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This paper presents a statistical-mechanics-inspired procedure for optimization of the sensor field configuration to detect mobile targets. The key idea is to capture the low-dimensional behavior of the sensor field configurations across the Pareto front in a multiobjective scenario for optimal sensor deployment, where the nondominated points are concentrated within a small region of the large-dimensional decision space. The sensor distribution is constructed using location-dependent energy-like functions and intensive temperature-like parameters in the sense of statistical mechanics. This low-dimensional representation is shown to permit rapid optimization of the sensor field distribution on a high-fidelity simulation test bed of distributed sensor networks.