Distributed active sensing is a new sensing paradigm, where active sensors and passive sensors are distributed in a field, and collaboratively detect and track the objects. "Exposure" of distributed active sensing networks (DASNs) quantifies the dimension limitations in detectability. It is important to deploy the sensors such that the exposure is minimized. Exposure minimization is shown to be NP-hard, and thus efficient heuristic algorithms are needed. In this paper, we propose a Genetic Algorithm (GA)-based solution that aims at achieving low exposure, scalability, and fast convergence. A novel flat binary chromosome encoding scheme and corresponding crossover and mutation operators are devised. Geometric knowledge is incorporated to significantly improve the convergence rate. Through extensive simulations, we demonstrate that the proposed algorithm outperforms a simple heuristic algorithm by up to 75%. The simulation results show that this algorithm is robust, self-adapti...