In this paper, a novel routing formation algorithm called Geometric programming based Energy Efficient Routing protocol (GEER) is proposed for hybrid ad-hoc network. It optimizes two sets of objectives: (i) maximize network lifetime and throughput, and (ii) minimize packet loss and routing overhead. The stated optimizations are done by the fusion of multi-objective optimization, geometric programming, and intuitionistic fuzzy set. The combination of stated techniques provides an effective tool that evaluates an optimal solution based on all objectives and estimates non-linear parameters of the network. The proposed method GEER is simulated in LINGO optimization software and validated with some existing methods in several scenarios. The outcomes of validation illustrate that the proposed method GEER outperforms the other existing methods based on several network metrics.