A matheuristic for a bi-objective demand-side optimization for cooperative smart homes

This paper proposes the demand-side management (C-DSM) of collaborative homes during one day. Some homes may have photovoltaic panels and batteries, other homes may have batteries, and the remaining homes are pure energy consumers. Homes are interconnected and connected to the main grid. The proposed C-DSM is formulated as a constrained bi-objective and mixed-integer linear optimization model with one objective related to the total net energy cost and the other related to discomfort caused by allowing flexibility of controllable loads within an acceptable comfort range. A matheuristic approach has been proposed to determine an efficient Pareto set for the problem, combining the non-dominated sorting genetic algorithm II (NSGAII) with an exact solver. In this approach, discrete decision variables are represented as partial chromosomes and an exact solver determines the continuous decision variables in an optimal way. A number of simulations are performed and compared with the weighted sum algorithm (WSA) under four cases for small to large number of homes. The results demonstrate the effectiveness of power cooperation among homes and show that our algorithm is able to obtain more Pareto solutions in a much shorter time that are far better than those obtained by the WSA. The proposed algorithm is suitable for large-sized C-DSM problem instances, promotes power cooperation between homes, reduces the dependency to the main grid and achieves individual fairness of energy net cost of each home without the need for installation of photovoltaic panels and batteries for all homes.