Cooperative optimization method and system for monitoring station site selection and rescue path planning

Abstract

The application relates to the technical field of post-disaster emergency response, and proposes a cooperative optimization method and system for monitoring station site selection and rescue path planning, which comprises the following steps: acquiring communication rescue information, including an emergency communication monitoring station candidate point position set, a node set and a disaster area demand quantity; constructing a double-target mixed integer nonlinear programming model through the communication rescue information, wherein the double targets include minimizing the total system rescue cost and minimizing the expected total rescue time; solving the double-target mixed integer nonlinear programming model by using a non-dominated sorting genetic algorithm, outputting an optimal solution set, and obtaining optimal decisions of the emergency communication monitoring station site selection and the rescue path. The application solves the cooperative optimization problem of communication support and rescue scheduling in disaster emergency response.

Description

Technical Field

[0001] This invention relates to the field of post-disaster emergency response technology, and in particular to a collaborative optimization method and system for monitoring station site selection and rescue route planning. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Disaster emergency response is a core component of disaster reduction and relief efforts. In recent years, natural disasters have become increasingly frequent and larger in scale globally. In emergencies, timely and efficient rescue is crucial for ensuring the safety of lives. In post-disaster response, emergency communication support and rescue dispatch are two key pillars of the disaster emergency response system. The rapid deployment and precise positioning capabilities of communication equipment are vital for the timely transmission of rescue information and the coordination of various rescue forces. Rational planning of rescue vehicle routes can effectively shorten rescue time, thereby maximizing the effectiveness of rescue forces. Currently, many researchers have studied improving communication coverage in search and rescue areas and vehicle dispatching schemes under different objectives through algorithm improvements and model building.

[0004] However, existing research reveals the following problems:

[0005] First, most current research is based on the ideal assumption that communication equipment will continue to operate normally after a disaster, failing to fully consider uncertainties such as equipment damage and power outages caused by disasters. This may lead to an overestimation of positioning accuracy and an underestimation of actual search and rescue time, affecting the accurate assessment of rescue efficiency. Second, although many studies have proposed optimization strategies for individual aspects such as the layout of emergency communication equipment or the route planning of rescue vehicles, there is a close coupling relationship between communication support and rescue dispatch in actual emergency response. For example, communication support provides key information support for rescue dispatch, ensuring that rescue forces can obtain real-time information about the disaster site in a timely and accurate manner, thereby formulating scientific and reasonable rescue routes and dispatch plans. However, current research still lacks exploration of the collaborative optimization mechanism between the two. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention discloses a collaborative optimization method and system for monitoring station site selection and rescue route planning. It constructs a bi-objective mixed integer nonlinear programming model and uses a non-dominated sorting genetic algorithm for multi-objective optimization to solve the collaborative optimization problem of communication support and rescue dispatch in disaster emergency response.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] The first aspect of this invention provides a collaborative optimization method for monitoring station site selection and rescue route planning, comprising:

[0009] Obtain communication rescue information, including the set of candidate locations for emergency communication monitoring stations, the set of nodes, and the required quantity in the disaster-stricken area;

[0010] A dual-objective mixed-integer nonlinear programming model is constructed using communication rescue information. The dual objectives include minimizing the total system rescue cost and minimizing the expected total rescue time.

[0011] The bi-objective mixed integer nonlinear programming model is solved using a non-dominated sorting genetic algorithm, and the optimal solution set is output to obtain the optimal decision for the location of the emergency communication monitoring station and the rescue route.

[0012] Furthermore, in the communication and rescue information, the node set includes a set of disaster-stricken areas and shelters.

[0013] Furthermore, the construction of a dual-objective mixed-integer nonlinear programming model using communication rescue information includes constructing a system rescue total cost objective function, an expected rescue total time objective function, and constraints.

