In recent years, the study of drone formation confrontation has emerged as a critical area in scientific research, particularly in scenarios where defensive drones must protect unarmed counterparts, such as those used for civilian, commercial, reconnaissance, cruise, or exploration purposes. However, research on the deployment of drone swarms for defense remains limited. This work addresses this gap by improving existing encoding and decoding schemes for heterogeneous drone formations. We establish a fitness function based on missile flight distance and the safety of unarmed drones, employing a genetic algorithm to optimize defensive drone formations. Our approach is tested against enemy formations of varying sizes and configurations, demonstrating rapid convergence to optimal solutions within 30 iterations. Through probabilistic effect assessment, we evaluate battle damage, showing that our defensive deployment strategy effectively minimizes losses, with an average loss rate of 18.75%. This methodology offers significant insights for drone swarm defense deployment research, leveraging multi-agent systems and evolutionary optimization techniques.
The evolution of drone technology since the early 20th century has enabled widespread applications in defense, disaster response, journalism, and scientific research. While single drones face limitations in search capability, observation range, and task complexity, multi-drone formations, enabled by multi-agent systems, provide a robust solution for complex, distributed tasks. Multi-agent technology, a branch of distributed artificial intelligence, has gained prominence since the late 1980s, with genetic algorithms being a popular tool for optimizing such systems. For instance, prior studies have applied genetic algorithms to air combat formation optimization, but these often assume homogeneous agents. In real-world scenarios, drone formations typically consist of 6 to 16 drones with heterogeneous characteristics, such as defensive and unarmed types. This complexity necessitates improved methods for formation optimization, as seen in modern military tactics like the U.S. Navy’s use of F-35 fighters guiding MQ-9 drones. Our research focuses on a 16-drone formation, aligning with practical operational needs, and aims to optimize defensive deployments to protect unarmed drones from adversarial interference.
To tackle this problem, we first refine the encoding and decoding schemes for drone formations. Traditional approaches use hierarchical encoding with basic four-drone formations—Wall Formation (WF), Finger-Four Formation (FT), Section Formation (ST), and Line Formation (LT)—as building blocks. Each basic formation is encoded in binary, as shown in Table 1, and combined into larger formations through a parent formation scheme. For a 16-drone formation, we use a 10-bit binary code: the first 2 bits represent the parent formation, and the next 8 bits represent the four sub-formations. To distinguish between defensive and unarmed drones, we append additional 4-bit binary codes to identify the indices of defensive drones, ranging from 0000 to 1111 (decimal 1 to 16). This extended encoding allows for precise representation of heterogeneous drone formations.
| Formation | Binary Code |
|---|---|
| Wall Formation (WF) | 00 |
| Finger-Four Formation (FT) | 01 |
| Section Formation (ST) | 10 |
| Line Formation (LT) | 11 |
The decoding process converts binary codes into spatial coordinates for each drone. It involves two steps: first, computing local coordinates for each basic formation centered at the origin, with inter-drone distances set to 200 meters, as illustrated in Figure 3; second, determining global coordinates based on parent formation adjustments. For each sub-formation, the center coordinates are calculated using:
$$ X_i’ = X_i \pm (L + 0.5L_i) $$
$$ Y_i’ = Y_i \pm (W + 0.5W_i) $$
where \( X_i’ \) and \( Y_i’ \) are the center coordinates of the \( i \)-th sub-formation, \( X_i \) and \( Y_i \) are local coordinates from the parent formation, \( L_i \) and \( W_i \) are the length and width of the sub-formation, and \( L \) and \( W \) are cumulative dimensions from other sub-formations. The individual drone coordinates are then derived as:
$$ x_{ij} = X_i’ \pm L_i $$
$$ y_{ij} = Y_i’ \pm W_i $$
where \( x_{ij} \) and \( y_{ij} \) are the coordinates of the \( j \)-th drone in the \( i \)-th sub-formation. Finally, defensive drone indices are extracted from the appended 4-bit codes. This encoding and decoding framework enables efficient representation and manipulation of heterogeneous drone formations for optimization.
