Method and system for layout optimization of emergency shelter based on multi-objective particle swarm optimization algorithm

Abstract

The present application relates to the technical field of urban disaster emergency management, and particularly relates to an emergency shelter layout optimization method and system based on a multi-objective particle swarm algorithm, and the steps are as follows: obtaining geographic information data, constructing an emergency shelter site selection optimization model with the objectives of minimizing evacuation distance, minimizing construction and evacuation cost, and maximizing distance from disaster hidden danger points, and an emergency shelter capacity optimization model with the objective of maximizing emergency shelter capacity; using a multi-objective particle swarm algorithm to jointly optimize the emergency shelter site selection optimization model and the emergency shelter capacity optimization model to obtain a Pareto solution set; and obtaining an emergency shelter layout scheme based on the Pareto solution set. The present application can form optimal emergency shelter layout schemes with different preferences according to the combination of geographic spatial characteristics and urban resident evacuation needs, so as to improve the overall emergency efficiency and scientificity of resource allocation of emergency shelters.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of urban disaster emergency management, in particular to an emergency shelter layout optimization method and system based on a multi-objective particle swarm algorithm. BACKGROUND

[0002] In the event of natural disasters, emergency shelters, as critical infrastructure, play an important role in protecting the lives of urban residents and reducing secondary disasters. However, in the actual planning of emergency shelters and disaster emergency management, the unreasonable site selection of emergency shelters, insufficient coverage, and poor accessibility of residents have seriously restricted the function of emergency shelters in the event of disasters, mainly in the following aspects: (1) The existing layout planning of emergency shelters treats the site selection and capacity allocation of emergency shelters as two isolated problems, lacks systematic linkage, which may lead to mismatch between capacity allocation and actual shelter demand, resulting in overloading or low utilization of emergency shelters, and weakening the disaster emergency response capability of emergency shelters; (2) In terms of site selection of emergency shelters, existing technologies only consider the shortest path or single cost minimization, ignoring the trade-off of multiple objectives in the facility site selection process, thus it is difficult to balance fairness and efficiency; (3) In the face of multi-objective conflict and complex constraint scenarios, traditional mathematical programming methods have obvious deficiencies in solving efficiency and quality of feasible solutions.

[0003] Therefore, there is an urgent need for an emergency shelter layout optimization method that can balance the supply and demand of emergency shelter site selection and capacity, has high solving efficiency, and can improve the overall accessibility, fairness, and emergency response efficiency of the shelter system. SUMMARY

[0004] The present application aims to provide an emergency shelter layout optimization method and system based on a multi-objective particle swarm algorithm to solve the technical problems pointed out in the background.

[0005] The present application is achieved by the following technical solution: An emergency shelter layout optimization method based on a multi-objective particle swarm algorithm, comprising the following steps:

[0006] Obtain geographic information data, and construct an emergency shelter site selection optimization model targeting at minimizing evacuation distance, minimizing construction and evacuation cost, and maximizing distance from disaster hazard points, and an emergency shelter capacity optimization model targeting at maximizing emergency shelter capacity;

[0007] Use a multi-objective particle swarm algorithm to jointly optimize the emergency shelter site selection optimization model and the emergency shelter capacity optimization model, and obtain a Pareto solution set;

[0008] Obtain an emergency shelter layout scheme based on the Pareto solution set.

[0009] According to a preferred embodiment, the geographic information data includes the coordinates of settlements, the coordinates of shelters, and the coordinates of disaster hazard points.

[0010] According to a preferred embodiment, the objective function expression for minimizing the evacuation distance is as follows:

[0011]

[0012] In the above formula, Indicates the first The weight of each settlement Indicates the first Coordinates of an emergency shelter Indicates the first The coordinates of the settlement Indicates emergency shelter with residential areas Euclidean distance, Indicates settlement Should we evacuate to the nearest emergency shelter? , Indicates a gathering of residents. This indicates an assembly of emergency shelters.