[0014] Furthermore, the objective function for the total cost of system rescue includes the site selection cost of candidate emergency communication monitoring stations and the system penalty cost caused by the inability to meet the needs of the disaster-stricken area after all candidate emergency communication monitoring stations allocated to the disaster-stricken area have failed. The objective function is as follows:

[0015]

[0016]

[0017]

[0018] in, For the disaster-stricken area, For the disaster-stricken areas, ; As a candidate site for emergency communication monitoring stations, This is a set of candidate sites for emergency communication monitoring stations. ; The total cost of the system rescue, The site selection cost for candidate emergency communication monitoring stations; The system penalty cost incurred when all candidate emergency communication monitoring stations allocated to the disaster area fail and the needs of the disaster area cannot be met; Candidate sites for the construction of emergency communication monitoring stations Required installation cost For binary decision variables; For the disaster-stricken area The unit penalty cost for wounded people who cannot receive rescue services; In the formula, represents the number of injured people trapped in the disaster area; This indicates all allocated to the disaster-stricken areas. Candidate sites for emergency communication monitoring stations The probability of all failures; As a binary decision variable, if the candidate point of the emergency communication monitoring station For the disaster-stricken area Providing monitoring services ,otherwise .

[0019] Furthermore, the objective function for constructing the total expected rescue time includes the search and rescue time spent by rescue vehicles in the disaster area and the total expected travel time between the various visited disaster areas. The objective function is as follows:

[0020]

[0021] in, The expected total rescue time; The time that rescue vehicles remain in the disaster area for search and rescue operations; The total expected travel time between the various disaster-stricken areas visited;

[0022] The search and rescue time that the rescue vehicles spend in the disaster area is expressed as follows:

[0023]

[0024]

[0025]

[0026]

[0027] in, For the disaster-stricken area To the candidate site of the emergency communication monitoring station The distance; This is a correction factor; As a binary decision variable, if the candidate point of the emergency communication monitoring station For the disaster-stricken area Providing monitoring services ,otherwise ; For the disaster-stricken area The monitoring accuracy is a dimensionless indicator that reflects the overall signal strength. This indicates the ideal accuracy conditions in the disaster area. The minimum rescue time, The quantity required for the disaster-stricken area, The rescue time for a single demand quantity under ideal accuracy conditions; Indicates the time increment coefficient; Indicates the decay rate; This indicates the probability that the disaster-stricken area will be visited by rescue vehicles; This represents the failure probability of each candidate emergency communication monitoring station.

[0028] Furthermore, the total expected travel time between the various visited disaster-stricken areas. It is divided into three parts: the expected travel time from the shelter to the first disaster-stricken area visited. Expected travel time from one disaster-stricken area to the next. And the expected travel time from the last visited disaster area back to the shelter. :

[0029]

[0030] Let the order in which the path visits the disaster-stricken area be: , Represents the first in this path Similarly, for each of the disaster-stricken areas visited, Represents the first in this path The visited disaster-stricken areas, and v>u The expression is as follows:

[0031]

[0032] in, It also indicates the disaster-stricken area being visited; Indicates the disaster-stricken area Being served This indicates that all disaster-stricken areas listed ahead of it have not been served. This indicates the distance from shelter 0 to the disaster-stricken area. Travel time;

[0033]

[0034] in, Indicates the disaster-stricken area and Being served Indicates all the affected areas between them. arrive None of them were served. Indicates from the disaster area arrive Travel time;

[0035]

[0036] in, Indicates the disaster-stricken area Being served This indicates that all disaster-stricken areas listed after it have not been served. Indicates from the disaster area Travel time to return to Vault 0.

[0037] Furthermore, the specific process of solving the bi-objective mixed-integer nonlinear programming model using a non-dominated sorting genetic algorithm includes:

[0038] Step 1: Chromosome Encoding and Population Initialization

[0039] Design a chromosome with a two-layer coding structure, including: a length of | The binary encoding and length of | are | | is an integer permutation encoding; during initialization, an initial population is generated randomly;

[0040] Step 2: Non-dominated sorting and crowding calculation:

[0041] For each individual in the population, calculate two objective function values: the total cost of system rescue and the expected total rescue time; use a fast non-dominated sorting strategy to divide the population into several non-dominated levels; calculate the crowding distance of individuals in each non-dominated level to measure the distribution density of the solution in the objective space;

[0042] Step 3: Select Operation:

[0043] A binary tournament selection mechanism is adopted, in which two individuals are randomly selected each time, and the individual with the higher non-dominant level is selected; if the levels are the same, the individual with the larger crowding distance is selected; the selection operation is repeated to form a parent population for crossover and mutation.

