Emergency facility site selection and service optimization model under facility failure and traffic jam conditions

Abstract

The invention discloses an emergency facility site selection and service optimization model under facility failure and traffic jam conditions, and relates to the technical field of comprehensive facility site selection, a pre-disaster planning decision model F1 is used for site selection decision of an emergency shelter and multi-level service distribution decision with priority; the dynamic optimization model F2 under the condition of failure of the post-disaster emergency shelter is used for redistributing services between a temporary rescue point and the shelter and adjusting a route of self-evacuation crowds under the condition of user balance UE; a pre-disaster planning decision model F1 and a dynamic optimization model F2 under the condition of failure of an emergency shelter after a disaster form a double-layer mixed integer nonlinear programming model MINLP based on a priority service distribution relation, and an equivalent single-layer mixed integer nonlinear programming model is deduced according to a KKT condition. The single-layer mixed integer nonlinear programming model comprises necessary conditions and sufficient conditions for the optimal flow value of the UE road section in the dynamic optimization model F2 under the condition of failure of the post-disaster emergency shelter.

Description

Technical Field

[0001] The present invention relates to the technical field of comprehensive facility site selection, and in particular to an emergency facility site selection and service optimization model under conditions of facility failure and traffic congestion. Background Art

[0002] Under major sudden disasters, emergency evacuation facilities themselves are likely to be affected by probabilistic interruptions due to various realistic factors. The problem involving location and allocation decisions in the case of facility service interruption is called the reliable facility location problem. The existing technology has established a reliable evacuation service planning path model by optimizing facility site selection decisions, path decisions and evacuation service allocation plans under disaster threats to minimize facility site selection costs, evacuee exposure risks and expected vehicle path costs; the existing technology has considered that interruptions may be related when facilities are subject to common hazards, and added an additional layer of support stations and facility connections to capture the correlation between facilities, and established a mixed integer programming model with the goal of minimizing expected system costs; the existing technology has considered the shared uncertainty of demand points, studied the emergency facility maximum coverage site selection-allocation decision problem, and took maximizing service quality as the optimization goal to improve the reliability and risk resistance of emergency facilities. Two-stage stochastic optimization is currently a hot topic in the research of reliable facility site selection. The existing technology has defined the site selection and allocation strategy in two stages, and constructed a planning model with the goal of minimizing the total cost; the existing technology has considered the two-stage random facility site selection problem with interruptions at the receiving end, the supplier end and the intermediate uncertainty conditions, introduced additional restrictions on the shortage risk, used the L-shaped method to solve it, and verified the feasibility of the model with the actual road network in the Gulf of Mexico.

[0003] Through the above prior art, it can be found that: (1) In post-disaster rescue operations, most studies focus on the evacuation of disaster victims by government organizations, and the transportation network only serves rescue vehicles, ignoring the actual situation (after a disaster, most victims have the ability to evacuate on their own, and the transportation network provides evacuation services for both self-evacuated people and government-organized evacuated victims). Therefore, adding the background flow of self-evacuation to conduct an in-depth analysis of the choice of evacuation routes for disaster victims has important practical significance.

[0004] (2) Despite the efforts made in their respective fields, current technology has not yet solved the interdependence between the location of emergency shelters, traffic congestion on the way, self-evacuation, and the risk of shelter interruption. Considering the above factors comprehensively, formulating a reasonable and effective emergency evacuation plan is an issue worthy of in-depth study. Summary of the invention

[0005] In view of this, the present invention intends to combine the actual situation and impact of sudden disasters on emergency rescue (such as the failure of built emergency service facilities, traffic congestion caused by a large number of people evacuating on their own in addition to the government-organized evacuation of the wounded, etc.), integrate the risk of shelter interruption, traffic congestion on the way and self-evacuation flow into a comprehensive facility site selection problem, and propose a two-layer random mixed integer nonlinear programming model based on priority service allocation relationship, in which facility site selection, disaster victim evacuation flow and service allocation decision are located in the upper layer, and traffic balance is located in the lower layer. Through programming on the GAMS platform, DICOPT is called to solve the mixed integer nonlinear programming model, and finally a case analysis is carried out on a 24-node test road network to verify the effectiveness and feasibility of the model and algorithm, in order to provide valuable reference for emergency departments to formulate emergency evacuation strategies to solve the problems raised in the background technology.

