Scheduling of sensor nodes in an energy-efficient manner is one of the most effective ways for extending the lifetime of wireless sensor networks (WSNs). In energy-efficient scheduling, only a subset of the deployed sensor nodes is enabled to monitor the targets. As sensor nodes have restricted communication and sensing range, coverage and network connectivity should be considered while scheduling with fewer sensor nodes. For guaranteed transmission of sensing data from every target point to the base station, connectivity and coverage are the most pivotal issues in the scheduling of sensor nodes. In this research article, we have presented the energy-efficient active/sleep scheduling of the sensor nodes using a genetic algorithm (GA) with Dither Creeping mutation in which only few sensors are activated that ensures the coverage to all targets as well as communication with the sensor nodes and base station (BS). The novelty of the proposed GA with crossover and Dither Creeping mutation (GACDCM) is that the mutation probability is generated randomly rather than the fixed value for each string. As a result, for the same generation, the various strings of the proposed algorithm will be subjected to various creeping mutation probabilities and the same string is subjected to various creeping mutation probabilities at successive generations. The proposed algorithm replaces the traditional bitwise mutation. For exploring the search space in case of extremely constrained problems, Dither Creeping Mutation is more efficient than bitwise mutation. We have simulated the proposed algorithm extensively with several WSN scenarios. the simulation results are analyzed with the existent algorithms to validate the efficiency of the presented algorithm. The experimental result showed that the lifetime of the suggested GACDCM is increased by 53.27% than traditional GA, 27.93% than GANCDCM, 13.23% than NSGA-II, and 4% than algorithm proposed by Harizan and Kuila (Wireless Netw 25(4):1995–2011, 2019). © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.