Edge computing minimizes latency and enhances real-time data processing compared to traditional cloud systems. However, efficient resource management and task scheduling remain complex due to dynamic workloads, heterogeneous nodes, and limited energy budgets. This study introduces a hybrid metaheuristic optimization and graph-based scheduling framework for adaptive resource management in edge environments. The proposed system integrates quasi-Sobol optimization with sigmoid fuzzy logic to balance computational load and minimize latency, while directed acyclic graph (DAG)-based scheduling ensures dependency-aware execution across edge nodes. Adaptive optimization control strengthens scalability and responsiveness under varying workload conditions. The framework is validated through simulation using edge server datasets and evaluated based on precision, recall, F1-score, latency, and energy consumption metrics. Experimental results demonstrate significant improvements in task allocation accuracy, resource utilization, and power efficiency compared to conventional scheduling methods. The approach offers a technically robust and scalable foundation for real-time, resource-efficient task scheduling in modern edge computing applications.