[0006] The present invention provides the following technical solution: an emergency facility location selection and service optimization model under conditions of facility failure and traffic congestion, comprising: Pre-disaster planning decision model F 1 , used for emergency shelter location decisions and multi-level service allocation decisions with priorities to minimize the total system cost; Dynamic optimization model for post-disaster emergency shelter failure 2 , under the condition of user equilibrium UE, it is used to redistribute services between temporary rescue points and shelters and adjust the routes of self-evacuated people to minimize traffic network congestion; Pre-disaster planning decision model F 1 Dynamic optimization model for emergency shelter failure after disasters 2 A two-level mixed integer nonlinear programming model MINLP based on the priority service allocation relationship is constructed, and an equivalent single-level mixed integer nonlinear programming model is derived according to the KKT condition. The single-level mixed integer nonlinear programming model includes a dynamic optimization model F under the condition of post-disaster emergency shelter failure. 2 The necessary and sufficient conditions for the optimal UE section flow value are formulated, with the optimization goal of minimizing the total system cost and achieving the balance of the transportation network.

[0007] Optimally, the pre-disaster planning decision model F 1 The total system cost to be minimized includes the cost of selecting the location of the emergency shelter, the cost of on-the-way traffic congestion in the event of service failure, and the system penalty cost caused by the inability of disaster victims at the temporary assembly point to obtain evacuation services after the emergency shelter fails. Specifically, it is: ; : Gather at temporary assembly points in disaster-stricken areas, ; : A set of candidate locations for emergency shelters, ; : The priority of evacuation of disaster victims from temporary assembly points to emergency shelters (if they are functioning normally), ; Refers to the priority level, The lower the value, the higher the priority; for example, for a temporary gathering point For the disaster victims, The emergency shelter at has the highest service priority; if the service at this point fails, then Emergency shelters at the level above 100 will serve as temporary assembly points Provide services, and so on; :Post-disaster evacuation transportation network The node set, ,in ; :Post-disaster evacuation transportation network Middle section collection, , Refers to the road section; : Site selection decision; if the candidate point is selected Building an emergency shelter is 1. Otherwise, 0; : Emergency Shelter construction costs; : Gather at a temporary gathering point evacuation flow of disaster victims; : Temporary meeting point The unit penalty cost of disaster victims being unable to obtain evacuation services; : Cost conversion coefficient per unit travel time; : Road section flow decision (government organization); passing road section evacuation flow of disaster victims; : Road section flow decision (self-evacuation); passing road section of self-evacuation traffic; : Based on priority service allocation decisions; if emergency shelters It is a temporary meeting point No. Level 1 refuge facilities ,otherwise ; : BPR function, calculate any scenario Lower section The actual travel time; : Emergency Shelter As the Level service facilities are temporary assembly points The probability of providing shelter services.

[0008] Preferably, for the pre-disaster planning decision model F 1 Constraints are imposed. The specific constraints are as follows: (3-1) means only emergency shelters are built Temporary meeting point Generate service allocation relationships with priorities; (3-2) Ensure that there is only one emergency shelter that can be used as a temporary assembly point No. Level service facilities; (3-3) Definition , indicating an emergency shelter As the Level service facilities are temporary assembly points The probability of providing shelter services, where For temporary meeting points Before Decisions on service allocation for emergency shelters Temporary meeting point Before The failure probability of the emergency shelter; (3-4) Give the road section The travel time; (3-5) Calculate road sections evacuation flow of disaster victims; (3-6) Define a temporary gathering point Evacuate to an emergency shelter The flow value of disaster victims; (3-7) Define the traffic flow values ​​at all temporary assembly points, emergency shelters, and other network nodes, where Is the node is the set of outflow segments starting from the starting point, Is the node The inflow section set of the terminal; (3-8) Define the pre-disaster planning decision model F 1 The decision variables in type; (3-9) Define the pre-disaster planning decision model F1 The decision variables in type; ; ; ; ; ; ; ; ; ; : Cost conversion coefficient per unit travel time; : Temporary meeting point of victims evacuated to emergency shelters Passing section evacuation flow of disaster victims; : From temporary meeting point Evacuate to an emergency shelter of victims evacuated; : Emergency Shelter The probability of service interruption failure; : Road section free flow travel time; : Road section capacity of traffic.

