  In an attempt to speed up the solution of the unit commitment (UC) problem,
both machine-learning and optimization-based methods have been proposed to
lighten the full UC formulation by removing as many superfluous line-flow
constraints as possible. While the elimination strategies based on machine
learning are fast and typically delete more constraints, they may be
over-optimistic and result in infeasible UC solutions. For their part,
optimization-based methods seek to identify redundant constraints in the full
UC formulation by exploring the feasibility region of an LP-relaxation. In
doing so, these methods only get rid of line-flow constraints whose removal
leaves the feasibility region of the original UC problem unchanged. In this
paper, we propose a procedure to substantially increase the line-flow
constraints that are filtered out by optimization-based methods without
jeopardizing their appealing ability of preserving feasibility. Our approach is
based on tightening the LP-relaxation which the optimization-based method uses
with a valid inequality related to the objective function of the UC problem and
hence, of an economic nature. The result is that the so strengthened
optimization-based method identifies not only redundant line-flow constraints
but also inactive ones, thus leading to more reduced UC formulations.