[0044] Step 4: Crossover and mutation operations:

[0045] For the crossover operation, a hybrid operation of simulated binary crossover and uniform crossover is used for the address selection substring and the service allocation substring; for the mutation operation, multinomial mutation is used for the binary encoded substring, and the mutation amplitude is controlled by adjusting the distribution exponent; the crossover and mutation probabilities remain fixed during the algorithm operation.

[0046] Step 5: Reorganization and Iteration Termination

[0047] The offspring population after crossover and mutation is merged with the parent population, and non-dominated sorting and crowding calculation are performed again. The top N elite individuals are selected to form a new generation population. The maximum number of iterations is set as the termination condition, and the optimal solution set is finally output.

[0048] A second aspect of the present invention provides a collaborative optimization system for monitoring station site selection and rescue route planning, comprising:

[0049] The information acquisition module is configured to acquire communication rescue information, including the set of candidate locations for emergency communication monitoring stations, the set of nodes, and the required quantity of disaster-stricken areas.

[0050] The model building module is configured to: construct a dual-objective mixed-integer nonlinear programming model using communication rescue information, wherein the dual objectives include minimizing the total system rescue cost and minimizing the expected total rescue time;

[0051] The model solving module is configured to use a non-dominated sorting genetic algorithm to solve the bi-objective mixed integer nonlinear programming model, output the optimal solution set, and obtain the optimal decision for the location of the emergency communication monitoring station and the rescue route.

[0052] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the collaborative optimization method for monitoring station site selection and rescue route planning as described in the first aspect of the present invention.

[0053] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the collaborative optimization method for monitoring station site selection and rescue route planning as described in the first aspect of the present invention.

[0054] The above one or more technical solutions have the following beneficial effects:

[0055] This invention constructs a dual-objective mixed-integer nonlinear programming model, aiming to minimize the total system rescue cost and the expected total rescue time. It comprehensively considers the two key factors of cost and time, and realizes the scientific site selection of emergency communication monitoring stations and the precise planning of rescue routes.

[0056] This invention employs the NSGA-II algorithm for multi-objective optimization. Through fast non-dominated sorting and crowding distance calculation, it effectively maintains the diversity and convergence of the solution set. The elite-preservation strategy significantly improves search efficiency, ensuring rapid location of the Pareto front in the complex solution space. Simultaneously, the algorithm's built-in constraint handling mechanism efficiently processes various complex constraints generated during site selection and path planning. By dynamically adjusting the solution generation and selection process, it ensures that the final optimized solution maintains high cost-effectiveness and time efficiency while satisfying all practical constraints. Under the condition of satisfying practical constraints, it generates an optimal decision set covering both cost and time objectives.

[0057] This invention verifies the practicality and effectiveness of the model and algorithm through case analysis, providing theoretical support and practical reference for the optimized design of disaster emergency response systems.

[0058] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0059] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0060] Figure 1 This is a schematic diagram of the method flow in Embodiment 1 of the present invention;

[0061] Figure 2 This is a Pareto front curve of the bi-objective optimization model in Embodiment 1 of the present invention;

[0062] Figure 3 This is a schematic diagram of the geographical deployment and coverage area of ​​the emergency communication monitoring station in Embodiment 1 of the present invention;

[0063] Figure 4 This is a schematic diagram illustrating the service allocation relationship between the emergency communication monitoring station and the disaster-stricken area in Embodiment 1 of the present invention;

[0064] Figure 5 This is a schematic diagram illustrating the composition of search and rescue time in each disaster-stricken area in Embodiment 1 of the present invention;

[0065] Figure 6 This is the final optimized rescue route map obtained in Embodiment 1 of the present invention. Detailed Implementation

[0066] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0067] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0068] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0069] Example 1