[0009] Optimized dynamic optimization model F for post-disaster emergency shelter failure 2 This includes taking into account the shortest path cost under the user equilibrium UE condition, optimizing the allocation of disaster evacuation traffic and self-evacuation traffic, and minimizing the total travel cost of the emergency evacuation network. Specifically: ; : The set of starting and ending point pairs of the self-evacuated crowd, ; :Origin and destination pair At the node Self-evacuation traffic on : Starting and ending points From the node Arrival at the destination The shortest path cost; : Self-evacuation groups at the starting and ending points Road sections during travel of self-evacuation traffic.

[0010] Preferably, a dynamic optimization model F for the failure of emergency shelters after disasters 2 Constraints are imposed. The specific constraints are as follows: (5-1) Calculate road sections evacuation flow of disaster victims; (5-2) is the network node flow conservation constraint; (5-3) Define any starting and ending points At the node The self-evacuation crowd flow demand at the node is the departure point (such as a temporary meeting point), then ; If it is a destination (such as an emergency shelter), then ; For any node other than the starting and ending points, ; (5-4) is the travel cost constraint, representing any starting and ending point Lower section The travel cost cannot be lower than the cost of the road section under the shortest path condition; (5-5) ensures the dual variables The non-negativity of (5-6) Define continuous decision variables; ; ; ; ; ; .

[0011] Preferably, the necessary and sufficient conditions for the optimal UE section flow value are as follows: (6-1) Given the road section capacity constraint, For road section Assigned to the starting and ending points The maximum flow capacity, ; (6-2) Given the path travel cost constraint, Starting and ending point On the road The relaxed upper bound on travel costs, ,in ; (6-3) ensures that any starting and ending points During the trip, any section of the road Non-negativity of path travel costs; (6-4) Define the decision variable type, when the starting and ending points Road sections for self-evacuation needs e If yes, the value is 1, otherwise it is 0; ; ; ; ; In the formula , the upper limit is ; , its upper limit is ,in .

[0012] The present invention has the following advantages: The emergency facility location selection and service optimization model designed by the present invention under the conditions of facility failure and traffic congestion includes a pre-disaster planning decision model F 1 Dynamic optimization model for emergency shelter failure after disasters 2 ; Pre-disaster planning decision model F 1 , used for emergency shelter location decisions and multi-level service allocation decisions with priorities to minimize the total system cost; Dynamic optimization model for post-disaster emergency shelter failure 2 , under the condition of user equilibrium UE, it is used to redistribute services between temporary rescue points and shelters and adjust the routes of self-evacuated people to minimize traffic network congestion; Pre-disaster planning decision model F 1 Dynamic optimization model for emergency shelter failure after disasters 2 A two-level mixed integer nonlinear programming model MINLP based on the priority service allocation relationship is constructed, and an equivalent single-level mixed integer nonlinear programming model is derived according to the KKT condition. The single-level mixed integer nonlinear programming model includes a dynamic optimization model F under the condition of post-disaster emergency shelter failure. 2 The necessary and sufficient conditions for the optimal UE section flow value in the optimization are to minimize the total system cost and achieve the balance of the traffic network as the optimization goal. Compared with the existing technology: 1. The present invention utilizes the actual situation (most of the victims have the ability to evacuate on their own after a disaster occurs, and the transportation network provides evacuation services for both the self-evacuated people and the government-organized evacuation of the victims). Therefore, the emergency facility site selection and service optimization model designed by the present invention under the conditions of facility failure and traffic congestion adds the background flow of self-evacuation to conduct an in-depth analysis of the choice of evacuation routes for the victims, which has important practical significance.

