Slime-Mould-Inspired Resilient Topology Construction Algorithm for UVC/RF Heterogeneous UAV Swarms

Abstract

Addressing the demand for highly reliable communication in unmanned aerial vehicle (UAV) swarms operating in extreme environments, this paper proposes a slime mold-inspired resilient topology construction algorithm for UVC/RF heterogeneous UAV networks, termed UVC-SMA. To overcome the limitations of conventional bio-inspired algorithms in UVC/RF heterogeneous network scenarios—including insufficient heterogeneous modeling, weak dynamic adaptability, long passive repair latency, and inadequate single-path reliability—the proposed algorithm integrates three core mechanisms. First, it constructs an energy-aware joint cost model for heterogeneous links and uses an exponential energy penalty factor to suppress energy hotspots in the network. Second, it designs a network state-driven parameter adaptation mechanism to dynamically balance the capabilities of global exploration and local exploitation. Third, it establishes an active key node protection framework with a hybrid degree-betweenness weighting, which shifts resilience optimization from post-failure reconfiguration to proactive pre-failure reinforcement and develops a K-shortest multipath routing method (K = 3) based on the reciprocal of conductivity to achieve millisecond-level path switching. The simulation results show that compared with the traditional slime mould algorithm (SMA), the UVC-SMA improves network robustness from 0.75 to 1.00, increases average residual energy by 19.5%, and reduces average node degree by 16.8%. The algorithm adopts a distributed architecture with a single iteration complexity of O(n²), which theoretically supports low-cost on-board deployment and is applicable to UAV swarm communication in highly dynamic and highly adversarial extreme environments. The reported robustness improvement from 0.75 to 1.00 is obtained under the baseline 50-node simulation configuration and cannot be guaranteed under arbitrary network or mobility conditions.

1. Introduction

The rapid expansion of the low-altitude economy and the modernization of national emergency management systems have driven the evolution of UAV swarms from single-platform operations to collaborative, standardized multi-UAV missions. Accordingly, extensive academic research has been conducted on reliable communication architectures for autonomous low-altitude UAV swarms, and modular hardware-algorithm co-design solutions have been widely verified to improve transmission stability in highly dynamic FANET scenarios [1,2]. In unstructured extreme scenarios such as earthquake rescue, border patrol and tactical reconnaissance, UAV ad hoc networks, featuring decentralization, self-organization and rapid deployment, serve as the only reliable communication backbone when ground communication infrastructure is fully paralyzed. However, existing technologies still face multiple challenges. Highly dynamic topologies force on-demand routing protocols to trigger full-network re-discovery frequently, resulting in high signaling overhead and slow convergence; the limited battery capacity of small UAVs makes unreasonable relay selection prone to form energy hotspots and cause network partitioning; single-RF links in complex electromagnetic environments can hardly meet the requirements of transmission distance, anti-interference, and concealment simultaneously. Existing studies have explored solutions from multiple dimensions: model predictive control for flight trajectory planning [3], hybrid energy systems for endurance improvement [4], and deep reinforcement learning frameworks for mobility-aware UAV network coordination [5].

To overcome the inherent defects of a single communication system, the heterogeneous integration of ultraviolet communication and radio frequency communication has attracted attention. Ultraviolet communication utilizes solar-blind scattering transmission, which naturally has the advantages of non-line-of-sight, anti-interference, and low probability of interception, and is suitable for short-range highly reliable relaying. Radio frequency communication relies on mature microwave technology to achieve wide-area coverage and high-speed data transmission. The two types of links are highly complementary in performance boundaries, opening up a new path for UAV swarm communication in extreme environments. However, the essential differences between the two in transmission mechanism, energy consumption characteristics, and spatial constraints also bring new theoretical challenges to the topology planning and routing optimization of heterogeneous networks.

Focusing on the routing problem of the above heterogeneous networks, existing studies mostly carry out channel modeling, power allocation, and link switching at the physical layer, confirming the performance gain of heterogeneous architectures compared with single-RF systems. Bio-inspired swarm intelligence algorithms have gradually become a mainstream solution for UAV dynamic optimization tasks owing to their inherent advantages of distributed architecture, self-organization, and strong robustness. Representative research includes the reinforcement learning-based artificial bee colony algorithm for 3D UAV path planning [6] and bird swarm intelligence variants applied to multiple UAV optimization scenarios: edge-based target detection with competitive swarm mechanisms [7] and path planning algorithms inspired by bird flock migration behavior [8]. There are also various well-established heuristic algorithms for UAV system optimization, such as metaheuristic reviews for drone delivery paths [9], the Stackelberg game-based heuristic approach for multi-UAV linear infrastructure protection [10], and the energy learning hyper-heuristic algorithm for heterogeneous UAV cooperative task allocation [11]. In recent years, machine learning and deep learning techniques have been extensively applied to UAV systems, demonstrating remarkable performance gains across multiple scenarios. Deep learning combined with depth cameras provides a mature solution for UAV environmental perception and autonomous obstacle avoidance [12]. In the field of visual inspection, such methods have been widely verified in typical scenarios such as UAV building facade defect detection [13] and aircraft skin defect detection tasks [14]. For instance, YOLO-series detection algorithms have been validated for rapid post-earthquake building damage detection using UAV remote sensing imagery [15]. For low-altitude agricultural scenarios, the improved Litchi-SORT tracking algorithm effectively addresses occlusion and motion instability, achieving accurate fruit tracking and counting in UAV aerial images [16].

However, the performance of data-driven models is limited by the number of labeled samples and on-board computing power, and cannot be directly applied to network-layer routing topology optimization scenarios. Graph theory and mathematical optimization methods are also widely used to solve optimal network topology and resource scheduling problems, relying on tools such as minimum spanning trees, connected dominating sets, and linear programming. Representative studies include a minimum spanning tree-based federated aggregation mechanism for UAV networks [17], and a linear programming approach combined with Petri net modeling for cyclic UAV logistics resource scheduling [18]. However, most graph theory and mathematical programming-based methods rely on static topology assumptions and global network state information, with a solution process dependent on a centralized computing architecture, making them difficult to adapt to highly dynamic, complex topologies. To address this limitation, distributed routing protocols and multi-agent deep reinforcement learning schemes have been developed for dynamic UAV ad hoc networks and swarm formation control [19,20]. The lime mould algorithm is one example of a swarm intelligence algorithm. It simulates the adaptive expansion and contraction of protoplasmic tubes along the nutrient gradient and shows natural compatibility with topology planning and path optimization. Nevertheless, directly applying existing slime mold algorithms to UVC/RF heterogeneous UAV scenarios exposes multiple deficiencies. Existing algorithms are all designed for single radio frequency links, without incorporating the spatial constraints and energy consumption differences of the two types of links into a unified quantification system, so joint optimization cannot be achieved. Fixed hyperparameter configurations cannot dynamically adjust the balance between global exploration and local exploitation according to the real-time network state, and are prone to premature convergence or performance degradation in time-varying topologies. Routing optimization remains based on passive repair logic; that is, reconfiguration occurs after a failure, and the approach lacks active identification and protection of key nodes, making it difficult to meet the rigid requirements of highly reliable communication. Moreover, the classic slime mould algorithm only outputs a single optimal path without redundancy design. Once the main path is interrupted, it needs to be re-iterated, which easily causes communication interruption.

In the broader field of UAV network resilience and survivable routing, existing research generally evolve along three paths. For single-path routing optimization, residual energy and link lifetime are core decision metrics, and surrogate modeling combined with heuristic algorithms has been validated to effectively reduce energy consumption in multi-trip UAV routing scenarios [21]. For multipath transmission, AOMDV-based redundancy mechanisms enable fast local switching between primary and backup paths, and improved protocols with stable node selection further enhance end-to-end transmission reliability [22]. Topology-aware active optimization methods can effectively enhance network survivability and resilience from the structural level. Representative approaches include joint optimization of network topology and timeslot resource allocation to maximize UAV communication capacity [23], and 3D path planning algorithms with adaptive sampling strategies to support dynamic topology adjustment [24]. However, the above three types of schemes generally rely on centralized optimization architectures and global topology information, and the passive repair paradigm makes it difficult to eliminate interruption delay. Resilience improvement and energy constraints are not coordinated, and adaptability is insufficient in highly dynamic and decentralized UAV swarm scenarios. Survivable routing and topology reinforcement schemes can effectively mitigate connectivity risks caused by node failures in steady-state network environments with slowly varying topologies and have well-recognized engineering application value. Representative studies cover multiple practical dimensions: holistic end-to-end congestion control for SAGIN-integrated UAV networks supports seamless aerial-terrestrial transmission [25] and cyber clone-driven blockchain architectures enhance both the security and operational efficiency of drone networks [26]. Most of these methods are built upon mature graph theory and mathematical optimization frameworks. Graph-theoretic approaches have been validated for cooperative rapid evasive target search in multi-UAV systems with global state information [27], and mathematical optimization models provide rigorous theoretical support for structured problem solving in centralized computing architectures [28]. Benefiting from such mature frameworks, these methods can quickly output network configurations that satisfy basic survivability requirements when global topology information is accessible. However, these schemes generally rely on centralized optimization or global topology information and have poor scalability in decentralized and high-speed-moving UAV swarms. The interruption delay caused by the passive repair paradigm is difficult to eliminate, and resilience improvement and energy constraints are considered separately. Indiscriminate redundancy design instead accelerates node energy depletion.

In response to the above research gaps, this paper proposes the UVC-SMA, which makes systematic improvements to the traditional slime mould algorithm. At the theoretical level, an energy-aware joint cost model for heterogeneous links is constructed, which unifies the quantification of link distance, height difference, and residual energy with an exponential penalty factor to enable the joint evaluation of UVC and RF links. A network state-driven parameter adaptation mechanism is designed to dynamically adjust the expansion rate, contraction rate, evaporation coefficient, and topology decision threshold according to real-time robustness, average node degree, and primary path length, so as to balance global exploration and local exploitation. An active key node protection framework with hybrid degree-betweenness weighting is established to shift the focus of resilience optimization from “post-failure repair” to “pre-failure prevention”. At the engineering level, the algorithm adopts a fully distributed architecture with low complexity and high adaptability, which theoretically supports deployment on low-cost on-board embedded platforms. Full hardware implementation and on-board performance verification remain part of our future work. Meanwhile, a K-shortest multipath routing generation method (K = 3) based on the reciprocal of conductance is proposed, which simultaneously generates a primary path and two backup paths without shared links. The theoretical switching delay is less than 10 ms, which significantly improves end-to-end communication reliability.

The core novelties that distinguish the UVC-SMA from existing swarm intelligence routing algorithms are summarized as follows. First, unlike traditional SMA and ACO algorithms designed for single-RF links, the UVC-SMA constructs a unified heterogeneous link cost model for UVC/RF dual links, enabling joint optimization of two types of links with complementary performance. Second, unlike fixed-parameter swarm intelligence algorithms, the UVC-SMA proposes a network state-driven parameter adaptation mechanism, which dynamically balances global exploration and local exploitation capabilities in dynamic topologies. Third, unlike the passive repair paradigm adopted by most existing routing algorithms, the UVC-SMA establishes an active key node protection framework coupled with conductivity-based K-disjoint multipath routing, shifting the focus of resilience optimization from post-failure reconfiguration to proactive pre-failure reinforcement.

2. System Model

This section constructs a complete mathematical model of spatiotemporal evolution for the 3D operational scenario of UVC/RF heterogeneous UAV swarms, and formalizes the engineering problem of resilient network construction into a multi-objective optimization problem with multiple constraints, providing rigorous theoretical support for subsequent algorithm design and performance verification. All model parameters and constraints are set based on the measured performance of commercial communication modules and the actual operation characteristics of UAVs, ensuring consistency between theoretical analysis and engineering practice.

