# The Spatial Optimization of Emergency Shelters Based on an Urban-Scale Evacuation Simulation
## 3 Theoretical Framework  
### Overall Research Framework  
This study was based on a detailed evacuation demand forecast via the use of an evacuation simulation model to analyze the supply and demand status of the site, and to obtain data regarding the remaining non-evacuated people at the plot scale, which can be used as a breakthrough point to construct a spatial optimization model. From the perspective of technical flow (Figure 1), it is mainly composed of the following three steps.  
Shelter demand analysis was the first step in the spatial layout evaluation and the key to the assessment of the supply and demand status of shelters. The POI data and residential unit data were mainly used to analyze daytime and nighttime shelter demand. The detailed methods and steps have been described in another study carried out by the present research team [12]. To avoid the duplication of work, the results of the previous demand analysis were directly used in the present study. Therefore, the main purpose of this article is to explore a method for evacuation simulation under the restriction of shelter capacity, as well as the spatial optimization of shelters.  
After obtaining the scale and spatial distribution of the shelter demand, an urban-scale evacuation simulation was carried out to obtain the supply and demand status of shelters, which can provide a data basis for the next step of spatial optimization. The balance of supply and demand in emergency shelters is important for effective disaster mitigation functions during disasters and in the evaluation of shelter service capacity. In the traditional practices of shelter planning, supply and demand are generally balanced by districts, rarely seen on streets. A problem that arises is that the probability is high that the supply and demand of certain small areas within the city may be unbalanced, and the service gap could be large. Therefore, we aimed to establish an evacuation simulation model between evacuees and shelters, and tried to simplify and implement complex and dynamic evacuation activities.  
Based on the results of the evacuation simulation, the scale and spatial distribution of the shelters were optimized. Because the core of the spatial optimization model is the realization of the redistribution of the remaining non-evacuated people at the demand point to the surrounding target plots, the parameters, functions, construction process, and solution of the model are similar to those of the evacuation simulation model. In other words, the evacuation simulation provides the necessary database for spatial optimization. Therefore, there is no need to describe the construction of the model in detail. Finally, the model calculation can yield the following information: the number of people allocated and the time spent on each route from each incomplete evacuation demand point to the nearby target plots; the number of remaining non-evacuated people from an incomplete evacuation demand point that are received in each target plot, and the time it takes for all people assigned to the target plot to complete their reallocation; the final state of each target plot, i.e., the number of non-evacuated people that are received.