Two advanced approaches (PA_1, and PA_2) based on a realistic 3D model of video sensor nodes (VSNs) deployed over a 2D target area are proposed to minimize energy consumption in the network maintaining area coverage and connectivity. Reducing the number of active VSNs decreases energy consumption, but lessens area coverage and connectivity too. These conflicting issues are resolved and an optimal solution is obtained by using an integer linear programming based approach PA_1. The problem being an NP-Hard one, PA_1 is not tractable for large instances, and a heuristic PA_2 based on an advanced genetic algorithm, is also developed to obtain the near-optimal solution. Simulation studies are carried out to compare the performance of PA_1, and PA_2 with the other three state-of-the-art approaches (APP_5, APP_6, and ET_3). Among three existing approaches, APP_6/(ET_3) is the best in energy consumption/(area coverage). It is observed that for the same simulation environment, both PA_1, and PA_2 guarantee higher network services, by reducing energy consumption by 40.85% and 33.34% respectively compared to the best existing approach APP_6; and as well as by increasing area coverage by 0.94% than the best existing approach ET_3 for the node density 150 on the target area of size 75x75 square meter. Between PA_1 and PA_2, PA_2 generates sub-optimal solution and PA_1 substantiates its superiority by reducing energy consumption by 11.26% than PA_2 without losing area coverage for the same simulation environment.