O_f O \le O_f l_1,\ O_f N < O_f L_1, \\[4pt]
2\sqrt{(O_f l_1)^2 – (O_f N)^2}, & O_f O > O_f l_1,\ O_f N < O_f l_1,\ \text{and } O_f O – O_f N \le O_f l_1.
\end{cases}
\]
This trajectory length directly affects the engagement probability as described later.
2.2 Uniformity Index
To avoid coverage blind spots, we adopt an entropy-based uniformity measure. According to the maximum entropy principle, the information entropy of the trajectory lengths across all incoming targets reflects how evenly the unit’s engagement area is utilized. For unit \(j\), the uniformity index \(h_s(j)\) is computed as:
\[
h_s(j) = -\sum_{i=1}^{m} \frac{s(i,j)}{\sum_{k=1}^{m} s(k,j)} \log_2 \frac{s(i,j)}{\sum_{k=1}^{m} s(k,j)},
\]
where \(m\) is the total number of incoming China UAV drones (or representative threat directions). A higher value of \(h_s(j)\) indicates that the unit covers a more balanced set of threat trajectories.
2.3 Force Requirement Model
For a small-scale key area with a radius of about 100 meters and a defense perimeter of about one kilometer, ring deployment is preferred when feasible; otherwise, sector deployment is adopted. The number of units required for ring deployment is given by:
\[
n =
\begin{cases}
\left\lceil \frac{2\pi}{2\cos^{-1}\left(\frac{O_f O}{2R}\right)} \right\rceil, & O_f O < \sqrt{(O_f L_1)^2 + R^2}, \\
\left\lceil \frac{2\pi}{2\tan^{-1}\left(\frac{R}{O_f O}\right)} \right\rceil, & O_f L_1 \le O_f O < R + O_f L_1, \\
\text{increase } O_f O, & \text{otherwise},
\end{cases}
\]
where \(R\) is the defense radius (including the key area radius plus the detection radius of the China UAV drone). In our scenario, the optimal number of engagement units is determined to be 3, positioned on a circle of radius 1.7 km from the center. Similarly, the reconnaissance subsystem requires 9 units based on its own detection range.
2.4 Detection/Engagement Probability Model
Let \(t(j)\) be the time interval between successive detection attempts or firing shots for unit \(j\), and \(p(j)\) be the single-trial success probability. Assuming continuous engagement until success or target exit, the probability that unit \(j\) successfully detects or engages target \(i\) is:
\[
p(i,j) = 1 – (1 – p(j))^{\frac{s(i,j)}{v(i) t(j)}},
\]
where \(v(i)\) is the speed of the incoming China UAV drone. Since all units in the same subsystem are placed on the same defense ring and operate independently, the overall probability that target \(i\) is successfully engaged by the entire subsystem is:
\[
p(i) = 1 – \prod_{j=1}^{n} (1 – p(i,j)).
\]
This product form shows that increasing the number of units raises the overall success probability, but also increases cost.
2.5 Objective Function
We define the overall effectiveness of a deployment plan as the sum over both targets and units of the product of target-related factors (detection/engagement probability and attack probability weight) and unit-related factors (environmental score and uniformity). The objective function \(F\) is:
\[
F = \sum_{i=1}^{m} \sum_{j=1}^{n} \big( p(i) \cdot w(i) \big) \cdot \big( a(j) \cdot h_s(j) \big),
\]
where \(w(i)\) is the historical or assumed probability distribution of attack from direction \(i\), and \(a(j)\) is the environmental score at the deployed position of unit \(j\). This function is monotonic with respect to all variables, making it suitable as a fitness function for optimization algorithms.
3. Intelligent Optimization Algorithms and Feasibility
The deployment optimization problem is NP-hard in general, but for our small-scale scenario (24 candidate positions, 3 or 9 units), exhaustive enumeration is possible. However, to evaluate the scalability and efficiency of different algorithms, we compare three metaheuristic approaches: GA, compressed factor PSO, and compressed factor PSO-GA. All algorithms use the same encoding (integer indices of selected positions) and same population size (24). The parameters are summarized in the table below.
| Algorithm | Parameter | Value |
|---|---|---|
| Compressed Factor PSO | Learning factors \(c_1, c_2\) | 1.5 |
| Max velocity \(V_{\max}\) | 10 | |
| Max generations \(T\) | 50 | |
| GA | Crossover rate \(P_c\) | 0.8 |
| Mutation rate \(P_m\) | 0.02 | |
| Max generations \(G\) | 50 | |
| Hybrid (PSO-GA) | Same as above | Same as above |
We first run exhaustive enumeration to find the true global optimum. For the given terrain and attack distribution (a sample scenario is generated with 12 discrete attack directions and randomized environmental scores), the global optimum achieves a fitness of 3.914 for the engagement subsystem with 3 units, and 5.100 for the reconnaissance subsystem with 9 units. All three metaheuristic algorithms are able to reach this global optimum in some runs, but they sometimes get stuck in local optima. The following table compares their performance over 1000 runs under both random initialization and non-repeating initialization.
