Symmetry breaking in MILP formulations for Unit Commitment problems

• Symmetry issues are discussed in the context of UC formulations.
• Three sets of SBC are proposed and analyzed.
• Three well-known UC MILP models are used to implement the SBC.
• The results presented are completely disruptive compared with the results presented in the literature.
• The SBC derived have a clear advantage over general methods available in two MILP solvers.

This paper addresses the study of symmetry in Unit Commitment (UC) problems solved by Mixed Integer Linear Programming (MILP) formulations, and using Linear Programming based Branch & Bound MILP solvers. We propose three sets of symmetry breaking constraints for UC MILP formulations exhibiting symmetry, and its impact on three UC MILP models are studied. The case studies involve the solution of 24 instances by three widely used models in the literature, with and without symmetry breaking constraints. The results show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed. The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers.