Relax-and-round strategies for solving the unit commitment problem with AC power flow constraints

Abstract The Unit Commitment problem with AC power flow constraints (UC-ACOPF) is a non-convex mixed-integer nonlinear programming (MINLP) problem encountered in power systems. Its combinatorial complexity, together with its non-convex and nonlinear constraints, makes it particularly challenging. A common approach to tackle this problem is to relax the integrality condition, but this often results in infeasible solutions. Consequently, rounding heuristics are frequently employed to restore integer feasibility. This paper addresses recent advances in heuristics aimed at quickly obtaining feasible points for the UC-ACOPF problem, focusing specifically on direct relax-and-round strategies. We propose a model-based heuristic that rescales the solution of the integer-relaxed problem before rounding. Furthermore, we introduce rounding formulas designed to enforce combinatorial constraints and with the aim of maintaining AC feasibility in the returned points. These methodologies are compared with standard direct rounding techniques in the literature, and applied to 6- and 118-bus test systems. Additionally, we integrate the proposed heuristics into an implementation of the Feasibility Pump (FP) method, demonstrating their utility and potential to enhance existing rounding strategies.