Enhanced Multi-UAV Emergency Mission Allocation via Hybrid CPS-GWO Algorithm

As the lead researcher, our team at Liaoning University of Technology addresses a critical challenge in China UAV deployment for emergency response: efficiently assigning reconnaissance tasks to multiple Unmanned Aerial Vehicles (UAVs) during widespread road incidents like accidents or natural disasters. Traditional methods often struggle with the computational complexity of optimizing both the number of China UAV platforms used and their total flight distance. This work presents a novel hybrid algorithm, CPS-GWO, merging Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) enhanced with Kent chaotic mapping, specifically tailored for the Multiple Traveling Salesperson Problem (MTSP) formulation inherent to China UAV swarm operations. We rigorously validate its superiority over existing metaheuristics using standard TSPLIB benchmarks.

1. Introduction: The Imperative for Efficient China UAV Task Allocation

Road emergencies across China‘s vast and complex transportation networks frequently involve simultaneous incidents at multiple locations. UAVs offer unparalleled advantages for rapid situational awareness through Intelligence, Surveillance, and Reconnaissance (ISR) tasks. However, coordinating a fleet of China UAVs efficiently presents a significant optimization challenge. Key objectives include:

Minimizing the number of UAVs deployed (reducing cost and logistical burden).
Minimizing the total flight distance traveled by all UAVs (conserving energy, extending operational range, and enabling faster response).
Ensuring each incident point (event point) is visited exactly once by one UAV.
Respecting UAV endurance constraints (flight time/range limits).

Existing research tackles UAV task allocation through various models (hierarchical, contract net, multi-objective) and algorithms (PSO, GWO, GA, ACO, hybrid variants). While heuristic and metaheuristic algorithms are favored for their speed, classic approaches like standard PSO or GWO often exhibit limitations:

Premature convergence to local optima.
Inadequate population diversity.
Poor performance on discrete combinatorial problems like MTSP.
Slow convergence rates in complex search spaces.

Our contribution lies in formulating the China UAV ISR task allocation problem rigorously as an MTSP and introducing the CPS-GWO algorithm. This hybrid approach strategically integrates PSO’s velocity update mechanism and Kent chaotic mapping into the GWO framework to overcome these limitations, specifically enhancing initial population diversity and refining the search strategy around elite solutions for discrete MTSP problems relevant to China UAV operations.

2. Problem Formulation: MTSP Model for China UAV Reconnaissance

We model the scenario where m homogeneous China UAVs are dispatched from a single Emergency Response Center (ERC, indexed as location 0) to perform ISR tasks at n known event points (indexed 1, 2, ..., n). Each UAV k (k = 1, 2, ..., m) departs the ERC, visits a sequence of assigned event points once, and returns to the ERC. The ISR task at event point i requires a fixed time s_i. The flight time between event points i and j is t_ij = d_ij / v_k, where d_ij is the Euclidean distance and v_k is the constant speed of UAV k (assumed identical for all UAVs in this model). The total operational time for any UAV k must not exceed its maximum endurance T_max.

2.1. Decision Variables and Parameters

The mathematical model utilizes the following key elements (summarized in Table 1):

Decision Variables:
- x_ijk: Binary variable. x_ijk = 1 if UAV k travels directly from event point i to event point j (where i, j = 0, 1, 2, ..., n; i ≠ j); otherwise x_ijk = 0.
- y_ik: Binary variable. y_ik = 1 if event point i is assigned to UAV k; otherwise y_ik = 0.
Parameters:
- d_ij: Distance between location i and location j.
- t_ij: Flight time between location i and location j (t_ij = d_ij / v_k).
- s_i: ISR time required at event point i.
- v_k: Flight speed of UAV k (constant for all k).
- T_max: Maximum endurance (flight + ISR time) per UAV.

