In this work, a novel energy efficient multi-objective resource allocation algorithm for heterogeneous cloud radio access networks (H-CRANs) is proposed where the trade-off between increasing throughput and decreasing operation cost is considered. H-CRANs serve groups of users through femtocell access points (FAPs) and remote radio heads (RRHs) equipped with massive multiple input multiple output (MIMO) connected to the base-band unit (BBU) pool via front-haul links with limited capacity. We formulate an energy-efficient multi-objective optimization (MOO) problem with a novel utility function. Our proposed utility function simultaneously improves two conflicting goals as total system throughput and operation cost. With this MOO, we jointly assign the sub-carrier, transmit power, access point (AP)(RRH/FAP), RRH, front-haul link, and BBU. To address the conflicting objectives, we convert the MOO problem into a single-object optimization problem using an elastic-constraint scalarization method. With this approach, we flexibly adjust trade-off parameters to choose between two objective functions.To propose an efficient algorithm, we deploy successive convex approximation (SCA) and complementary geometric programming (CGP) approaches. Finally, via simulation results we discuss how to select the values of trade-off parameters, and we study their effects on conflicting objective functions (i.e., throughput and operation cost in MOO problem). Simulation results also show that our proposed approach can offload traffic from C-RANs to FAPs with low transmit power and thereby reduce operation costs by switching off the under-utilized RRHs and BBUs. It can be observed from the simulation results that the proposed approach outperforms the traditional approach in which each user is associated to the AP (RRHs/FAPs) with the largest average value of signal strength. The proposed approach reduces operation costs by 30% and increases throughput index by 25% which in turn leads to greater energy efficiency (EE).INDEX TERMS 5G, multi-objective optimization problem, elastic-constraints method.