[0070] like Figure 1 As shown, this embodiment discloses a collaborative optimization method for monitoring station site selection and rescue route planning, including:

[0071] S1: Obtain communication and rescue information, including the set of candidate emergency communication monitoring stations, the set of disaster-stricken areas, the number of disaster-stricken areas in need, and the location of shelters;

[0072] S2: Construct a dual-objective mixed-integer nonlinear programming model using communication rescue information, including minimizing the total system rescue cost and minimizing the expected total rescue time;

[0073] S3: The bi-objective mixed integer nonlinear programming model is solved using a non-dominated sorting genetic algorithm, and the optimal solution set is output to obtain the optimal decision on the location of the emergency communication monitoring station and the rescue route.

[0074] In this embodiment, the following is first set:

[0075] 1) The locations of the disaster area, candidate emergency communication monitoring stations, and shelters are all known, as is the required number of disaster areas. 2) The probability of each emergency communication monitoring station failing is independent, and the possibility of a station continuing to provide service after failure is not considered. 3) Rescue vehicles travel at a constant speed. 4) Each disaster area can only be visited by a rescue vehicle once at most.

[0076] In step S1, let As a candidate site for emergency communication monitoring stations, This is a set of candidate sites for emergency communication monitoring stations. The disaster-stricken area is defined as follows: , For the disaster-stricken areas, Assume the required quantity in the disaster-stricken area is... This indicates the affected area. The scale of demand; Assume For shelters (the starting and ending points of rescue vehicle routes); For the set of all nodes, .

[0077] In addition, due to uncontrollable factors after a disaster, emergency communication monitoring stations often fail, and each candidate emergency communication monitoring station... The failure probability is ( ).

[0078] In step S2, a dual-objective mixed-integer nonlinear programming model is constructed using communication rescue information. The dual objectives specifically include minimizing the total system rescue cost and minimizing the expected total rescue time. The model construction process is as follows:

[0079] S2.1: Construct the objective function for the total cost of system rescue. Including candidate sites for emergency communication monitoring stations Site selection costs And due to allocation to disaster-stricken areas Candidate sites for emergency communication monitoring stations The system penalty cost incurred when all systems fail and trapped disaster victims cannot be rescued. .

[0080] Total system rescue cost = site selection cost + system penalty cost, that is:

[0081]

[0082] S2.1.1: Constructing candidate sites for emergency communication monitoring stations The expression for the location cost:

[0083]

[0084] In the formula, Candidate sites for the construction of emergency communication monitoring stations Required installation cost For binary decision variables, if the candidate point is chosen... The value is 1 if an emergency communication monitoring station is installed at the location, otherwise it is 0.

[0085] S2.1.2: When allocated to disaster-stricken areas Candidate sites for emergency communication monitoring stations After all of them fail, the affected area will then be... With zero monitoring accuracy, rescue workers will face prolonged search and rescue times and high costs, at which point rescue vehicles will abandon accessing the disaster area. Heading to the next disaster area and assume responsibility for the disaster-stricken areas The penalty cost of wounded soldiers not receiving aid. Construct the system penalty cost expression:

[0086]

[0087] in, For the disaster-stricken area The unit penalty cost for wounded people who cannot receive rescue services; In this formula, the number of injured people trapped in the disaster area is represented; This indicates all allocated to the disaster-stricken areas. Candidate sites for emergency communication monitoring stations The probability of all failures; As a binary decision variable, if the candidate point of the emergency communication monitoring station For the disaster-stricken area Providing monitoring services ,otherwise .

[0088] S2.2: Construct the objective function for the expected total rescue time This includes rescue vehicles remaining in the disaster area. Search and rescue time And traveling through various disaster-stricken areas visited. Total expected travel time between .

