K–β Risk-Threshold Optimization for Multistage Adaptive Task Assignment and Recovery of Heterogeneous UAVs

This study addresses multistage task assignment and recovery for heterogeneous unmanned aerial vehicle (UAV) teams under progressively revealed disruptions and epistemic parameter uncertainty. A finite scenario tree is used to represent the sequential revelation of service demand and persistent UAV unavailability. Assignment and routing decisions are indexed by information nodes and linked through nonanticipativity, allowing a policy to adapt after new information becomes available without using future observations. Unit-distance fuel consumption is represented by normal uncertain variables, whereas service effectiveness is driven by node-specific lognormal uncertain factors. The resulting formulation incorporates heterogeneous capabilities, task completion, cross-stage collaboration, route continuity, flight-range limits, and consumable-payload capacities. A K–β risk model is developed to minimize the fuel-consumption and weighted service-deficit thresholds at prescribed belief levels. Inverse and generalized inverse uncertainty distributions yield a deterministic multiobjective reformulation while preserving the efficient policy set. A branch-risk-aware multiobjective evolutionary algorithm based on decomposition (BRA–MOEA/D) is designed as a structure-compatible solution method for the resulting combinatorial problem. On the tested medium and large benchmark instances, computational experiments produce feasible nondominated policies with distinct fuel–service tradeoffs; these results are evidence at the investigated scales rather than a general claim of algorithmic superiority or scalability. Mechanism comparisons show that adaptive branching and event-triggered recovery materially change the attainable risk-threshold front, while a sensitivity analysis confirms that the two belief levels separately regulate fuel-risk and service-risk conservatism. The model thereby links sequential adaptation and recovery decisions with belief-based risk control in heterogeneous UAV service operations.