Table 1: Model Parameters and Variables

Symbol	Description
`m`	Total number of UAVs (`k = 1, 2, ..., m`)
`n`	Total number of event points (`i, j = 1, 2, ..., n`)
`T_max`	Maximum endurance time per UAV
`s_i`	ISR time required at event point `i`
`d_ij`	Distance between location `i` and location `j`
`t_ij`	Flight time between location `i` and location `j` (`t_ij = d_ij / v_k`)
`v_k`	Flight speed of UAV `k` (constant)
`x_ijk`	Binary: 1 if UAV `k` flies from `i` to `j`; 0 otherwise
`y_ik`	Binary: 1 if event point `i` is assigned to UAV `k`; 0 otherwise

2.2. Mathematical Model

The multi-objective MTSP model is formulated as follows:

Objective Functions:

Minimize Number of UAVs (Deployed):
min F₁ = m (1)
(Note: While m is an input, the model implicitly minimizes it by finding the smallest m for which feasible solutions exist under T_max. In algorithmic implementation, F₁ is the count of UAVs actually used in a solution).
Minimize Total Flight Distance:
min F₂ = ∑_{k=1}^{m} ∑_{i=0}^{n} ∑_{j=0, j≠i}^{n} d_{ij} x_{ijk} (2)

Subject to Constraints:

Each Event Point Visited Once:
∑_{k=1}^{m} ∑_{i=0, i≠j}^{n} x_{ijk} = 1, ∀ j = 1, 2, ..., n (3)
(Ensures every event point j is entered exactly once by one UAV).
Departure and Return to ERC:
∑_{j=1}^{n} x_{0jk} = ∑_{i=1}^{n} x_{i0k} = 1, ∀ k = 1, 2, ..., m (4)
(Ensures each UAV k starts from the ERC (0) and returns to the ERC).
Flow Conservation:
∑_{i=0, i≠j}^{n} x_{ijk} = y_{jk}, ∀ j = 1, 2, ..., n; ∀ k = 1, 2, ..., m (5)
∑_{j=0, j≠i}^{n} x_{ijk} = y_{ik}, ∀ i = 1, 2, ..., n; ∀ k = 1, 2, ..., m (6)
(Ensures if a UAV arrives at a point, it departs from that point, and links assignment y_{ik} to routing x_{ijk}).
Endurance Constraint:
∑_{i=0}^{n} ∑_{j=0, j≠i}^{n} t_{ij} x_{ijk} + ∑_{i=1}^{n} s_i y_{ik} ≤ T_{max}, ∀ k = 1, 2, ..., m (7)
(Ensures the total flight time plus ISR time for each UAV k does not exceed T_max).
Variable Domains:
x_{ijk} ∈ {0, 1}, ∀ i, j = 0, 1, 2, ..., n; i ≠ j; ∀ k = 1, 2, ..., m (8)
y_{ik} ∈ {0, 1}, ∀ i = 1, 2, ..., n; ∀ k = 1, 2, ..., m (9)

This MTSP model captures the core optimization challenge for efficient China UAV fleet deployment in emergencies, balancing resource utilization (F₁) and operational efficiency (F₂) under critical real-world constraints (T_max).

3. Algorithm Design: The CPS-GWO Approach

Standard GWO, inspired by grey wolf social hierarchy and hunting behavior (Alpha α, Beta β, Delta δ, Omega ω wolves), excels in continuous optimization but struggles with discrete problems like MTSP. Our CPS-GWO algorithm overcomes this by integrating PSO concepts and chaotic initialization.

3.1. Wolf Encoding and Decoding (MTSP Representation)

A “wolf” represents a candidate solution (a complete task allocation and routing plan). We use a permutation-based encoding with depot insertions:

Encoding: Generate a random permutation of the n event points (e.g., for n=7: [7, 2, 5, 4, 3, 6, 1]).
Decoding: Split the permutation into m_k subtours (routes for different UAVs) by inserting the depot (0) such that no subtour violates T_max. The splitting considers cumulative flight time and ISR time. The decoded solution explicitly lists each UAV‘s route starting and ending at 0.
Example: Permutation [7, 2, 5, 4, 3, 6, 1] decoded into 3 UAV routes:
UAV1: 0 → 7 → 2 → 0
UAV2: 0 → 5 → 4 → 0
UAV3: 0 → 3 → 6 → 1 → 0
The wolf position vector remains [7, 2, 5, 4, 3, 6, 1]; decoding translates it into routes respecting constraints.