[0013] 2. The present invention comprehensively considers the interdependence between the site selection of emergency shelters, traffic congestion on the way, self-evacuation and the risk of shelter interruption, and formulates a reasonable and effective emergency facility site selection and service optimization model under the conditions of facility failure and traffic congestion. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A schematic diagram of the emergency rescue network structure provided in this embodiment; wherein (a) is a normal operation state, and (b) is a failure scenario; Figure 2 A schematic diagram of the proportion of each cost provided in this embodiment; Figure 3 A schematic diagram of a 24-node test road network provided by the present invention; Figure 4 A schematic diagram of the disaster victim service distribution relationship (r=1) of the 24-node experimental road network provided by the present invention; Figure 5 A schematic diagram of the service distribution relationship (r=2) for disaster victims in a 24-node experimental road network provided by the present invention; Figure 6 Schematic diagram of the disaster victim service allocation relationship (r=3) of the 24-node experimental road network provided by the present invention. DETAILED DESCRIPTION

[0015] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] The present invention provides an emergency facility location selection and service optimization model under the conditions of facility failure and traffic congestion. The model is based on the following assumptions: Assumption 1: The areas affected by the disaster are divided and a certain area (such as a village, town or community) is used as a temporary rescue point.

[0017] Assumption 2: The locations and numbers of candidate emergency shelters and temporary rescue points are known.

[0018] Assumption 3: The capacity constraints of emergency shelters are not considered during the evacuation process.

[0019] Assumption 4: There are sufficient emergency evacuation vehicles, which depart from temporary rescue points and transport the wounded to emergency shelters.

[0020] Assumption 5: The probability of service failure of each emergency shelter is the same, and the situation where the emergency shelter can continue to improve its service after failure is not considered.

[0021] The model includes: Pre-disaster planning decision model F 1 , used for emergency shelter location decisions and multi-level service allocation decisions with priorities to minimize the total system cost; Dynamic optimization model for post-disaster emergency shelter failure 2 , under the condition of user equilibrium UE, it is used to redistribute services between temporary rescue points and shelters and adjust the routes of self-evacuation of people to minimize traffic network congestion; Pre-disaster planning decision model F 1 Dynamic optimization model for emergency shelter failure after disasters 2 A two-level mixed integer nonlinear programming model MINLP based on the priority service allocation relationship is constructed, and an equivalent single-level mixed integer nonlinear programming model is derived according to the KKT condition. The single-level mixed integer nonlinear programming model includes a dynamic optimization model F under the condition of post-disaster emergency shelter failure. 2 The necessary and sufficient conditions for the optimal UE section flow value are formulated, with the optimization goal of minimizing the total system cost and achieving the balance of the transportation network.

[0022] Pre-disaster planning decision model F 1 The total system cost to be minimized includes the cost of selecting the location of the emergency shelter, the cost of on-the-way traffic congestion in the event of service failure, and the system penalty cost caused by the inability of disaster victims at the temporary assembly point to obtain evacuation services after the emergency shelter fails. Specifically, it is: ; : Gather at temporary assembly points in disaster-stricken areas, ; : A set of candidate locations for emergency shelters, ; : The priority of evacuation of disaster victims from temporary assembly points to emergency shelters (if they are functioning normally), ; Refers to the priority level, The lower the value, the higher the priority; for example, for a temporary gathering point For the disaster victims, The emergency shelter at has the highest service priority; if the service at this point fails, then Emergency shelters at the level above 100 will serve as temporary assembly points Provide services, and so on; :Post-disaster evacuation transportation network The node set, ,in ; :Post-disaster evacuation transportation network Middle section collection, , Refers to the road section; : Site selection decision; if the candidate point is selected Building an emergency shelter is 1. Otherwise, 0; : Emergency Shelter construction costs; : Gather at a temporary gathering point evacuation flow of disaster victims; : Temporary meeting point The unit penalty cost of disaster victims being unable to obtain evacuation services; : Cost conversion coefficient per unit travel time; : Road section flow decision (government organization); passing road section evacuation flow of disaster victims; : Road section flow decision (self-evacuation); passing road section of self-evacuation traffic; : Based on priority service allocation decisions; if emergency shelters It is a temporary meeting point No. Level 1 refuge facilities ,otherwise ; : BPR function, calculate any scenario Lower section The actual travel time; : Emergency Shelter As the Level service facilities are temporary assembly points The probability of providing shelter services.

