This paper presents the development of a heuristic-based algorithm for a Home Electric Energy Management System (HEEMS). The novelty of the proposal resides in the fact that solutions of the Pareto front, minimizing both the energy consumption and cost, are obtained by a Genetic Algorithm (GA) considering the renewable energy availability as well as the user activity level (AL) inside the house. The extensive solutions search characteristic of the GAs is seized to avoid the calculation of the full set of Pareto front solutions, i.e., from a reduced set of non-dominated solutions in the Pareto sense, an optimal solution with the best fitness is obtained, reducing considerably the computational time. The HEEMS considers models of the air conditioner, clothes dryer, dishwasher, electric stove, pool pump, and washing machine. Models of the wind turbine and solar PV modules are also included. The wind turbine model is written in terms of the generated active power exclusively dependent on the incoming wind profiles. The solar PV modules model accounts for environmental factors such as ambient temperature changes and irradiance profiles. The effect of the energy storage unit on the energy consumption and costs is evaluated adapting a model of the device considering its charge and discharge ramp rates. The proposed algorithm is implemented in the Matlab® platform and its validation is performed by comparing its results to those obtained by a freeware tool developed for the energy management of smart residential loads. Also, the evaluation of the performance of the proposed HEEMS is carried out by comparing its results to those obtained when the multi-objective optimization problem is solved considering weights assigned to each objective function. Results showed that considerable savings are obtained at reduced computational times. Furthermore, with the calculation of only one solution, the end-user interaction is reduced making the HEEMS even more manageable than previously proposed approaches.