Exact and Evolutionary Algorithms for Sequential Multi-Objective Transmission Topology Planning

TL;DR

This paper presents exact and evolutionary algorithms for day-ahead transmission topology planning, optimizing multiple operational objectives, with the exact method providing a complete Pareto front and serving as a benchmark.

Contribution

It introduces a novel block enumeration algorithm for exact Pareto front computation and a tailored NSGA-III-based evolutionary heuristic for multi-objective transmission topology planning.

Findings

The block algorithm computes the full Pareto front in under three minutes for a congested day.

The evolutionary algorithm converges towards the Pareto front but does not fully recover it.

The methods are validated using real data from the Dutch high-voltage grid.

Abstract

We address day-ahead transmission topology planning and congestion management as a sequential, multi-objective optimization problem and develop two complementary algorithms for it: an exact enumeration method and a tailored evolutionary heuristic. The problem is formulated with four operational objectives reflecting real TSO decision criteria: worst-case line loading under $N-1$ security, topological depth, number of switching actions, and time spent in non-reference topologies, over a 24-hour horizon. We introduce the block algorithm, an exact method that exploits the temporal block structure of feasible strategies to enumerate the complete Pareto front; for fixed operational bounds on depth and switch count, its evaluation count grows polynomially with the planning horizon. We complement it with a multi-objective evolutionary algorithm based on NSGA-III, with structure-guided initialization and problem-specific variation operators tailored to the topology-planning structure. Using real operational data from the Dutch high-voltage grid operated by TenneT TSO, we show that the block algorithm computes the full Pareto front for a highly congested day in under three minutes, and that the evolutionary algorithm converges toward but does not recover the exact front. The block algorithm thus provides both a practical decision-support tool and a ground-truth benchmark for future heuristic and learning-based methods on this problem class.