Stigmergy-based systems (e.g., ant colony optimization) rely on indirect coordination via environmental modifications. While they exhibit self-organization, their strategies are typically predefined and static, lacking the capacity for online strategy generation. Environmental feedback is implicit and delayed, limiting adaptability in dynamic scenarios.

MARL-based swarm cooperation enables agents to learn policies through trial-and-error interactions. Although MARL supports adaptive strategy acquisition, it often requires centralized training or extensive simulation, and the learned policies are usually fixed after deployment. Strategy generation is thus offline and computationally intensive, with limited interpretability and scalability in open-ended environments.

CE&SG pursues online, self-organized strategy generation through a hyper-heuristic (HH) mechanism whose interaction structure was loosely inspired by biological self-organization. Strategies are not preprogrammed but emerge from local interactions among embodied agents, driven by real-time environmental feedback. This enables continuous adaptation, scalability, and interpretability—3 long-standing challenges in swarm robotics.

Automated strategy design. PIHH achieves the automatic generation and optimization of advanced strategies through the interaction of base strategy network architectures. This process requires no manual intervention at the strategy composition level or complex algorithm debugging; the system can screen and strengthen effective strategies based on environmental feedback, significantly reducing the engineering burden of algorithm design and adjustment.

Dynamic environmental adaptability. PIHH simulates the iterative evolution of natural populations during training, enabling dynamic environment-driven strategy adaptation in response to factors such as sudden tasks, robot failures, and task changes. More importantly, PIHH can perceive environmental shifts, task requirements, and swarm status in real time, generating robust strategies that adapt to diverse types and intensities of disturbances.

Scalability of problem size. Unlike common centralized preplanning methods, PIHH employs a distributed mechanism that effectively mitigates computational explosion issues arising from expanding problem scales in centralized approaches. Experiments demonstrate that PIHH maintains stable performance and low computational costs across both small-scale and large-scale tasks and swarm configurations.

Strategy interpretability. The generated advanced strategies are dynamically composed of semantically explicit base strategies, such as distance, resource matching, and task sequencing. Engineers can understand the decision logic by analyzing strategy activation frequencies. This modular design approach enhances strategy transparency and credibility, facilitating deployment in practical systems.

From a high-frequency perspective, Strategies 11 and 13 are the most commonly used across all problems in task allocation decisions. Strategies 6, 16, 17, and 18 also show relatively high usage frequencies on average, playing important roles in decision-making. Collectively, these high-frequency strategies (Strategy 11: distance between tasks; Strategy 13: proportion of UAVs functionally suited to a task; Strategy 6: proportion of UAVs with the same function; Strategy 16: task execution sequence; Strategies 17 and 18: historical heuristic/random element) elucidate the primary decision factors underpinning PIHH’s strategy generation: intertask spatial relationships, resource-task functional matching, collaborative potential, temporal constraints, and necessary exploratory behavior. These factors align with engineering intuition, such as prioritizing spatially proximate tasks, ensuring functional compatibility, maintaining reasonable grouping, and adhering to task sequences.

From a low-frequency perspective, the 3 least activated strategies are Strategies 5, 8, and 15, indicating their relatively lower importance in task allocation decisions. These low-frequency strategies (Strategy 5: number of UAV functions; Strategy 8: remaining resources of a UAV; Strategy 15: resources required by a task) suggest that, due to the complexity of swarm heterogeneity and task coupling, PIHH-generated strategies do not simply rely on static resource counts or function enumeration. Instead, they focus more on dynamic matching relationships and collaborative efficiency.

Initial phase (Round 0): At this stage, the swarm is in a relatively balanced state. The generated strategy is primarily dominated by high-frequency base policies, such as base strategy 11 (task-to-task distance) and base strategy 13 (proportion of UAVs matching task functionality). As shown in Fig. 7A, these policies carry the highest weight in the heuristic value. This leads to a decision logic that tends to select the spatially closest and functionally matched idle UAV for new tasks—a coordination strategy based on local optima that may lack robustness in dynamic environments. The corresponding self-attention matrix in Fig. 7B reveals a relatively concentrated strategy interaction network. Core strategy 13, as the central node, attracts the majority of attention from both core strategy 11 and itself, forming a singular decision pattern dominated by proximity.