Next, we construct a fitness function to evaluate the effectiveness of defensive drone formations. The fitness function considers two key factors: missile flight distance and safety of unarmed drones. For a given enemy drone, unarmed drone, and defensive drone, the interception process is modeled. Let \( R \) be the distance from the defensive drone to the interception point, \( S_1 \) the distance from the enemy drone to the interception point, and \( S_2 \) the distance from the unarmed drone to the interception point. We define a missile flight distance metric:
$$ \alpha_1 = \frac{R}{S_1} $$
This ratio represents the relative flight distance of the intercept missile to the enemy missile. A smaller \( \alpha_1 \) reduces interception difficulty by shortening the intercept missile’s travel, enhancing guidance accuracy and reducing environmental interference. For unarmed drone safety, we consider damage from missile explosions. The peak overpressure from an explosion decreases with distance, and we define an explosion damage metric:
$$ \alpha_2 = e^{-S_2} $$
This exponential function decreases as \( S_2 \) increases, minimizing damage to unarmed drones. The combined fitness function for a single scenario is:
$$ \alpha = \frac{1}{k_1 \alpha_1 + k_2 \alpha_2} $$
where \( k_1 \) and \( k_2 \) are weight coefficients dependent on missile warhead types (e.g., \( k_1 > k_2 \) for penetrative warheads, \( k_1 < k_2 \) for explosive warheads). To ensure balanced defense coverage across all unarmed drones, we optimize the fitness using a scaling function:
$$ \alpha_i = f\left( \sum_{j=1}^{q(i)} \alpha_{ij} \right) $$
$$ f(x) = \frac{2}{1 + e^{-2x}} – 1 $$
where \( \alpha_i \) is the fitness for the \( i \)-th unarmed drone, \( \alpha_{ij} \) is the fitness for the \( j \)-th enemy drone attacking it, and \( q(i) \) is the number of enemy drones targeting it. The function \( f(x) \) saturates as \( x \) increases, promoting equitable defense distribution. The overall formation fitness is:
$$ \lambda = \sum_{i=1}^{n} \alpha_i $$
where \( n \) is the number of unarmed drones. Additionally, we impose practical constraints, such as limiting defensive drones to protect only drones in front or to the sides, ignoring rear areas due to missile launch direction limitations.
We employ a genetic algorithm to optimize drone formation based on this fitness function. The algorithm parameters are set as follows: maximum generations = 30, population size = 100, crossover probability = 0.6, mutation probability = 0.01, and distance between formations = 10 km. The optimization process involves encoding formation candidates, evaluating fitness, and applying selection, crossover, and mutation operations to evolve optimal solutions. The genetic algorithm is chosen for its ability to handle complex encoding, heuristic search capabilities, parallelizability, and flexibility with fitness functions. We simulate five distinct combat scenarios to validate our approach, each with varying enemy formation sizes, configurations, and attack angles, as well as different ratios of defensive to unarmed drones. The scenarios are:
- Enemy 16-drone single formation vs. 10 defensive drones + 6 unarmed drones.
- Enemy 8-drone single formation vs. 10 defensive drones + 6 unarmed drones.
- Enemy 8-drone dual formation vs. 10 defensive drones + 6 unarmed drones.
- Enemy 4-drone quadruple formation vs. 10 defensive drones + 6 unarmed drones.
- Enemy 16-drone single formation vs. 12 defensive drones + 4 unarmed drones.
For each scenario, we consider multiple attack directions (e.g., frontal, 30° right, 30° left, 60° right). The genetic algorithm consistently converges to optimal fitness values within 30 generations, demonstrating rapid optimization. The optimized drone formations show improved defensive layouts, with defensive drones positioned to minimize interception distances and maximize safety for unarmed drones. For instance, in Scenario 1, the optimized formation places defensive drones in forward positions to shield unarmed drones from frontal attacks, while in Scenario 2, defensive drones are more dispersed to cover broader angles. The convergence curves indicate stable evolution, with fitness values plateauing after 20-25 generations, confirming the algorithm’s efficiency.
