Emergency shelters location-allocation problem concerning uncertainty and limited resources: a multi-objective optimization with a case study in the Central area of Beijing, China

The special planning for shelters is an integral part of overall city planning and is a key issue in solving the urban security problem. During the planning of earthquake emergency shelters, it is usually necessary to prioritize the designated shelters to avoid wasting resources. However, in previous research initiatives, special attention has been given to the general location-allocation model without prior consideration of the designated shelters. This article presents a multi-objective supplemental location-allocation optimization model for earthquake emergency shelters that addresses the concerns related to the designated shelters. This model is believed to remain more consistent with the knowledge of shelter planners and policy makers by incorporating the uncertainties of the temporal dynamics of population distribution and the spatially heterogeneous distribution of evacuees under various earthquake damage scenarios by using the elliptical attenuation model for seismic intensity into the location-allocation problem. A case study of the central area of Beijing, China is presented. A modified particle swarm optimization algorithm is applied to solve the supplemental location-allocation model and the general location-allocation model, and the solutions obtained from the two models are then compared. The results show that the solutions of the supplemental location-allocation model significantly minimized the shelter area by prioritizing the designated shelters. By contrast, without prior consideration of the designated shelters, the shelter areas significantly increased, which slightly decreased the evacuation distance in the general location-allocation model. The policy makers could select solutions from the obtained minimal-area scheme using the supplemental location-allocation model that ensures acceptable evacuation distances and minimal budgets by prioritizing the designated shelters during the phased planning of shelters in Beijing.