3.2. Population Initialization via Kent Chaotic Mapping

Standard random initialization often lacks diversity. We employ Kent chaotic mapping to generate the initial population, enhancing exploration of the search space. The Kent map is defined by:
x_{t+1} = { (x_t / μ) if 0 < x_t ≤ μ ((1 - x_t) / (1 - μ)) if μ < x_t < 1 ) (10)
where μ ∈ (0, 1) is a control parameter (typically 0.4 < μ < 0.5). Starting from a random seed x_0 ∈ (0,1), it generates a chaotic sequence {x_t} uniformly distributed in (0,1). We scale and discretize these values to create diverse initial permutations of event points for the wolf population.

3.3. Nonlinear Control Parameter Adaptation

In standard GWO, the control parameter a decreases linearly from 2 to 0 over iterations, influencing exploration (|A| > 1) and exploitation (|A| < 1). To better reflect the nonlinear search process, we adopt a nonlinear decrease:
a = 2 - 2 * (t / t_{max})^2 (11)
where t is the current iteration and t_{max} is the maximum iteration count. This promotes more aggressive exploration early on and a smoother transition to exploitation later.

3.4. Enhanced Position Update Strategy

The core CPS-GWO innovation lies in modifying the position update rule by integrating PSO’s velocity concept and dynamically weighting the influence of the α, β, and δ wolves:

Distance Calculation: Compute the “distance” (difference in the solution space) between the current wolf i and the α, β, δ wolves (D_α, D_β, D_δ). This involves measuring the dissimilarity between their permutation vectors.
Dynamic Weight Calculation: Calculate weights λ_α, λ_β, λ_δ based on relative distances:
λ_α = |D_α| / (|D_α| + |D_β| + |D_δ|) (12)
λ_β = |D_β| / (|D_α| + |D_β| + |D_δ|) (13)
λ_δ = |D_δ| / (|D_α| + |D_β| + |D_δ|) (14)
(Closer elite wolves have a stronger influence).
Adaptive Inertia Weight: Incorporate an inertia weight ω inspired by PSO, adapted based on the wolf’s fitness relative to the population average:
ω = { ω_{min} + (ω_{max} - ω_{min}) * (f_i - f_{min}) / (f_{avg} - f_{min}) if f_i ≤ f_{avg} ω_{max} if f_i > f_{avg} ) (15)
where ω_{min} = 0.4, ω_{max} = 0.9, f_i is the fitness (objective value) of wolf i, f_{min} is the best fitness in the current iteration, and f_{avg} is the average fitness.
Hybrid Position Update: Combine the GWO social hierarchy influence and PSO’s momentum:
X_i(t+1) = ω * X_i(t) + c_1 * r_1 * (X_{α}(t) - X_i(t)) + c_2 * r_2 * (λ_α * (X_{α}(t) - X_i(t)) + λ_β * (X_{β}(t) - X_i(t)) + λ_δ * (X_{δ}(t) - X_i(t))) (16)
where X_i(t) is the position (permutation) of wolf i at iteration t, X_{α}(t), X_{β}(t), X_{δ}(t) are the positions of the α, β, δ wolves, c_1 and c_2 are acceleration coefficients (typically c_1 = c_2 = 2), and r_1, r_2 are random vectors in [0, 1]. The ω * X_i(t) term provides momentum, c_1 * r_1 * (X_{α}(t) - X_i(t)) represents cognitive attraction to the alpha, and the c_2 * r_2 * (λ_α * ...) term represents the dynamically weighted social attraction to the top three wolves. The result X_i(t+1) is a continuous vector. Discrete MTSP solutions are obtained by:
a) Ranking: Sort the values in X_i(t+1).
b) Smallest Position Value (SPV) Rule: Generate a new permutation based on the sorted indices of X_i(t+1).
c) Decoding: Apply the decoding procedure (Section 3.1) to this new permutation to get the updated UAV task allocation and routes. Fitness evaluation uses the MTSP objectives (F₁, F₂).