To assess the effectiveness of our optimized drone formation, we conduct a probabilistic evaluation using real missile parameters. We model the interception process with the “Vanguard-2” portable air defense missile, which has a speed of 600 m/s, weight of 11.32 kg, and warhead weight of 1.42 kg. Assuming drones fly at 20 m/s and missiles travel linearly, we compute interception probabilities. The interception point coordinates are calculated as:
$$ x_3 = x_4 + x_2 \times (x_1 – x_4) $$
$$ y_3 = y_4 + y_2 \times (y_1 – y_4) $$
where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_4, y_4) \) are coordinates of enemy, defensive, and unarmed drones, respectively. The time to interception is \( t = S_1 / v \), with \( v = 600 \) m/s. Updated positions after time \( t \) are used to compute distances \( a \), \( S_2 \), and \( R \). The interception probability \( P \) is modeled as:
$$ \theta = \arccos\left( \frac{S_2^2 + R^2 – a^2}{2 \times S_2 \times R} \right) $$
$$ P = | -\beta \times \theta + 1 |, \quad \theta \in (\theta_1, \theta_2] $$
where \( \theta \) is the angle between intercept and enemy missile paths, and \( \beta \) is a probability constant. The expected number of intercepted missiles \( E_1 \) is:
$$ E_1 = \sum_{i=0} X_i \times P(X_i) $$
where \( P(X_i) \) is the probability of intercepting \( i \) missiles. The remaining enemy missiles \( Q = W – E_1 \), with \( W \) as total launched missiles. The probability of hitting unarmed drones is:
$$ P’ = | -\beta \times \theta + 1 |, \quad \theta = \pi $$
$$ P(Y_i) = C_i^Q \times (P’)^i \times (1 – P’)^{Q-i} $$
The expected number of lost drones \( E_2 \) is:
$$ E_2 = \sum_{i=0} Y_i \times P(Y_i) $$
and the remaining drones \( T = M – E_2 \), with \( M \) as total friendly drones. We simulate loss curves for all scenarios, as summarized in Table 2. The results show maximum losses of 6 drones, minimum of 0, average of 3, and an average loss rate of 18.75%. This confirms the efficacy of our defensive drone formation strategy.
| Scenario | Attack Direction | Losses (Drones) |
|---|---|---|
| 1: Enemy 16 vs. 10+6 | Frontal | 4 |
| 30° Right | 5 | |
| 30° Left | 5 | |
| 60° Right | 6 | |
| 2: Enemy 8 vs. 10+6 | Frontal | 0 |
| 30° Right | 1 | |
| 30° Left | 1 | |
| 60° Right | 0 | |
| 3: Enemy 8 Dual vs. 10+6 | Dual 30° Approach | 5 |
| 4: Enemy 4 Quad vs. 10+6 | Quad Approach | 6 |
| 5: Enemy 16 vs. 12+4 | Frontal | 3 |
| 30° Right | 3 | |
| 30° Left | 3 | |
| 60° Right | 4 |
The optimization of drone formation through genetic algorithms offers several advantages over other methods like neural networks or machine learning. Genetic algorithms excel at handling complex encoding problems, perform heuristic searches without reliance on empirical data, support parallel processing, and accommodate diverse fitness functions. Our improved encoding scheme allows for precise representation of heterogeneous drone formations, while the fitness function balances interception efficiency and safety. The rapid convergence within 30 generations demonstrates the algorithm’s suitability for real-time applications in dynamic combat environments. Furthermore, the probabilistic assessment validates that optimized formations significantly reduce losses, even against larger enemy forces. This work underscores the importance of drone formation optimization in multi-agent systems, with potential extensions to adaptive strategies for changing battlefield conditions.
In conclusion, we have developed a robust framework for optimizing heterogeneous drone formation for defense purposes. By refining encoding and decoding techniques and designing a comprehensive fitness function, we enable genetic algorithms to efficiently generate optimal formations. Our simulations across diverse scenarios show consistent convergence and effective defense, with loss rates kept low. Future work will focus on integrating real-time adaptation mechanisms, exploring hybrid optimization algorithms, and extending the approach to larger-scale drone swarms for both defensive and offensive operations. The insights from this study contribute to advancing drone swarm deployment strategies, enhancing the autonomy and effectiveness of multi-drone systems in complex missions.