Metaheuristic Optimization of Hybrid Renewable Energy Systems Under Asymmetric Cost-Reliability Objectives: NSGA-II and MOPSO Approaches
Amal Hadj Slama, Lotfi Saïdi, Majdi Saidi, Mohamed Benbouzid
Abstract
This study investigates the asymmetric trade-off between cost and reliability in the optimal sizing of stand-alone Hybrid Renewable Energy Systems (HRESs) composed of photovoltaic panels (PV), wind turbines (WT), battery storage, a diesel generator (DG), and an inverter. The optimization is formulated as a multi-objective problem with Cost of Energy (CoE) and Loss of Power Supply Probability (LPSP) as conflicting objectives, highlighting that those small gains in reliability often require disproportionately higher costs. To ensure practical feasibility, the installation roof area limits both the number of PV panels, wind turbines, and batteries. Two metaheuristic algorithms—NSGA-II and MOPSO—are implemented in a Python-based framework with an Energy Management Strategy (EMS) to simulate operation under real-world load and resource profiles. Results show that MOPSO achieves the lowest CoE (0.159 USD/kWh) with moderate reliability (LPSP = 0.06), while NSGA-II attains a near-perfect reliability (LPSP = 0.0008) at a slightly higher cost (0.179 USD/kWh). Hypervolume (HV) analysis reveals that NSGA-II offers a more diverse Pareto front (HV = 0.04350 vs. 0.04336), demonstrating that explicitly accounting for asymmetric sensitivity between cost and reliability enhances the HRES design and that advanced optimization methods—particularly NSGA-II—can improve decision-making by revealing a wider range of viable trade-offs in complex energy systems.