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.

提出了一种基于物理信息的分层图卷积网络（PI-GCN）用于神经潜伏，通过学习电力系统各组成部分的底层特征来寻找高质量的变量分配；采用基于 MIP 模型的图卷积网络（MB-GCN）用于神经分支，在 B＆B 树的每个节点上选择最优变量进行分支；将神经潜伏和神经分支集成到现代 MIP 求解器中构建一个创新的神经 MIP 求解器，用于处理大规模的 UC 问题。数值研究表明，相较于基线 MB-GCN，PI-GCN 在神经潜伏方面具有更好的性能和可扩展性；此外，将神经 MIP 求解器与我们提出的神经潜伏模型和基线神经分支模型相结合，可以获得最低的运营成本，并在所有测试日中优于现代 MIP 求解器。

基于物理信息图学习解决大规模机组组合问题

Solve Large-scale Unit Commitment Problems by Physics-informed Graph  Learning

Finding a high-quality feasible solution to a combinatorial optimization (CO)
problem in a limited time is challenging due to its discrete nature. Recently,
there has been an increasing number of machine learning (ML) methods for
addressing CO problems. Neural diving (ND) is one of the learning-based
approaches to generating partial discrete variable assignments in Mixed Integer
Programs (MIP), a framework for modeling CO problems. However, a major drawback
of ND is a large discrepancy between the ML and MIP objectives, i.e., variable
value classification accuracy over primal bound. Our study investigates that a
specific range of variable assignment rates (coverage) yields high-quality
feasible solutions, where we suggest optimizing the coverage bridges the gap
between the learning and MIP objectives. Consequently, we introduce a post-hoc
method and a learning-based approach for optimizing the coverage. A key idea of
our approach is to jointly learn to restrict the coverage search space and to
predict the coverage in the learned search space. Experimental results
demonstrate that learning a deep neural network to estimate the coverage for
finding high-quality feasible solutions achieves state-of-the-art performance
in NeurIPS ML4CO datasets. In particular, our method shows outstanding
performance in the workload apportionment dataset, achieving the optimality gap
of 0.45%, a ten-fold improvement over SCIP within the one-minute time limit.

研究通过优化变量分配的覆盖率，建立深度神经网络模型以实现高质量的可行解，在组合优化问题中实现了最先进的性能表现。

阈值感知学习生成混合整数规划可行解

Threshold-aware Learning to Generate Feasible Solutions for Mixed  Integer Programs

Finding a better feasible solution in a shorter time is an integral part of
solving Mixed Integer Programs. We present a post-hoc method based on Neural
Diving to build heuristics more flexibly. We hypothesize that variables with
higher confidence scores are more definite to be included in the optimal
solution. For our hypothesis, we provide empirical evidence that confidence
threshold technique produces partial solutions leading to final solutions with
better primal objective values. Our method won 2nd place in the primal task on
the NeurIPS 2021 ML4CO competition. Also, our method shows the best score among
other learning-based methods in the competition.

使用基于神经深潜的后处理方法提高启发式的灵活性，并通过置信得分确定最优解的一部分解，以找到更好、更快的可行解。该方法在 NeurIPS 2021 ML4CO 竞赛中获得了第二名，且在同类基于学习的方法中获得了最佳成绩。