2.1. Solar-Blind UVC Communication Principle

Solar ultraviolet radiation in the 200–280 nm band is strongly absorbed by stratospheric ozone molecules, resulting in extremely low background radiation noise in this band near the ground. This naturally forms a “solar-blind” transmission window with inherent low interception probability and anti-interference properties. Unlike traditional radio frequency communication, which relies on line-of-sight transmission, ultraviolet signals can form non-line-of-sight propagation paths through the multiple scattering effects of atmospheric molecules and aerosols. The transceiver can establish a communication link without strict alignment, enabling effective adaptation to attitude jitter and temporary occlusion during the highly dynamic maneuvering of UAV swarms.

A typical airborne ultraviolet communication system adopts a separate transceiver structure, consisting of a transmitter, an atmospheric channel, and a receiver. The operating principle of the system is shown in Figure 1.

The transmitter uses an ultraviolet LED array as the radiation source. After the on-board data unit completes data encoding and encapsulation, the baseband signal is loaded onto the LED array through the modulation driver module to complete electro-optical conversion and radiate solar-band optical signals into the atmospheric space. Affected by molecular scattering, ozone absorption, and aerosol attenuation in the atmospheric channel, optical signals form spatially dispersed propagation paths through multiple scattering, which is the internal mechanism by which ultraviolet communication can establish links without strict pointing alignment. The receiver converges weak optical signals through an ultraviolet lens, removes out-of-band stray light through a solar-blind filter, completes photoelectric conversion by a photodetector and demodulates and recovers the original data through the signal processing unit.

This architecture, utilizing non-line-of-sight transmission and anti-interference characteristics, can provide highly reliable short-range relaying in complex electromagnetic environments. However, restricted by atmospheric attenuation, the single-hop transmission distance is generally on the order of hundreds of meters, making it difficult to independently support wide-area UAV swarm networking. For this reason, this paper adopts a heterogeneous fusion networking system of ultraviolet and radio frequency links, utilizing the complementary advantages of the two types of links in coverage capability and survivability resilience.

2.2. Three-Dimensional UAV Network Scenario Model

Consider a UAV swarm network deployed in a three-dimensional Euclidean space region $\mathsf{\Omega }=\left[0,300\right]\times \left[0,300\right]\times \left[30,150\right] {\mathrm{m}}^3$. Define the node set as N = {1, 2,…, n}, where n = 50 is the total number of network nodes. Designate node 1 as the data source node S, node 50 as the data destination node D, and the remaining nodes as relay nodes. The initial coordinates of the source node are fixed as [0,0,50]^T, the initial coordinates of the destination node are fixed as [300,300,50]^T, and the initial coordinates of relay nodes are randomly and uniformly distributed in the space region $\mathsf{\Omega }$.

A random walk mobility model with boundary damping constraints is used to simulate the dynamic flight characteristics of UAVs. The three-dimensional velocity vectors of nodes follow independent normal distributions, with a horizontal velocity standard deviation of 1 m/s and a vertical velocity standard deviation of 0.1 m/s, and the time step dt = 2.0 s. To avoid excessively frequent changes in network topology, node positions are updated every 20 iterations, and mobility is only activated after the number of iterations is greater than 30. When a node moves beyond the space boundary, the velocity component in the corresponding direction is reversed and multiplied by a damping coefficient of 0.8 and the coordinates are constrained within the boundary range.

A differentiated node energy initialization strategy is adopted. As the core communication endpoints of the network, the source node and destination node are configured with an initial energy of 1000 J, and the initial energy of relay nodes follows a uniform distribution from 500 J to 800 J. The residual energy of nodes dynamically decreases with the continuous operation of communication links. When the energy drops to 0, the node completely fails and loses all communication capabilities. The specific 3D UAV scenario is shown in Figure 2.

2.3. UVC/RF Heterogeneous Communication Link Model

Based on the physical characteristics of UVC scattering transmission and RF electromagnetic wave transmission, the heterogeneous link accessibility criteria and energy-aware joint cost model are established. For any two nodes i and j, a UVC link is accessible if and only if the Euclidean distance between the nodes is in the range from 50 m to 150 m, and the flight heights of both nodes are lower than the 100 m ozone layer boundary. An RF link is accessible if and only if the Euclidean distance between the nodes is in the range of 20 m to 300 m. Both types of links adopt multiple-input multiple-output (MIMO) antenna arrays to achieve spatial diversity gain, which improves link capacity and anti-multipath fading capability without additional transmit power, and provides physical-layer support for parallel multi-link routing optimization of the subsequent slime mold algorithm. Figure 3 shows the on-board hemispherical MIMO model.

On this basis, a joint cost model for heterogeneous links is constructed, comprehensively considering link distance, height difference, and node residual energy. First, an exponential energy factor is introduced:

$${\epsilon }_{ij}(t)=exp\left(-{\displaystyle \frac{min\left(E_i\right(t),E_j(t\left)\right)}{500}}\right)$$

(1)

This factor can produce a significant cost increase when the node energy is nearly exhausted, thereby naturally suppressing low-energy nodes from becoming relay nodes at the routing selection level.

For the UVC scattering transmission characteristics, a cost function including distance cost, height-difference cost, and an energy penalty term is designed:

$$C_{uv}(i,j,t)=\left[{\left({\displaystyle \frac{d_{ij}\left(t\right)}{150}}\right)}^2+0.3\cdot {\left({\displaystyle \frac{\mid z_i\left(t\right)-z_j\left(t\right)\mid }{50}}\right)}^2\right]\cdot (1+0.2\cdot {\epsilon }_{ij}(t))+0.05 \cdot {\displaystyle \frac{\mid z_i\left(t\right)-z_j\left(t\right)\mid }{50}}$$

(2)

The distance cost adopts a quadratic form to reflect the rapid attenuation of UVC transmission quality with distance. The weight of height-difference cost is set to 0.3 to reflect the significant impact of vertical distance on scattering links. The weight of energy factor is set to 0.2 to reflect the higher energy consumption characteristics of UVC communication modules.

For the RF air–ground propagation characteristics, a cost function including a 1.5th power distance cost, a sigmoid-shaped long-distance additional cost, and an energy penalty term is designed:

$$C_{rf}(i,j,t)=\left[{\left({\displaystyle \frac{d_{ij}\left(t\right)}{300}}\right)}^{1.5}+0.1\cdot {\displaystyle \frac{1}{1+exp(-d_{ij}(t)/100)}}\right]\cdot (1+0.1\cdot {\epsilon }_{ij}(t))+0.05\cdot {\displaystyle \frac{\mid z_i\left(t\right)-z_j\left(t\right)\mid }{50}}$$

(3)

All key thresholds and weighting coefficients are grounded in physical characteristics, commercial device specifications, and published experimental data.

The 50–150 m UVC operating range and 100 m altitude threshold align with the typical performance of commercial solar-blind UV-C transceivers in the near-ground atmospheric boundary layer. The lower bound of 50 m matches the minimum operating distance of near-field ultraviolet scattering links, while the upper bound of 150 m aligns with the maximum reliable transmission range of low-power solar-blind LED modules. The 100 m altitude threshold reflects the upper boundary of the near-ground ozone mixing layer, below which solar-blind background noise remains at an ultra-low level and UVC links maintain stable performance [1].

The 20–300 m RF communication range follows widely adopted standard FANET simulation configurations for small, low-power UAV platforms. The 20 m minimum distance avoids near-field signal saturation, and the 300 m maximum range matches the typical communication radius of 2.4 GHz low-power transceivers on miniature UAVs [1].

The 500 J energy normalization constant in Equation (1) is calibrated to the typical battery capacity of small reconnaissance UAVs, serving as the baseline for the exponential energy penalty mechanism. The initial energy settings (1000 J for endpoint nodes, 500–800 J for relay nodes) match the power configuration of common small UAV platforms, where core mission nodes carry larger battery packs. The per-link energy consumption values (0.5 J/s for UVC, 0.3 J/s for RF) are derived from measured power dissipation of commercial ultraviolet LED modules and RF transceivers, respectively.

The weighting coefficients in Equations (2) and (3) reflect the relative contribution of each physical factor to link quality. Their influence on network performance is verified through sensitivity analysis presented in Section 4.3.3. The energy factor weight is set to 0.1 to reflect the higher energy efficiency of RF communication modules. A unified global height-difference penalty term is added to both link types to ensure the vertical stability of the network topology. When both UVC and RF links are accessible between two nodes, the link with the lower cost is automatically selected as the active transmission link.

Sensitivity analysis confirms that varying these weighting coefficients within a reasonable range produces a variation of less than 2.1% in final robustness, verifying that the baseline parameter settings are robust and not arbitrarily chosen.

2.4. Topology Generation and Energy Evolution Mechanism

A conductivity-driven topology generation mechanism is constructed based on the above link cost model. First, all candidate links with conductivity greater than the preset threshold are screened. Conductivity reflects the transmission quality and importance of the link and is dynamically updated by the iteration process of the subsequent slime mold algorithm. For each candidate link, its link type is determined according to the accessibility criterion and sorted by conductivity from high to low. To avoid node communication overload, the maximum number of node connections is limited according to node type: source and destination nodes can establish up to 8 connections, and ordinary relay nodes can establish up to 6 connections. Connections are established sequentially from high to low conductivity until all nodes reach the maximum number of connections or all candidate links are processed. This mechanism can prioritize retaining links with higher transmission quality while maintaining a reasonable connection density, achieving a balance between network performance and resource consumption.

To accurately characterize the impact of communication routing decisions on network energy distribution and lifetime, a heterogeneous link energy consumption model is constructed. Per unit time, each UVC link consumes 0.5 J of energy, and each RF link consumes 0.3 J of energy. The energy consumption of each link is equally shared by the two end nodes. When the residual energy of a node drops to 0, all its communication links are automatically disconnected. To enhance network resilience, an active key node protection mechanism is introduced. Key node identification and protection operations are performed every 30 iterations to add redundant connections for core nodes in the network. For each additional protection connection, the nodes at both ends of the connection consume 5 J of energy each, and a protection connection is added only when the residual energy of the node is greater than 100 J. Each key node can add up to 3 protection connections.

Based on the above conductivity-driven topology generation rules and the active key node protection mechanism with hybrid degree-betweenness weighting, the UVC-SMA can adaptively generate a hierarchical heterogeneous resilient topology that meets energy constraints and connectivity requirements, as shown in Figure 4. The key nodes in the topology are reinforced with additional protection links, which significantly reduces the probability of partitioning caused by single-point failure. The backup paths generated by the K-shortest method are link-disjoint, meaning they share no common communication links. This ensures that a single link failure does not affect more than one path. However, the paths are not guaranteed to be fully node-disjoint, so failure of a critical relay node may still disrupt multiple paths simultaneously. The key node protection mechanism mitigates this risk by reinforcing high-betweenness nodes, and the overall architecture ensures continuous communication through redundant relay paths, laying a foundation for reliable communication in extreme environments.

2.5. Quantitative Evaluation System of Network Resilience

Network resilience is a core indicator of the ability of UAV swarms to maintain core communication services in extreme environments. This paper constructs a quantitative evaluation system from three dimensions: connectivity, survivability, and topological stability. Source-destination connectivity is defined as the probability that there is at least one valid transmission path between the source node and the destination node at any time, reflecting the basic communication capability of the network.

Network robustness is defined as the probability that the source node and destination node remain connected under a given node failure ratio. To ensure the statistical significance of the evaluation results, 20 independent node failure tests are performed within each simulation run, and the average connectivity probability is taken as the final robustness value for that run. The node failure ratio is dynamically adjusted according to the real-time topological density of the network: 20% when the average node degree is greater than 10, 18% when it is between 6 and 10, and 15% when it is less than or equal to 6.

The average degree is defined as the average number of neighbors per node in the network, reflecting the connection density and redundancy of the network. In this study, it is controlled at about 2.9 through the topology decision mechanism. The average link conductivity is defined as the average value of the conductivity of all valid links in the network, reflecting the overall transmission quality of the network. The number of available paths is defined as the number of valid disjoint paths between the source node and the destination node, reflecting the path redundancy of the network. This study sets the maximum number of paths to 3, that is, 1 primary path and 2 backup paths.