[0023] For the pre-disaster planning decision model F 1 Constraints are imposed. The specific constraints are as follows: (3-1) means only emergency shelters are built Temporary meeting point Generate service allocation relationships with priorities; (3-2) Ensure that there is only one emergency shelter that can be used as a temporary assembly point No. Level service facilities; (3-3) Definition , indicating an emergency shelter As the Level service facilities are temporary assembly points The probability of providing shelter services, where For temporary meeting points Before Decisions on service allocation for emergency shelters Temporary meeting point Before The failure probability of the emergency shelter; (3-4) Give the road section The travel time; (3-5) Calculate road sections evacuation flow of disaster victims; (3-6) Define a temporary gathering point Evacuate to an emergency shelter The flow value of disaster victims; (3-7) Define the traffic flow values ​​at all temporary assembly points, emergency shelters, and other network nodes, where Is the node is the set of outflow segments starting from the starting point, Is the node The inflow section set of the terminal; (3-8) Define the pre-disaster planning decision model F 1 The decision variables in type; (3-9) Define the pre-disaster planning decision model F 1 The decision variables in type; ; ; ; ; ; ; ; ; ; : Cost conversion coefficient per unit travel time; : Temporary meeting point of victims evacuated to emergency shelters Passing section evacuation flow of disaster victims; : From temporary meeting point Evacuate to an emergency shelter of victims evacuated; : Emergency Shelter The probability of service interruption failure; : Road section free flow travel time; : Road section capacity of traffic.

[0024] Dynamic optimization model for post-disaster emergency shelter failure 2 This includes taking into account the shortest path cost under the user equilibrium UE condition, optimizing the allocation of disaster evacuation traffic and self-evacuation traffic, and minimizing the total travel cost of the emergency evacuation network. Specifically: ; : The set of starting and ending point pairs of the self-evacuated crowd, ; :Origin and destination pair At the node Self-evacuation traffic on : Starting and ending points From the node Arrival at the destination The shortest path cost; : Self-evacuation groups at the starting and ending points Road sections during travel of self-evacuation traffic.

[0025] Dynamic optimization model for post-disaster emergency shelter failure 2 Constraints are imposed. The specific constraints are as follows: (5-1) Calculate road sections evacuation flow of disaster victims; (5-2) is the network node flow conservation constraint; (5-3) Define any starting and ending points At the node The self-evacuation crowd flow demand at the node is the departure point (such as a temporary meeting point), then ; If it is a destination (such as an emergency shelter), then ; For any node other than the starting and ending points, ; (5-4) is the travel cost constraint, representing any starting and ending point Lower section The travel cost cannot be lower than the cost of the road section under the shortest path condition; (5-5) ensures the dual variables The non-negativity of (5-6) Define continuous decision variables; ; ; ; ; ; .

[0026] The necessary and sufficient conditions for the optimal UE section flow value are as follows: (6-1) Given the road section capacity constraint, For road section Assigned to the starting and ending points The maximum flow capacity, ; (6-2) Given the path travel cost constraint, Starting and ending point On the road The relaxed upper bound on travel costs, ,in ; (6-3) ensures that any starting and ending points During the trip, any section of the road Non-negativity of path travel costs; (6-4) Define the decision variable type, when the starting and ending points Road sections for self-evacuation needs e If yes, the value is 1, otherwise it is 0; ; ; ; ; In the formula , the upper limit is ; , its upper limit is ,in .

