In this paper a multi-objective genetic algorithm is used to solve a multi-objective model to optimize the time allocation of domestic loads within a planning period of 36 h, in a smart grid context. The management of controllable domestic loads is aimed at minimizing the electricity bill and the end-user's dissatisfaction concerning two different aspects: the preferred time slots for load operation and the risk of interruption of the energy supply. The genetic algorithm is similar to the Elitist NSGA-II (Non-dominated Sorting Genetic Algorithm II), in which some changes have been introduced to adapt it to the physical characteristics of the load scheduling problem and improve usability of results. The mathematical model explicitly considers economical, technical, quality of service and comfort aspects. Illustrative results are presented and the characteristics of different solutions are analyzed.