This paper proposes a comprehensive mathematical optimization framework for techno-economic demand side management (DSM) in hybrid energy systems (HESs), with a focus on standalone configurations. The framework incorporates load growth projections and the probabilistic uncertainties of renewable energy sources to enhance planning robustness. To identify high-quality near-optimal solutions, several advanced metaheuristic algorithms were employed, including the Exponential Distribution Optimizer (EDO), Teaching-Learning-Based Optimization (TLBO), Circle Search Algorithm (CSA), and Wild Horse Optimizer (WHO). The results highlight substantial economic and environmental improvements, with battery integration yielding a 69.7% reduction in total system cost and an 84.3% decrease in emissions. Additionally, this study evaluated the influence of future load growth on fuel expenditure, offering realistic insights into the techno-economic viability of HES deployment.