Based on the above model, the construction of UVC/RF heterogeneous UAV-resilient networks can be formalized as a multi-objective optimization problem with multiple constraints: maximize the comprehensive network resilience (i.e., the average value of the resilience index over the entire simulation period), minimize the total network energy consumption, and minimize the average end-to-end transmission delay. The constraints to be satisfied include link accessibility (Section 2.3), upper limits on node connections (source/destination nodes ≤ 8, relay nodes ≤ 6), non-negative node residual energy, and conductivity between 0.05 and 1.0. This is an NP-hard combinatorial optimization problem characterized by high dimension, multiple constraints, and dynamics, and is difficult to solve using traditional mathematical optimization methods within a limited time. The slime mould algorithm, with its distributed computing, self-organization, adaptability, and strong robustness, can effectively deal with such dynamic optimization problems. Formal NP-hardness proof: The resilient topology construction problem under UVC/RF heterogeneous constraints can be reduced to the classical k-connectivity augmentation problem, a well-known NP-hard combinatorial optimization problem. Formally, the resilient topology construction problem can be reduced to the minimum-cost k-vertex-connected spanning subgraph problem, a well-established NP-hard combinatorial optimization problem for $k\ge 2$. Our formulation introduces additional constraints, including heterogeneous edge costs, node degree limits, and energy-aware weighting, which further increase computational hardness. This provides a formal theoretical justification for adopting a swarm intelligence heuristic approach.

3. Design of the UVC-SMA

Targeting the multi-objective optimization problem formulated in Section II, UVC-SMA is proposed with systematic enhancements to traditional SMA. By simulating the foraging and self-organizing behavior of Physarum polycephalum, the algorithm enables distributed heterogeneous UAV topology construction and routing optimization. Three core innovations are integrated: network state adaptive parameter tuning, hybrid degree–betweenness critical node protection, and conductivity-based K-disjoint multipath routing.

Table 1. UVC-SMA algorithm parameters.

Parameter Symbol	Parameter Name	Value Range	Baseline Value
αbase	Base tube expansion rate	[0.1, 0.25]	0.15
βbase	Base tube contraction rate	[0.01, 0.05]	0.03
${\mathsf{\gamma }}_{\mathrm{base}}$	Base pheromone evaporation coefficient	[0.9, 0.98]	0.95
${\mathsf{\theta }}_{\mathrm{base}}$	Base topology decision threshold	[0.2, 0.5]	0.35
Q	Pheromone intensity	[1.0, 2.0]	1.5
K	Number of multipath routes	[2, 5]	3
wd/wb	Degree-betweenness weight ratio	[0.5/0.5, 0.8/0.2]	0.7/0.3

summarizes all standardized algorithm parameters.

3.1. Overall Framework of the UVC-SMA Algorithm

This algorithm is designed to meet the demand for highly reliable communication in UVC/RF heterogeneous UAV swarms in dynamic environments. It achieves self-organizing optimization and resilience enhancement of distributed network topologies by simulating the adaptive expansion and contraction of protoplasmic tubes during the foraging process of Physarum polycephalum. The inputs to the algorithm include node 3D positions, mobility speeds, communication parameters, etc. It integrates four mechanisms: energy-aware heterogeneous link cost, network state-driven parameter adaptation, active key node protection, and multipath redundant routing, and outputs the optimal topology and routing paths that meet resilience and energy efficiency constraints.

The algorithm first completes global initialization: the slime mold tube conductivity matrix C_ij is randomly initialized to 0.3~1.0, node energy, pressure field and data rate vectors are assigned initial values, and the source node pressure P_source = 10 and destination node pressure P_dest = −5 are set to form the initial driving force for protoplasmic flow. In the main iteration, to simulate dynamic UAV mobility, node positions are updated only when the number of iterations is greater than 30 and every 20 iterations, and boundary damping reflection is adopted. Then, parameter adaptive adjustment is performed: according to the current network robustness, average degree and primary path length, the algorithm dynamically adjusts the tube expansion rate α, contraction rate β, evaporation coefficient $\gamma$ and topology decision threshold $\theta$. The preset base parameters are used in the initial stage.

The slime mold growth dynamic engine is the core computing module. The algorithm first updates the pressure of all relay nodes (determined by the sum of its own data rate and neighbor conductivity), and then calculates the protoplasmic flow rate of each tube based on Poiseuille’s law, with the flow direction determined by the pressure difference at both ends. When the flow is positive, the tube expands by α; when the flow is negative, the tube contracts by β. At the same time, pheromone evaporation and distance reward are introduced to make neighboring nodes more likely to establish stable connections. All conductivities are constrained within [0.05, 1.0] and remain symmetric. Based on the updated conductivity, the topology decision filters candidate links above the threshold $\theta$, determines the link type according to UVC/RF accessibility, and imposes differentiated limits on the maximum number of node connections (source/destination nodes ≤ 8, relay nodes ≤ 6) to avoid load overload.

To enhance survivability, active key node protection is triggered when the number of iterations is greater than 50 and every 30 iterations: key nodes are identified with 7:3 weighted degree centrality and betweenness centrality, and up to 3 redundant protection links are established for them, each consuming 5 J of energy from both end nodes. Energy evolution calculates consumption according to link type: 0.5 J for UVC links and 0.3 J for RF links, with energy consumption equally shared by both ends; nodes fail when energy drops to 0. Based on the current topology, an improved Dijkstra and a simplified Yen’s algorithm are used to generate K = 3 disjoint paths (1 primary path and 2 backup paths), using the reciprocal of conductivity, 1/C_ij, as the cost to achieve millisecond-level switching.

At the end of each iteration, robustness and connectivity are evaluated through 20 independent random node failure tests. When the number of iterations is greater than 80, the robustness standard deviation of the last 20 iterations is <0.03, the average degree standard deviation is <0.2, and the source-destination connectivity is always 1, the algorithm converges and terminates early; otherwise, it continues to the maximum number of iterations T_max. Finally, the optimal primary path, backup path set, optimal robustness, average residual energy, and hop count of the optimal path are output.

The UVC-SMA algorithm adopts a fully distributed architecture intended for embedded on-board deployment across UAV platforms and operates without any centralized control node for its core functional loop. The previously cited per-iteration complexity of O(n²), where n stands for the number of one-hop neighbors surrounding each node, applies only to the core slime mold growth and conductivity update engine, which covers three sub-processes: pressure field update, flow rate calculation, and conductivity adjustment. This core engine can run in a completely distributed fashion across all nodes in the swarm: each UAV stores its own local copy of the conductivity matrix, neighbor position table, and residual energy status locally, and performs all core computations using only information exchanged with its immediate adjacent nodes, with only periodic low-rate beacon transmissions required between neighboring nodes to maintain state consistency.

Supplementary operations, including key node protection, K-shortest-path computation, and robustness evaluation are designed as modular add-on functions with differentiated execution frequencies, which is fully consistent with the step sequence specified in the pseudocode in

Table 2. Energy-aware adaptive slime mold algorithm for heterogeneous UAV-resilient network construction (UVC-SMA).

UVC-SMA

Input: Node 3D position sequence pi(t), velocity sequence vi(t), communication parameters Ruv, Rrf, Hozone, algorithm parameters ${\mathrm{T}}_{\max }, {\mathsf{\alpha }}_{\mathrm{base}}, {\mathsf{\beta }}_{\mathrm{base}}, {\mathsf{\gamma }}_{\mathrm{base}}$$, {\mathsf{\theta }}_{\mathrm{base}}$, Q, K energy parameters Einit, Econsume uvc, Econsume rf

Output: Optimal primary path from source to destination Pprimany, backup path set ${\mathrm{P}}_{\mathrm{backup}}, \mathrm{optimal} \mathrm{network} \mathrm{robustness} \mathrm{R}*, \mathrm{average} \mathrm{residual} \mathrm{energy} {\mathrm{E}}_{\mathrm{avg}}^{\mathrm{*}}$, optimal path hop count L*

1:  Initialization: conductivity matrix C ← 0.3~1.0, node energy E ← Einit, pressure P ← 0, data rate D ← 0

2:  Set source node pressure Psource ← 10, destination node pressure Pdest ← −5 3:  for iter = 1 to Tmax do 4:  if iter > 30 and mod(iter, 20) = 0 then

5:  Update node positions: pi← pi +vi · Δt (boundary damping reflection)

6:  end if

7:  if iter > 1 then

8:  Adaptively adjust parameters:$\mathsf{\alpha },\mathsf{\beta },\mathsf{\gamma },\mathsf{\theta }\leftarrow \mathrm{adaptive}\left(\mathrm{R},\overline{\mathrm{d}},{\mathrm{L}}_{\mathrm{path}}\right)$

9:  else

10:  $\mathsf{\alpha }\leftarrow {\mathsf{\alpha }}_{\mathrm{base}},\mathsf{\beta }\leftarrow {\mathsf{\beta }}_{\mathrm{base}},\mathsf{\gamma }\leftarrow {\mathsf{\gamma }}_{\mathrm{base}},\mathsf{\theta }\leftarrow {\mathsf{\theta }}_{\mathrm{base}}$

11:  end if

12:  Slime mold growth iteration: update node pressure field P

13:  for each link (i,j) do

14:  Calculate flow rate:${\mathrm{F}}_{\mathrm{i}\mathrm{j}}\leftarrow {\mathrm{C}}_{\mathrm{i}\mathrm{j}}\cdot \left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{j}}\right)$

15:   if${\mathrm{F}}_{\mathrm{i}\mathrm{j}}>0$ then

16:   Tube expansion:${\mathrm{C}}_{\mathrm{i}\mathrm{j}}\leftarrow {\mathrm{C}}_{\mathrm{i}\mathrm{j}}+\mathsf{\alpha }\cdot \left|{\mathrm{F}}_{\mathrm{i}\mathrm{j}}\right|\cdot \left(1-{\mathrm{C}}_{\mathrm{i}\mathrm{j}}\right)$

17:   else

18:   Tube contraction:${\mathrm{C}}_{\mathrm{i}\mathrm{j}}\leftarrow {\mathrm{C}}_{\mathrm{i}\mathrm{j}}-\mathsf{\beta }\cdot \left|{\mathrm{F}}_{\mathrm{i}\mathrm{j}}\right|\cdot {\mathrm{C}}_{\mathrm{i}\mathrm{j}}$

19:   end if

20:   Conductivity update:${\mathrm{C}}_{\mathrm{i}\mathrm{j}}\leftarrow \mathsf{\gamma }\cdot {\mathrm{C}}_{\mathrm{i}\mathrm{j}};{\mathrm{C}}_{\mathrm{i}\mathrm{j}}\leftarrow {\mathrm{C}}_{\mathrm{i}\mathrm{j}}+\left(1-\mathsf{\gamma }\right)\cdot \mathrm{Q}/\left(1+{\mathrm{d}}_{\mathrm{i}\mathrm{j}}\right)$

21:   Constrain conductivity: clamp ${\mathrm{C}}_{\mathrm{i}\mathrm{j}}\in \left[0.05,1.0\right]$, maintain matrix symmetry

22:   end for

23:   Topology decision: generate adjacency matrix and link type Ltp (based on $\mathsf{\theta }$ and accessibility)

24:   if iter > 50 and mod(iter,30) = 0 then

25:  Key node protection: degree-betweenness weighted identification Si, add redundant links and update energy E

26:  end if

27:  Energy update:$\mathrm{E}\leftarrow \mathrm{E}-{\displaystyle \frac{1}{2}}\sum \left({\mathrm{E}}_{\mathrm{consume}\_\mathrm{uvc}}\cdot \mathbb{I}\left(\mathrm{L}=1\right)+{\mathrm{E}}_{\mathrm{consume}\_\mathrm{rf}}\cdot \mathbb{I}\left(\mathrm{L}=2\right)\right)$

28:  K-shortest path generation: solve Pprimary and Pbackup based on 1/Cij

29:  Robustness evaluation: random node failure test, calculate Rcur and connectivity ${\mathsf{\xi }}_{\mathrm{cur}}$

30:  if iter > 80 and convergence conditions are met then

31:  break

32:  end if

33:  end for

34:  return optimal primary path Pprimary, backup paths Pbackup, ${\mathrm{R}}^{\mathrm{*}},{\mathrm{E}}_{\mathrm{avg}}^{\mathrm{*}},{\mathrm{L}}^{\mathrm{*}}$

. Key node protection is triggered only every 30 iterations, remains inactive before the 50th iteration, and the global betweenness centrality calculation it relies on functions as a low-frequency offline post-processing step. K-shortest-path generation updates at every iteration but operates entirely on each node’s local conductivity matrix and does not depend on centralized coordination or global network information. Robustness evaluation is conducted at each iteration exclusively for performance monitoring and result verification and is not an essential component for real-time routing operation; this module can be turned off in actual on-board deployment to further reduce computational load.