[0089] Expected total rescue time = Expected search and rescue time + Expected travel time, i.e.:

[0090]

[0091] S2.2.1: Each disaster-stricken area One or more candidate emergency communication monitoring stations Monitoring is conducted, and the accuracy of the monitoring depends on the disaster-stricken area. Candidate sites for emergency communication monitoring stations The distance between them determines the outcome, so for any disaster-stricken area... In this context, monitoring accuracy is expressed as:

[0092]

[0093] In the formula, For the disaster-stricken area To the candidate site of the emergency communication monitoring station The distance; This is a correction factor; For binary decision variables; if the candidate points of the emergency communication monitoring station For the disaster-stricken area Providing monitoring services ,otherwise ; For the disaster-stricken area The monitoring accuracy is a dimensionless indicator that reflects the overall signal strength. Higher monitoring accuracy provides better protection for the affected area. The more accurately the location of the injured is pinpointed, the more likely rescue workers will remain in the disaster area. The lower the accuracy of the monitoring, the shorter the rescue time. Conversely, the lower the accuracy of the monitoring, the less time rescuers can find in the disaster area. The longer the rescue time, the better.

[0094] Build for disaster-stricken areas The expression for the rescue time is shown below:

[0095]

[0096] In the formula, This indicates the ideal accuracy conditions in the disaster area. The minimum rescue time, The quantity required for the disaster-stricken area, For a single demand quantity under ideal accuracy conditions, then ; This represents the time increment coefficient, indicating the intensity of the impact of decreased control precision on rescue time. It represents the decay rate and reflects the accuracy sensitivity.

[0097] set up Indicates the disaster-stricken area The probability of being visited by rescued vehicles (i.e., the candidate emergency communication monitoring stations assigned to disaster-stricken area i) At least one is operating normally. The calculation formula is:

[0098]

[0099] Rescue vehicles departed from shelter "0" and headed to various disaster-stricken areas. Rescuing trapped disaster victims, the rescue team eventually returned to shelter "0". This occurred when rescue vehicles visited the disaster area. Search and rescue time will be generated during this process. The expression for the total expected search and rescue time is constructed as follows:

[0100]

[0101] S2.2.2: In disaster emergency response, the core uncertainty in rescue vehicle route planning lies in: the availability of candidate locations for emergency communication monitoring stations. Random failures, affecting the disaster-stricken areas served. This could result in a loss of communication support and inaccessibility (i.e., being "skipped"). In this embodiment, the optimization objective is to find a route that accesses all affected areas, given the known probability of each affected area being served. The prior path ensures that when rescue vehicles travel along this path, they bypass unserved disaster areas (i.e., service disaster areas). Emergency communication monitoring station When all [parts] fail, its expected travel time is minimized.

[0102] Based on the above theory, when considering candidate sites for emergency communication monitoring stations In the event of failure, the total expected travel time for the rescue vehicle route is calculated as follows:

[0103] It is necessary to specify a requirement to visit all disaster-stricken areas. Given a prior path, let the order in which this path visits the disaster-stricken area be: ,in Represents the first in this path The visited disaster-stricken areas; similarly, Represents the first in this path The visited disaster-stricken areas, and v>u The total expected travel time consists of three parts:

[0104] (1) Part 1: From the shelter (0) to the first disaster-stricken area visited The expression for expected travel time:

[0105]

[0106] This expression represents the disaster-stricken area. It is the probability that the first path is visited (i.e.) Served And all the disaster-stricken areas ahead of it. arrive None were served ; Similarly, the number of disaster-stricken areas visited is multiplied by the distance from the shelter (0) to that disaster-stricken area. travel time .

[0107] (2) Part Two: From the disaster-stricken areas to the disaster area The expression for the expected travel time (v>u):

[0108]

[0109] This expression represents the disaster-stricken area. and All were visited, and the affected areas It is the disaster area The probability of the next visited node (i.e., the affected area) and Served And all the disaster-stricken areas between them. arrive None were served ), multiplied from the disaster-stricken area arrive travel time .

[0110] (3) Part Three: From the last disaster-stricken area visited Expected travel time to return to shelter (0):

[0111]

[0112] This expression represents the disaster-stricken area. It is the probability that the last item in the path is visited (i.e. Served And all the disaster-stricken areas following it. arrive None were served ), multiplied from the disaster-stricken area Travel time to return to the shelter (0) .