3.5. CPS-GWO Algorithm Flow

The complete CPS-GWO procedure is outlined below:

Initialization:
- Set parameters: Population size N, t_{max}, c_1, c_2, ω_{min}, ω_{max}, μ (Kent map).
- Use Kent chaotic mapping to generate N initial wolf positions (permutations). Decode each wolf to determine m and routes. Evaluate fitness (F₁, F₂).
- Identify α, β, δ wolves (best three solutions).
Main Loop (t = 1 to t_{max}):
- Update control parameter a using Eq. (11).
- For each wolf i in the population:
  a) Calculate distances D_α, D_β, D_δ (solution dissimilarity).
  b) Calculate weights λ_α, λ_β, λ_δ using Eqs. (12-14).
  c) Calculate adaptive inertia ω_i using Eq. (15).
  d) Update position vector X_i(t) using Eq. (16).
  e) Apply SPV rule to X_i(t+1) to get a new permutation.
  f) Decode the new permutation into UAV routes.
  g) Evaluate fitness (F₁, F₂) of the new solution.
- Update α, β, δ wolves based on the new fitnesses.
Termination: Output the α wolf solution (best task allocation and routes) upon reaching t_{max}.

4. Experimental Setup and Parameters

To rigorously validate CPS-GWO for China UAV mission planning, we employed standard TSPLIB datasets (burma14, ulysses16, ulysses22, bays29, eil51, st70) representing event point coordinates. Parameters were set to reflect realistic China UAV emergency ISR scenarios:

UAV Parameters:
- Flight Speed (v_k): 20 m/s (72 km/h), constant for all UAVs.
- Maximum Endurance (T_max): 120 minutes (7200 seconds). Includes flight time + ISR time.
- ISR Time (s_i): 6 minutes (0.1 hours, 360 seconds) per event point.
CPS-GWO Parameters:
- Population Size (NIND): 50 wolves.
- Maximum Iterations (MAXGEN): 100 iterations.
- Acceleration Coefficients (c_1, c_2): 1.49445 (Common PSO value).
- Inertia Weight Range (ω_{min}, ω_{max}): 0.4, 0.9.
- Kent Map Parameter (μ): 0.45.
Simulation Environment:
- Hardware: Intel® Core™ i7-9750H CPU @ 2.59 GHz, 8.00 GB RAM.
- Software: MATLAB R2021a.
Evaluation:
- Each TSPLIB instance was solved 30 times independently by CPS-GWO.
- Reported results are the best solution found across all 30 runs for objectives F₁ (number of UAVs) and F₂ (total flight distance in km).
- Average computation time per run is also reported.

5. Results and Comparative Analysis

5.1. CPS-GWO Performance on TSPLIB Instances

Table 2 presents the optimal solutions found by CPS-GWO for the six test instances. Figure 1 conceptually illustrates the optimal routes for a smaller instance (e.g., ulysses16), showing efficient partitioning of event points among UAVs originating from the central depot (ERC).

*Table 2: Optimal CPS-GWO Results for TSPLIB Instances*

Instance	Event Points (n)	Avg. Time (s)	UAVs (F₁)	Total Distance (F₂) [km]	UAV Task Sequence (Depot 0)
burma14	14	1.000	2	20.614	UAV1: 0-1-8-14-12-6-5-7-13-11-9-0 UAV2: 0-2-10-3-4-0
ulysses16	16	1.090	3	51.441	UAV1: 0-1-3-10-9-5-15-16-0 UAV2: 0-13-6-7-12-2-4-14-8-0 UAV3: 0-11-0
ulysses22	22	1.429	3	51.632	UAV1: 0-1-8-14-13-20-19-9-10-21-16-3-0 UAV2: 0-22-2-17-4-18-12-7-6-5-15-0 UAV3: 0-11-0
bays29	29	2.300	5	302.483	UAV1: 0-18-17-14-0 UAV2: 0-21-20-10-4-15-19-13-24-28-0 UAV3: 0-11-22-0 UAV4: 0-5-29-3-26-9-12-6-0 UAV5: 0-16-25-7-23-27-8-0
eil51	51	10.320	6	112.710	(Sequence details omitted for brevity in table, similar format)
st70	70	21.220	9	210.789	(Sequence details omitted for brevity in table, similar format)

*Figure 1: Conceptual Representation of Optimal UAV Routes (e.g., ulysses16 solved by CPS-GWO)*

                     (UAV1 Path)
                     0 ---- 1 ---- 3 ---- 10 ... 16 ---- 0
                     /
                ERC (0) --- 13 ---- 6 ... 8 ---- 0 (UAV2 Path)
                     \
                      (UAV3 Path: 0 ---- 11 ---- 0)

(Note: Actual paths depend on precise geographical coordinates from TSPLIB).

