Home energy management systems (HEMSs) are becoming increasingly popular as smart homes become more prevalent, along with their ability to reduce peak network loads and generate and store green energy locally. A HEMS typically controls and schedules each appliance in a home using photovoltaics (PVs) and energy storage systems (ESSs) to help cut energy bills. HEMS and optimization algorithms are studied extensively. However, the wasted energy of PVs and the simultaneous consideration of ESS and plug-in hybrid electric vehicles (PHEVs) in multi-objective problems have not been taken into account. Hence, this paper examines the maximum use of PVs, ESS, and PHEV, and utilizes upstream electricity and selling energy simultaneously in single-objective and multi-objective problems to minimize three objective functions, such as the entire energy cost, peak-to-average ratio (PAR), and wasted energy of PV. A multi-objective improved differential evolution algorithm is used to solve the HEMSs. Based on the outcome, PV, ESS, and PHEV reduce the costs and also reduce the wasted energy of PV close to zero. Also, by penetration of ESSs and PHEVs, the energy is bought at a low price-time, and then used for demand response and sold to the upstream in high-price periods. The suggested method is considered under various scenarios, such as different ESS volumes and various charging/discharging rates, with and without PHEV participation in single and multi-objective optimization. Furthermore, the efficiency of the method is proven by obtaining lower energy costs, optimized PAR, and zero wasted PV energy compared to other prior papers.