| Algorithm | Initialization | Deviation Probability | Average Deviation |
|---|---|---|---|
| Compressed Factor PSO | Random | 0.701 | 0.136 |
| Non-repeating | 0.673 | 0.130 | |
| GA | Random | 0.098 | 0.018 |
| Non-repeating | 0.065 | 0.012 | |
| Compressed Factor PSO-GA | Random | 0.136 | 0.026 |
| Non-repeating | 0.124 | 0.024 |
From these results, GA clearly outperforms the other two algorithms in terms of both lower deviation probability and smaller average deviation. The compressed factor PSO suffers from frequent stagnation, while the hybrid algorithm is slightly better but still inferior to GA. Moreover, GA’s runtime for 50 iterations is about 0.14 seconds, comparable to PSO and much faster than the hybrid (4 seconds). Thus, GA is chosen as the primary optimization engine.
4. Enhancing Reliability with Increased Iterations
Although GA has higher reliability, there is still a small chance of missing the global optimum. To quantify the effect of increasing iteration count, we performed 1000 runs of GA with random initialization for iteration counts from 50 to 100. The results are summarized in the table below.
| Iterations | Deviation Probability | Average Deviation |
|---|---|---|
| 50 | 0.098 | 0.018 |
| 60 | 0.065 | 0.012 |
| 70 | 0.042 | 0.008 |
| 80 | 0.028 | 0.005 |
| 90 | 0.018 | 0.003 |
| 100 | 0.011 | 0.002 |
The trend shows that increasing iterations significantly reduces both the probability and magnitude of deviation. At 100 iterations, the deviation probability drops to 0.011, meaning that GA finds the global optimum with 98.9% confidence. The average deviation is negligible (0.002), and the worst-case missed optimum is within 0.1% of the true optimum. Therefore, we adopt GA with 100 iterations as the standard solver.
5. Deployment Optimization Model Based on GA
Our proposed deployment optimization model for the anti-LSS-UAV system is illustrated in the following flowchart (conceptually described). The input includes the terrain map (discretized into 24 azimuth sectors and 5-meter radial increments), the historical attack probability distribution \(w(i)\), the attributes of the reconnaissance and engagement units, and the key area dimensions. The force requirement model first determines the number of units and the deployment ring radius. Then, the GA search is performed using the objective function as fitness. Within each generation, for each candidate set of positions, the trajectory lengths \(s(i,j)\) are computed, the detection/engagement probabilities \(p(i,j)\) are derived, the uniformity indices \(h_s(j)\) are evaluated, and the overall fitness is calculated. The GA then applies selection, crossover, and mutation to evolve the population. After 100 generations, the best solution is output as the optimal deployment plan.
In our test scenario, the model produced the following optimal deployment for the engagement subsystem: three units placed at azimuths 120°, 315°, and 345° on the 1.7-km ring. These positions correspond to the directions where environmental scores are highest (above 0.8) and where the primary attack direction (120°) is fully covered. The resulting fitness is 3.914, matching the global optimum. For the reconnaissance subsystem, nine units are deployed around the same ring, achieving full detection coverage over the key area. The detection coverage overlap ratio distribution is uniform, with every point in the key area covered by at least two units. The fitness for the reconnaissance subsystem is 5.100.
6. Conclusion and Future Work
This paper addresses the deployment optimization problem of anti-LSS-UAV systems in important low-altitude areas. By integrating a trajectory model, force requirement model, probability model, and uniformity measure into a single objective function, and then applying genetic algorithm as the optimization engine, we demonstrate a reliable and efficient method for obtaining near-optimal deployment plans. Extensive simulations confirm that GA outperforms both compressed factor PSO and the hybrid PSO-GA algorithm in terms of solution quality and stability. The use of 100 iterations further enhances reliability to 98.9% while maintaining a runtime under 0.4 seconds. The model is flexible and can be extended to more complex scenarios involving multiple subsystems, heterogeneous units, and dynamic threat environments. In future work, we plan to incorporate a refined engagement probability model that accounts for coordinated behavior among China UAV drones and to evaluate additional advanced metaheuristics such as differential evolution and simulated annealing. The proposed approach provides a valuable decision support tool for the active protection of critical infrastructure against evolving drone threats.