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The communication problem is to select a minimal set of placed sensor devices in a service area so that the entire service area is accessible by the minimal set of sensors. Finding the minimal set of sensors is modeled as a vertex cover problem, where the vertex cover set facilitates the communications between the sensors in a multi-hop fashion keeping in mind the limited communication range and battery lifespan of all sensors. The vertex cover set is a subset of the coverage set of sensors; therefore, we transform the search space from continuous into discrete space. We encoded the vertex cover problem into the evolutionary domain, where the objective function is to select a minimal set of sensors out of the coverage sensors to act as a vertex cover so that the communication range of the vertex cover set covers the entire service area. The experimental results demonstrate the feasibility of our evolutionary approach in finding minimal vertex cover set; which is less than 16% of total sensors used as communication sensors; in under 5 minutes seconds with 91% coverage of the sensor nodes in wireless sensor network.