Learning-aided Bigraph Matching Approach to Multi-Crew Restoration of Damaged Power Networks Coupled with Road Transportation Networks

The resilience of critical infrastructure networks (CINs) after disruptions, such as those caused by natural hazards, depends on both the speed of restoration and the extent to which operational functionality can be regained. Allocating resources for restoration is a combinatorial optimal planning problem that involves determining which crews will repair specific network nodes and in what order. This paper presents a novel graph-based formulation that merges two interconnected graphs, representing crew and transportation nodes and power grid nodes, into a single heterogeneous graph. To enable efficient planning, graph reinforcement learning (GRL) is integrated with bigraph matching. GRL is utilized to design the incentive function for assigning crews to repair tasks based on the graph-abstracted state of the environment, ensuring generalization across damage scenarios. Two learning techniques are employed: a graph neural network trained using Proximal Policy Optimization and another trained via Neuroevolution. The learned incentive functions inform a bipartite graph that links crews to repair tasks, enabling weighted maximum matching for crew-to-task allocations. An efficient simulation environment that pre-computes optimal node-to-node path plans is used to train the proposed restoration planning methods. An IEEE 8500-bus power distribution test network coupled with a 21 square km transportation network is used as the case study, with scenarios varying in terms of numbers of damaged nodes, depots, and crews. Results demonstrate the approach's generalizability and scalability across scenarios, with learned policies providing 3-fold better performance than random policies, while also outperforming optimization-based solutions in both computation time (by several orders of magnitude) and power restored.

Bigraph Matching Weighted with Learnt Incentive Function for Multi-Robot Task Allocation

Most real-world Multi-Robot Task Allocation (MRTA) problems require fast and efficient decision-making, which is often achieved using heuristics-aided methods such as genetic algorithms, auction-based methods, and bipartite graph matching methods. These methods often assume a form that lends better explainability compared to an end-to-end (learnt) neural network based policy for MRTA. However, deriving suitable heuristics can be tedious, risky and in some cases impractical if problems are too complex. This raises the question: can these heuristics be learned? To this end, this paper particularly develops a Graph Reinforcement Learning (GRL) framework to learn the heuristics or incentives for a bipartite graph matching approach to MRTA. Specifically a Capsule Attention policy model is used to learn how to weight task/robot pairings (edges) in the bipartite graph that connects the set of tasks to the set of robots. The original capsule attention network architecture is fundamentally modified by adding encoding of robots' state graph, and two Multihead Attention based decoders whose output are used to construct a LogNormal distribution matrix from which positive bigraph weights can be drawn. The performance of this new bigraph matching approach augmented with a GRL-derived incentive is found to be at par with the original bigraph matching approach that used expert-specified heuristics, with the former offering notable robustness benefits. During training, the learned incentive policy is found to get initially closer to the expert-specified incentive and then slightly deviate from its trend.