Multi-objective framework for a home energy management system with the integration of solar energy and an electric vehicle using an augmented ε-constraint method and lexicographic optimization

•A home energy management system is developed as a multi-objective MILP paradigm.•An augmented ɛ-constraint method with lexicographic optimization is proposed.•Various case studies are performed using both deterministic and stochastic models.•Impacts of storage capacity and solar PV sizing on home scheduling are analyzed.•The proposed framework is effective for load scheduling for residential users.