The full end-to-end complexity that accounts for all auxiliary modules amounts to O(N³) per evaluation window, where N denotes the total number of nodes in the entire network. For real-time on-board operation scenarios, only the core O(n²) engine needs to run continuously on each node.

The core engine alone meets the real-time routing update requirements of on-board embedded platforms, while fully distributed on-board implementation of all auxiliary modules remains part of our future work.

Under the 50-node scale, the core conductivity matrix occupies less than 50 KB of memory. Combined with the low per-iteration computational overhead, this result theoretically supports the feasibility of stable deployment on low-cost embedded microcontroller units (MCUs) commonly used in small UAVs.

To validate the real-time performance of the algorithm on low-cost on-board platforms, we conduct runtime measurements across three typical node scales (20, 50, and 80 nodes) on a standard embedded microcontroller unit (ARM Cortex-M4, 168 MHz, 128 KB SRAM). The test targets the core per-iteration slime mold growth engine, which is the time-critical module executed at every iteration.

The measured average per-iteration runtime is 0.82 ms for the 20-node scale, 2.10 ms for the 50-node baseline scale, and 4.58 ms for the 80-node scale. The runtime grows approximately quadratically with node count, consistent with the theoretical O(n²) complexity analysis. Even at the 80-node scale, the per-iteration latency is far shorter than the 2 s topology update interval, ensuring that the algorithm completes all core computations within each time slot and maintains stable tracking of dynamic topology changes.

The four mechanisms collaborate for optimization to achieve the global optimum of network resilience, energy efficiency and transmission performance under dynamic topology and random node failure scenarios. The pseudocode of the algorithm is shown in Table 2.

3.2. Design of Core Modules

3.2.1. Network State-Driven Adaptive Parameter Adjustment Mechanism

Conventional slime mold algorithms adopt fixed core parameter configurations, making it difficult for them to adapt to the dynamic topology changes of UAV networks. To solve this problem, this paper proposes a network state-driven adaptive parameter adjustment mechanism, which dynamically associates the tube expansion rate α, contraction rate β, pheromone evaporation coefficient $\gamma ,$ and topology decision threshold $\theta$ with the real-time operation status of the network, realizing a dynamic balance between global exploration and local exploitation capabilities. Parameter adjustment is performed at the beginning of each iteration. In the initial stage (the number of iterations less than 20), the base parameter configuration α₀ = 0.15, β₀ = 0.03, ${\gamma }_0=0.95$, ${\theta }_0=0.35$ is adopted. When the number of iterations is greater than 20, parameters are dynamically adjusted according to the network state.

According to network operation characteristics, network states are divided into four typical scenarios, and the corresponding parameter adjustment rules are designed. Parameters are updated at the beginning of each iteration using fixed step sizes: 0.01 per iteration for α, β, and $\theta$, and 0.005 for $\gamma$. An explicit priority order is defined for the four state triggers to handle simultaneous activation. When multiple conditions are met at the same time, the highest-priority rule is applied first, and lower-priority adjustments are executed only if parameters remain within the defined boundary ranges. The lowest-priority low connectivity state applies when robustness is below 0.7 and average degree is below 3, indicating insufficient network connectivity: the tube expansion rate is increased, contraction rate decreased, and topology decision threshold lowered to enhance the algorithm’s global exploration capability. The second-priority high redundancy state applies when robustness exceeds 0.9 and average degree is above 4, indicating excessively high connection redundancy: the expansion rate is decreased, contraction rate increased, and threshold raised to enhance local exploitation. The third-priority deteriorating state applies when robustness shows a downward trend over 10 consecutive iterations, and current robustness is below 0.8: the expansion rate is increased and the threshold is lowered to rapidly restore connectivity. The highest-priority low efficiency state applies when the length of the primary path exceeds 5 hops, and the average degree is below 4: the threshold is lowered to increase connection density and shorten transmission paths. Strict boundary constraints are enforced for all parameters to ensure algorithm stability: $\alpha \in \left[0.1,0.25\right]$, $\beta \in \left[0.01,0.05\right]$, $\gamma \in \left[0.9,0.98\right]$, $\theta \in \left[0.2,0.5\right]$. This mechanism enables the algorithm to automatically adjust behavior patterns according to network states and maintain excellent optimization performance in dynamic topology scenarios. The specific operation of the dynamic adjustment mechanism is shown in Figure 5.

3.2.2. Slime Mold Growth Dynamic Engine

The slime mold growth dynamic engine is the core of the UVC-SMA algorithm, which achieves the adaptive optimization of network topology by simulating the expansion and contraction process of protoplasmic tubes. The engine consists of three interconnected links: node pressure field establishment, tube flow calculation, and conductivity update.

First, establish the node pressure field. The source node and destination node in the network are set as high-pressure and low-pressure nodes, respectively, providing driving force for protoplasmic flow. The pressure of the source node is fixed at P_S = 10, and the pressure of the destination node is fixed at P_D = −5.

The energy-aware link cost defined in Equations (2) and (3) exerts its influence on topology formation and routing through a two-level mapping mechanism embedded in the conductivity evolution framework. At the topology evolution level, the link cost implicitly sets the initial conductivity distribution and modulates the conductivity update dynamics: links with lower energy-aware cost are assigned higher initial conductivity and receive stronger distance-based reward during iterative updates, so they are preferentially retained in the subsequent topology decision step. In this way, the energy penalty factor naturally suppresses low-energy nodes from being selected as relays, as high cost reduces their conductivity and thus their probability of included in the active topology. The pressure of relay nodes is jointly determined by the conductivity of their neighbor nodes and their own data rate:

$$P_i(t)=D_i-0.1{\displaystyle \sum _{j=1}^n}{C}_{ij}(t)$$

(4)

where D_i is the data rate of node i (source node set to 10, destination node set to −5, relay nodes random between 0.3 and 1.0), and C_ij(t) is the tube conductivity between node i and node j. This pressure field can guide protoplasm to flow from the source node to the destination node, and at the same time make nodes with higher data rate obtain higher pressure and prioritize the establishment of transmission paths.

The pressure field defined in Equation (4) is a heuristic potential that drives protoplasmic flow in the slime mold algorithm, rather than a physical communication quantity such as voltage or hydraulic pressure. It follows the standard Physarum-inspired routing framework, where pressure differences across links drive protoplasmic flow, and flow, in turn, modulates link conductivity through the positive feedback mechanism.

The differentiated value scales across source, destination and relay nodes are an intentional design of the global flow-driving mechanism. The fixed high pressure at the source node and fixed low pressure at the destination node establish a steady global gradient that directs overall flow from source to destination. For relay nodes, the pressure is dynamically determined by both the local data injection rate and the aggregated conductivity of neighboring links, so that nodes with higher traffic demand and better connectivity naturally maintain higher pressure and prioritize path establishment.

The data rate term and the neighbor conductivity term are normalized to the same order of magnitude through the 0.1 scaling coefficient, ensuring balanced contributions of both factors to the pressure field. The stability of this scaling coefficient is verified through quantitative sensitivity analysis presented in Section 4.3.3.

Based on Poiseuille’s law, the protoplasmic flow rate in the tube is jointly determined by the pressure difference between the two end nodes and the tube conductivity [29]:

$$F_{ij}\left(t\right)=C_{ij}\left(t\right)\cdot \left(P_i\right(t)-P_j(t\left)\right)$$

(5)

where F_ij(t) is the flow rate from node i to node j. The sign of the flow rate indicates the flow direction, and the absolute value indicates the flow magnitude.

Following the flow positive feedback mechanism, tubes with net inflow expand, and tubes with net outflow contract. The flow F_ij is a directed quantity defined from node i to node j, but the conductivity update is enforced to remain symmetric at all times, such that C_ij = C_ji independent of node ordering. Specifically, if $F_{ij}>0$ (net flow from i to j), the link conductivity increases by $\alpha \cdot \left|F_{ij}\right|\cdot \left(1-C_{ij}\right)$; if $F_{ij}<0$ (net flow from j to i), the conductivity decreases by $\beta \cdot \left|F_{ij}\right|\cdot C_{ij}$. The identical adjustment is applied to C_ji simultaneously to preserve symmetry after each update step. The conductivity update rule is [30] as follows:

$$C_{ij}(t+1)=\left\{\begin{array}{cc}{C}_{ij}\left(t\right)+\alpha \cdot \mid F_{ij}\left(t\right)\mid \cdot (1-C_{ij}(t\left)\right),& F_{ij}\left(t\right)>0,\\ C_{ij}\left(t\right)-\beta \cdot \mid F_{ij}\left(t\right)\mid \cdot C_{ij}\left(t\right),& F_{ij}\left(t\right)<0.\end{array}\right.$$

(6)

with $C_{ij}\left(t+1\right)=C_{ji}\left(t+1\right)$ enforced after each update step.

Following the flow-based expansion and contraction step described in Equation (6), two additional operations are applied sequentially to every link conductivity, in exact accordance with the execution order in the pseudocode (Table 2, Line 20): first, uniform pheromone evaporation, then distance-based reward.

First, pheromone evaporation is applied to attenuate all conductivities uniformly on the basis of the expanded/contracted values:

$$C_{ij}\left(t+1\right)=\gamma \cdot C_{ij}{\left(t+1\right)}_{\mathrm{after} \mathrm{expansion} \mathrm{and} \mathrm{contraction}}$$

(7a)

Then, a distance-based reward is added to strengthen shorter links, consistent with the distance-dependent attenuation characteristic of wireless channels:

$$C_{ij}\left(t+1\right)=C_{ij}\left(t+1\right)+\left(1-\gamma \right)\cdot {\displaystyle \frac{Q}{1+d_{ij}\left(t\right)}}$$

(7b)

After both steps, the conductivity of each link is clamped to the interval [0.05, 1.0], and the conductivity matrix is enforced to remain symmetric.

Where Q denotes the pheromone intensity, and d_ij(t) denotes the Euclidean distance between node i and node j at time t. This mechanism makes spatially closer nodes more likely to form and maintain stable connections, which is consistent with the operational properties of practical communication networks.

After both steps, the conductivity of each link is clamped to the interval [0.05, 1.0], and the conductivity matrix is enforced to remain symmetric.

Based on the bounded conductivity property and positive feedback mechanism of the slime mold growth dynamic, the convergence of the proposed algorithm can be formally analyzed following the standard martingale convergence framework for stochastic search heuristics.

The conductivity of each link is bounded within [0.05, 1.0], and the positive feedback mechanism ensures that links with higher flow rates monotonically increase in conductivity, while links with lower flow rates monotonically decrease. Since the total number of links is finite, and the conductivity values are bounded, the sequence of network conductivity matrices forms a bounded stochastic process with monotonic improvement in the objective function. By the martingale convergence theorem, as the number of iterations approaches infinity, the core slime mold growth dynamics converge almost surely to a locally optimal stationary topology.

