A Symmetry-Driven Inverse Design Framework for Multi-Agent Cooperative Deployment Under Line-of-Sight Constraints

Cooperative deployment of mobile agents under geometric and line-of-sight constraints gives rise to high-dimensional constrained optimization problems whose underlying physical configuration often exhibits exploitable structure. This paper develops a symmetry-driven inverse design framework that leverages two structural features of the engagement geometry—the Z2×Z2 mirror symmetries of the extended target silhouette and a closed-form forward–inverse correspondence between line-of-sight-aligned burst locations and physical agent parameters—to construct low-dimensional seeds for subsequent physical parameter optimization. The framework is developed and validated on a representative naval defense instance in which a fleet of unmanned aerial vehicles (UAVs) releases spherical obscuration payloads to interrupt the line of sight between incoming mobile threats and a cylindrical extended target. Instead of searching only over the four-dimensional UAV parameter space (heading angle, speed, drop time, fuse delay), the method first specifies a desired burst location in a two-dimensional inverse space and analytically back-calculates feasible agent parameters, which are then refined by multi-start Nelder–Mead optimization in the physical parameter space. A conservative three-dimensional cylindrical line-of-sight obscuration model is developed by constructing four extreme tangent sightlines from the missile to the cylindrical target and verifying whether the spherical smoke cloud simultaneously blocks all of them. A hierarchical multi-agent task allocation framework combines a performance matrix, assignment enumeration, and joint multi-start refinement. Numerical experiments on five progressively complex sub-problems demonstrate obscuration durations of 1.362s (single fixed shot), 4.580s (optimized shot), 7.324s (three-shot relay), 11.140s (three-UAV cooperation), and 20.652s (full five-UAV three-missile assignment). Additional high-dimensional benchmarks, sensitivity tests, and error analyses clarify the reproducibility and limitations of the approach.