[0113] The total expected travel time is calculated by combining the above three parts as shown below:

[0114]

[0115] S2.3: Establish a bi-objective mixed integer nonlinear programming model to minimize the total cost of system rescue while minimizing the expected total rescue time.

[0116] Minimize the total cost of system rescue objective function :

[0117]

[0118] Minimize the objective function of the expected total rescue time T :

[0119]

[0120] S2.4: Construct constraints.

[0121] (1) Define the following binary decision variables, continuous decision variables, and integer variables respectively:

[0122]

[0123]

[0124]

[0125] in, These are binary decision variables; if rescue vehicles visit the disaster area but ,otherwise ; For binary decision variables, if the vehicle travels directly from node m to node n, then... ,otherwise ,in , ; For continuous decision variables, representing the disaster-stricken area The overall monitoring accuracy obtained; For integer variables, Let be a set of positive integers, representing the disaster-stricken areas. Ranking of access order in the rescue route .

[0126] (2) To ensure that only emergency communication monitoring stations are candidate sites Distribution to disaster-stricken areas will only occur after installation. And the disaster-stricken area Candidate sites for emergency communication monitoring stations The distance between them should not be greater than that of the candidate points for emergency communication monitoring stations. Given the service radius, the following constraints are established:

[0127]

[0128] in, Emergency communication monitoring station The service radius.

[0129] (3) To ensure that each disaster-stricken area Must be a candidate point for at least one emergency communication monitoring station Provide testing services and establish the following constraints:

[0130]

[0131] (4) If rescue vehicles visit the disaster area To ensure that there is at least one candidate site for emergency communication monitoring station The monitoring services are assigned to this area, with the following constraints:

[0132]

[0133] (5) For the disaster-stricken areas To ensure the ideal state (i.e., candidate sites for emergency communication monitoring stations providing services) Under normal operating conditions, the initial monitoring accuracy is not lower than the specified threshold, and the following constraints are established:

[0134]

[0135] in, For the disaster-stricken area The lowest precision threshold.

[0136] (6) Define the formula for calculating travel time:

[0137]

[0138] in, Let m be the travel time from node m to node n, where m is the travel time from node m to node n. ; Let be the distance traveled between node m and node n, where ; This represents the average speed of the rescue vehicles.

[0139] (7) To ensure that there is exactly one path starting from shelter (0), the following constraints are established:

[0140]

[0141] (8) To ensure that there is exactly one path back to shelter (0), the following constraints are established:

[0142]

[0143] (9) To ensure traffic balance along the path, i.e. for any disaster-stricken area being visited. Rescue vehicles are allowed only one entry and one exit; for any unvisited disaster areas... If no rescue vehicle arrives, the following constraints are established:

[0144]

[0145]

[0146] (10) To prevent sub-loops from forming in the path, the following constraints are established:

[0147]

[0148]

[0149] In step S3, the solution process for the bi-objective mixed-integer nonlinear programming model constructed in this embodiment faces two main challenges: first, there are conflicts between objective functions; and second, the model itself has high complexity. In multi-objective optimization problems, there is usually no single global optimum, but rather a set of Pareto optima to characterize the trade-offs between different objectives. To efficiently obtain the Pareto front solution set, this embodiment uses a non-dominated sorting genetic algorithm (NSGA-II) with an elitist retention strategy to solve the model. The overall algorithm flow is as follows:

[0150] S3.1: Chromosome Encoding and Population Initialization

[0151] To fully represent the two types of decisions—site selection for emergency communication monitoring stations and rescue route planning—a chromosome with a two-layer coding structure is designed. The first substring is of length | The binary encoding of | indicates whether an emergency communication monitoring station is installed at each candidate location; the second substring is of length | The integer permutation code represents the order in which rescue vehicles visit different disaster-stricken areas. During initialization, an initial population is generated randomly, ultimately forming an initial population of size N.

