Grid modernization and digitalization gradually alter the traditional operation of power systems. Demand side management has attained significant attention and the deployment of smart meters creates opportunities for new data-driven services. Towards this direction, home energy management systems (HEMS) can play a pivotal role by enabling residential demand response applications. This paper introduces a HEMS aiming at low energy cost, improved thermal comfort and scheduling of appliance operation according to end-user habits. To this end, a multi-objective optimization problem is formulated by employing a non-intrusive load monitoring mechanism and a control scheme for heat pumps. The conducted analysis investigates the effect of each objective on the overall system performance under different dynamic tariff schemes.