Graph-Enhanced Adaptive Reinforcement Learning for Multi-Objective Task Allocation and Power Optimization in Edge Computing

Edge computing (EC) has emerged as a critical paradigm for enabling low-latency, real-time applications, yet the distributed and resource-constrained nature of edge infrastructure poses significant challenges for energy-efficient task allocation. Traditional heuristic and reinforcement learning (RL) approaches may not explicitly represent the changing relationships among edge servers, potentially limiting their effectiveness in energy-aware task allocation and load balancing. This paper proposes Graph-Enhanced Adaptive Reinforcement Learning (GEA-RL), a framework that integrates Graph Neural Networks (GNNs) with Deep Q-Networks (DQN) for task allocation and migration in EC systems. Unlike conventional approaches that treat servers as independent entities, GEA-RL explicitly models server relationships and resource dependencies through dynamic graph structures, enabling more intelligent allocation decisions. Our method formulates the optimization problem as a Markov Decision Process with realistic power consumption models incorporating both static and dynamic components while considering resource constraints and migration costs. We evaluate GEA-RL through simulations under multiple workload scenarios and compare its performance with heuristic and RL baselines in terms of power consumption, load balancing, and response time. Simulation results across multiple workload scenarios reveal that GEA-RL achieves an average response time of 99 ms, compared with 121 ms for the Worst-Fit baseline, representing an 18.2% reduction. The framework also achieves a service availability of 99.82%, compared with 99.41% for Worst-Fit, and reduces power consumption by 3.0% under the evaluated settings. These results indicate that incorporating graph-structured information into RL-based resource management can improve response time, service availability, and energy efficiency in the simulated EC environment.