For the full constrained problem with degree limits, energy penalties, and adaptive parameters, global optimality is not theoretically guaranteed. However, empirical results across 10 independent random seeds consistently converge to the same stable solution with less than 1.2% variance in robustness, demonstrating strong practical convergence.

3.2.3. Conductivity-Driven Topology Generation Mechanism

Based on the conductivity matrix formed during the slime mold growth process, this paper proposes a conductivity-driven topology generation mechanism, which controls the network connection density while ensuring network connectivity and survivability and avoids excessive energy consumption. The specific steps are as follows: first, filter all candidate links with conductivity higher than the current topology decision threshold $\theta$; for each candidate link, determine its link type according to the link accessibility criteria (if both UVC and RF link accessibility conditions are met, prioritize the link with the lower cost); sort all candidate links by conductivity in descending order, and prioritize establishing links with higher transmission quality; to avoid node communication load overload, impose differentiated limits on the maximum number of node connections (source and destination nodes establish up to 8 connections, ordinary relay nodes establish up to 6 connections); establish connections sequentially from high to low conductivity until all nodes reach the maximum number of connections or all candidate links are processed.

This mechanism can automatically retain the most important links for network transmission while eliminating links with high redundancy, achieving the optimal balance between network performance and resource consumption. The simulation results show that this mechanism can stabilize the average node degree in the optimal interval around 2.9.

3.2.4. Active Key Node Protection Mechanism with Hybrid Degree-Betweenness Weighting

Most traditional routing algorithms adopt the passive optimization paradigm of “failure occurrence–route reconfiguration”, which cannot fundamentally avoid single-point-of-failure risks. To solve this problem, this paper proposes an active key node protection mechanism based on hybrid degree-betweenness weighting, shifting the focus of network resilience optimization from post-failure repair to pre-failure prevention. This mechanism is executed every 30 iterations and only activated after the number of iterations exceeds 50.

First, construct a node importance evaluation system through weighted fusion of degree centrality and betweenness centrality:

$$S_i=0.7\cdot {\displaystyle \frac{d_i}{\mathrm{m}\mathrm{a}\mathrm{x}\left(d_i\right)}}+0.3\cdot {\displaystyle \frac{b_i}{\mathrm{m}\mathrm{a}\mathrm{x}\left(b_i\right)}}$$

(8)

where d_i is the degree centrality of node i, and b_i is the betweenness centrality of node i (simplified calculation based on the source-destination shortest path). The weight coefficients 0.7 and 0.3, respectively, reflect the contribution of local connection density and global routing bottleneck to node importance. Then, filter nodes with importance score greater than 0.3 from non-endpoint nodes as key nodes and select up to 5 for protection.

Screen optimal redundant connection candidates for each key node. Candidate nodes must meet the following conditions: distance from the key node less than 250 m, current number of connections less than 6, and residual energy greater than 100 J. The score of candidate connections is jointly determined by conductivity, distance factor and energy factor: ${\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}_{ij}=C_{ij}\left(t\right)\cdot \left(1-d_{ij}/300\right)\cdot \min \left(E_i,E_j\right)/500$. Select the candidate node with the highest score to establish a protection connection, and each key node can add up to 3 protection connections. For each additional protection connection, the nodes at both ends of the connection consume 5 J of energy each for link establishment and maintenance.

This mechanism can effectively improve the survivability of key nodes without significantly increasing the overall network energy consumption, and greatly reduce the probability of network partitioning. The simulation results show that after introducing this mechanism, the network robustness is improved by 7.6% on average.

It is worth noting that adding redundant protection links for key nodes introduces non-negligible energy overhead. We conduct comparative experiments for different maximum numbers of allowable protection connections per key-node (0, 1, 2, 3) across low-energy, baseline-energy, and high-energy scenarios. When allowing up to 3 protection links (baseline setting in this work), the network obtains an average robustness gain of 7.6%, accompanied by a 6.4% reduction in overall network lifetime. Restricting to maximum 2 protection connections yields 5.1% robustness improvement while only sacrificing 3.2% network lifetime, which is more suitable for energy-constrained deployments. Setting zero additional protection links eliminates this extra energy cost but removes most of the proactive resilience gain. The maximum-protection-connection parameter serves as an adjustable trade-off knob for practical configuration, balancing survivability requirements and the available node energy budget.

3.2.5. Conductivity-Based K-Shortest Multipath Routing Generation

Traditional slime mold algorithms can only generate a single optimal transmission path, which cannot meet the highly reliable communication requirements in extreme scenarios. To solve this problem, this paper proposes a conductivity-based K-shortest multipath routing generation method, which synchronously generates primary and backup paths based on slime mold topology evolution. This method uses the reciprocal of conductivity as the path cost metric, meaning links with higher conductivity correspond to lower path cost and higher energy efficiency. This routing metric is fully consistent with the energy-aware cost structure defined earlier, so minimizing the sum of 1/C_ij along a path is equivalent to selecting a high-quality, energy-efficient transmission route.

First, use the improved Dijkstra algorithm to solve the shortest path from the source node to the destination node as the primary path:

$$\mathrm{if} \mathrm{dist}[v]>\mathrm{dist}[u]+{\displaystyle \frac{1}{C_{uv}\left(t\right)}} \mathrm{then} \mathrm{dist}[v]=\mathrm{dist}[u]+{\displaystyle \frac{1}{C_{uv}\left(t\right)}}$$

(9)

where $\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\left[v\right]$ is the shortest path cost from the source node to node v. Then use the simplified Yen’s algorithm to generate K − 1 backup paths: for each generated path, sequentially block each link in the path, recalculate the shortest path, and filter candidate paths that share no links with the generated paths. Sort all candidate paths by cost from low to high, and select the first K − 1 as backup paths. This paper sets K = 3, that is, it generates 1 primary path and 2 backup paths.

This method can quickly switch to available backup paths when the primary path is disconnected due to link interruption or node failure, without re-initiating route discovery. The reported failover delay refers to routing-layer path switching latency, defined as the time from failure detection to the backup path being activated in the local forwarding table. Under the assumption of an ideal MAC with no retransmission overhead, this delay consists of failure detection latency (negligible for precomputed backup paths, as link conductivity drops are detected locally within one iteration) and forwarding table update time. On typical low-power embedded microcontrollers, the forwarding table update for 3 precomputed paths takes approximately 5–10 ms, consistent with the reported millisecond-level values. This delay does not include physical-layer retransmission time, packet queuing delay, or end-to-end propagation delay. The K paths in operation are shown in Figure 6.

4. Simulation Results and Performance Analysis

4.1. Simulation Environment and Parameter Settings

All simulation network scenarios comprise 50 heterogeneous UAV nodes (except for node scale expansion experiments), with nodes randomly distributed in a 300 m × 300 m × 150 m three-dimensional space. The basic horizontal mobility speed of nodes is 1.0 m/s, and the vertical speed is 0.1 m/s. The boundary is processed with reflection and damping. The main simulation parameters are shown in

Table 3. Simulation parameters.

Parameter Category	Value	Parameter Category	Value
Network Topology		Communication Parameters
Number of UAV nodes N	50	UVC energy consumption	0.5 J/s
Source node coordinates	(0, 0, 50)	RF energy consumption	0.3 J/s
Destination coordinates	(300, 300, 50)	Energy Model
Basic mobility speed	(1.0, 1.0, 0.1) m/s	Source/destination	1000 J
Communication Parameters		Relay nodes	500~800 J
Maximum UVC range Ruv	150 m	Robustness Evaluation
Maximum RF range Rrf	300 m	Random failure ratio	15%~20%
UVC altitude threshold HUV	100 m	Failure test repetitions	20
Minimum UVC distance	50 m
Minimum RF distance	20 m

, which are completely consistent with the initialization values in the MATLAB code to ensure the reproducibility of experiments.

For performance evaluation, the following packet-level communication parameters and traffic model are adopted consistently across all algorithms. A constant bit rate (CBR) traffic model is used: the source node generates data packets continuously at a fixed rate, with a fixed packet size of 1000 bits. The RF link transmission rate is 1 Mbps, and the UVC link transmission rate is 100 kbps. For topology-level routing evaluation, the media access control (MAC) layer adopts an ideal channel access assumption without collisions. Each node maintains a single first-in-first-out (FIFO) queue with negligible per-hop processing delay. No retransmission is performed during path failover, and routing-layer switching relies on pre-computed backup paths. The reported millisecond-level failover delay refers to routing-table switching latency at the network layer, which operates on a completely different time scale from the 2 s simulation iteration step. The 2 s iteration interval defines the topology update and node mobility time step, while failover is a local software operation on the embedded microcontroller: link conductivity drops are detected locally within one iteration, and the forwarding table update for three precomputed paths takes approximately 5–10 ms on typical low-power embedded MCUs. This switching delay is orders of magnitude shorter than the 2 s topology update interval, meaning failover completes fully within a single iteration cycle and does not conflict with the simulation time step definition. This delay does not include physical-layer retransmission time, packet queuing delay, or end-to-end propagation delay.

4.2. Comparison Algorithms and Performance Evaluation Indicators

This section constructs a core evaluation system from three dimensions: network survivability, energy efficiency, and topological structure. For horizontal comparison with similar algorithms, it further supplements transmission service quality and fault response capability indicators to form a complete performance verification framework. All experiments are repeated 10 times with independent random seeds for node initialization and mobility to ensure statistical robustness. All performance indicators (robustness, energy, degree, PDR) are reported as mean ± standard deviation across these 10 independent simulation runs. The 20 failure tests used for robustness evaluation are intra-run injections, not separate simulation runs. For cross-algorithm comparisons, paired two-sample t-tests are used instead of independent t-tests, as all algorithms are tested under identical initial conditions, node positions, and random seed sequences. A significance level of α = 0.05 is used for all statistical tests, and 95% confidence intervals are provided for key cross-algorithm performance differences.

For fair comparison across all algorithms, a unified two-tier stopping criterion framework is adopted consistently across all scenarios and all benchmark algorithms.

First, for all ablation experiments and cross-algorithm comparison experiments, all algorithms run for exactly 200 fixed iterations without early termination, and all performance metrics, including residual energy, robustness and the packet delivery ratio (PDR), are uniformly recorded at the 200th iteration. This eliminates bias introduced by different convergence speeds when comparing energy consumption and steady-state performance.

Second, the early convergence stopping rule used in standalone algorithm verification follows an identical 20-iteration sliding window framework across all configurations: convergence is declared when the robustness standard deviation over the last 20 iterations is below 0.03, the average node degree standard deviation is below 0.2, and source-destination connectivity remains at 1 for all 20 iterations. This rule is applied identically to UVC-SMA, all ablation variants, and all benchmark algorithms, with no algorithm-specific adjustment.

The first core indicator is network robustness R, defined as the probability that the source and destination nodes remain connected under a given random node failure ratio (the failure ratio is dynamically adjusted to 15%~20% according to the real-time average node degree of the network). Each group of experiments repeats 20 independent random failure tests and takes the average value. This indicator directly reflects the network’s survivability under extreme disturbances.

The second core indicator is average residual energy, E_avg, that is, the arithmetic mean of residual energy of all nodes when the algorithm converges, which is used to measure the network energy utilization efficiency and life cycle length.

The third core indicator is average node degree d = 2L/n, where L is the total number of valid links and n is the total number of nodes. This indicator reflects the connection density and topological structure balance of the network. Excessively high average degree leads to energy waste, while excessively low affects connectivity.

Two extended indicators are supplemented for horizontal comparison: one is the packet delivery ratio (PDR), defined as the ratio of the number of data packets successfully received by the destination node to the total number sent by the source node, which quantifies the actual end-to-end transmission service quality; the other is failover delay, defined as the total duration from primary path failure trigger to backup path resuming normal communication, which reflects the network’s dynamic response speed to failures.

4.3. Simulation Results and In-Depth Analysis

4.3.1. Horizontal Comparison with Traditional Slime Mold Algorithm

Under the same network scale, energy configuration, communication parameters and environmental disturbances, the traditional slime mold algorithm is compared with the UVC-SMA algorithm. Each group of experiments is repeated 10 times, and the results are reported as mean ± standard deviation.

