In modern warfare, the role of Unmanned Aerial Vehicle systems has evolved from supporting elements to critical assets, as demonstrated in conflicts such as Nagorno-Karabakh and the Russia-Ukraine war. Reconnaissance-strike integrated Unmanned Aerial Vehicle swarms, capable of performing both surveillance and attack missions, represent a significant advancement. However, the complexity of multi-objective task allocation under temporal constraints poses a substantial challenge. Traditional methods often fail to address the dynamic and coupled nature of task assignment and path planning for Unmanned Aerial Vehicle clusters. In this paper, we propose a hybrid optimization algorithm combining Discrete Particle Swarm Optimization (DPSO) and Genetic Algorithm (GA) to solve the multi-objective task allocation problem for reconnaissance-strike integrated Unmanned Aerial Vehicle swarms. Our approach models the sequential constraints of “verify-before-strike” operations and enhances global exploration and convergence precision through adaptive mechanisms. Simulation results validate the superiority of our method over standard DPSO and GA algorithms in terms of convergence speed, stability, and reliability.
The task allocation problem involves coordinating a swarm of N homogeneous reconnaissance-strike integrated Unmanned Aerial Vehicles, denoted as U = {U1, U2, …, UN}, to engage M targets, T = {T1, T2, …, TM}. Each Unmanned Aerial Vehicle carries a payload vector Ri = ⟨Rzc_i, Rdj_i⟩, where Rzc_i and Rdj_i represent the number of reconnaissance and strike payloads, respectively. Targets are categorized into four types based on priority: core, key, important, and general, with task requirements given by Tj = ⟨Rzc_j, Rdj_j⟩, indicating the required number of reconnaissance and strike missions. A critical temporal constraint mandates that reconnaissance must precede strike missions for any target requiring both, though these tasks can be performed by different Unmanned Aerial Vehicles to minimize latency. The command center aims to optimize task allocation to minimize the maximum mission completion time across the swarm while adhering to all constraints.
The objective function F is formulated to minimize the longest mission duration among all Unmanned Aerial Vehicles, incorporating penalty terms for constraint violations:
$$ \min F = F_1 + \lambda \sum_{g=1}^{4} r_g $$
Here, F1 represents the time cost function, λ is a penalty coefficient (set to 1000 to eliminate infeasible solutions), and rg are binary indicators for constraint violations (0 if satisfied, 1 otherwise). The time cost for each Unmanned Aerial Vehicle Ui is calculated as:
$$ F_1 = \frac{D_{iu}}{V_u} + \alpha_1 \delta_1 + \alpha_2 \delta_2 $$
where Diu is the total distance traveled by Unmanned Aerial Vehicle Ui, Vu is its velocity, α1 and α2 are the counts of reconnaissance and strike missions performed, and δ1 and δ2 are the durations for single reconnaissance and strike tasks, including information flow and damage assessment times, set to 5 and 3 minutes, respectively.
Constraints are defined as follows:
- Temporal Constraints: For any target Tj with both reconnaissance and strike tasks, the reconnaissance must be completed before the strike: t_{Tj}^{zc} < t_{Tj}^{dj}. The execution times are derived from the mission sequences and travel distances.
- Mission Completion Constraints: All reconnaissance and strike tasks must be fulfilled. The number of strikes on each target type must achieve a minimum damage threshold Hi, computed as 1 – (1 – α)^{C_{ti}} ≥ Hi, where α is the single-strike effectiveness (0.75), and C_{ti} is the minimum strikes required. For example, core targets (H1=0.9) require at least 2 strikes.
- Range Constraints: The total distance Diu for each Unmanned Aerial Vehicle must not exceed the maximum range Dmax.
- Payload Constraints: The number of strike missions per Unmanned Aerial Vehicle cannot exceed its carried strike payloads: ∑_{j=1}^{M} x_{ij}^{dj} U_{ij}^{dj} ≤ R_i^{dj}.
