[Paper Review] Optimal Transmission Switching: Improving Solver Performance Using Heuristics

Anton Hinneck, David Pozo|arXiv (Cornell University)|Jun 23, 2021

Optimal Power Flow Distribution4 citations

TL;DR

This paper proposes a novel asynchronous parallel framework that accelerates exact mixed-integer linear programming (MILP) solution of the Optimal Transmission Switching Problem (OTSP) by concurrently running a full OTSP formulation and heuristic-based incumbent solution generation. The method significantly reduces solution time—achieving optimal solutions up to 30 times faster than standard solvers—while maintaining global optimality guarantees through dynamic lower bound updates.

ABSTRACT

The optimal transmission switching problem (OTSP) is an established problem of changing a power grid's topology to obtain an improved operation by controlling the switching status of transmission lines. This problem was proven to be NP-hard. Proposed solution techniques based on mixed-integer formulations can guarantee globally optimal solutions but are potentially intractable in realistic power grids. Heuristics methods cannot guarantee global optimality but can provide tractable solution approaches. This paper proposes solving the OTSP using exact formulations alongside parallel heuristics that generate good candidate solutions to speed up conventional branch-and-bound algorithms. The innovative aspect of this work is a new asynchronous parallel algorithmic architecture. A solver instance solving the full OTSP formulation is run in parallel to another process that asynchronously generates solutions to be injected into the full OTSP solution procedure during run time. Our method is tested on 14 instances of the pglib-opf library: The largest problem consisting of 13659 buses and 20467 branches. Our results show a good performance for large problem instances, with consistent improvements over off-the-shelf solver performance. We find that the method scales well with an increase in parallel processors.

Motivation & Objective

• To address the computational intractability of large-scale OTSP instances, which are NP-hard and difficult to solve with exact methods alone.
• To overcome the limitation of heuristic-only approaches, which lack optimality guarantees and lower bounds.
• To improve the performance of exact branch-and-bound algorithms by injecting high-quality heuristic solutions in real time.
• To design a scalable, asynchronous parallel architecture compatible with standard MILP solvers like Gurobi and CPLEX.
• To evaluate the method on realistic power system cases from the pglib-opf library, including large systems with over 13,000 buses.

Proposed method

• A master solver instance runs the full OTSP MILP formulation using a commercial MIP solver (e.g., Gurobi), while multiple worker processes asynchronously generate candidate solutions via problem-specific heuristics.
• The heuristic workers use a line selection criterion (lpsc) based on power transfer distribution factors to prioritize promising transmission lines for switching.
• Solutions from the heuristic workers are injected into the master solver’s branch-and-cut process in real time, improving the incumbent upper bound and tightening the optimality gap.
• The architecture is asynchronous and supports dynamic load balancing across multiple processors, with each worker rank assigned to a subset of CPU cores.
• The method leverages rich APIs of modern solvers and MPI-based parallel computing to enable efficient communication and integration.
• The framework is general-purpose and compatible with any MILP solver, allowing plug-in use of various heuristic strategies.

Experimental results

Research questions

• RQ1 Can parallel heuristic solution generation significantly accelerate the convergence of exact MIP solvers for large-scale OTSP instances?
• RQ2 How does the integration of real-time incumbent solutions from heuristics affect the optimality gap and solution time in branch-and-cut algorithms?
• RQ3 To what extent does the proposed asynchronous parallel architecture scale with increasing numbers of processors on realistic power system test cases?
• RQ4 Can the method achieve near-optimal or optimal solutions within practical time limits for large systems (e.g., 13,659 buses) where standard solvers fail?
• RQ5 How does the performance of the proposed method compare to off-the-shelf solvers in terms of solution quality and computation time?

Key findings

• The proposed P-OTSP framework achieved optimal solutions for the 1354_pegase case in under 30 seconds, a 30-fold improvement over the baseline off-the-shelf solver.
• For the largest test case (13659 buses, 20467 branches), the method found solutions within 0.86% of the global optimum in less than 15 minutes, except for the 6470_rte case.
• With three parallel worker processes, the method reduced computation time by a factor of 30 compared to the standard solver, demonstrating strong scalability.
• The integration of heuristic solutions significantly improved the incumbent upper bound, accelerating convergence and reducing the optimality gap.
• The asynchronous architecture effectively utilized all available cores, outperforming the stock solver even when using the same number of cores.
• The method maintains global optimality guarantees by continuously updating the lower bound, enabling quantification of remaining improvement potential.