[0013] According to a preferred embodiment, the objective function expression for minimizing construction and evacuation costs is as follows:

[0014]

[0015] In the above formula, Indicates emergency shelter The unit construction cost Indicates emergency shelter capacity, Indicate whether to build emergency shelters , Indicates settlement To emergency shelter The per capita evacuation cost.

[0016] According to a preferred embodiment, the objective function expression for maximizing the distance from disaster-prone points is as follows:

[0017]

[0018] In the above formula, Indicates potential disaster sites coordinates Indicates potential disaster sites The weight.

[0019] According to a preferred embodiment, the method further comprises setting constraints for the emergency shelter location optimization model, the constraints comprising:

[0020] an emergency shelter selection constraint, expressed as wherein the above equation indicates that each residential area must be evacuated to the nearest emergency shelter;

[0021] an emergency shelter quantity constraint, expressed as wherein, represents the number of emergency shelters that can be built.

[0022] According to a preferred embodiment, the objective function for maximizing the capacity of emergency shelters is expressed as:

[0023]

[0024] wherein, is a minimum value, .

[0025] According to a preferred embodiment, the method further comprises setting constraints for the emergency shelter capacity optimization model, the constraints comprising:

[0026] an emergency shelter capacity supply-demand matching constraint, expressed as wherein the above equation indicates that the capacity of each emergency shelter should meet the demand of the surrounding residential areas;

[0027] a regional emergency shelter total capacity supply-demand matching constraint, expressed as wherein the above equation indicates that the total capacity of emergency shelters should be greater than the total demand in the region .

[0028] According to a preferred embodiment, the emergency shelter location optimization model and the emergency shelter capacity optimization model are jointly optimized using a multi-objective particle swarm algorithm, and the solving process is as follows:

[0029] Each particle is coded as a vector to represent the coordinates and capacity of the emergency shelter;

[0030] The speed and position of each particle are updated, and after each iteration of the particle swarm position update, the coordinates of the emergency shelter are called to the emergency shelter capacity optimization model to optimize the capacity of the emergency shelter ;

[0031] Through the alternative iteration of the emergency shelter location optimization model and the emergency shelter capacity optimization model, a set of Pareto solutions that are complementary to each other in the multi-objective space are output.

[0032] The application further provides an emergency shelter layout optimization system based on a multi-objective particle swarm algorithm, which is applied to the emergency shelter layout optimization method based on the multi-objective particle swarm algorithm.

[0033] A model construction module is configured to acquire geographic information data, and construct an emergency shelter site selection optimization model with the objectives of minimizing evacuation distance, minimizing construction and evacuation cost, and maximizing distance from a disaster hazard point, and an emergency shelter capacity optimization model with the objective of maximizing emergency shelter capacity.

[0034] A joint optimization module is configured to jointly optimize the emergency shelter site selection optimization model and the emergency shelter capacity optimization model by using a multi-objective particle swarm algorithm to obtain a Pareto solution set.

[0035] A solution module is configured to acquire an emergency shelter layout scheme based on the Pareto solution set.

[0036] The technical scheme of the emergency shelter layout optimization method and system based on the multi-objective particle swarm algorithm provided by the application has at least the following advantages and beneficial effects: (1) the optimal emergency shelter layout scheme with different preferences can be formed according to the combination of geographic spatial features and urban resident evacuation demand, so as to improve the overall emergency efficiency of the emergency shelter and the scientific nature of resource allocation; (2) the multi-objective particle swarm algorithm is used to jointly optimize the emergency shelter site selection optimization model and the emergency shelter capacity optimization model, so as to provide an efficient and flexible solution for the multi-objective optimization problem of emergency shelter layout, balance convergence and diversity, generate a high-quality Pareto optimal solution set, and assist decision makers in making trade-offs under complex constraints; and (3) the dynamic adjustment mechanism of inertia weight, individual learning factor, group learning factor and local learning factor is established, so as to improve the convergence efficiency and global search ability of the particle swarm algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 A flowchart of the emergency shelter layout optimization method based on the multi-objective particle swarm algorithm provided for the embodiment 1 of the application is shown in the figure.