[0152] S3.2: Non-dominated ordering and crowding calculation

[0153] For each individual in the population, two objective function values ​​are calculated: the total cost of system rescue and the expected total rescue time. A fast non-dominated sorting strategy is used to divide the population into several non-dominated levels; the higher the level, the better the individual. Based on this, to maintain the distribution of the solution set, the crowding distance of individuals within each non-dominated level is calculated to measure the distribution density of solutions in the objective space. The larger the crowding distance, the lower the solution density in the individual's region, and the greater its contribution to diversity.

[0154] S3.3: Select Operation

[0155] A binary tournament selection mechanism is used for individual selection. Specifically, in each selection process, two individuals are randomly selected from the current population for comparison. First, individuals with higher non-dominated levels are prioritized; these are those that perform better in multi-objective optimization and are not dominated by other individuals, ensuring the population converges towards the optimal solution. If two individuals have the same non-dominated level, their crowding distance is further compared, and the individual with the larger crowding distance is selected. This helps maintain population diversity and avoids premature convergence to a local optimum. By repeating the selection process, a parent population is gradually built for subsequent crossover and mutation operations, thus ensuring both convergence and population diversity during evolution.

[0156] S3.4: Crossover and Mutation Operations To effectively improve population diversity and enhance search capabilities, a hybrid operation (SBX_UX_cc) is used for both the location substring and the path order substring for crossover. This operation can handle crossovers of binary and continuous variables simultaneously. For mutation, multinomial mutation (PM) is employed, with the mutation magnitude controlled by adjusting the distribution exponent. The crossover and mutation probabilities remain constant throughout the algorithm's execution to ensure search stability.

[0157] S3.4: Recombination and Iterative Termination. The offspring population, after crossover and mutation, is merged with the parent population. Non-dominated sorting and crowding calculation are performed again to select the top N elite individuals and construct a new generation population. The algorithm sets a maximum number of iterations as the termination condition and finally outputs the Pareto optimal solution set.

[0158] In this embodiment, an experimental study conducted in a certain city is used as an example to further verify the effectiveness and practicality of the model and algorithm proposed in this embodiment.

[0159] A connected road network with 13 nodes was selected as the experimental background. Location A was designated as a refuge (the starting and ending point for rescue vehicles), and the remaining 12 nodes were designated as disaster areas, numbered A1–A12, covering various functional types such as residences, schools, and shopping malls. Table 1 shows the geographical distribution of the nodes and the number of nodes required.

[0160] Table 1 Data on shelters and disaster-stricken areas

[0161]

[0162] To reflect the diversity of emergency communication equipment, this study sets up three types of emergency communication monitoring stations. Their installation costs, failure probabilities, and service radii are shown in Table 2, to reflect the trade-off between "low cost - small coverage - high failure" and "high cost - large coverage - low failure".

[0163] Other parameter settings are as follows: 25 candidate emergency communication monitoring stations, unit penalty cost. The value is 15,000 yuan, and the precision threshold is... The value is 2, and the affected area is... Single demand rescue time The average speed of the rescue vehicle is 0.2 hours. For 20 km / h, correction factor Values Time increment coefficient A value of 3 indicates the decay rate. It is 0.1.

[0164] Table 2 Basic Data of Different Types of Emergency Communication Monitoring Stations

[0165]

[0166] Implement a non-dominated sorting genetic algorithm using Python programming, such as... Figure 2 As shown, the Pareto front of the bi-objective optimization model is obtained. The results indicate a clear trade-off between the total system cost and the expected rescue time: reducing the total system rescue cost often leads to a longer expected rescue time, while shortening the rescue time requires higher costs to improve communication coverage reliability. This phenomenon aligns with the urgency of the "golden rescue time" and the limited resources in disaster relief. As investment in emergency communication monitoring stations increases, the marginal improvement in rescue time gradually weakens, indicating the need for a scientific balance between equipment configuration and route planning within a limited budget.