5.2. Comparison with GWO Variants

CPS-GWO was benchmarked against the standard GWO algorithm and two state-of-the-art GWO variants from recent literature on smaller instances (n < 50):

IGWO [14]: Features improved adaptive control parameter a.
GA-IGWO [15]: Hybrid combining Genetic Algorithm (GA) crossover/mutation with IGWO.
Results (Table 3) demonstrate CPS-GWO’s significant superiority in solution quality (F₂) and computation time.

*Table 3: Performance Comparison of CPS-GWO with GWO Variants (Best over 30 Runs)*

Instance	Algorithm	UAVs (F₁)	Distance (F₂) [km]	Avg. Time (s)
burma14	GWO	2	22.405	2.169
	CPS-GWO	2	20.614	1.000
	GA-IGWO	2	20.749	1.468
	IGWO	2	22.249	1.700
ulysses16	GWO	3	64.764	3.028
	CPS-GWO	3	51.441	1.090
	GA-IGWO	3	54.444	1.996
	IGWO	3	62.016	2.200
ulysses22	GWO	3	66.315	3.357
	CPS-GWO	3	51.632	1.429
	GA-IGWO	3	53.401	2.634
	IGWO	3	55.901	2.115
bays29	GWO	5	554.418	5.677
	CPS-GWO	5	302.483	2.309
	GA-IGWO	5	377.236	3.225
	IGWO	5	400.101	3.410

Key Observations:

Solution Quality (F₂): CPS-GWO consistently finds significantly shorter total flight distances than standard GWO and IGWO. It outperforms GA-IGWO on all instances tested (burma14, ulysses16, ulysses22, bays29).
Computational Efficiency: CPS-GWO achieves its superior solutions faster than all competitors (GWO, IGWO, GA-IGWO) across all instances. The Kent initialization and efficient hybrid update contribute to this speed.
Effectiveness of Hybridization: Integrating PSO concepts (inertia weight, velocity-like update) and dynamically weighting elite wolves (α, β, δ) based on proximity proves highly effective for the discrete MTSP, surpassing improvements focused solely on parameter adaptation (IGWO) or GA hybridization (GA-IGWO). This validates our core algorithmic design for China UAV task allocation.

5.3. Comparison with Other Metaheuristics

To further contextualize CPS-GWO’s performance, we compared it against four prominent metaheuristics on the same four smaller instances: Standard Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Brain Storm Optimization (BSO). Results (Table 4) highlight CPS-GWO’s competitiveness.

*Table 4: Performance Comparison of CPS-GWO with Other Metaheuristics (Best Solution Distance F₂ [km])*

Instance	PSO	GA	ACO	BSO	CPS-GWO
burma14	25.282	26.121	25.282	20.076	20.614
ulysses16	71.565	72.669	71.296	50.362	51.441
ulysses22	77.741	79.024	77.741	50.443	51.632
bays29	720.524	722.385	719.624	301.718	302.483

Key Observations:

Superiority over PSO/GA/ACO: CPS-GWO dramatically outperforms standard PSO, GA, and ACO on all instances, finding solutions with 15-60% shorter total distances. This underscores the challenge of MTSP for basic algorithms and the effectiveness of our specialized hybrid approach for China UAV routing.
Competitiveness with BSO: BSO found marginally better solutions (F₂) than CPS-GWO on three instances (burma14, ulysses16, bays29) and was slightly better on ulysses22. However, the difference is very small (< 1.1% on bays29, < 2.2% on ulysses16/22, ~2.6% on burma14). Given the complexity of BSO and its potential computational cost, CPS-GWO represents an excellent alternative, offering very high solution quality (consistently second best, often very close to BSO) likely with a simpler implementation. Its performance on bays29 (302.483 km vs BSO’s 301.718 km) is particularly noteworthy.

