The electricity demand growth is one of the main problems in the power grid scenario, as this situation increases the electricity supply complexity. Simultaneously, environmental issues creates the need for non-pollutant, renewable solutions. With the advent of smart grids, which consists of integrating information and communication technologies (ICT) to a traditional grid, the demand management can be improved by the consumer participation. This process is defined as Demand Response, which is a program that aims to alter the consumer's electricity consumption patterns through incentives or benefits, either based on changes in the electricity price over time or when the power grid operation needs any intervention. Price-based DR programs are the most common schemes, in which a tariff model is used to help the consumer adjust his energy consumption based on electricity price variation. With the increased insertion of distributed generation and the microgrids, the management on the demand-side needs to consider the home appliances usage, as well as the distributed energy resources utilization, considering both the operational characteristics of these elements and the consumer preferences. In this work, a preference-based, demand response (DR) many-objective optimization model based on real-time electricity price is presented to solve the problem of optimal residential load management. The purpose of such a model are: 1) to minimize the costs associated with consumption; 2) to minimize the inconvenience caused to consumers; 3) to minimize environmental pollution; 4) to minimize the occurrence of rebound peaks. Potential solutions to the underlying many-objective optimization problem are subject to a set of electrical and operational constraints related to home appliances categories and the utilization of distributed energy resources (DER) and energy storage systems (ESS). The use of the proposed model is illustrated in a realistic microgrid scenario where suitable solutions were found by the Non-Dominated Sorting Genetic Algorithm III (NSGA-III). These solutions determine new operational periods for home appliances as well as the utilization of DER and ESS for the planning horizon while considering consumer preferences. Besides helping consumers to take advantage of the benefits offered by DR, the experimental results show that the many-objective DR model together with the NSGA-III algorithm can effectively minimize energy-consumption costs as well as reduce inconvenience costs, environmental pollution and rebound peaks.