[0027] This embodiment provides an emergency rescue network consisting of "temporary rescue points-emergency shelters", with special attention to the optimization problem in the post-disaster large-scale evacuation scenario. In the post-disaster scenario, a large number of carless disaster victims are usually gathered at temporary rescue points and transferred to safe emergency shelters by rescue vehicles. Figure 1 (a) shows how to select the location of emergency shelters, the route planning of rescue vehicles, and the evacuation routes of people who evacuate themselves (people with cars). However, due to major damage caused by sudden disasters or human factors (such as water and power outages), some emergency shelters may become ineffective, forcing victims to find alternative shelters. In this case, victims will face a higher risk of exposure and may not even be able to obtain effective evacuation services.

[0028] Figure 1 (b) in the figure shows how the affected victims readjust their routes to seek alternative shelter services in the scenario of emergency shelter failure. For evacuation planning in disaster-prone areas, on the one hand, it is necessary to optimize the location of emergency shelters to ensure that they can effectively cover the evacuation needs of potential disaster-affected areas; on the other hand, it is also necessary to predict the possible emergency shelter failure scenarios when actual disasters occur, as well as the dynamic adjustment process of affected victims' reselection of shelters. At the same time, the behavior of self-evacuation people may have a significant impact on the evacuation activities organized by the government, and this mutual influence also needs to be fully considered in planning. Therefore, in addition to the site selection, route and allocation decisions under normal circumstances, the real evacuation planning problem also needs to face a more complex dimension: when some emergency shelters are interrupted, the backup emergency shelter allocation plan and the self-evacuation route replanning strategy. All these complexities make the planning of evacuation services more challenging, because the system should be both cost-effective and reliable.

[0029] This embodiment uses GAMS programming and calls the DICOPT solver to solve and numerically analyze the mixed integer nonlinear programming model. A 24-node test road network in a certain city is selected to test the effectiveness of the model, and the optimization results of the 24-node test road network are analyzed in detail to propose management insights for optimizing resource allocation and improving evacuation efficiency, providing a scientific basis and practical guidance for evacuation path planning and resource allocation in emergency management.

[0030] Basic data settings: The unit construction cost of the emergency shelter is set to 10,000 yuan, the travel time value coefficient α is 10 yuan, the unit penalty cost τ is 15,000 yuan, the interruption probability q=5%, the proportion of disaster evacuation flow and self-evacuation flow is 40% and 60% respectively, the number of temporary rescue points is 17, the number of emergency shelters is 7, the allocation priority R=3, and there are 8 self-evacuation routes.

[0031] Analysis of test results: Taking a 24-node road network as an example to analyze the optimization plan, the proportion of each cost is as follows Figure 2 As shown in Figure 2. Among them, the site selection cost accounts for only 5.54%, which is at a relatively low level, while the total transportation cost accounts for as high as 89.40%, which occupies an absolute dominant position in the total system cost. Specifically, the cost of evacuating disaster victims accounts for 11.32%. This cost is the travel cost incurred by disaster victims in the process of traveling from temporary gathering points to emergency shelters due to factors such as traffic congestion. In particular, the cost of self-evacuation is as high as 78.08%, which occupies a dominant position in transportation costs. This phenomenon is mainly due to the fact that the proportion of self-evacuated people in the urban population is large and there is a lack of scientific and reasonable travel planning. In view of this, this data should be highly valued in order to explore effective cost reduction strategies, such as optimizing evacuation routes, reasonably regulating the ratio of disaster victims to self-evacuation, and implementing precise and effective guidance and management for self-evacuated people to avoid the situation where costs rise due to traffic congestion. Finally, the penalty cost accounts for only 5.06%, the lowest among the four costs, which may imply that in the current system, the cost impact caused by the penalty measures is relatively weak. However, its rationality and effectiveness still need to be carefully considered to ensure the balance and rationality of various costs. In general, in-depth insight into the composition and importance of different costs provides an intuitive and powerful basis for the precise formulation of relevant strategies and measures, which in turn helps to improve the operating efficiency and benefits of the overall system.

