Surveillance Radar Placement on Digital Elevation Models: A Constraint Optimization Model with a Lexicographic Coverage Objective

Ground surveillance radars on rugged terrain must be placed so that a few units observe as much of the area as possible, preferably with redundancy, while remaining able to communicate. Existing models either prescribe the multiple-coverage level in advance or rely on heuristics without optimality guarantee. We formulate radar placement on a digital elevation model as a constraint optimization problem that combines line-of-sight viewsheds with antenna height and radar horizon, distance and line-of-sight constraints between radars, and a lexicographic objective that maximizes the observed area first and multiple coverage next, without a prescribed coverage level or weights. We solve it exactly with backtracking, an improved search with symmetry breaking and bounding, and a CP-SAT model, and compare them with greedy and genetic-algorithm baselines on 30 synthetic and 10 real terrains. The line-of-sight computation agrees with GDAL on 99.4% of the cells. Requiring every pair of radars to communicate directly limits the mean coverage to at most 38% on the synthetic terrains, whereas multi-hop connectivity reaches 75% with ten radars, close to the unconstrained optimum. The improved exact search solves 99 of 100 instances with up to 900 candidate locations within 300 s.