In this work, we present an improved viral-inspired optimization algorithm, termed IH5N1-SASM, designed to address the complex three-dimensional path planning problem for China drone. The original H5N1 metaheuristic suffers from premature convergence and limited adaptive balancing between exploration and exploitation, especially in highly nonlinear and constrained landscapes typical of real-world China drone missions. To overcome these deficiencies, we propose three synergistic mechanisms: a State-Aware Search Mechanism (SASM) that dynamically evaluates population diversity and improvement rate to classify the search state (diffusion, aggregation, or stagnation); an Information-Guided Self-Decomposition strategy (IGSD) that focuses perturbation on high-variance dimensions based on individual performance; and a Multi-Time-scale Dynamic Search mechanism (MTDS) that triggers strong perturbations via Cauchy jumps or elite-guided backtracking when stagnation is detected. We validate the proposed algorithm on the CEC2017 benchmark suite and a realistic three-dimensional terrain path planning simulation for China drone. Extensive comparisons with seven state-of-the-art algorithms demonstrate that IH5N1-SASM achieves significantly better optimization accuracy, faster convergence, and higher stability. The results confirm its effectiveness for complex constrained optimization and China drone path planning applications.
We begin by formulating the China drone path planning as a multi-objective constrained optimization problem. The three-dimensional environment is constructed using a Digital Elevation Model (DEM) with terrain heights \(H(x,y)\) and multiple cylindrical threat zones representing obstacles. The flight path is discretized into a sequence of waypoints: \(\mathbf{P} = \{ \mathbf{p}_0, \mathbf{p}_1, \ldots, \mathbf{p}_n, \mathbf{p}_{n+1} \}\), where \(\mathbf{p}_i = (x_i, y_i, z_i)\) is the \(i\)-th waypoint, \(\mathbf{p}_0\) is the start, and \(\mathbf{p}_{n+1}\) is the target. The path must satisfy spatial bounds and altitude constraints:
\[
x_{\min} \le x_i \le x_{\max}, \quad y_{\min} \le y_i \le y_{\max}, \quad z_{\min} \le z_i \le z_{\max}.
\]
Threat zones are modeled as vertical cylinders: \(T_j = (x_j, y_j, R_j)\) with radius \(R_j\). A collision penalty is imposed when the path intersects any cylinder. The overall cost function is a weighted sum of four sub-objectives:
\[
J = w_1 F_1 + w_2 F_2 + w_3 F_3 + w_4 F_4,
\]
where
\[
\begin{aligned}
F_1 &= \sum_{i=0}^{n} \| \mathbf{p}_{i+1} – \mathbf{p}_i \| \quad (\text{path length}),\\
F_2 &= \sum_{i=0}^{n} \sum_{j=1}^{m} \text{penalty}(\mathbf{p}_i, T_j) \quad (\text{threat avoidance}),\\
F_3 &= \sum_{i=1}^{n} \max(0, |z_i – z_{\text{target}}| – \Delta z_{\max}) \quad (\text{altitude constraint}),\\
F_4 &= \sum_{i=1}^{n-1} \left( \Delta\psi_i^2 + \Delta\theta_i^2 \right) \quad (\text{smoothness}),
\end{aligned}
\]
with weights \(w_1 = 30, w_2 = 100, w_3 = 10, w_4 = 50\). This formulation captures the essential requirements for safe and efficient China drone flight.
The above figure illustrates a typical China drone mission scenario over a complex terrain with multiple threat cylinders. The green surface represents the digital elevation model, and the blue columns denote no-fly zones. Our goal is to find a collision-free, smooth, and economical path from the start to the target point.
1. Proposed IH5N1-SASM Algorithm
We now describe the three core mechanisms we introduce to enhance the original H5N1 viral-inspired metaheuristic. The baseline H5N1 algorithm updates each individual via an attack-adaptation scheme:
\[
\mathbf{x}_i^{t+1} = \mathbf{p}_{\text{mp}}^k + \mathbf{r}_i \odot (\mathbf{x}_{\text{best}}^t – \mathbf{x}_i^t),
\]
where \(\mathbf{p}_{\text{mp}}^k\) is a randomly permuted position, \(\mathbf{r}_i \in (0,1)^d\) is a random vector, and \(\mathbf{x}_{\text{best}}^t\) is the global best. The adaptation phase applies \(\mathbf{x}_i^{t+1} = \frac{c}{2}(\mathbf{x}_i^t + \mathbf{x}_{\text{best}}^t)\) with a decreasing coefficient \(c\).
1.1 State-Aware Search Mechanism (SASM)
We define three real-time metrics to capture the search state:
- Population diversity: \(D(t) = \frac{1}{d}\sum_{j=1}^d \frac{\text{std}(\mathbf{x}_j^{(t)})}{u_j – l_j}\), where \(u_j, l_j\) are dimension bounds.
- Improvement rate: \(R_{\text{imp}}(t) = \frac{|f_{\text{best}}^{(t)} – f_{\text{best}}^{(t-1)}|}{|f_{\text{best}}^{(t-1)}| + \varepsilon}\).