To address this NP-hard problem, we develop a hybrid DPSO-GA algorithm that leverages the global search capability of GA and the rapid convergence of DPSO. The algorithm employs a two-layer particle encoding scheme: the first layer is a task sequence listing all reconnaissance and strike missions, and the second layer specifies the Unmanned Aerial Vehicle indices assigned to each task. This encoding captures the complex mappings in multi-UAV协同 operations, including “one-to-many” and “many-to-one” scenarios.
The particle update formula integrates mutation, individual learning, and global learning operations:
$$ x_i^{t+1} = \omega \cdot f_1(x_i^t) \oplus c_1 \cdot f_2(E_i^t, P_i(t)) \oplus c_2 \cdot f_3(F_i^t, P_g(t)) $$
Here, ω is the inertia weight, c1 and c2 are learning factors, f1 is a mutation operator, f2 learns from the individual best Pi(t), and f3 learns from the global best Pg(t). The operators are defined as:
- Mutation Operator f1: With probability ω, either reshuffles the task layer (for global exploration) or randomly alters one Unmanned Aerial Vehicle index in the execution layer (for local refinement).
- Individual Learning f2: Performs crossover by dividing the task set into two subsets, copying one subset from the current particle and the other from Pi(t), preserving order.
- Global Learning f3: Uses an adaptive threshold ρ to copy elements from Pg(t) to the offspring, with ρ increasing over iterations to favor convergence.
We enhance the algorithm with adaptive adjustments:
- Inertia Weight ω: Updated using a cosine function to balance exploration and exploitation:
$$ \omega = \omega_{\min} + (\omega_{\max} – \omega_{\min}) \cos^2\left(\frac{\pi t}{2T}\right) $$
where ωmin=0.3, ωmax=0.95, t is the current iteration, and T is the maximum iterations.
- Learning Factors c1 and c2: Adjusted linearly to emphasize individual exploration early and social learning later:
$$ c_1 = c_{1\max} – (c_{1\max} – c_{1\min}) \frac{t}{T} $$
$$ c_2 = c_{2\min} + (c_{2\max} – c_{2\min}) \frac{t}{T} $$
with c1max=0.9, c1min=0.3, c2max=0.9, c2min=0.3.
- Threshold ρ: Increases from ρmin=0.1 to ρmax=0.9 to control the replication of global best elements.
Fitness evaluation involves decoding each particle into a task assignment, clustering targets, and using a greedy strategy for path planning. The fitness value is the maximum mission time, with penalties applied for constraint violations.
We conduct simulations in a 300 km × 300 km × 5000 m airspace with 8 Unmanned Aerial Vehicles and 12 targets. The Unmanned Aerial Vehicles’ initial positions and payloads, and target locations and requirements, are randomized but summarized in Tables 1 and 2. Parameters include Vu=50 m/s, Dmax=500 km, δ1=5 min, δ2=3 min, and α=0.75. The algorithm runs for 1000 iterations with a population size of 200.
| Target ID | X (km) | Y (km) | Z (km) | Type | Reconnaissance | Strike |
|---|---|---|---|---|---|---|
| 1 | 156.83 | 267.24 | 0 | Core | 1 | 2 |
| 2 | 89.69 | 207.25 | 0 | Core | 1 | 2 |
| 3 | 21.54 | 76.12 | 0 | Key | 1 | 2 |
| 4 | 202.55 | 50.93 | 0 | Key | 1 | 2 |
| 5 | 97.96 | 169.32 | 0 | Key | 1 | 2 |
| 6 | 240.13 | 237.95 | 0 | Important | 1 | 1 |
| 7 | 116.25 | 256.53 | 0 | Important | 1 | 1 |
| 8 | 227.13 | 147.03 | 0 | Important | 1 | 1 |
| 9 | 22.43 | 244.49 | 0 | General | 0 | 1 |
| 10 | 74.65 | 175.60 | 0 | General | 1 | 0 |
| 11 | 220.09 | 139.67 | 0 | General | 1 | 0 |
| 12 | 278.15 | 167.32 | 0 | General | 0 | 1 |
| UAV ID | X (km) | Y (km) | Z (km) | Reconnaissance | Strike |
|---|---|---|---|---|---|
| 1 | 167.96 | 62.26 | 5.56 | 1 | 4 |
| 2 | 184.64 | 168.75 | 7.34 | 1 | 3 |
| 3 | 233.36 | 114.14 | 3.01 | 1 | 2 |
| 4 | 285.47 | 60.96 | 6.45 | 1 | 1 |
| 5 | 34.11 | 235.78 | 6.04 | 1 | 0 |
| 6 | 227.74 | 179.53 | 3.34 | 1 | 2 |
| 7 | 205.38 | 41.40 | 6.41 | 1 | 2 |
| 8 | 47.09 | 164.48 | 5.46 | 1 | 4 |
After 50 simulation runs, the best fitness value achieved is 1.222698 hours, with the corresponding task allocation detailed in Table 3. The results show that 6 out of 8 Unmanned Aerial Vehicles handle multiple tasks, and 4 targets require coordinated strikes from multiple JUYE UAVs, demonstrating the algorithm’s ability to model complex mappings. All constraints, including temporal sequences, are satisfied. The three-dimensional path planning for the Unmanned Aerial Vehicle swarm is visualized, indicating efficient routes and balanced workloads.