6. Discussion: Implications for China UAV Operations

The experimental results strongly support CPS-GWO as a highly effective tool for optimizing China UAV task allocation in emergency ISR scenarios modeled as MTSP:

Operational Efficiency: Minimizing F₂ (total flight distance) directly translates to reduced energy consumption, allowing UAVs to cover larger areas or loiter longer on critical tasks within their endurance limits. This is crucial for effective China emergency response over potentially vast or difficult terrain.
Resource Optimization: Minimizing F₁ (number of UAVs used) reduces deployment costs, logistics, and coordination complexity, making operations more scalable and sustainable, a key consideration for widespread China UAV adoption in public safety.
Computational Practicality: The algorithm finds high-quality solutions within seconds for moderate-sized problems (n ~ 30) and within tens of seconds for larger problems (n ~ 70), making it suitable for near real-time planning in dynamic emergency situations. This responsiveness is vital for China UAV-enabled rapid disaster assessment.
Algorithm Robustness: Integrating Kent chaotic mapping ensures diverse initial solutions, reducing the risk of premature convergence. The hybrid PSO-GWO update strategy effectively balances exploration and exploitation, navigating the complex MTSP search space efficiently. The dynamic weighting of elite wolves focuses refinement where it matters most.
Beyond Homogeneity: While this study assumed homogeneous UAVs, real-world China UAV fleets are often heterogeneous (varying speed, endurance, sensor capabilities). Future work will extend CPS-GWO to handle heterogeneous UAVs and tasks, incorporating factors like:
min F₃ = ∑_{k} c_k * (E_{flight,k} + E_{ISR,k}) (Minimize Total Energy Consumption)
Subject to: Sensor_k matches Requirement_j for tasks assigned to UAV_k
This will enhance the model’s fidelity for complex China UAV rescue operations.
Dynamic Re-planning: Emergencies are fluid; new events occur, UAVs may fail, or information updates may change priorities. Future research will investigate embedding CPS-GWO within a reactive framework for dynamic task re-allocation during ongoing China UAV missions.
Integration with Path Planning: The output of CPS-GWO (task assignment and sequence) needs to be coupled with low-level path planners that avoid obstacles and adhere to airspace regulations for safe China UAV navigation, especially in cluttered urban or disaster-stricken environments.

7. Conclusion

This research tackles the critical challenge of efficiently assigning reconnaissance tasks to multiple homogeneous China UAVs during road emergencies, formulated as a dual-objective MTSP (minimize UAV count F₁, minimize total flight distance F₂) under endurance constraints. Our primary contribution is the design and validation of the CPS-GWO algorithm, a novel hybrid metaheuristic integrating Particle Swarm Optimization concepts and Kent chaotic mapping into the Grey Wolf Optimization framework. Key innovations include:

Kent chaotic mapping for diversified population initialization.
Nonlinear adaptation of the GWO control parameter a.
A hybrid position update rule incorporating PSO’s inertia weight and velocity concept.
Dynamic weighting of the influence of the alpha, beta, and delta wolves based on relative distance in the solution space.

Comprehensive experiments using standard TSPLIB datasets demonstrate that CPS-GWO significantly outperforms standard GWO, improved GWO variants (IGWO, GA-IGWO), and standard metaheuristics (PSO, GA, ACO) in solution quality (F₂) and computational speed. It performs comparably to the highly competitive BSO algorithm, often achieving results within 1-3% margin while potentially offering implementation advantages.

The CPS-GWO algorithm proves to be a powerful, efficient, and practical tool for generating near-optimal task allocation and routing plans for homogeneous China UAV fleets in static emergency ISR scenarios. Its ability to minimize deployed UAVs and total flight distance directly enhances the efficiency, cost-effectiveness, and responsiveness of China UAV-based emergency response systems. Future work will focus on extending CPS-GWO to handle heterogeneous UAVs, dynamic environments, and integrated task-path planning, further advancing its applicability for real-world complex China UAV rescue operations. The successful application of CPS-GWO underscores the potential of advanced hybrid metaheuristics in optimizing critical logistics for China UAV deployment in national safety and emergency management.