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The assessment of grid-connected systems depends on their cost efficiency, reliability, and greenhouse gas (GHG) reduction potential. This study presents a multi-objective optimization framework for designing a grid-connected photovoltaic (PV) and battery energy storage (BES) system integrated with an electric vehicle (EV) for a household in Riyadh, Saudi Arabia. The framework aims to minimize the Cost of Energy (COE) and Loss of Power Supply Probability (LPSP) while maximizing the Renewable Energy Fraction (REF). Additionally, GHG emissions are evaluated as a result of these objectives. The EV operates in Vehicle-to-Home (V2H) mode, enhancing system flexibility and energy management. The optimization process employs two advanced metaheuristic techniques, Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Harris Hawks Optimization (MOHHO), to identify Pareto front solutions. Fuzzy logic is then applied to determine a balanced compromise among the economically optimal (minimum COE), renewable energy-oriented (maximum REF), and environmentally optimal (minimum GHG emissions) solutions. Simulation results show that the proposed system achieves a COE of USD 0.0554/kWh, a LPSP of 1.96%, and an REF of 92.55%. Although the COE is slightly higher than that of the grid, the system provides significant environmental and renewable energy benefits. This study highlights the potential of integrating dynamic EV management and advanced optimization techniques to enhance the performance of grid-connected systems. The findings demonstrate the effectiveness of combining Pareto-based optimization with fuzzy logic to achieve balanced solutions addressing economic, environmental, and renewable energy objectives, paving the way for sustainable energy systems in urban households. Full article