On the influence of problem definition in sensor placement optimization

Abstract

The combinatorial nature of sensor placement optimization has motivated the use of heuristic algorithms to avoid the high computational costs of finding global optima by focusing instead on satisfactory local optima. Transition of an optimization strategy from research to practice should involve a detailed inquiry into the dependence of its results on the representation of realistic scenarios. A sampling method was used to examine how the specification of a sensor placement problem for optimization affects the statistical properties of various ensembles of optimum networks produced by a heuristic algorithm. Features sampled in each ensemble were the resolution of the grid used for computing network coverage, the range of each sensor, and the dimensions of obstacles to line-of-sight sensing. The candidate placement grid also was sampled to examine the consequences of being unable to place sensors at a subset of a regularly spaced grid. The objective function was the number of sensors required to exceed a probability of detection threshold throughout the coverage area. The relative importance of variability in each parameter was found to depend on the widths and baseline values of the assumed variability ranges. Important length scale ratios were identified for ensuring the feasibility and integrity of the optimization process.