Energy consumption is a vital issue when optimum usage and carbon footprint are all considered in today’s Internet of Things (IoT) environments. Considering edge computing, that becomes too critical in terms of wireless devices with limited battery power. Especially in healthcare applications, the defined IoHT approach requires sustainability while future massive solutions may result negative outputs in terms of carbon footprint. So, optimum energy consumption seems positive in terms of multiple ways. In the literature, one trendy method is using clustering for lowering the energy consumption within the Internet of Healthcare Things (IoHT) environment on edge computing. In this study, optimization of energy consumption in IoHT was done via improved Genetic Electro-Search Optimization (GESO) algorithm. According to the obtained findings in the performed applications, GESO was effective enough in finding optimum conditions of energy consumption for an active IoHT setup.