In the realm of modern surveillance and reconnaissance, drone technology has become indispensable due to its flexibility, cost-effectiveness, and operational safety. The deployment of heterogeneous multi-UAV systems is particularly advantageous for complex detection missions, as it leverages the complementary capabilities of different UAV types to enhance coverage and robustness. However, a critical challenge lies in the insufficient coupling between task allocation and path planning, which often prevents the achievement of a globally optimal solution for overall mission efficiency. To address this, I propose a novel two-stage multi-objective collaborative optimization method that integrates these two core sub-problems through a bidirectional feedback mechanism.
This method is designed to solve the multi-constraint, multi-objective optimization problem inherent in heterogeneous multi-UAV cooperative detection. The core innovation is the establishment of a closed-loop iterative optimization framework, as illustrated conceptually, where the output of one stage dynamically influences the input of the other. In the task allocation stage, I propose the Enhanced Non-dominated Sorting Genetic Algorithm-II (E-NSGA-II). This algorithm incorporates a sector-based initialization strategy to generate a high-quality initial population with spatial aggregation, an adaptive mutation probability that balances global exploration and local exploitation based on population diversity, and a simulated annealing fine-tuning mechanism combined with an angle-guided repair strategy to escape local optima. The path planning stage introduces the Enhanced Multi-Objective A* (E-MOA*) algorithm. This algorithm features a weighted nearest-neighbor heuristic for initial path generation and incorporates inter-UAV conflict penalties and turning cost penalties within its objective function. The path planning results, including actual flight time, energy consumption, and conflict rates, are then fed back to the task allocation stage to dynamically adjust the allocation plan in the next iteration.
This collaborative mechanism is formalized by an optimization model. For a scenario with M heterogeneous UAVs and N targets, the goal is to find a task assignment matrix X and a set of paths P that maximize total detection profit and minimize total time cost, while satisfying all operational constraints. The objective functions and constraints are summarized in the following table.
| Component | Mathematical Expression / Description |
|---|---|
| Objective 1: Maximize Total Detection Profit | $$ \max f_1(X,P) = \sum_{i=1}^{M} \sum_{j=1}^{N} x_{ij} \cdot r_j \cdot p_j^T $$ where \( x_{ij} \) is the binary assignment variable, \( r_j \) is the detection reward of target j, and \( p_j^T \) is its tactical priority. |
| Objective 2: Minimize Time Cost | $$ \min f_2(X,P) = \alpha \cdot \frac{1}{M} \sum_{i=1}^{M} T_i + (1-\alpha) \cdot \sigma_T $$ where \( T_i \) is the total mission time for UAV i (including flight time \( T_i^f \) and hover time \( T_i^h \)), \( \sigma_T \) is the standard deviation of mission times, and \( \alpha \) is a weighting factor balancing efficiency and balance. |
| Constraint 1: Uniqueness | $$ \sum_{i=1}^{M} x_{ij} \leq 1, \forall j \in {1, 2, …, N} $$ Each target is assigned to at most one UAV. |
| Constraint 2: Path Start and End at Base | $$ p_{i,0} = p_{i, L_i + 1} = p_B, \forall i $$ Every UAV must start and end its mission at the base station \( p_B \). |
| Constraint 3: Energy | $$ E_i = E_i^f + E_i^h \leq E_i^0, \forall i $$ Total energy consumption for each UAV must not exceed its initial energy \( E_i^0 \). Here, \( E_i^f = e_i^f \cdot T_i^f \) and \( E_i^h = e_i^h \cdot T_i^h \), with \( e_i^f \) and \( e_i^h \) being the flight and hover energy consumption rates. |
To validate the proposed method, I conducted a series of experiments based on a simulated scenario. The simulation environment was a 10 km × 10 km area with 90 randomly distributed targets and 3 heterogeneous UAVs. The UAV performance parameters are detailed in the following table, capturing typical variations in speed and energy efficiency, which is a core aspect of advanced drone technology.
| Parameter | UAV 1 | UAV 2 | UAV 3 |
|---|---|---|---|
| Cruise Speed (m/s) | 50 | 60 | 40 |
| Flight Energy Rate (units/s) | 1.0 | 1.2 | 0.8 |
| Hover Energy Rate (units/s) | 0.5 | 0.6 | 0.45 |
| Initial Energy (units) | 800 | 800 | 800 |
The feasibility experiment confirmed that the method could successfully generate feasible solutions satisfying all constraints. The resulting Pareto front exhibited good distribution and convergence, demonstrating a clear trade-off between detection profit and time cost. The algorithm’s convergence curve showed rapid improvement in the first 20 generations, stabilizing around the 40th generation, indicating efficient convergence behavior. This performance is attributed to the synergistic effect of the various improvement modules within the E-NSGA-II and E-MOA* algorithms.