[0038] Figure 2 A flowchart of the multi-objective particle swarm algorithm provided for the embodiment 1 of the application is shown in the figure.

[0039] Figure 3 A structural block diagram of the emergency shelter layout optimization system based on the multi-objective particle swarm algorithm provided for the embodiment 2 of the application is shown in the figure. DETAILED DESCRIPTION

[0040] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0041] Embodiment 1

[0042] The present embodiment provides an emergency shelter layout optimization method based on a multi-objective particle swarm algorithm, Figure 1 For the flowchart of the emergency shelter layout optimization method, see Figure 1 The emergency shelter layout optimization method comprises the following steps:

[0043] Step S01, obtain geographic information data, and construct an emergency shelter site selection optimization model with the objectives of minimizing evacuation distance, minimizing construction and evacuation cost, and maximizing distance from disaster hazard points, and an emergency shelter capacity optimization model with the objective of maximizing emergency shelter capacity;

[0044] Through government public platforms, professional agency databases, remote sensing and surveying and mapping technologies, and field research, geographic information data including resident point coordinates, shelter coordinates, and disaster hazard point coordinates are obtained. The emergency shelter site selection optimization model and the emergency shelter capacity optimization model are constructed according to the geographic information data such as resident point coordinates, shelter coordinates, and disaster hazard point coordinates.

[0045] The emergency shelter site selection optimization model has the objectives of minimizing evacuation distance, minimizing construction and evacuation cost, and maximizing distance from disaster hazard points. The expressions of the objective functions are as follows:

[0046] The expression of the objective function of minimizing evacuation distance is as follows:

[0047]

[0048] In the above formula, represents the weight of the i-th resident point, represents the coordinates of the j-th emergency shelter, represents the coordinates of the i-th resident point, represents the Euclidean distance between the emergency shelter and the resident point, represents whether the resident point is evacuated to the nearest emergency shelter, ​​​​​​​represents a set of residential areas, represents a set of emergency shelters.

[0049] The objective function expression for minimizing the construction and evacuation cost is as follows:

[0050]

[0051] In the above formula, represents the unit construction cost of an emergency shelter , represents the capacity of an emergency shelter , represents whether to build an emergency shelter , represents the per capita evacuation cost of a residential area to an emergency shelter .

[0052] The objective function expression for maximizing the distance from the disaster hazard point is as follows:

[0053]

[0054] In the above formula, represents the coordinates of a disaster hazard point , represents the weight of a disaster hazard point , the higher the disaster hazard point danger level, the larger .

[0055] Further, the constraint conditions are set for the emergency shelter site optimization model, including the emergency shelter selection constraint and the number of constructible emergency shelters constraint; wherein the expression of the emergency shelter selection constraint is , which indicates that each residential area must evacuate to the nearest emergency shelter; the expression of the number of constructible emergency shelters constraint is , is the number of constructible emergency shelters, which indicates that the number of emergency shelters constructed should be limited within the limit number.

[0056] The emergency shelter capacity optimization model aims to maximize the capacity of the emergency shelter, and the expression of the objective function is as follows:

[0057]

[0058] In the above formula, is a minimum value, to avoid zero errors.

[0059] Furthermore, constraints are set for the emergency shelter capacity optimization model, including supply-demand matching constraints for emergency shelter capacity and supply-demand matching constraints for the total regional emergency shelter capacity; wherein, the expression for the emergency shelter capacity supply-demand matching constraint is as follows: This constraint states that the capacity of each emergency shelter should meet the needs of surrounding residential areas; the expression for the supply-demand matching constraint of the total capacity of regional emergency shelters is: This constraint states that the total capacity of emergency shelters should be greater than the total demand in the region. .

