Non-Submodular Cooperation in UAV Swarms for Active Missile Defense

Defending high-value assets against precision-guided missiles is among the hardest problems in modern autonomous systems, and cooperative swarms of low-cost unmanned aerial vehicles (UAVs) are rapidly changing how this defense can be mounted. We study such a swarm tasked with deploying smoke screen countermeasures, formulating its coordination as a high-dimensional, non-concave optimal control problem in which the objective of maximizing the union of obscuration intervals is inherently non-additive. We prove that the underlying discrete selection layer is monotone but not submodular, so agent contributions cannot be assessed in isolation and greedy or auction-based allocation carries no near-optimality guarantee, a structural result that motivates joint planning and generalizes beyond the present application. To navigate the resulting 40-dimensional decision space, we propose a joint planning framework driven by an enhanced metaheuristic algorithm (SBOA-Pro). Our simulations demonstrate that optimized cooperation yields a substantial improvement in defensive effectiveness over unoptimized baselines, achieving a total obscuration of 28.73 seconds. Our analysis identifies the empirical signature of this non-submodular structure, a counter-intuitive emergent principle termed Phantom Synergy, in which agents with zero measurable individual contribution can nonetheless be indispensable to the collective solution. This challenges additive agent valuation methods and indicates that in complex cooperative tasks the utility of an agent is defined not by its isolated output but by its role within the system-level solution. A sensitivity analysis further reveals an asymmetric robustness profile. The collective strategy retains roughly 95% of its efficacy under a 6.7% variation in threat velocity, yet remains markedly sensitive to internal execution errors, indicating that its viability depends more on platform execution precision than on external threat uncertainty.