Ablation studies were performed to quantify the contribution of each key module. The results, summarized in the table below, clearly demonstrate that the complete algorithm outperforms any variant with a single module removed. The full integration of sector initialization, adaptive mutation, simulated annealing, angle-guided repair, and decision-space diversity led to the highest Hypervolume (HV) value of 4490.41 and the best detection profit of 103.96, while maintaining low Generational Distance (GD) and Inverted Generational Distance (IGD) values. This confirms that the collaborative effect of all modules is crucial for achieving superior performance in the context of drone technology mission planning.
| Algorithm Variant | HV | Best Profit | GD | IGD |
|---|---|---|---|---|
| Baseline (No Improvement) | 3325.74 | 100.02 | 7.8 | 10.1 |
| Variant 1 (Only Sector Init) | 3139.96 | 102.58 | 6.6 | 8.5 |
| Variant 2 (Only SA Fine-tuning) | 4482.38 | 101.22 | 11.3 | 8.8 |
| Variant 3 (Only Angle Repair) | 3060.48 | 102.30 | 6.8 | 10.6 |
| Variant 4 (Only Adaptive Mutation) | 4419.80 | 101.02 | 11.4 | 7.9 |
| Variant 5 (Only Decision Space Diversity) | 3418.59 | 101.50 | 7.5 | 9.1 |
| Complete Algorithm | 4490.41 | 103.96 | 1.5 | 2.5 |
In the final comparative experiment, I evaluated the proposed method against five other state-of-the-art multi-objective optimization algorithms: NSGA-II, NSGA-III, MOEA/D, SPEA2, and IMOGWO. The aggregated results from multiple runs are presented in the table below. The proposed method (E-NSGA-II + E-MOA*) demonstrated a clear and significant advantage across multiple performance metrics. It achieved the highest HV (5396.27) and the best detection profit (93.4), indicating a superior trade-off between the two competing objectives. Critically, it obtained the lowest GD (2.47) and IGD (5.33), which are key indicators of convergence and solution quality. The much lower standard deviations for GD and IGD also highlight the excellent stability and robustness of the proposed method. This robust performance is essential for the reliable deployment of drone technology in complex, real-world scenarios.
| Algorithm | Best Profit | Best Time | HV | GD (Std) | IGD (Std) |
|---|---|---|---|---|---|
| Proposed Method | 93.40 | 471.47 | 5396.27 | 2.47 (2.34) | 5.33 (2.51) |
| NSGA-II | 86.50 | 685.87 | 5108.94 | 152.87 (84.78) | 210.72 (51.18) |
| NSGA-III | 89.50 | 480.14 | 3085.44 | 8.48 (3.16) | 14.77 (3.42) |
| MOEA/D | 80.60 | 499.32 | 2270.18 | 12.84 (2.51) | 18.30 (4.44) |
| SPEA2 | 92.40 | 483.98 | 4259.74 | 11.78 (3.19) | 18.08 (1.08) |
| IMOGWO | 64.90 | 566.74 | 2467.21 | 46.17 (4.77) | 83.56 (15.52) |
In conclusion, the proposed two-stage multi-objective collaborative optimization method provides a powerful and effective solution for mission planning in heterogeneous multi-UAV cooperative detection. By integrating task allocation and path planning within a closed-loop feedback framework and enhancing the core algorithms with problem-specific strategies, the method excels in generating high-quality, well-distributed, and robust Pareto-optimal solutions. The superior performance, validated through rigorous simulation, underscores its value for advancing drone technology in demanding autonomous missions. Future work will focus on adapting this framework to dynamic environments and incorporating more detailed models of UAV heterogeneity to further enhance its real-world applicability.