[0060] Step S02: Use the multi-objective particle swarm optimization algorithm to jointly optimize the emergency shelter site selection optimization model and the emergency shelter capacity optimization model to obtain the Pareto solution set;

[0061] Specifically, step S02 can be further subdivided into the following sub-steps:

[0062] Step S21: Encode each particle as a vector This indicates the coordinates and capacity of the emergency shelter;

[0063] Step S22: Update the velocity and position of each particle, and after each iteration of particle swarm position update, update the coordinates of the emergency shelter. The emergency shelter capacity optimization model is invoked to optimize emergency shelter capacity. ;

[0064] The particle update mechanism is as follows:

[0065] The velocity is updated for each particle, as shown in the following expression:

[0066]

[0067] In the above formula, express Moment Particle speed, express Moment Particle speed, Indicates inertia weight, Represents individual learning factors. Represents particles The known optimal position of an individual Represents the group learning factor. Represents particles The known global optimal position Represents the local learning factor. Represents particles Known local optimal location, , with for a uniform random number within an interval, denotes the position of a particle at a time instant;

[0068] wherein the inertia weight and the individual learning factor are iterated in a linearly decreasing manner, and the expression is as follows:

[0069]

[0070]

[0071] In the above formula, denotes the upper limit value of the inertia weight, denotes the lower limit value of the inertia weight, denotes the upper limit value of the individual learning factor, denotes the lower limit value of the individual learning factor, denotes the number of iterations of the particle swarm algorithm, denotes the maximum number of iterations of the particle swarm algorithm.

[0072] It should be noted that the inertia weight and the individual learning factor encourage the particles to fully explore the space at the initial stage of algorithm iteration, and improve the diversity of solutions, and accelerate the convergence to the optimal region at the later stage of iteration.

[0073] The swarm learning factor is iterated in a linearly increasing manner, so that the particles explore the global optimal solution at the later stage of iteration, accelerate the weighted convergence speed, and improve the quality of the solution, and the expression is as follows:

[0074]

[0075] In the above formula, denotes the upper limit value of the swarm learning factor, denotes the lower limit value of the swarm learning factor.

[0076] The local learning factor is iterated in a fixed value, which is helpful to avoid the particles falling into local optimum, thereby improving the stability of global search of the particles.

[0077] It should be noted that the embodiment improves the convergence efficiency and global search ability of the particle swarm algorithm by establishing the dynamic adjustment mechanism of the inertia weight, the individual learning factor, the swarm learning factor, and the local learning factor.

[0078] ​Further, the position of each particle is updated, and the expression is as follows:

[0079]

[0080] Step S23, by alternately iterating the emergency shelter site optimization model and the emergency shelter capacity optimization model, a Pareto solution set that is complementary to each other in the multi-objective space is output.

[0081] Specifically, after updating the position of the particle swarm in each iteration, the coordinates of the emergency shelter The emergency shelter capacity optimization model is called to optimize the capacity of the emergency shelter ; by alternately iterating the emergency shelter site optimization model and the emergency shelter capacity optimization model, a Pareto solution set that is complementary to each other in the multi-objective space is output.

[0082] Referring to Figure 2 , the embodiment jointly optimizes the emergency shelter site optimization model and the emergency shelter capacity optimization model by constructing and using a multi-objective particle swarm algorithm, provides an efficient and flexible solution for the multi-objective optimization problem of emergency shelter layout, balances convergence and diversity to generate a high-quality Pareto optimal solution set, and assists decision makers in making trade-offs under complex constraints.

[0083] In some embodiments of the embodiment, the Pareto solution set is generated according to a non-dominated sorting mechanism, and the specific process is as follows:

[0084] In the solving process, each solution in the particle swarm is non-dominantly sorted according to the dominance relationship , wherein f i (x) represents the i-th objective function, x i represents the i-th decision variable of the solution x, and x i (x) represents the i-th decision variable of the solution x.

[0085] After multiple iterations, a Pareto solution set X P is generated , which satisfies , X represents the set of all generated solutions in the iteration process of the particle swarm, and contains candidate solutions generated in each iteration, and x i (x) represents the i-th decision variable of the solution x.

