The exponential growth of data generated by various aspects of life, particularly through internet-enabled devices, has introduced significant challenges in processing such data within strict time constraints. Cloud computing has emerged as a potential solution due to its ability to handle heterogeneous, energy-constraint, and non-cooperative data. However, the task scheduling problem in cloud computing, being NP-hard, demands efficient solutions that balance system performance and energy consumption. Current methods often fail to address the imbalanced system loads and fluctuating cloud requests effectively, leading to increased energy usage and degraded performance. This paper tackles these challenges by proposing an energy-efficient load balancing strategy coupled with an optimized cloud requests placement method. Task scheduling is approached using the binary chaotic Jaya (BCJaya) algorithm, which leverages evolutionary techniques to ensure high performance. The proposed algorithm is evaluated against key metrics, including Makespan, virtual machine (VM) utilization, energy consumption, and load balancing rate. Additionally, the BCJaya algorithm's efficacy is demonstrated using a real-world benchmark dataset and is compared against established baselines. The results show that BCJaya consistently outperforms alternative methods, particularly in scenarios involving increasing tasks and VMs, making it a robust solution for cloud scheduling challenges.