Dynamic response phase (Round 1): Events d₁ and d₃ drastically altered the environmental landscape. The meta-algorithm detected the emergence of new target T_new and the failure of U₄, triggering a new round of strategy generation. At this point, the attention weight of base strategy 8 (UAV remaining resources) surged sharply, as shown in Fig. 7A, as the system urgently needed to assess remaining strike capabilities and avoid resource conflicts. As evident in Fig. 7C, the self-attention matrix undergoes significant changes: the attention to base strategy 8 substantially increases and forms a new strong interactive connection with base strategy 6. This drives the generation of a temporary strategy prioritizing the assignment of strike tasks to UAVs with sufficient remaining resources and fewer co-functional partners. Simultaneously, owing to incomplete information, this round is accompanied by a temporary peak in the weight of base strategy 18 (random constant), prompting the system to engage in some blind exploration.

Rearrangement phase (Rounds 2 and 3): The system gradually converges toward the feasible solution space through multiple rounds of interaction. The role of base strategy 17 (historical heuristic value) intensifies, guiding the strategy to search near the previous round’s optimal solution. Simultaneously, base strategy 5 (number of UAV functions) is significantly activated. This is a base strategy with extremely low activation frequency in static analysis, as shown in Fig. 5. The self-attention matrices in Fig. 7D and E reveal its critical role: from Round 2 to 3, a triangular interaction pattern emerged among base strategies 5, 13, and 11, establishing a critical decision logic: when strike units are damaged, prioritize dispatching integrated UAVs to execute critical strike tasks—even if this may not represent the optimal functional match for that UAV. While this strategy appears to assign suboptimal tasks to versatile UAVs, it globally resolves strike capability bottlenecks, functioning as a leverage strategy.

Stable phase (Round 4): Ultimately, the system converged to a new stable strategy combination, as shown in Fig. 7F. The new strategy composition balances base efficiency (base strategies 11 and 13), functional fault tolerance (base strategies 5 and 6), and sustained exploration capability (base strategies 17 and 18). The corresponding self-attention matrix exhibits a balanced, redundant network structure: base strategy 13 and Strategy 11 remain the foundation for efficient matching, though their dominance diminishes; base strategy 5 is firmly integrated as a specialized module for handling functional deficiencies; and the interaction weights between base strategies 17 and 18 revert to baseline levels. At this stage, the swarm establishes a new cooperative paradigm: reconnaissance UAV swarms handle new target detection, while the remaining strike UAVs and integrated UAVs dynamically form teams to collaboratively execute subsequent strike and assessment tasks through functional substitution.

Low-frequency strategies are not ineffective. Base strategy 5 (number of UAV functions) and base strategy 8 (remaining resources) exhibit low activation frequencies under static or simple dynamic conditions (Fig. 5) and are often underestimated. However, in this dynamic scenario with missing features, the attention weights of these strategies rapidly increase after dynamic triggering, becoming pivotal hubs within the strategy interaction network (see Fig. 7C to E). They dominate critical decisions such as feature substitution and resource re-evaluation. This underscores that strategy potential must be assessed dynamically and context-dependently; static priority lists are inadequate for complex, evolving environments. This case illustrates a broader methodological point: aggregate performance metrics alone would indicate that PIHH recovered from the UAV failure, but would not reveal how the recovery was achieved. It is the per-round traceability of strategy weights (Fig. 7A) and the topological visibility of the interaction network (Fig. 7B to F) that expose the lever mechanism—Strategy 5 transitioning from a dormant state to a coordination hub. Such diagnostic insights are structurally unavailable in methods where decision logic is distributed across opaque neural network parameters (e.g., E2E-MoE, CTED-MAPPO, and DNC-A2C).

Exploratory behavior exhibits time sensitivity. Activation of the base strategy 18 (random constant) is not uniformly distributed. It shows a distinct peak during the initial dynamic trigger phase (Round 1) in Fig. 7C, when system information is highly uncertain and requires increased exploration to escape potentially trapped invalid solution spaces. During recovery and stabilization phases, its contribution rapidly diminishes, yielding to more information-rich strategies. In this SEAD task, exploration behavior concentrates during phases of high information uncertainty. This indicates that the exploration–exploitation balance in this scenario is time-sensitive, rather than fixed at a predetermined ratio.

Leverage strategy relies on global perception. Generated decisions underutilize one specialized UAV, yet prove efficient for the entire swarm by alleviating system bottlenecks. The emergence of such locally suboptimal yet globally efficient leverage strategies hinges on direct and indirect robotic connections in CE&SG. This mechanism enables strategies to perceive real-time global swarm states—such as the functional workload ratio reflected in base strategy 6 (proportion of UAVs with identical functions) and the spatial clustering implied by base strategy 11 (task distance), thereby facilitating collaborative decisions that transcend local fields of view.

