Iterative Coupling of Interior-Point and Tabu Search Methods for Large-Scale Stochastic Mixed-Integer Problems

The secure and efficient operation of power systems involves both continuous and discrete decision variables, subject to operational uncertainties and intricate topological constraints. Such problems are naturally formulated as stochastic mixed-integer nonlinear programs (MINLPs), whose direct solution is computationally prohibitive due to their nonconvex structure and high dimensionality. This paper proposes a hybrid continuous discrete optimization framework that integrates predictor–corrector interior point methods with combinatorial search techniques of the Tabu Search type, designed to address preventive and corrective decision-making under uncertainty in a unified manner. Unlike conventional hybrid approaches, the proposed method establishes a formal iterative coupling between the continuous and discrete level, wherein marginal sensitivities derived from the Karush–Kuhn–Tucker (KKT) conditions of the interior-point block directly guide the combinatorial exploration process. This reciprocal exchange of analytical information eliminates the need for binary relaxations and endows the heuristic component with a mathematically grounded rationale. The methodology is validated on power systems of different scales, including the IEEE-118 and PEGASE-9241 networks, demonstrating its ability to consistently represent continuous and discrete operational decisions within a unified framework for secure power system operation under uncertainty. Mathematics Subject Classification (2020) 90C11 · 90C90 · 49M37 · 65K05