A Multi-objective Model for the Location of the Emergency Facilities and the Selection of the Rescue Path Based on the Restoration of the Damaged Edges

: In this paper, an equivalence theorem is given, that is, in a weighted graph, the maximum value of the minimum edge weights of all minimal edge cut sets between two points is equal to the minimum value of the maximum edge weights of all paths between the two points. On this basis, the recovery time between two points in the network is defined from the perspective of the minimal edge cut set and the path, respectively, and the equivalence of the two definitions is shown. Two models are established to optimize the partial recovery of network functions, by taking the damaged road network after the earthquake as the scene, based on the definition of the network recovery time and the total network time. Model 1 includes three objective functions, which are the sum of the failure levels between all pairs of the demand points and the facilities serving them, the total network time and the total cost. Different priorities were set for solving these three objectives. Since such a hierarchical model is not conducive to the optimization of the objective functions with lower priorities, model 1 is modified appropriately. The sum of the failure levels is combined with the total network time into an integrated objective function by weighting, and the minimization of this new function is taken as the highest-priority objective and the minimization of the total cost is taken as the secondary-priority objective, in order to achieve the balance between the sum of the failure levels and the total network time. Thus, model 2 is obtained. A case study is used to test the two models and verify their effectiveness.