International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4277 2020 2020 Department of Computer Science, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia Abdulnaser Abdulnaser Energy consumption in large-scale distributed computing has become a first-order design constraint, affecting operational costs, carbon emissions, and service reliability. This paper proposes a hybrid optimization framework that combines Linear Programming (LP) for feasible solution seeding with a Hybrid Genetic–Simulated Annealing (HGSA) metaheuristic for global search. The objective is to minimize total energy while preserving Quality of Service (QoS) and Service-Level Agreement (SLA) constraints. We adopt a widely used server power model that relates power to utilization and extend it with an optional carbon-aware objective that weights power by time- and location-varying grid carbon intensity. Decision variables include task–node–time assignments and, optionally, per-host frequency states for dynamic voltage and frequency scaling (DVFS). The proposed HGSA leverages LP-based seeding to accelerate convergence, applies crossover and mutation operators to explore the search space, and uses simulated annealing to refine solutions and escape local optima. We evaluate the approach using Google Cluster traces and CloudSim Plus, reporting standard metrics such as total energy (kWh), carbon emissions (kgCO₂e) when applicable, SLA violations (%), and makespan. A percentage-reduction indicator quantifies improvements over baselines (e.g., Round Robin and First-Fit). The framework is designed to be reproducible and extensible, with an experimental template specifying workload preprocessing, simulator configuration, and evaluation protocols. Results demonstrate consistent reductions in energy alongside improved utilization balancing, while respecting SLA constraints; when carbon-aware weighting is enabled, the scheduler further shifts flexible work to cleaner intervals without compromising throughput. The contributions include: (i) a unified energycarbon objective with explicit constraints; (ii) an LP-seeded HGSA tailored to task scheduling; (iii) a dataset-driven evaluation recipe using realistic traces; and (iv) a practical measurement protocol that reports both absolute values and percentage reductions to facilitate cross-study comparison. 2026 2026 504 510 10.54216/IJNS.270241 https://www.americaspg.com/articleinfo/21/show/4277