- Fitness diversity: \(D_f(t) = \frac{\text{std}(f_i^{(t)})}{|\text{mean}(f_i^{(t)})| + \varepsilon}\).
Based on these metrics, the search state is classified as:
| State | Condition | Action |
|---|---|---|
| Diffusion | \(D(t) \ge \tau_{\text{div}}^{\text{high}}\) | Promote exploration (increase attack probability) |
| Aggregation | \(D(t) < \tau_{\text{div}}^{\text{high}}\) and \(R_{\text{imp}}(t) > \tau_{\text{imp}}\) | Enhance local exploitation (increase adaptation weight) |
| Stagnation | \(R_{\text{imp}}(t) < \tau_{\text{imp}}\) for \(K\) consecutive generations | Trigger MTDS (see Section 1.3) |
1.2 Information-Guided Self-Decomposition (IGSD)
IGSD dynamically decomposes the population into explorers and exploiters based on historical fitness ranking. Individuals with rank in the bottom \(\rho N\) (we use \(\rho = 0.3\)) are designated as explorers; the rest are exploiters. Furthermore, we compute the standard deviation of each dimension across the population and select the top \(\alpha d\) dimensions (we set \(\alpha = 0.4\)) as key dimensions \(\mathcal{D}_K\). Explorers apply perturbation only on \(\mathcal{D}_K\) to enhance search efficiency, while exploiters perform standard updates on all dimensions.
1.3 Multi-Time-scale Dynamic Search (MTDS)
MTDS operates on a slow time scale, triggered either every \(T_s\) generations (we set \(T_s = 20\)) or immediately when SASM detects stagnation. A fraction \(p_{\text{slow}} = 0.25\) of the population (weighted towards explorers) is selected to undergo one of two complementary perturbations on the key dimensions \(\mathcal{D}_K\):
- Cauchy heavy-tailed jump:
\[
\mathbf{x}_{i,\mathcal{D}_K}^{(t+1)} = \mathbf{x}_{\text{best},\mathcal{D}_K}^{(t)} + \beta_t \cdot \mathbf{c},
\]
where \(\mathbf{c}_j = \tan(\pi(u_j – 0.5))\) with \(u_j \sim U(0,1)\), and \(\beta_t\) decays linearly with iterations. - Elite-guided backtracking:
\[
\mathbf{x}_{i,\mathcal{D}_K}^{(t+1)} = \mathbf{x}_{i,\mathcal{D}_K}^{(t)} + \beta_t (\mathbf{x}_{\text{elite},\mathcal{D}_K} – \mathbf{x}_{i,\mathcal{D}_K}^{(t)}) + \eta \boldsymbol{\varepsilon},
\]
with \(\boldsymbol{\varepsilon}\) being Gaussian noise and \(\eta = 0.1\).
The complete pseudo-code of IH5N1-SASM is summarized below:
Initialize population, best solutions, elite archive
for t = 1 to MaxIter:
Compute D(t), R_imp(t), D_f(t)
Determine search state via SASM
if state == Stagnation or mod(t, T_s) == 0:
Select slow-scale individuals
Perform MTDS (Cauchy or elite update) on key dimensions
else:
for each individual i:
if i is explorer:
Apply IGSD: update only on key dimensions with attack-adaptation
else:
Apply standard H5N1 attack-adaptation
Evaluate fitness, update personal best, global best, and elite archive
Adjust parameters based on state
2. Experimental Results on CEC2017 Benchmarks
We evaluate IH5N1-SASM on six representative functions from the CEC2017 test suite (F5, F8, F13, F18, F28, F30) in 30 dimensions. All algorithms run 20 independent trials with population size 50 and 500 iterations. Parameter settings for comparison algorithms are listed in the table below.
| Algorithm | Parameter Configuration |
|---|---|
| IH5N1-SASM | \(P_1 = 0.8; P_2 = 0.85; p_{\text{slow}} = 0.25; \tau_{\text{div}}^{\text{high}} = 0.2\) |
| H5N1 | \(P_1 = 0.8; P_2 = 0.85\) |
| PSO | \(c_1 = 2; c_2 = 2\) |
| GWO | \(\vec{a} = 2\) (linearly decreased to 0) |
| WOA | \(a_2 \in [-2, -1]; b = 1\) |
| HHO | \(E_1 = 2(1 – t/T)\) |
| DBO | \(p_{\text{rol}} = p_{\text{egg}} = p_{\text{bab}} = p_{\text{stc}} = 0.25\) |
| SSA | \(P_L = 0.5; V_0 = 0\) |
Table below reports the mean and standard deviation of the best fitness obtained over 20 runs for each function. The theoretical optimal values are \(100 \times i\) for function \(F_i\).