| UAV ID | Targets | Tasks | Total Time (h) | Distance (km) |
|---|---|---|---|---|
| 1 | 9 | Strike | 1.35 | 233.21 |
| 2 | 1, 7 | Reconnaissance + Strike ×2, Strike | 1.04 | 144.31 |
| 3 | 3 | Reconnaissance + Strike ×2 | 1.38 | 215.20 |
| 4 | 4, 8 | Reconnaissance, Reconnaissance + Strike | 1.23 | 182.71 |
| 5 | 2, 10 | Reconnaissance, Reconnaissance | 1.30 | 188.52 |
| 6 | 11, 12, 6 | Reconnaissance, Strike, Reconnaissance + Strike | 1.30 | 185.10 |
| 7 | 5 | Reconnaissance | 1.33 | 205.86 |
| 8 | 5, 4 | Strike ×2, Strike ×2 | 1.36 | 209.08 |
We compare our hybrid DPSO-GA algorithm with standard DPSO and GA algorithms. The convergence curves and fitness distributions over 50 runs are analyzed. Key performance metrics are summarized in Table 4. Our algorithm achieves an average fitness of 1.399414, which is 50.0% lower than DPSO (2.797139) and 10.7% lower than GA (1.566487). The variance is reduced by 95.7% compared to DPSO and 79.9% compared to GA, indicating superior stability. The confidence interval width for DPSO-GA is only 20.7% of DPSO and 44.8% of GA, highlighting higher reliability and consistency. These results confirm that our method effectively addresses the limitations of both algorithms, providing a robust solution for Unmanned Aerial Vehicle swarm task allocation.
| Algorithm | Average | Max | Min | Variance | Coefficient of Variation | Standard Deviation | CI Lower | CI Upper |
|---|---|---|---|---|---|---|---|---|
| DPSO-GA | 1.399414 | 1.533107 | 1.222698 | 0.006935 | 0.059508 | 0.083276 | 1.375748 | 1.423081 |
| DPSO | 2.797139 | 3.790750 | 2.036251 | 0.161812 | 0.143811 | 0.402258 | 2.682818 | 2.911459 |
| GA | 1.566487 | 2.278882 | 1.200434 | 0.034484 | 0.118544 | 0.185697 | 1.513713 | 1.619262 |
In conclusion, our hybrid DPSO-GA algorithm successfully models the complex task allocation problem for reconnaissance-strike integrated Unmanned Aerial Vehicle swarms, adhering to temporal and other constraints. The adaptive mechanisms ensure a balance between global exploration and local exploitation, resulting in high-quality solutions. Future work will focus on extending this approach to heterogeneous Unmanned Aerial Vehicle swarms, including electronic warfare and kamikaze JUYE UAVs, to address real-time multi-task planning in dynamic environments. This research contributes to the intelligent advancement of Unmanned Aerial Vehicle cluster operations, enhancing their effectiveness in modern warfare.