The results demonstrate that the conventional slime mold algorithm fails to achieve stable convergence within 200 iterations, with a final robustness of 0.75 ± 0.028, average residual energy of 382.7 ± 11.3 J, and average node degree as high as 3.51 ± 0.12. The UVC-SMA algorithm fully converges at 200 iterations, with a final robustness of 1.000 ± 0.000, an average residual energy increased to 457.3 ± 9.6 J, and an average node degree optimized to 2.92 ± 0.07.

Compared with the traditional slime mold algorithm, UVC-SMA improves robustness by 33.3%, increases average residual energy by 19.5%, and reduces average node degree by 16.8%. The 95% confidence intervals for the three improvements are [28.7%, 37.9%], [15.2%, 23.8%], and [13.1%, 20.5%], respectively. Two-sample t-tests confirm that all three performance differences are statistically significant (p < 0.01).

The experiments confirm that the energy-aware link cost can automatically avoid low-energy nodes and avoid energy hotspots; the dynamic parameter adaptation mechanism adjusts the balance between exploration and exploitation in real time according to network status and accelerates convergence; key node protection accurately identifies and reinforces topological cores and greatly improves survivability; multipath redundant routing switches quickly when the primary path fails and ensures communication continuity. The traditional slime mold algorithm, lacking the above mechanisms, has excessively high link redundancy, fast energy consumption, and vulnerable key nodes, so its comprehensive performance is significantly lower than UVC-SMA. Figure 7 illustrates the final robustness comparison between the two algorithms, while Figure 8 presents the comparison of average residual energy and average node degree, with the two metrics displayed in panel (a) and panel (b), respectively. The iteration count at convergence is reported quantitatively in the preceding analysis.

4.3.2. Ablation Experiments of Each Improved Module

To quantify the contribution of each improved module, five groups of progressive ablation comparisons are designed: traditional SMA; energy-aware improved SMA (SMA-E), which introduces only the heterogeneous link energy penalty mechanism; energy-aware adaptive-parameter improved SMA (SMA-EA), which adds network state-driven dynamic parameter adjustment on top of SMA-E; energy-aware adaptive parameter with key node protection improved SMA (SMA-EAK), which further adds the hybrid degree-betweenness weighted key node protection framework on top of SMA-EA; and finally the complete UVC-SMA with multipath redundancy. Network scale, energy configuration, and environmental disturbance are kept consistent across all groups, and each group includes 10 independent repeated simulations.

The results show that traditional SMA does not converge within 200 iterations, with a robustness of 0.75 ± 0.028, an average residual energy of 382.7 ± 11.3 J, and an average degree of 3.51 ± 0.12. After introducing energy awareness, robustness rises to 0.82 ± 0.024, the average residual energy reaches 421.5 ± 10.1 J, and the average degree drops to 3.28 ± 0.10. After adding dynamic parameter adaptation, the iteration count at convergence is reduced to 185 ± 6, with robustness of 0.92 ± 0.018, residual energy of 438.9 ± 9.2 J, and degree of 3.05 ± 0.08. After adding key node protection, iteration count at convergence are 172 ± 5, with robustness of 0.99 ± 0.007, residual energy of 449.6 ± 8.8 J, and degree of 2.95 ± 0.07. The complete UVC-SMA with multipath redundancy reaches a robustness of 1.000 ± 0.000, residual energy of 457.3 ± 9.6 J, and degree of 2.92 ± 0.07 at 200 iterations.

All module contributions are statistically significant (p < 0.05), indicating that each mechanism has independent and superimposed performance gains.

All four modules produce significant positive contributions and have synergistic effects: energy awareness mainly improves energy efficiency, dynamic parameters accelerate convergence, key node protection enhances robustness, and multipath improves communication reliability. The complete algorithm improves robustness by 33.3%, average residual energy by 19.5%, and average node degree by 16.8% compared with traditional SMA. Figure 9 presents the robustness comparison across all ablation configurations, and Figure 10 summarizes the corresponding energy and degree metrics, with average residual energy in panel (a) and average node degree in panel (b).

4.3.3. Parameter Performance Analysis

To evaluate the generalization ability of UVC-SMA under different network conditions, respectively change the node scale, node mobility speed, and node initial energy.

(1)

Influence of Node Scale

Experiments are carried out for three typical node scales: 20, 50, and 80. Each group includes 10 independent repeated simulations, and the robustness evolution curve over the full iteration period is shown in Figure 11.

From the evolution trend, the algorithm shows convergence characteristics of rapid rise and gradual stabilization under all three scales. The 20-node small-scale scenario is limited by topological redundancy, with low initial robustness. The final steady-state robustness is 0.938 ± 0.015, the average residual energy is 511.4 ± 10.2 J, and the average degree is 2.90 ± 0.08. Under the 50-node baseline scenario, topological redundancy and energy cost achieve the optimal balance, and the steady-state robustness rises to a peak of 1.000 ± 0.000, with an average residual energy of 457.3 ± 9.6 J and an average degree of 2.92 ± 0.07. Under the 80-node medium-large scale scenario, link redundancy is significantly improved, and convergence speed is significantly accelerated. It enters the steady-state interval at about 95 iterations. The final steady-state robustness is maintained at 0.972 ± 0.011, the average residual energy is 556.1 ± 10.8 J, and the average degree is 2.90 ± 0.09.

Experiments show that node scale is positively correlated with convergence speed; link redundancy provided by high-density nodes can effectively offset the impact of local failures; 50 nodes are at the peak of service load, with the most significant energy consumption. The average degree of the algorithm is stable at around 2.9 under different scales, and the fluctuation range of 10 simulation results is less than 1.2%, indicating excellent topological construction balance. Figure 11 presents the robustness evolution trends, and Figure 12 shows the corresponding residual energy and node degree results, with the two metrics displayed in panel (a) and panel (b) respectively.

To further validate the parameter choices in the link cost model and pressure field formulation, we conduct additional sensitivity analysis on key weighting coefficients, in addition to the convergence threshold verification.

For the distance-to-height-difference weight ratio in Equation (2), tested ratios from 0.1/0.9 to 0.9/0.1 produce less than 2.1% variation in final robustness, verifying that the baseline 0.7/0.3 ratio is robust and not arbitrarily chosen. For the 0.1 scaling coefficient in Equation (4), values ranging from 0.05 to 0.2 yield less than 1.8% variation in final robustness, confirming a stable balance between the data rate and conductivity contributions to the pressure field.

To verify the robustness of the conclusions to threshold choices and Monte Carlo noise, we conduct sensitivity analysis on the convergence stopping thresholds. Three sets of threshold levels are tested across all node scale, mobility speed and initial energy scenarios: tight thresholds (robustness std < 0.02, degree std < 0.15), baseline thresholds (robustness std < 0.03, degree std < 0.2), and loose thresholds (robustness std < 0.04, degree std < 0.25).

The results show that the final steady-state robustness values differ by less than 1.2% across the three threshold settings, and the average node degree values differ by less than 0.8%. This confirms that the performance conclusions are robust to both threshold choices and inherent Monte Carlo noise in the random node failure tests.

(2)

Influence of Node Mobility Speed

Three sets of scenarios with speed coefficients of 0.2×, 0.5×, and 1.0× are constructed, each with 10 independent repeated simulations. The statistical results show that the low-speed scenario (0.2×) requires 200 iterations to reach stability, with a robustness of 0.900 ± 0.021, an average residual energy of 458.3 ± 9.8 J, and an average node degree of 2.88 ± 0.08. The medium-speed scenario (0.5×) also requires 200 iterations, with a robustness of 1.000 ± 0.000, an average residual energy of 457.3 ± 9.6 J, and an average node degree of 2.92 ± 0.07. The high-speed scenario (1.0×) converges in only 116 ± 4 iterations, with a robustness of 0.900 ± 0.023, an average residual energy of 552.8 ± 10.5 J, and an average node degree of 2.88 ± 0.09.

Under the drastic 1.5× speed coefficient scenario, rapid node movement induces frequent link breakages. The algorithm still maintains basic source–destination connectivity, but the steady-state robustness drops to 0.811 ± 0.026, with an average residual energy of 574.2 ± 11.3 J and an average node degree of 2.87 ± 0.09. The convergence speed further increases to 94 ± 5 iterations.

The algorithm exhibits excellent adaptive capability to dynamic topology changes: performance peaks at medium speed with full robustness; at high speed, it automatically enters a fast-response mode with greatly accelerated convergence.

For consistent cross-speed comparison, all energy, robustness, and degree metrics are recorded at the 200th iteration (equivalent to 400 s of physical time, with dt = 2.0 s per iteration) across all speed scenarios. The reported convergence iteration count reflects only convergence speed, not the measurement point of energy. Under this unified time framework, cross-speed energy comparisons are valid, as all scenarios share identical per-iteration energy consumption rates and total simulation duration. Under this standard, high-speed scenarios show slightly higher residual energy due to shorter effective topology formation time.

The fluctuation of average node degree across all speed settings is less than 1.4% over 10 simulation runs, indicating strong topological stability.

These results define the applicable mobility boundary of UVC-SMA: the algorithm maintains excellent robustness and stability for scenarios with a mobility speed coefficient ≤ 1.0×. Beyond this range, ultra-drastic mobility causes topology changes to outpace the algorithm’s update period, leading to notable resilience degradation. Addressing such extreme scenarios will require integration of a node trajectory prediction module to pre-adjust conductivity prior to link breakage, which is outlined as future work.

Figure 13 presents the robustness evolution under different speed coefficients, and Figure 14 shows the corresponding residual energy and node degree results, with the two metrics displayed in panel (a) and panel (b), respectively.

(3)

Influence of Initial Node Energy

To eliminate the interference of initial total energy difference on energy consumption evaluation and verify the energy performance robustness of the algorithm under different energy storage conditions, normalized average residual energy (i.e., the ratio of network average residual energy to average initial energy) is adopted as a unified evaluation indicator. Three groups of simulation scenarios are set, including low energy (200~300 J), baseline energy (500~800 J), and high energy (1000~1500 J), and each group carries out 10 independent repeated simulations.

The low-energy configuration requires 200 iterations, with a normalized average residual energy of 0.655 ± 0.021, a network robustness of 0.950 ± 0.018, and an average node degree of 2.91 ± 0.08. The baseline-energy configuration requires 200 iterations, with a normalized average residual energy of 0.703 ± 0.019, a network robustness of 1.000 ± 0.000, and an average node degree of 2.92 ± 0.07. The high-energy configuration only requires 128 ± 5 iterations, with a normalized average residual energy of 0.916 ± 0.015, a robustness of 0.900 ± 0.020, and an average node degree of 2.90 ± 0.08.

The algorithm exhibits energy adaptive characteristics: when energy is limited, it automatically enters survival priority mode and still maintains a high robustness of 0.950; when energy is sufficient, it switches to efficiency priority mode, greatly shortening the convergence time, and energy consumption only accounts for 8.3% of the initial value. The fluctuation of average degree under different energy conditions is less than 0.7%, and topological balance is not affected by energy conditions. Figure 15 presents the final robustness under different initial energy levels, and Figure 16 shows the corresponding normalized residual energy and node degree results, with the two metrics displayed in panel (a) and panel (b), respectively.

4.3.4. Comparative Verification with HLP-ACO Heterogeneous Routing Algorithm

To comprehensively verify the comprehensive performance boundary and applicable scenarios of UVC-SMA in UVC/RF heterogeneous UAV scenarios, the hybrid link-aware and predictive ant colony optimization algorithm (HLP-ACO) for similar 3D heterogeneous UAV networks is selected as the horizontal comparison benchmark.

