## 1 Introduction  
The frequency and intensity of extreme weather events have significantly increased over the last decade, with the National Oceanic and Atmospheric Administration reporting a more than twofold increase in number of billion-USD weather and climate disasters compared to that in the previous decade in the USA alone [1]. One such event was Hurricane Ida in September 2021, which hit Louisiana, USA, and caused 902,000 customers to lose electricity. Even after 15 days of restoration efforts, more than 10% of customers were still without power. The state faced significant infrastructure damage, including approximately 30,000 poles, 36,000 spans of wire, and 6000 transformers affected [2, 3]. These types of extreme weather events, exacerbated by climate change, are ever-increasing and pose severe threats to power networks. The cascading and widespread outages due to extreme weather events result in massive power outage costs. These costs become even more prominent when critical load points, such as hospitals, fire stations, data centers, etc., are affected. Researchers have proposed various infrastructure hardening and operational management strategies to enhance the resilience of power systems against extreme weather events [4; 5; 6; 7]. However, given the unpredictable nature of the intensity and frequency of such events, it is generally anticipated that power systems will inevitably be affected by these extremes, even after employing resilience enhancement methods. Consequently, it is a usual practice to prioritize resource allocation in the restoration of critical loads during these events. A wide range of research methods have been explored for restoring critical loads in extreme event situations. System planning measures, such as the installation of distributed energy resources (DER) and microgrid formation for supplying critical loads during extreme events, as well as operational strategies to minimize their adverse impacts, have received considerable attention [8; 9]. The authors of References [6; 10] utilize DER for the restoration of critical loads in a distribution system. A graph-theoretic framework is utilized in [10] to determine the available path between the DER and the critical load to facilitate the fast restoration of critical loads. Reference [6] formulates an optimization problem to minimize the critical load curtailment in a microgrid based on the penalty cost for the load curtailed. References [11; 12] utilize electric vehicles (EV) as mobile energy storage to restore critical loads. In Reference [11], EVs parked at residential and commercial parking lots are used as an energy storage source to form a microgrid to supply the critical loads, whereas Reference [12] assesses the real-time traffic conditions and congestion following an extreme event to strategically plan the optimal routes for EV and repair crews to reach critical loads. Reference [13] suggests a dynamic strategy for restoring priority loads, wherein the restoration plan is regularly updated on an hourly basis. This updating process takes into account the current demand of the load and the availability of resources, ensuring an efficient restoration process. References [14; 15] propose an intentional islanding scheme in a reconfigurable distribution system to improve the resilience of critical loads. Reference [16] presents a combination of long-term hardening measures and short-term operational measures to restore the supply to the critical loads. The section comprising the distribution systems consisting of priority loads is undergrounded before the event. Following the event, mobile generators are deployed to supply power to critical components within the system. References [7; 17; 18] propose a targeted hardening of infrastructures based on the location of essential load points to enhance the resilience of power systems against disastrous events. Various researchers have proposed several metrics to quantify resilience, but there is still no universally accepted standard.