Cloud Computing is the significant paradigm responsible for the massive migration of enterprise applications in the information world. The resource allocation and scheduling in data centers of the cloud is one of the predominant optimization issues in clouds. Diversified numbers of static and dynamic allocation schemes were propounded for handling the problem of resource allocation. However, the conventional resource management schemes are not adequate to handle resource allocation based on the demands received from the tasks of the client in a reliable and intelligent manner. In this paper, a Hybrid Simulated Annealing and Spotted Hyena Optimization Algorithm (HSA-SHOA) is proposed as a significant bio-inspired resource management and task scheduling technique that plays an anchor role in the cloud environment. This HSA-SHOA-based resource management technique facilitates the option of task allocation to the individual virtual machines in an effective way based on the benefits of Spotted Hyena Optimization Algorithm (SHOA). It is propounded for maintaining the balance between exploitation and exploration involved in the task of optimizing resources, such that virtual machines are never underloaded or overloaded. Further, the management of resources that includes memory and CPU is handled based on the demands introduced by the tasks based on the incorporation of Simulated Annealing (SA) with SHOA. Simulation experiments conducted through CloudSim demonstrated the superior performance of the proposed HSA-SHOA-based resource management scheme over the benchmarked bio-inspired scheme evaluated based on enhanced reliability, makespan, energy consumption, minimized mean response time and cloud resources utilization rate.