The HLP-ACO benchmark algorithm is implemented following its original hybrid link-aware and predictive ant colony framework, with only minimal adaptation to fit the UVC/RF heterogeneous scenario [31]. The core ant colony optimization mechanism, pheromone update rules, and topology prediction logic remain identical to the original publication. Adaptations are limited to modality-specific link accessibility criteria, per-link energy consumption calculation, and matching initial conditions to the UVC-SMA experiments. HLP-ACO is selected as the primary quantitative benchmark because it belongs to the same swarm intelligence topology optimization paradigm, enabling a controlled apples-to-apples comparison. To contextualize the results against broader FANET solutions, we also provide qualitative comparison with classical standard multipath routing protocols (AOMDV, OLSR, MAODV). These network-layer protocols follow a route discovery–maintenance–repair paradigm with fundamentally different optimization time scales and metrics, making direct quantitative comparison inappropriate. All implementation details below are fully consistent with our MATLAB code.

Parameter configuration*: The algorithm uses five ants per iteration. The pheromone importance factor α = 1, the heuristic factor β = 1, and the energy factor $\gamma =1$. The pheromone evaporation coefficient is set to $\rho =0.2$, the topology prediction weight is $\omega =0.7$, and the pheromone intensity coefficient Q = 100. The initial pheromone value on all accessible links is uniformly set to 1.0, consistent with the upper initial conductivity range of UVC-SMA.

Initialization and random seed control: All HLP-ACO experiments use identical node initial positions, 3D mobility velocity profiles, energy configurations, and random seed sequences as those used for the UVC-SMA. This ensures that performance differences arise only from algorithm mechanisms, not initial conditions.

Heterogeneous scenario adaptation: The original single-modality HLP-ACO is adapted to the UVC/RF heterogeneous environment. Link accessibility follows the same criteria as the UVC-SMA: UVC links are available when distance is between 50 m and 150 m and both nodes are below 100 m altitude; RF links are available when distance is between 20 m and 300 m. Ants evaluate link quality separately for each modality and automatically select the lower-cost link type when both are accessible. Energy consumption is calculated per link type, consistent with the UVC-SMA energy model.

Topology prediction mechanism: topology prediction is updated every five iterations with a prediction time step of 2 s, using linear extrapolation of node velocity. The combined heuristic value integrates 70% predicted position information and 30% current position information, guiding ants to adapt to dynamic topology changes in advance.

Stopping criterion: HLP-ACO adopts exactly the same two-tier stopping framework as the UVC-SMA: fixed 200 iterations for all comparison experiments, and the same convergence rule for standalone verification.

For consistent comparison, all HLP-ACO experiments run for exactly 200 iterations, as in the UVC-SMA. The MATLAB simulation code for both algorithms will be made publicly available upon manuscript acceptance to ensure full reproducibility.

Both algorithms belong to the swarm intelligence routing framework, but there are essential differences in optimization orientation: HLP-ACO takes single-path transmission efficiency as the core optimization objective, while the UVC-SMA focuses on global topological resilience and fast fault recovery.

This comparison is carried out from five dimensions: random node failure survivability, failover response capability, scale expansion adaptability, steady-state transmission efficiency, and network-wide energy efficiency. Two core indicators, network layer connectivity robustness and transport layer packet delivery ratio, are collected simultaneously. All experimental groups uniformly control the 3D operation scenario, heterogeneous link parameters, node energy configuration and random walk mobility model to be completely consistent. Each group of experiments is independently repeated 10 times under different random seeds. All performance indicators are reported as mean ± standard deviation, and two-sample t-tests are used to verify the statistical significance of performance differences, with a significance level of α = 0.05. This ensures the fairness of the comparison process and the statistical credibility of the results.

(1)

Comparison of Resilience Evolution Under Random Node Failure

To improve the physical fidelity of fault injection, we adopt a modality-specific failure model that reflects the distinct degradation mechanisms of UVC and RF links. Three distinct failure events are defined and used consistently throughout the analysis:

First, link interruption: a single communication link becomes temporarily unavailable due to channel fading, atmospheric obscuration, or interference, affecting only one specific link of either modality.

Second, node failure: a UAV node loses all communication capability, either temporarily (energy depletion) or permanently (hardware failure), disabling all connected links.

Third, modality-specific failure: systematic degradation affecting all links of one communication modality across the entire network.

Two categories of fault scenarios are tested for comparison: single-link random interruption and dual-link concurrent interruption, corresponding to conventional link disturbance and multi-point concurrent failures under strong interference, covering mild to severe failure levels. The single relay node failure scenario that highly overlaps with the link failure mechanism is eliminated to streamline the comparison dimensions.

To quantify the modality-specific failure mechanisms, we define explicit probability functions for both link types, calibrated against near-ground atmospheric and electromagnetic measurement data.

For the UVC links, failure probability depends on both link distance and node altitude:

$$p_{\mathrm{uv}}\left(d,h\right) = p_{\mathrm{uv},0}\cdot \exp \left({\alpha }_{\mathrm{uv}}\cdot {\displaystyle \frac{d - d_{\mathrm{uv},\min }}{d_{\mathrm{uv},\max } - d_{\mathrm{uv},\min }}}\right)\cdot \left(1 + {\beta }_{\mathrm{uv}}\cdot {\displaystyle \frac{\max \left(0,\hspace{0.17em}h - h_{\mathrm{th}}\right)}{h_{\mathrm{th}}}}\right)$$

(10)

where the baseline failure probability $p_{\mathrm{uv},0}=0.02$, distance coefficient ${\alpha }_{\mathrm{uv}}=1.2$, altitude coefficient ${\beta }_{\mathrm{uv}}=0.8$, and $h_{\mathrm{th}}=100 \mathrm{m}$ is the ozone layer altitude threshold. Failure probability grows exponentially with distance and rises sharply above the altitude boundary, consistent with atmospheric scattering physics.

For the RF links, failure probability scales with link distance and local node density:

$$p_{\mathrm{rf}}\left(d,\rho \right) = p_{\mathrm{rf},0}\cdot {\left({\displaystyle \frac{d}{d_{\mathrm{rf},\max }}}\right)}^{{\gamma }_{\mathrm{rf}}}\cdot \left(1 + {\delta }_{\mathrm{rf}}\cdot \rho \right)$$

(11)

where the baseline failure probability $p_{\mathrm{rf},0}=0.015$, distance exponent ${\gamma }_{\mathrm{rf}}=1.5$, and node density coefficient ${\delta }_{\mathrm{rf}}=0.3$. This captures the distance-dependent path loss and density-dependent electromagnetic interference characteristics of RF channels.

For the node failure events, energy depletion disables the UVC links first when residual energy drops below 20% of initial capacity and disables both link types at 0% energy. Complete hardware failure disables both link types simultaneously, with a probability of 0.01 per node per 10 iterations.

Directed fault injection is triggered every 10 iterations during the full iteration period of the algorithm, and all failures are applied to the current main transmission path. The end-to-end communication recovery delay and average packet delivery ratio are counted to compare the fault response speed and transmission continuity of the two algorithms. The results are shown in Figure 17, with network robustness evolution in panel (a) and packet delivery ratio evolution in panel (b). Each group of scenarios is independently repeated 20 tests and the statistical mean is taken to ensure consistent comparison benchmarks. All experiments are rerun under this modality-specific failure model, and the comparative conclusions remain statistically consistent.

As can be seen from Figure 17a, the UVC-SMA shows evolution characteristics of rapid rise and high-level stabilization after convergence under all three failure scenarios. Under 5% mild failure, the algorithm reaches robustness of 0.964 at 60 iterations and converges to 1.000 after 140 iterations. Under 15% typical failure, it breaks through 0.95 at 80 iterations and stabilizes at 1.000 after 160 iterations. The degree-betweenness weighted key node protection mechanism effectively offsets the connectivity impact of node failures. Under the 15% node failure ratio, UVC-SMA achieves a steady-state robustness of 1.000 ± 0.000 and a PDR of 0.951 ± 0.011, while HLP-ACO achieves 0.758 ± 0.031 and 0.712 ± 0.029 respectively. The robustness advantage of UVC-SMA is 24.2 percentage points, with a 95% confidence interval of [19.8, 28.6] percentage points; the PDR advantage is 23.9 percentage points, with a 95% confidence interval of [18.7, 29.1] percentage points. Two-sample t-tests confirm both advantages are statistically significant (p < 0.001).

Under 25% severe damage, the steady-state robustness of UVC-SMA still maintains 0.917 ± 0.019, only attenuated by 8.3% compared with the 15% scenario. The optimization rate of HLP-ACO is significantly lagging. The convergence process is accompanied by continuous small oscillations, and the higher the failure intensity, the more significant the performance attenuation. The steady-state robustness is about 0.878 under 5% failure, only 0.758 under 15% failure, and has fallen below 0.5 at 25% failure, unable to guarantee basic connectivity services.

The evolution law of packet delivery ratio in Figure 17b is highly consistent with that of robustness. The delivery ratio of the UVC-SMA increases synchronously with topology optimization, and the steady-state PDR under the three scenarios are 0.982, 0.951 and 0.873 respectively. Effective data transmission can still be maintained under severe damage scenarios. The delivery ratio of HLP-ACO rises slowly and the steady-state value is low. It oscillates in the range of 0.4~0.5 for a long time under 25% failure, making it difficult to form stable end-to-end transmission capability.

The core of performance difference lies in different optimization paradigms. UVC-SMA adopts pre-defense logic, pre-emptively eliminates single point of failure risks through active reinforcement of key nodes, and achieves millisecond-level failover combined with primary and backup paths without shared links. Packet loss is only concentrated in the very short switching interval. HLP-ACO relies on passive route reconfiguration after failure, lacks resilience design at the global topology level, and node failures are likely to cause cascading path interruptions. Packets are continuously lost during route re-discovery, so both indicators deteriorate synchronously with the increase of failure intensity.

(2)

Comparison of Failover Delay and Transmission Continuity

Set two types of failure scenarios: single-link random interruption and dual-link concurrent interruption, respectively corresponding to conventional link disturbance and multi-point concurrent failures under strong interference, covering mild to severe failure levels. The single relay node failure scenario that highly overlaps with the link failure mechanism is eliminated to streamline the comparison dimensions. Trigger directed fault injection every 10 iterations during the full iteration period of the algorithm, and all failures are applied to the current main transmission path. Count the end-to-end communication recovery delay and average packet delivery ratio, and compare the fault response speed and transmission continuity of the two algorithms. The results are shown in Figure 18, with the end-to-end recovery delay shown in panel (a) and the packet delivery ratio shown in panel (b). Each group of scenarios is independently tested 20 tests and the statistical mean is calculated to ensure consistent comparison benchmarks.

From the evolution law of recovery delay in Figure 18a, the UVC-SMA maintains millisecond-level fault response capability throughout the iteration process. When the topology is not stable in the early iteration, the recovery delays of single-link and dual-link failures are 17.2 ms and 22.5 ms respectively. As the topology gradually converges, the delay decreases rapidly and stabilizes. After convergence, the recovery delay of single-link interruption is only 7.8 ± 0.9 ms, and that of dual-link concurrent failure is only 11.3 ± 1.2 ms, meeting the requirement of seamless switching throughout the process. The failover delay advantage of the UVC-SMA over HLP-ACO is statistically significant (p < 0.001).

The failover delay of HLP-ACO shows the characteristics of high in the early stage and gradual decline. In the initial stage of iteration, pheromone accumulation is insufficient, and full ant colony route discovery needs to be restarted after failure. The single-link interruption delay reaches 362.4 ms and exceeds 800 ms in case of dual-link concurrent failure. As the pheromone concentration gradually increases, the pathfinding efficiency is improved, but limited by the single-path architecture, it still maintains at the hundred-millisecond level after convergence, with a gap of 1~2 orders of magnitude from UVC-SMA.

The evolution trend of packet delivery ratio in Figure 18b is consistent with the delay results. UVC-SMA relies on pre-stored multipath redundancy, with very little packet loss during failover. The steady-state PDR under the two types of fault scenarios can reach 0.991 and 0.972 respectively, both maintaining at a high level. HLP-ACO has a very low delivery ratio in the early iteration, and the initial PDR is less than 0.11 under dual-link concurrent failures. The delivery ratio rises slowly as the route gradually converges, but restricted by the passive reconfiguration mechanism, the steady-state PDR of the two types of failures is only 0.788 and 0.618, with significant loss of transmission continuity.

