Multi-UAV Data & Semantic Forwarding MOP

• The paper introduces DCSFMOP, a framework that jointly maximizes raw data throughput, enhances semantic delivery, and minimizes UAV energy consumption in post-disaster scenarios.
• It employs a hybrid methodology combining greedy clustering, NSGA-II for UAV positioning and beamforming, and LLM-guided parameter tuning to improve convergence and performance.
• Implications include scalable multi-UAV networks with improved spectral efficiency and robust semantic transmission, vital for efficient disaster relief communications.

The Data Collection and Semantic Forwarding Multi-Objective Optimization Problem (DCSFMOP) is a formal optimization framework designed to coordinate multi-UAV systems for post-disaster communications, capturing the joint trade-offs among raw data throughput, semantic information delivery, and strict UAV energy budgets. It is central to enabling scalable, efficient, and resilient low-altitude multi-UAV-assisted wireless networks for disaster relief, where UAVs must collect and semantically compress user data, organize into clusters for collaborative transmission, and optimize positions and transmissions with energy constraints. DCSFMOP is inherently a mixed-integer nonlinear program (MINLP) with dynamically varying variable dimensionality and NP-hardness, reflecting the multifaceted design challenges of modern multi-UAV post-disaster networks (Zheng et al., 22 Jan 2026).

1. System Architecture and Data Flow

DCSFMOP is formulated within a post-disaster, low-altitude multi-UAV-assisted data collection and semantic forwarding network architecture, which has the following stages:

• Ground Users and UAV Associations: A set of $N_U$ users $u\in\{1,...,N_U\}$ each hold textual data $S_u$. UAVs, typically operating at 60–120 m altitude, use a nearest-UAV association rule based on three-dimensional distance $d_{u,v}$ for raw data retrieval.
• UAV Clustering and Semantic Extraction: Once UAV $v$ gathers $S_{v}$ from its associated users, UAVs self-organize into $N_{cluster}$ clusters $\{C_1, ..., C_{N_{cluster}}\}$; within each, members aggregate their raw data and invoke an intra-cluster semantic encoder (e.g., DeepSC), yielding semantic symbols $x_c = C_{\beta}(S_{\alpha}(S_c))$ with cluster-wise symbolization.
• Virtual Antenna Array and Backhaul Transmission: Each cluster executes collaborative beamforming (CB) by treating its UAVs as a virtual antenna array (VAA), adjusting per-vehicle excitation weights $w_{v,c}$ for joint transmission to a remote base station (BS), yielding gain $G_c(\theta,\phi)$ and SNR $SNR_{c,bs}$.

This sequence supports both spatial diversity in data acquisition and spectral efficiency in backhaul forwarding, essential for post-disaster recovery (Zheng et al., 22 Jan 2026).

2. Decision Variables and Constraints

DCSFMOP covers a suite of coupled decision variables:

Variable	Type	Domain/Description
UAV clustering $c_v$	Integer	$\{1,...,N_{cluster}\}$ per UAV
UAV positions $q_v=(x_v,y_v,z_v)$	Continuous	$\mathbb{R}^3$, subject to flight region $\mathcal{R}$
VAA weights $w_{v,c}$	Continuous	Complex, bounded $[w_{min},w_{max}]$
Semantic symbols per word $k_{c,bs}$	Integer	$[k_{min},k_{max}]$ per cluster
UAV trajectories $Q(t)$, power allocations	Continuous	Implicit, mission interval $[0,T]$

Typical constraints include region-bounded UAV placement ($q_v \in \mathcal{R}$), pairwise UAV separation ($\|q_{v_i}-q_{v_j}\| \geq d_{min}$), non-empty clusters, semantic similarity thresholds ($\xi_{c,bs} \geq \xi_{th}$), and integer-bounded symbolization ($k_{c,bs}$) (Zheng et al., 22 Jan 2026).

3. Mathematical Problem Formulation

DCSFMOP targets simultaneous optimization of three performance metrics:

• User Data Collection Rate:

$$R_{user}(Q) = \sum_{u=1}^{N_U} R_{u,v_u^*} \ R_{u,v} = B \log_2(1+\mathrm{SINR}_{u,v})$$

with $\mathrm{SINR}_{u,v}$ defined by user transmit power, path loss $L_{u,v}$, and noise, reflecting link quality from user to assigned UAV.

• Semantic Forwarding Rate:

$$R_{semantic}(c,Q,w,k) = \sum_{c=1}^{N_{cluster}} SR_{c,bs}$$

$$SR_{c,bs} = \frac{B I}{k_{c,bs} L} \cdot \xi_{c,bs} \cdot \log_2(1+\mathrm{SNR}_{c,bs})$$

where the semantic similarity $\xi_{c,bs}$ is a function of both compression ($k_{c,bs}$) and CB link SINR, linking rate and semantic preservation.

