Wireless Body Area Network (WBAN) is an interconnection of tiny biosensors that are organized in/on several parts of the body. The developed WBAN is used to sense and transmit health-related data over the wireless medium. Energy efficiency is the primary challenges for increasing the life expectancy of the network. To address the issue of energy efficiency, one of the essential approaches i.e., the selection of an appropriate relay node is modelled as an optimization problem. In this paper, energy efficient routing optimization using Multiobjective-Energy Centric Honey Badger Optimization (M-ECHBA) is proposed to improve life expectancy. The proposed M-ECHBA is optimized by using the energy, distance, delay and node degree. Moreover, the Time Division Multiple Access (TDMA) is used to perform the node scheduling at transmission. Therefore, the M-ECHBA method is used to discover the optimal routing path for enhancing energy efficiency while minimizing the transmission delay of WBAN. The performances of the M-ECHBA are analyzed using life expectancy, dead nodes, residual energy, delay, packets received by the Base Station (BS), Packet Loss Ratio (PLR) and routing overhead. The M-ECHBA is evaluated with some classical approaches namely SIMPLE, ATTEMPT and RE-ATTEMPT. Further, this M-ECHBA is compared with the existing routing approach Novel Energy Efficient hybrid Meta-heuristic Approach (NEEMA), hybrid Particle Swarm Optimization-Simulated Annealing (hPSO-SA), Energy Balanced Routing (EBR), Threshold-based Energy-Efficient Routing Protocol for physiological Critical Data Transmission (T-EERPDCT), Clustering and Cooperative Routing Protocol (CCRP), Intelligent-Routing Algorithm for WBANs namely I-RAW, distributed energy-efficient two-hop-based clustering and routing namely DECR and Modified Power Line System (M-POLC). The dead nodes of M-ECHBA for scenario 3 at 8000 rounds are 4 which is less when compared to the dead nodes of EBR.