The Sweet Spot of Bound Tightening for Topology Optimization
Salvador Pineda, Juan Miguel Morales
TL;DR
The paper tackles the computational difficulty of DC-OTS in fully switchable transmission networks by introducing topology-aware bound tightening (TBT). By maintaining integrality for a carefully selected subset of lines within a level-$k$ neighborhood of each target line, TBT preserves local physical constraints (e.g., Kirchhoff-like relations) while relaxing distant decisions to improve bound quality without excessive cost. Empirical results on the IEEE 118-bus system show that a moderate neighborhood size (notably $k=2$) yields the best trade-off, halving the number of unsolved instances and reducing total solve time by around 45% compared with strong baselines. The approach thus enhances scalability and robustness of topology optimization in power systems with high renewable penetration, providing a practical path to tighter MILP reformulations and faster solutions.
Abstract
Topology optimization has emerged as a powerful and increasingly relevant strategy for enhancing the flexibility and efficiency of power system operations. However, solving these problems is computationally demanding due to their combinatorial nature and the use of big-M formulations. Optimization-based bound tightening (OBBT) is a well-known strategy to improve the solution of mixed-integer linear programs (MILPs) by computing tighter bounds for continuous variables. Yet, existing OBBT approaches in topology optimization typically relax all switching decisions in the bounding subproblems, leading to excessively loose feasible regions and limited bound improvements. In this work, we propose a topology-aware bound tightening method that uses network structure to determine which switching variables to relax. Through extensive computational experiments on the IEEE 118-bus system, we find that keeping a small subset of switching variables as binary, while relaxing the rest, strikes a sweet spot between the computational effort required to solve the bounding problems and the tightness of the resulting bounds.