[0086] Step S03, based on the Pareto solution set, an emergency shelter layout scheme is obtained.

[0087] ​​​​In summary, the technical solution provided in the embodiment can form an optimal layout scheme of emergency shelters with different preferences according to the combination of geographical spatial features and evacuation needs of urban residents, so as to improve the overall emergency efficiency and scientificity of resource allocation of the emergency shelters.

[0088] Embodiment 2

[0089] Based on the technical solution provided in Embodiment 1, the embodiment provides an emergency shelter layout optimization system based on a multi-objective particle swarm algorithm. The system is applied to the emergency shelter layout optimization method based on the multi-objective particle swarm algorithm as described in Embodiment 1, as shown in Figure 3 The system includes:

[0090] A model construction module is configured to acquire geographical information data, and construct an emergency shelter site selection optimization model with the objectives of minimizing evacuation distance, minimizing construction and evacuation cost, and maximizing distance from disaster hazard points, and an emergency shelter capacity optimization model with the objective of maximizing emergency shelter capacity.

[0091] A joint optimization module is configured to perform joint optimization on the emergency shelter site selection optimization model and the emergency shelter capacity optimization model by using a multi-objective particle swarm algorithm, to obtain a Pareto solution set.

[0092] A solution module is configured to acquire an emergency shelter layout scheme based on the Pareto solution set.

[0093] The functions of each module of the emergency shelter layout optimization system based on the multi-objective particle swarm algorithm in the embodiment are the same as the explanation of the embodiment of the emergency shelter layout optimization method based on the multi-objective particle swarm algorithm, and the technical effects are the same, which will not be repeated here.

[0094] The above is only a preferred embodiment of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. An emergency shelter layout optimization method based on a multi-objective particle swarm algorithm, characterized in that, The method comprises the following steps: obtaining geographic information data containing coordinates of residential areas, coordinates of shelters and coordinates of disaster hidden points, constructing an emergency shelter site selection optimization model with the objectives of minimizing evacuation distance, minimizing construction and evacuation cost and maximizing distance from disaster hidden points, and an emergency shelter capacity optimization model with the objective of maximizing emergency shelter capacity, wherein the evacuation distance is the Euclidean distance between the coordinates of residential areas and the coordinates of shelters, the construction cost is the construction cost of shelters, and the evacuation cost is the cost from residential areas to shelters; jointly optimizing the emergency shelter site selection optimization model and the emergency shelter capacity optimization model by using a multi-objective particle swarm algorithm to obtain a Pareto solution set; obtaining an emergency shelter layout scheme based on the Pareto solution set; the constraint conditions of the emergency shelter site selection optimization model include an emergency shelter selection constraint and a number of constructible emergency shelters constraint, wherein the emergency shelter selection constraint is that each residential area must be evacuated to the nearest emergency shelter; the constraint conditions of the emergency shelter capacity optimization model include an emergency shelter capacity supply-demand matching constraint and a regional emergency shelter total capacity supply-demand matching constraint; the particle updating mechanism of the multi-objective particle swarm algorithm is as follows: updating the speed of each particle, and the expression is as follows: In the above formulae, denotes the velocity of the particle at time , denotes the velocity of the particle at time , denotes the inertia weight, denotes the individual learning factor, denotes the known individual best position of the particle , denotes the swarm learning factor, denotes the known global best position of the particle , denotes the local learning factor, denotes the known local best position of the particle , , and are uniform random numbers in the interval [0, 1], denotes the position of the particle at time ; where the inertia weight and individual learning factor The iteration is performed in a linearly decreasing manner, expressed as follows: In the above formula, represents an upper limit value of the inertia weight, represents a lower limit value of the inertia weight, represents an upper limit value of the individual learning factor, represents a lower limit value of the individual learning factor, represents the number of iterations of the particle swarm algorithm, represents the maximum number of iterations of the particle swarm algorithm; Group learning factor The iterations are performed in a linearly increasing manner, expressed as follows: In the above formulae, represents an upper limit value of the group learning factor, represents a lower limit value of the group learning factor; Local learning factor Iteration with fixed values. 2.The multi-objective particle swarm optimization algorithm based emergency shelter layout optimization method according to claim 1, wherein, the expression of the objective function of the minimum evacuation distance is as follows: In the above formulae, denotes the weight of the nth settlement, denotes the coordinates of the nth emergency shelter, denotes the coordinates of the nth settlement, denotes the Euclidean distance of the emergency shelter to the settlement, denotes whether the settlement is evacuated to the nearest emergency shelter , denotes the set of settlements, denotes the set of emergency shelters.​ 3.The multi-objective particle swarm optimization algorithm based emergency shelter layout optimization method according to claim 2, wherein, the expression of the objective function of the minimum construction and evacuation cost is as follows: In the above formula, represents the unit construction cost of the emergency shelter , represents the capacity of the emergency shelter , represents whether to build an emergency shelter , represents the per capita evacuation cost of the residential area to the emergency shelter . 4.The multi-objective particle swarm optimization algorithm based emergency shelter layout optimization method according to claim 3, wherein, the expression of the objective function of the maximum distance from disaster hidden points is as follows: In the above formula, represents a coordinate of a disaster risk point, represents a weight of a disaster risk point, represents a set of disaster risk points.​​ 5. The multi-objective particle swarm optimization algorithm based emergency shelter layout optimization method of claim 4, wherein, The method further comprises setting constraint conditions for the emergency shelter site selection optimization model, and the constraint conditions include: Emergency shelter selection constraints, expressed as ; The number of emergency shelters constraint is expressed as In the above equation, where N is the number of emergency shelters that can be built.