• UAV Flight Energy Consumption:

$$E_{UAV}(Q) = \sum_{v=1}^{N_V} \int_0^T [P_v^{xy}(\|\mathbf{V}_v^{xy}(t)\|) + P_v^{z}(V_v^z(t))]\ dt$$

The complete MINLP formulation is:

$$\max_{c,Q,w,k} \{f_1=R_{user}(Q),\; f_2=R_{semantic}(c,Q,w,k),\; -f_3=-E_{UAV}(Q)\}$$

subject to region, separation, clustering, symbolization, and semantic similarity constraints (Zheng et al., 22 Jan 2026).

4. Problem Complexity and Structural Properties

DCSFMOP exhibits several challenging characteristics:

• Mixed Variable Types: Simultaneous optimization over continuous (UAV positions, CB weights), discrete/integer (clustering variables $c_v$, symbol levels $k_{c,bs}$), and implicitly time-indexed variables (trajectories, power allocation).
• Nonlinearity: Nonlinear dependencies include logarithmic rate expressions, channel models with distance- and beamforming-dependent path loss, semantic similarity functions, and mobility-induced energy integrals.
• NP-hardness: Even with fixed continuous variables, optimizing the clustering assignment is a $k$-means-style combinatorial problem, and the presence of variable-dimensional decision vectors (as $N_{cluster}$ is also optimized) compounds the difficulty.
• Dynamic Dimensionality: The length of the $k_{c,bs}$ vector changes with $N_{cluster}$, requiring dynamic rescaling of the problem’s feasible set.

These properties necessitate advanced, hybrid optimization techniques and preclude reliance on simple convex or greedy heuristics (Zheng et al., 22 Jan 2026).

5. LLM-Enabled Alternating Optimization Approach (LLM-AOA)

The designated solution methodology, LLM-AOA, decomposes the joint optimization as follows:

1. Greedy Clustering Assignment (GCA): Fixing $Q$, $w$, $k$, iteratively merge cluster pairs if this improves the semantic rate $f_2$, terminating when no further gain is observed. The complexity is $\mathcal{O}(N_V^4)$ in the worst case but converges rapidly for moderate $N_V$.
2. Joint UAV Position & Beamforming Weight Optimization: Given clustering and symbolization, employ NSGA-II (a multi-objective genetic algorithm) to evolve UAV positions and CB weights across $T_{local}$ generations. A LLM (e.g., ChatGPT 5.0) receives population diversity/convergence metrics (spread $SP$, uniformity $M_3^*$) and recommends adjustments to crossover and mutation rates to foster convergence stability and solution diversity.
3. Greedy Symbol Optimization (GSO): For each cluster, sweep $k_{c,bs}$ in $[k_{min},k_{max}]$ and select the value maximizing semantic rate.
4. Population Assessment: All candidate solutions undergo non-dominated sorting on $(f_1, f_2, -f_3)$; the population is truncated by crowding distance to maintain cardinality and solution spread.

This iterative process returns a Pareto-optimal front, balancing user rate, semantic rate, and energy consumption (Zheng et al., 22 Jan 2026).

6. Empirical Results and System-Level Insights

Key insights and benchmark outcomes:

• Simulation Parameters: $N_U=500$ users over a $1\,\mathrm{km} \times 1\,\mathrm{km}$ area, $N_V=8$ UAVs, BS at $(5000,5000,0)\,\mathrm{m}$, population $M=30$, $T_{AO}=50$, $T_{local}=10$, LLM=ChatGPT 5.0.
• Performance: LLM-AOA improves user transmission rate $f_1$ to $1.10\times10^8\,\mathrm{bps}$ (26.8% over AOA baseline), semantic rate $f_2$ to $4.12\times10^6\,\mathrm{suts/s}$ (22.9% improvement), with energy $f_3$ comparable or lower at efficient points.
• UAV Placement: Optimal positioning balances proximity to user clusters and cluster tightness for CB, supporting efficient data collection and robust backhaul transmission.
• Pareto Efficiency: Non-dominated solutions illustrate explicit trade-offs; enhancement in semantic rate is sometimes constrained by energy or by the need for raw throughput.

A plausible implication is that LLM-guided parameter control confers meaningful acceleration and robustness over fixed-rule evolutionary strategies, as evidenced by the sustained improvement in both transmission and semantic rates (Zheng et al., 22 Jan 2026).

7. Significance, Context, and Research Directions

DCSFMOP provides a unified optimization formalism for multi-UAV-enabled post-disaster networks, essential for large-scale, real-world deployments where mission success depends on mutual optimization of throughput, semantics, and energy. The integration of semantic compression, clusterwise CB, and adaptive LLM-guided optimization defines a new methodological standard for handling high-dimensional and dynamically structured MINLPs in low-altitude wireless network control.

DCSFMOP serves as an exemplar for MINLPs with dynamic variable sets, suggesting wider applicability in mobile ad hoc networking, cooperative sensing, and energy-constrained multi-agent coordination. Further exploration of LLM-enhanced optimization regimes and semantic communication-aware network control appear to be promising avenues for ongoing research (Zheng et al., 22 Jan 2026).