Symmetry issues in mixed integer programming based Unit Commitment

• Symmetry breaking method is applied to MILP based UC problems with identical units.
• Elements that generate symmetry in UC are identified.
• The B&C algorithm under the presence of symmetry is evaluated.
• Addition of constraints to set generator status variable priorities is proposed.
• Results show that this method leads to a substantial reduction in computation cost.

A mixed integer linear problem is called symmetric if the variables can be permuted without changing the structure of the problem. Generally, these problems are difficult to solve due to the redundant solutions which populate the enumeration tree. In Unit Commitment problems the symmetry is present when identical generators have to be scheduled. This article presents a way to reduce the computational burden of the Branch and Cut algorithm by adding appropriate inequalities into the mixed-linear formulation of the Unit Commitment problem. In the examples considered, this approach leads to a substantial reduction in computational effort, without affecting the objective value.