6. The method of claim 1 to 5, wherein, the expression of the objective function of the maximum emergency shelter capacity is as follows: In the above formulae, is a minimum value, .

7. The multi-objective particle swarm optimization algorithm based emergency shelter layout optimization method of claim 6, wherein, The method further comprises setting constraint conditions for the emergency shelter capacity optimization model, and the constraint conditions include: The capacity supply-demand matching constraint of the emergency shelter is expressed as The above formula indicates that the capacity of each emergency shelter should meet the demand of the surrounding residential area. The total capacity of the regional emergency shelter supply-demand matching constraint is expressed as The above formula indicates that the total capacity of the emergency shelter should be greater than the total demand in the region . 8.The multi-objective particle swarm optimization algorithm based emergency shelter layout optimization method according to claim 7, wherein, jointly optimizing the emergency shelter site selection optimization model and the emergency shelter capacity optimization model by using a multi-objective particle swarm algorithm, and the solving process is as follows: Encoding each particle as a vector to represent the coordinates and capacity of the emergency shelter; performing velocity update and position update for each particle, and after each iteration of the particle swarm position update, obtaining the coordinates of the emergency shelter calling a capacity optimization model of the emergency shelter to optimize the capacity of the emergency shelter ; complementary Pareto solution sets in a multi-objective space are output by alternately iterating the emergency shelter site selection optimization model and the emergency shelter capacity optimization model.

9. An emergency shelter layout optimization system based on a multi-objective particle swarm optimization algorithm, characterized in that, The system is applied to the multi-objective particle swarm algorithm-based emergency shelter layout optimization method according to any one of claims 1 to 8, and the system comprises: a model construction module configured to obtain geographic information data and construct an emergency shelter site selection optimization model with the objectives of minimizing evacuation distance, minimizing construction and evacuation cost and maximizing distance from disaster hidden points, and an emergency shelter capacity optimization model with the objective of maximizing emergency shelter capacity; a joint optimization module configured to jointly optimize the emergency shelter site selection optimization model and the emergency shelter capacity optimization model by using a multi-objective particle swarm algorithm to obtain a Pareto solution set; a solving module configured to obtain an emergency shelter layout scheme based on the Pareto solution set.

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