This research is aimed to investigate the Evolutionary paradigm for minimizing power consumption in wireless sensor networks (WSN) at the design stage. This work incorporated required connectivity and energy-conservation constraints while finding optimal sensor network designs. The optimization process considered four energy consumption levels for cluster heads, sensors in high and low level signal locations and inactive sensors. Energy consumption has to be minimized to ensure maximum battery life span for the sensors without compromising the Quality of Service that is required for any specific application. This work investigates the efficiency of genetic algorithmic approach to search for an acceptable solution in a large solution space which is a non-polynomial problem.