Learning-based hyper-heuristic (DRL-HH). DRL-HH employs a deep Q-network to dynamically select among a set of predefined low-level heuristics. In the USAD environment, this approach encounters 2 primary difficulties. First, the continuous state-action space induced by physical dynamics and collision avoidance substantially expands the Q-network’s input domain, leading to sample inefficiency and requiring extensive online fine-tuning. Second, the heuristic selection policy, once trained, remains relatively static during deployment, offering limited adaptability to unforeseen environmental perturbations. Consequently, DRL-HH exhibits the lowest objective values among all compared methods across all 3 scales, accompanied by elevated collision rates that escalate sharply as M increases.

Multiobjective hyper-heuristic (CBHH). CBHH augments the HH framework with a compass-guided multiobjective selection mechanism, enabling simultaneous consideration of task efficiency and spatial distribution. While this dual-objective design partially mitigates congestion, CBHH still relies on a fixed set of base heuristics whose relative importance is determined offline. In dynamic environments where the urgency of task completion and the severity of collision risk fluctuate unpredictably, the static weighting scheme proves insufficient. CBHH achieves marginally better performance than DRL-HH but remains significantly behind PIHH, particularly in collision avoidance.

Primate-inspired metaheuristic (RSOA). RSOA mimics the hierarchical social structure and foraging behavior of golden snub-nosed monkeys, employing a leader–follower mechanism to guide population-based search. Despite sharing a biological inspiration with PIHH, RSOA’s strategy space is confined to continuous parameter optimization rather than discrete task allocation. When adapted to the USAD problem, RSOA must discretize its continuous solutions, introducing quantization errors and losing the fine-grained coordination required for collision-free trajectory assignment. The resulting performance is the poorest among all evaluated methods, with collision rates exceeding 13 events at M = 18.

Multiagent reinforcement learning (E2E-MoE, CTED-MAPPO, and DNC-A2C). These 3 MARL methods represent the current frontier in learned multiagent coordination. E2E-MoE’s mixture-of-experts architecture facilitates modular policy decomposition, CTED-MAPPO benefits from centralized training, and DNC-A2C leverages external memory to retain historical context. Despite their theoretical expressiveness, all 3 MARL approaches face a common challenge in the USAD setting: the sim-to-real gap between discrete-time training and continuous-time execution. The physical simulator introduces sensor noise, actuation delays, and unmodeled aerodynamic disturbances that are absent during policy optimization. As a result, the learned policies require substantial online adaptation, manifesting as elevated collision rates and suboptimal task completion. Notably, the performance degradation becomes more pronounced as the problem scale increases, indicating that the learned coordination strategies do not generalize robustly to larger swarm sizes.

Heterogeneous multirobot task allocation via reinforcement learning (HMRTA-RL). HMRTA-RL employs an attention-based encoder–decoder architecture with multihead attention (8 heads, 128-dimensional embedding) and gated linear units, trained via REINFORCE with a POMO-style baseline. As the method most specifically designed for heterogeneous robot task allocation among the MARL baselines, HMRTA-RL achieves the strongest MARL performance across all USAD scales. Its attention mechanism effectively captures cross-dependencies among heterogeneous UAVs and spatially distributed tasks, and the constrained flashforward mechanism reduces deadlocks during training. However, HMRTA-RL was originally designed for 2D grid environments with constant-speed agents and does not natively account for continuous 6-DOF kinematics or collision avoidance. PIHH’s collision penalty augments [Eqs. (26) and (27)] and fission–fusion interaction structure confers additional advantages in the physically constrained USAD setting, explaining the 4.2% to 4.5% performance margin maintained by PIHH across scales.

PIHH (ours). In contrast to the aforementioned approaches, PIHH’s CE&SG architecture offers 3 distinct advantages in physically constrained environments. First, the base strategy set is semantically grounded in real-time sensor measurements (e.g., relative distances and functional compatibility), allowing the self-attention mechanism to natively incorporate collision risk as a weighted factor without architectural modification. Second, the fission–fusion interaction structure enables local subgroups of UAVs to temporarily coordinate their trajectories, preventing the global propagation of congestion that plagues fully decentralized methods. Third, the event-triggered meta-algorithm reactively adjusts task assignments in response to near-miss events, effectively closing the loop between perception and replanning. As evidenced in Table 4, PIHH achieves the highest objective values across all scales while maintaining the lowest collision counts. The performance gap widens with increasing M, underscoring the scalability of the self-organizing strategy generation mechanism.