[0032] Figure 3 The experimental road network is 24 nodes, of which 1, 4, 6, 12, 19, and 24 are emergency shelters, and the remaining nodes are temporary assembly points. The location of emergency shelters, the service allocation relationship with priority levels, and the optimal self-evacuation route are as follows: Figure 4 , Figure 5 , Figure 6 As shown in the figure, it can be clearly seen that for node 9, node 4, node 6, and node 19 are its first, second, and third level emergency shelters respectively. The temporary assembly point and the emergency shelter present a one-to-many service allocation relationship. For example, in the case of r = 1, node 3, node 5, node 9, and node 11 will go to node 4 to seek shelter. Figure 3-Figure 6, it can clearly understand the distribution of temporary assembly points, the location of emergency shelters, the service allocation between them and the path of self-evacuation in the test road network, providing an intuitive visual reference and basic basis for further analyzing the efficiency of the evacuation system and optimizing the evacuation plan.

[0033] In the face of the evacuation needs of people without cars under sudden disasters, this embodiment designs an emergency rescue network consisting of two nodes: "rescue point-shelter". Taking into account the probability of emergency shelter service interruption and traffic congestion during evacuation under actual circumstances, a two-layer random mixed integer nonlinear programming model based on the priority service allocation relationship is established with the minimum expected total system cost as the optimization goal, which collaboratively optimizes the emergency shelter site selection, rescue and evacuation paths and service allocation decisions. GAMS programming is used for the problem under study, and the DICOPT solver is called to solve the model. Finally, combined with actual cases, the feasibility of the model is further verified to provide decision makers with auxiliary decision-making references for emergency evacuation plans for people without cars under sudden disasters.

[0034] This example only studies the optimization of emergency shelter site selection, emergency rescue and evacuation of disaster victims under sudden disasters. In practice, the dispatch of emergency materials after disasters also needs to be considered. In addition, the uncertainty of rescue point demand is also a research direction worth exploring in the future to further improve the robustness and feasibility of the optimization scheme.

[0035] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. Emergency facility location selection and service optimization model under the conditions of facility failure and traffic congestion, characterized by: include: Pre-disaster planning decision model F1 is used for the location decision of emergency shelters and multi-level service allocation decision with priority to obtain the minimum total system cost; The dynamic optimization model F2 in the case of post-disaster emergency shelter failure is used to reallocate services between temporary rescue points and shelters and adjust the routes of self-evacuated people under the condition of user equilibrium UE to minimize traffic network congestion; The pre-disaster planning decision model F1 and the dynamic optimization model F2 in the case of post-disaster emergency shelter failure constitute a two-layer mixed integer nonlinear programming model MINLP based on the priority service allocation relationship. According to the KKT condition, an equivalent single-layer mixed integer nonlinear programming model is derived. The single-layer mixed integer nonlinear programming model includes the necessary and sufficient conditions for the optimal UE section flow value in the dynamic optimization model F2 in the case of post-disaster emergency shelter failure, with the optimization goal of minimizing the total system cost and achieving the balance of the transportation network.