In essence, the UVC-SMA adopts the pre-redundancy design of “synchronously generating primary and backup paths with topology evolution”. After a fault is triggered, communication can be restored only by locally switching the forwarding table, without additional iterative calculation. HLP-ACO only outputs a single optimal path with no pre-configured backup capacity. The ant colony pathfinding process must be restarted after the primary path is interrupted, which cannot eliminate the inherent overhead of route discovery. Therefore, the higher the fault intensity, the more obvious the performance attenuation.

(3)

Comparison of Performance Scalability Under Different Node Scales

Select three groups of typical node scales (20, 50, and 80), uniformly apply 15% random node failure ratio, and compare the connectivity resilience and transmission performance of the two algorithms in the 0~200 iteration period to verify the performance retention capability of the algorithm with network scale expansion. The results are shown in Figure 19, with network robustness evolution in panel (a) and packet delivery ratio evolution in panel (b). All experimental groups keep the 3D operation area, mobility model and energy configuration completely consistent. Failed nodes are randomly selected from the relay node set to ensure unified comparison benchmarks.

From the evolution law of robustness in Figure 19a, the UVC-SMA shows a trend of first increasing and then slowly decreasing with the increase of node scale, and maintains fast convergence speed and small steady-state fluctuation under all scales. The 20-node small-scale scenario is limited by topological redundancy, with steady-state robustness of 0.938 ± 0.016. Under the 50-node baseline scenario, topological redundancy and energy cost achieve the optimal balance, and robustness rises to a peak of 1.000 ± 0.000. When expanded to the 80-node medium-large scale scenario, the robustness is still maintained at 0.972 ± 0.012, only attenuated by 2.8% compared with the peak, and the performance attenuation is very gentle.

The robustness of HLP-ACO continues to decrease with the increase of node scale, from 0.882 ± 0.027 for 20 nodes to 0.798 ± 0.033 for 80 nodes, with a total attenuation of 9.5%. Moreover, the larger the scale, the slower the convergence speed, and the more significant the performance fluctuation during iteration.

The scale evolution law of packet delivery ratio in Figure 19b is highly consistent with robustness. The steady-state PDR of the UVC-SMA reaches a peak of 0.951 at 50 nodes, and still maintains 0.937 when expanded to 80 nodes, only attenuated by 1.5% compared with the peak. The scale stability of transmission quality is excellent. The steady-state PDR of HLP-ACO continues to decrease from 0.805 for 20 nodes to 0.714 for 80 nodes, with a total attenuation of 11.3%. Transmission quality degradation is obvious in large-scale scenarios.

The core of performance difference lies in the different scalability of algorithm optimization architecture. The global topology evolution of the UVC-SMA based on the conductivity matrix has natural parallel adaptability. The degree-betweenness key node protection and multipath redundancy mechanisms can be dynamically adjusted with network scale. The link redundancy gain brought by scale expansion can effectively offset the negative impact of increased failed nodes. The ant colony search space of HLP-ACO increases approximately squarely with the number of nodes, the optimization quality continues to decline under a fixed number of iterations, and path stability is further reduced, eventually leading to simultaneous attenuation of robustness and delivery ratio with increasing scale. This result confirms that the UVC-SMA has more stable resilience performance and stronger engineering adaptability in UAV swarms of different scales.

(4)

Comparison of Steady-State Transmission Efficiency

To further clarify the performance applicable boundaries of the two algorithms, supplement the comparison of end-to-end transmission efficiency in fault-free steady-state scenarios. Take the 50-node baseline scenario as the research object, count the average end-to-end transmission delay (including propagation delay and transmission delay) of the current optimal path every 10 iterations, and compare the transmission efficiency convergence characteristics of the two algorithms. The results are shown in Figure 20.

From the evolution curve in Figure 20, the end-to-end delay of both algorithms shows a monotonic downward trend with the progress of iteration, with a fast decline rate in the early stage and gradual stabilization in the later stage. In the early iteration, UVC-SMA relies on the link pre-screening mechanism of initial conductivity, and the delay decline rate is slightly faster than HLP-ACO. With the deepening of iteration, the positive feedback mechanism of HLP-ACO with path length and delay as direct optimization objectives gradually shows advantages. The final steady-state delay drops to 38.2 ± 2.1 ms, about 21.6% lower than UVC-SMA’s 48.7 ± 2.4 ms, with clear transmission efficiency advantages.

The core of this difference lies in the different optimization orientations of the two algorithms. HLP-ACO takes end-to-end delay and path length as the core basis for pheromone update, and the optimization process always converges to the shortest transmission path without reserving additional overhead for topological redundancy, so better steady-state transmission efficiency can be achieved. The UVC-SMA takes global topological resilience as the primary optimization objective. To ensure path redundancy and fast switching in fault scenarios, the primary path is not strictly the geometric shortest path, and a certain degree of link redundancy needs to be maintained, so the steady-state transmission delay increases slightly.

This result further confirms the scenario differentiation characteristics of the two algorithms. HLP-ACO has low computational overhead and high single-path transmission efficiency, and is more suitable for routine inspection and data backhaul scenarios with stable topology and gentle electromagnetic environment. UVC-SMA exchanges acceptable steady-state delay cost for 1~2 orders of magnitude improvement in switching speed and robustness gain in fault scenarios, and is more suitable for high-dynamic, high-confrontation extreme operation environments such as emergency rescue and tactical reconnaissance.

(5)

Comparison of Network-wide energy efficiency

To comprehensively measure the resource consumption level of the two algorithms, based on 10 independent repeated experiments, count the average residual energy of all nodes in the network under steady state and compare their energy utilization efficiency. The results are shown in Figure 21. All experimental groups have exactly the same initial energy configuration. The initial energy of relay nodes follows a uniform distribution of 500~800 J, and the simulation period is uniformly 200 iterations.

From the statistical results in Figure 21, HLP-ACO has certain advantages in terms of steady-state energy efficiency. The average residual energy of 10 experiments is 513.4 ± 10.5 J, about 12.3% higher than UVC-SMA’s 457.3 ± 9.6 J. This difference is determined by their architectural designs. HLP-ACO is a single-path routing mechanism. Only links on the main transmission path generate communication and maintenance energy consumption, without bearing the additional overhead of redundant topology. UVC-SMA takes topological resilience as the core optimization objective. To support key node protection links and multipath redundant backups, richer network connections need to be maintained, so the overall energy consumption increases slightly.

Combined with the previous performance comparison, the two algorithms present a clear performance trade-off relationship. HLP-ACO enables efficient single-path transmission with low energy overhead and is suitable for normal operation scenarios with stable topology and low failure probability. The UVC-SMA trades a modest increase in energy consumption for a significant improvement in robustness and millisecond-level failover capability under node failure scenarios, and is more suitable for high-dynamic, high-risk extreme mission environments.

To further clarify the positioning of the UVC-SMA in the broader FANET research landscape, we qualitatively compare it with three classical state-of-the-art multipath routing protocols: AOMDV, OLSR, and MAODV.

Classical FANET routing protocols operate at the network layer, following the route discovery–maintenance–repair paradigm. AOMDV and MAODV are reactive multipath protocols that discover routes on demand and maintain backup paths through periodic hello packets; OLSR is a proactive protocol that precomputes routes through multipoint relays. These protocols excel at fast packet forwarding under stable topologies, but their route re-discovery process introduces significant latency and packet loss when topology changes rapidly or node failures occur.

In contrast, the UVC-SMA operates at the topology construction layer, optimizing the overall network connectivity structure through slime mold dynamics. Instead of reacting to failures after they occur, it proactively reinforces key nodes and precomputes disjoint backup paths embedded in the topology. This brings orders-of-magnitude faster failover and higher robustness under high-dynamics and high-failure scenarios, at the cost of slightly higher steady-state delay and energy overhead.

Direct quantitative comparison between the two categories is not straightforward: classical routing protocols are optimized for packet-level forwarding latency and control overhead, whereas the UVC-SMA targets topological resilience and structural energy efficiency. The optimization time scales and core indicator systems are fundamentally different. Therefore, we take HLP-ACO, a peer swarm intelligence topology optimization algorithm, as the primary quantitative benchmark, and provide this qualitative comparison to contextualize the results against broader FANET solutions.

5. Conclusions

To meet the highly reliable communication requirements of UVC/RF heterogeneous UAV swarms in extreme, highly dynamic environments, this paper proposes a slime-mold-inspired heterogeneous UAV-resilient network construction algorithm, UVC-SMA. The algorithm is specifically designed from three perspectives: first, according to the physical differences between ultraviolet scattering and radio frequency transmission, a heterogeneous link cost model with an exponential energy penalty factor is constructed to enable collaborative evaluation of the two types of links; second, a network state-driven parameter adaptation mechanism is established to dynamically adjust core parameters based on real-time robustness, average node degree, and primary path length, balancing global exploration and local exploitation; third, an active key node protection framework with hybrid degree-betweenness weighting is introduced and is combined with the K-shortest multipath method based on reciprocal conductivity to advance resilience optimization from post-failure repair to pre-failure active reinforcement and ensure millisecond-level fast switching of faulty paths.

Multiple groups of simulation results show that, compared with the conventional slime mould algorithm (SMA), the UVC-SMA improves network robustness from 0.75 to 1.00, increases the average residual energy by 19.5%, reduces the average node degree by 16.8%, and can converge stably within 200 iterations. Note that such full robustness cannot be guaranteed under arbitrary extreme mobility or energy-starved conditions. Ablation experiments verify the positive contribution and synergistic effect of each improved module. Parameter sensitivity analysis shows that the algorithm can maintain balanced topological performance under different node scales, mobility speeds, and initial energy conditions.

A horizontal comparison with the similar ant colony routing algorithm HLP-ACO shows that UVC-SMA has more advantages in connectivity resilience and packet delivery ratio under random node failure scenarios, with failover delay 1~2 orders of magnitude lower, and the performance attenuation with network scale expansion is more gentle. Meanwhile, HLP-ACO shows better transmission efficiency and energy efficiency in fault-free steady-state scenarios. The two algorithms present clear scenario adaptation differentiation characteristics. Overall, UVC-SMA exchanges acceptable steady-state delay and energy cost for significant resilience gains in extreme fault environments, and is more suitable for highly dynamic, high-confrontation UAV operation scenarios.

Limitations of simulation-based evaluation should be noted. All results in this manuscript originate from MATLAB-level numerical simulation with several simplifying assumptions. An ideal collision-free MAC-layer channel-access model is adopted without accounting for packet collisions, hidden-terminal interference, and retransmission overhead. UVC/RF link attenuation follows theoretical formulas, while practical atmospheric turbulence, random obscuration, and hardware noise introduce additional stochastic link failures. Node mobility follows the Gauss-Markov random-walk model, without real-world flight-controller constraints, obstacle-avoidance logic, and mission-waypoint restrictions. These simplifications will create performance gaps between simulated results and physical field deployment. Hardware-based field experiments will be pursued in our future research.

The algorithm adopts a fully distributed architecture with a per-iteration complexity of O(n²), which demonstrates the theoretical feasibility of low-cost on-board embedded deployment and can serve as a technical reference for UAV swarm communication in extreme scenarios. Full hardware implementation and field verification will be carried out in future work. In future work, two specific research directions will be further explored. First, a node trajectory prediction mechanism based on the Gauss-Markov mobility model will be introduced to enable pre-adjustment of topology conductivity before node position changes, further reducing performance fluctuation caused by dynamic topology. Second, an adaptive transmit power control mechanism for heterogeneous links will be developed that dynamically adjusts UVC and RF transmit power according to real-time link quality and node residual energy, so as to achieve more refined joint optimization of energy efficiency and network resilience.