Review of Symmetry-Breaking Options on Mathematical Programming Models with Rolling Horizons Procedure

The rolling horizons procedure is widely used both in industry and in scientific research for the resolution of mathematical programming models. It allows reducing the size of the models to be solved in the times allowed with the available computational capacities. It takes into consideration the closest information with less uncertainty. But programming models can have symmetries, when they have variables that can be permuted without changing the structure of the problem. These symmetries increase the search spaces for possible solutions, increasing the need for computation and presenting alternative solutions with equivalent results in the objective function. The symmetry can generate different solutions with equivalent values in the objective function but that can imply very different results in the long term with the rolling horizons procedure. This paper presents the proposed actions to symmetry break that have been applied to the rolling horizons procedure. The work provides the different proposals identified to break the symmetry.