2. The model for emergency facility location selection and service optimization under conditions of facility failure and traffic congestion according to claim 1 is characterized by: The pre-disaster planning decision model F1 includes the minimization of the total system cost, which includes the cost of emergency shelter site selection, the cost of on-the-way traffic congestion in the service failure scenario, and the system penalty cost caused by the inability of disaster victims at temporary assembly points to obtain evacuation services after the emergency shelter fails. Specifically, it is: ; : Gather at temporary assembly points in disaster-stricken areas, ; : A set of candidate locations for emergency shelters, ; : Under normal operation, the priority order of evacuation of disaster victims from temporary assembly points to emergency shelters, ; :Post-disaster evacuation transportation network The node set, ,in ; :Post-disaster evacuation transportation network Middle section collection, Refers to the road section; : Site selection decision; if the candidate point is selected Building an emergency shelter is 1. Otherwise, 0; : Emergency Shelter construction costs; : Gather at a temporary gathering point evacuation flow of disaster victims; : Temporary meeting point The unit penalty cost of disaster victims being unable to obtain evacuation services; : Cost conversion coefficient per unit travel time; : Government decision-making on road traffic; evacuation flow of disaster victims; : The traffic flow of the road section is self-evacuated; of self-evacuation traffic; : Based on priority service allocation decisions; :BPR function, calculate any scene Lower section The actual travel time; : Emergency Shelter As the Level service facilities are temporary assembly points The probability of providing shelter services.

3. The model for emergency facility location selection and service optimization under conditions of facility failure and traffic congestion according to claim 2 is characterized by: Constraints are imposed on the pre-disaster planning decision model F1. The specific constraints are as follows: (3-1) means only emergency shelters are built Temporary meeting point Generate service allocation relationships with priorities; (3-2) Ensure that there is only one emergency shelter that can be used as a temporary assembly point No. Level service facilities; (3-3) Definition , indicating an emergency shelter As the Level service facilities are temporary assembly points The probability of providing shelter services, where For temporary meeting points Before Decisions on service allocation for emergency shelters Temporary meeting point Before The failure probability of the emergency shelter; (3-4) Give the road section The travel time; (3-5) Calculate road sections evacuation flow of disaster victims; (3-6) Define a temporary meeting point Evacuate to an emergency shelter The flow value of disaster victims; (3-7) Define traffic flow values ​​at all temporary assembly points, emergency shelters, and other network nodes; (3-8) Define the types of decision variables in the pre-disaster planning decision model F1.

4. The model for emergency facility location and service optimization under conditions of facility failure and traffic congestion according to claim 1 is characterized by: The dynamic optimization model F2 under the condition of post-disaster emergency shelter failure includes minimizing the total travel cost of the emergency evacuation network under the condition of user equilibrium UE, specifically: ; : The set of starting and ending point pairs of the self-evacuated crowd, ; :Origin and destination pair At the node Self-evacuation flow on : Starting and ending points From the node Arrival at the destination The shortest path cost; : Self-evacuation groups at the starting and ending points Road sections during travel of self-evacuation traffic.

5. The model for emergency facility location selection and service optimization under conditions of facility failure and traffic congestion according to claim 4 is characterized by: The dynamic optimization model F2 is constrained in the case of post-disaster emergency shelter failure. The specific constraints are as follows: (5-1) Calculate road sections evacuation flow of disaster victims; (5-2) is the network node flow conservation constraint; (5-3) Define any starting and ending points At the node The self-evacuation crowd flow demand at the node is the departure place, If it is the destination, then ; For any node other than the starting and ending points, ; (5-4) is the travel cost constraint, representing any starting and ending point Lower section The travel cost cannot be lower than the cost of the road section under the shortest path condition; (5-5) ensures the dual variables The non-negativity of (5-6) Define continuous decision variables.

6. The model for emergency facility location selection and service optimization under conditions of facility failure and traffic congestion according to claim 1 is characterized by: The necessary and sufficient conditions for the optimal UE section flow value are as follows: (6-1) Given the road section capacity constraint, For road section Assigned to the starting and ending points The maximum flow capacity, ; (6-2) Given the path travel cost constraint, Starting and ending points On the road The relaxed upper bound on travel costs, ,in ; (6-3) ensures that any starting and ending points Any section of the journey Non-negativity of path travel costs; (6-4) Define the decision variable type, when the starting and ending points Road sections for self-evacuation needs e If yes, the value is 1, otherwise it is 0.

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