The optimization of energy consumption, with consequent costs reduction, is one of the main challenges in present and future smart grids. Of course, this has to occur keeping the living comfort for the end-user unchanged. In this work, an approach based on the mixed-integer linear programming paradigm, which is able to provide an optimal solution in terms of tasks power consumption and management of renewable resources, is developed. The proposed algorithm yields an optimal task scheduling under dynamic electrical constraints, while simultaneously ensuring the thermal comfort according to the user needs. On purpose, a suitable thermal model based on heat-pump usage has been considered in the framework. Some computer simulations using real data have been performed, and obtained results confirm the efficiency and robustness of the algorithm, also in terms of achievable cost savings.Index Terms-Dynamic residential scenarios, energy and task scheduling, mixed-integer linear programming (MILP), optimal home energy management, smart grid, thermal comfort.

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