Solve Large-scale Unit Commitment Problems by Physics-informed Graph
  Learning
Jingtao Qin Nanpeng Yu
Unit commitment (UC) problems are typically formulated as mixed-integer
programs (MIP) and solved by the branch-and-bound (B&B) scheme. The recent
advances in graph neural networks (GNN) enable it to enhance the B&B algorithm
in modern MIP solvers by learning to dive and branch. Existing GNN models that
tackle MIP problems are mostly constructed from mathematical formulation, which
is computationally expensive when dealing with large-scale UC problems. In this
paper, we propose a physics-informed hierarchical graph convolutional network
(PI-GCN) for neural diving that leverages the underlying features of various
components of power systems to find high-quality variable assignments.
Furthermore, we adopt the MIP model-based graph convolutional network (MB-GCN)
for neural branching to select the optimal variables for branching at each node
of the B&B tree. Finally, we integrate neural diving and neural branching into
a modern MIP solver to establish a novel neural MIP solver designed for
large-scale UC problems. Numeral studies show that PI-GCN has better
performance and scalability than the baseline MB-GCN on neural diving.
Moreover, the neural MIP solver yields the lowest operational cost and
outperforms a modern MIP solver for all testing days after combining it with
our proposed neural diving model and the baseline neural branching model.