Communication delays cause the self-attention mechanism to compute weights from outdated peer strategy vectors. This misaligns Query–Key matching: UAV i evaluates its strategy affinity against UAV j’s prior state, potentially inducing oscillatory weight reassignments if j has since changed its strategy profile. In the fission–fusion topology, staleness can induce erroneous subgroup joining or delayed fission, and convergence time increases with delay because subgroup consensus requires communication round-trips. Above a critical threshold, the swarm may remain in a perpetual transient state. As a concrete mitigation, we propose a decentralized bounded-staleness synchronization policy: each UAV attaches a local timestamp to broadcast vectors and, upon reception, computes an age-dependent confidence weight that exponentially decays stale peer contributions before Softmax normalization. Features exceeding a maximum staleness threshold can be supplemented with linear extrapolation from recent history. This scheme is fully decentralized and introduces negligible computation overhead.

On resource-constrained platforms, the per-event pipeline may exceed the interevent interval under high event rates, creating a backlog of decisions that operate on stale state. Stale decisions reduce swarm efficiency, triggering more events and further backlog. To mitigate this, the pipeline can be partitioned into 2 tiers. The critical tier (per-event) handles candidate strategy feature evaluation, K × K attention, heuristic scoring, and task selection. The background tier (asynchronous) handles global strategy weight recalibration, subgroup membership evaluation, and exploration budgeting. Newly triggered events interrupt background computation, bounding critical-tier latency. An adaptive mode can temporarily promote strategy recalibration to the critical tier during rapid environmental transients.

Residual sensor noise propagates to distance-based features (S1 to S3, S11, and S12) in proportion to position estimation error. Uncorrelated random noise across UAVs is partially averaged out by Softmax relative normalization over multiple decision cycles. Correlated noise, such as Global Positioning System (GPS) multipath, is more consequential: a coherent position bias across the swarm can systematically distort attention weight distributions. An extended Kalman filter fusing inertial measurement unit (IMU), visual odometry, and GPS can mitigate this as a preprocessing module without modifying PIHH. A robust attention variant with sublinear scaling of outlier features is a direction for future algorithmic work.

Scope of the constraint. Manual base strategy design is a one-time per-problem-class investment following a principled decomposition template, distinct from per-instance parameter tuning. The SEAD-to-USAD portability (see the “PIHH deployment to the USAD mission” section) shows that the vocabulary can be reused when domains share task model and spatial semantics. When domain semantics diverge substantially, the vocabulary requires reidentification.

Cross-domain transferability: limitations and compensatory directions. The current base strategy set was designed through “3-dimensional decomposition, per-dimension enumeration”. The decomposition template—agent status, task characteristics, and exploratory behavior—is domain-agnostic, but it specifies only the dimensional framework, not what to place within each dimension. When the target domain’s task semantics diverge substantially from SEAD—e.g., area coverage lacks a discrete “task completion” concept, whereas warehouse logistics closely resembles SEAD—decision heuristics in that dimension must be reidentified. The SEAD-to-USAD migration succeeded with only semantic reinterpretation precisely because the 2 domains happen to be semantically isomorphic on this dimension—a favorable special case, not a general capability. Two directions may reduce the manual design burden. First, per-dimension strategy enumeration can be formalized as a set of guiding questions, turning creative design into guided completion. Second, a large language model (LLM) prompted with the domain description and guiding questions can propose candidate heuristics; the proposed heuristics are screened through lightweight simulation, and the human role shifts from proposer to reviewer. Neither direction eliminates manual involvement; both reduce the per-dimension design cost.

LLM can assist in base strategy design. Given a target domain description and the decomposition template, an LLM can propose candidate heuristics drawing on patterns learned during pretraining. A retrieval-augmented generation component can further ground these proposals against validated robotic planning literature, reducing the risk of generating strategies untethered from practical constraints. After candidate strategies are screened through lightweight discrete-event simulation—eliminating variants that violate battery constraints, kinematic limits, or causal logic—surviving strategies can be fed back to the LLM to refine subsequent generation, forming an iterative improvement loop. This pipeline faces 2 practical difficulties requiring sustained effort: some LLM-generated strategies may be superficially plausible but physically infeasible and must be rigorously filtered in simulation; and the structured corpus of validated heuristics that retrieval-augmented generation depends on is currently at an early stage of development. On a longer time scale, base strategies could be modeled as learnable parametric functions and optimized concurrently with attention weights, forming a meta-learning loop over the strategy space. We note that the following kinds of tacit knowledge in base strategy design resist automation in the foreseeable future: kinematic intuitions about specific hardware platforms, experiential judgment about nonlinear interactions among multiple constraints, and recognition of boundary conditions not explicitly modeled in the task semantics. The realistic near-term goal, therefore, is not to eliminate human involvement but to shift the human role from direct strategy designer to reviewer and validator guided by the decomposition template.