| Function | Metric | IH5N1-SASM | H5N1 | PSO | GWO | WOA | HHO | DBO | SSA |
|---|---|---|---|---|---|---|---|---|---|
| F5 | Mean | 508.60 | 517.04 | 515.41 | 515.78 | 554.99 | 547.17 | 538.52 | 529.16 |
| Std | 2.60 | 3.18 | 6.83 | 10.13 | 19.90 | 13.34 | 12.48 | 10.52 | |
| F8 | Mean | 809.51 | 817.82 | 813.18 | 815.39 | 846.34 | 830.87 | 832.20 | 829.43 |
| Std | 3.69 | 3.38 | 5.34 | 6.97 | 19.33 | 8.24 | 12.15 | 8.47 | |
| F13 | Mean | 2140.39 | 3542.35 | 6595.15 | 10725.32 | 20377.78 | 17034.37 | 12973.61 | 11034.34 |
| Std | 1730.27 | 2585.47 | 5859.46 | 6565.50 | 18291.07 | 15225.11 | 13636.25 | 10535.74 | |
| F18 | Mean | 3160.03 | 9916.40 | 15502.48 | 26643.18 | 14973.39 | 15582.65 | 25397.22 | 7954.50 |
| Std | 1718.54 | 5569.11 | 15448.61 | 14365.75 | 8962.75 | 11645.66 | 16074.08 | 6842.73 | |
| F28 | Mean | 3146.46 | 3236.82 | 3286.20 | 3376.29 | 3430.87 | 3359.78 | 3330.41 | 3274.87 |
| Std | 100.69 | 145.65 | 144.23 | 83.31 | 201.19 | 122.70 | 128.31 | 136.49 | |
| F30 | Mean | 20610.69 | 42988.24 | 212431.34 | 1014025.81 | 675599.00 | 1731754.76 | 587172.86 | 444309.16 |
| Std | 17016.39 | 26620.96 | 400867.62 | 1726182.52 | 914037.51 | 2192840.63 | 525325.56 | 561693.62 |
The results clearly show that IH5N1-SASM consistently achieves the lowest mean fitness across all tested functions, particularly on the complex hybrid and composition functions F13, F18, and F30, where our algorithm outperforms the original H5N1 by a large margin. The standard deviations are also among the smallest, indicating superior robustness. The improvement on F30 is dramatic: a mean of 20610.69 versus 42988.24 for H5N1—a reduction of approximately 52%.
3. Strategy Contribution Analysis
To isolate the contribution of each component, we conduct ablation experiments on the China drone path planning test case. Table below shows the mean, best, and standard deviation of the total path cost over 20 independent runs, with population size 100, 15 waypoints, and 1000 iterations.
| Algorithm | Mean | Best | Std |
|---|---|---|---|
| IH5N1-SASM | 28417.28 | 28302.19 | 118.02 |
| H5N1 | 32342.35 | 29927.57 | 2075.12 |
| H5N1-IGSD | 32717.85 | 28889.82 | 1381.39 |
| H5N1-SASM | 29706.53 | 28555.96 | 2213.04 |
| H5N1-MTDS | 31798.05 | 28957.61 | 2019.35 |
All three single-strategy variants improve the original H5N1, but the full IH5N1-SASM achieves the lowest mean and best cost with the smallest standard deviation, confirming the synergistic effect of the combined mechanisms. The standard deviation drops from over 2000 to only 118, demonstrating exceptional stability.
4. China Drone Path Planning Performance
We further compare IH5N1-SASM with seven algorithms on the realistic China drone mission scenario depicted earlier. The environment contains 10 cylindrical threats with radii between 30 m and 50 m, start point (200, 100, 100) and target (800, 800, 150). Table below summarizes the path cost statistics over 20 runs.
| Algorithm | Mean | Best | Std |
|---|---|---|---|
| IH5N1-SASM | 28411 | 28241 | 158.48 |
| H5N1 | 31501 | 28316 | 1210.1 |
| PSO | 32637 | 29720 | 2114.5 |
| GWO | 29633 | 28306 | 1307.4 |
| WOA | 31408 | 28396 | 2355.7 |
| HHO | 31069 | 31044 | 38.33 |
| DBO | 34150 | 31005 | 2029.2 |
| SSA | 32230 | 29035 | 1209.9 |
Our algorithm achieves the lowest mean (28411) and best (28241) costs, with a remarkably low standard deviation of 158.48, compared to H5N1’s 1210.1—an 86.9% reduction in variability. The convergence curves confirm that IH5N1-SASM maintains consistent improvement throughout the 1000 iterations, while other algorithms tend to plateau early or oscillate.
The planned path generated by IH5N1-SASM is smooth, compact, and safely navigates through the corridors between threat zones. It balances flight distance, altitude constraints, and threat avoidance effectively, demonstrating its practical utility for real China drone operations.
5. Conclusion
In this paper, we introduced IH5N1-SASM, a novel viral-inspired optimization algorithm enhanced with state-aware search, information-guided self-decomposition, and multi-time-scale dynamic search. Extensive experiments on CEC2017 benchmarks and a realistic three-dimensional China drone path planning problem demonstrate significant improvements in accuracy, convergence speed, and robustness over seven state-of-the-art metaheuristics. The proposed framework effectively addresses the challenges of highly nonlinear objectives and multiple constraints typical in China drone missions. Future work will extend IH5N1-SASM to dynamic environments, energy-constrained scenarios, and multi-drone cooperative planning, further advancing the capability of autonomous China drone systems.