[0167] The experiment set up 25 candidate emergency communication monitoring stations (ES1–ES25). The final optimization results showed that a total of 15 emergency communication monitoring stations needed to be installed, including 2 Type 1 devices, 8 Type 2 devices, and 5 Type 3 devices. Type 2 devices accounted for the highest proportion, indicating that the system achieved a balance between cost and reliability—this type of device provides a relatively good service radius and failure control at a moderate cost. Figure 3 The geographical deployment and coverage of the emergency communication monitoring stations are shown (horizontal and vertical coordinates are not marked). It can be seen that most disaster-stricken areas are effectively covered, and the distribution of equipment is largely consistent with the spatial distribution of needs.

[0168] Figure 4 This further demonstrates the service allocation relationship between emergency communication monitoring stations and disaster-stricken areas. For example, emergency communication monitoring stations ES11 and ES22 each serve three disaster-stricken areas, demonstrating high resource utilization; although disaster-stricken area A3 is served by only ES8, its monitoring accuracy is high due to its proximity; while A4, A8, and A9 are each provided with monitoring services by three monitoring stations, further improving service reliability.

[0169] The search and rescue time structure for each disaster-stricken area is as follows: Figure 5 As shown in the diagram. It is noteworthy that although the number of people needed in disaster-stricken areas A1, A7, and A12 was the same (5 each), their search and rescue times were 2.41 hours, 3.09 hours, and 3.36 hours, respectively. The difference mainly stemmed from variations in monitoring accuracy. Similarly, the disaster-stricken area A6 (12 people), which had the highest need, had a search and rescue time only 0.2 hours longer than disaster-stricken area A2 (8 people). This was because disaster-stricken area A6 had higher monitoring accuracy, reflecting the crucial impact of communication quality on rescue efficiency.

[0170] The final optimized rescue route is as follows: Figure 6As shown, rescue vehicles depart from the shelter, visit the disaster-stricken areas in sequence (A2-A1-A3-A4-A5-A6-A7-A8-A9-A11-A12-A10), and finally return to the shelter. Figure 6 (Horizontal and vertical coordinates not labeled). This route, ensuring that all covered areas are rescued, has a total travel time of only 1.87 hours, demonstrating the model's efficiency in route planning.

[0171] Example 2

[0172] This embodiment discloses a collaborative optimization system for monitoring station site selection and rescue route planning, including:

[0173] The information acquisition module is configured to acquire communication rescue information, including the set of candidate locations for emergency communication monitoring stations, the set of nodes, and the required quantity of disaster-stricken areas.

[0174] The model building module is configured to: construct a dual-objective mixed-integer nonlinear programming model using communication rescue information, wherein the dual objectives include minimizing the total system rescue cost and minimizing the expected total rescue time;

[0175] The model solving module is configured to use a non-dominated sorting genetic algorithm to solve the bi-objective mixed integer nonlinear programming model, output the optimal solution set, and obtain the optimal decision for the location of the emergency communication monitoring station and the rescue route.

[0176] Example 3

[0177] The purpose of this embodiment is to provide a computer-readable storage medium.

[0178] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the collaborative optimization method for monitoring station site selection and rescue route planning as described in Embodiment 1 of this disclosure.

[0179] Example 4

[0180] The purpose of this embodiment is to provide an electronic device.

[0181] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the collaborative optimization method for monitoring station site selection and rescue route planning as described in Embodiment 1 of this disclosure.

[0182] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0183] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0184] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A collaborative optimization method for monitoring station site selection and rescue route planning, characterized in that, include: Obtain communication rescue information, including the set of candidate locations for emergency communication monitoring stations, the set of nodes, and the required quantity in the disaster-stricken area; A dual-objective mixed-integer nonlinear programming model is constructed using communication rescue information, including: Construct the objective function for the total system rescue cost, the objective function for the expected total rescue time, and the constraints; The objective function for the total rescue cost of the system is as follows: in, For the disaster-stricken area, For the disaster-stricken areas, ; As a candidate site for emergency communication monitoring stations, This is a set of candidate sites for emergency communication monitoring stations. ; The total cost of the system rescue, The site selection cost for candidate emergency communication monitoring stations; The system penalty cost incurred when all candidate emergency communication monitoring stations allocated to the disaster area fail and the needs of the disaster area cannot be met; Candidate sites for the construction of emergency communication monitoring stations Required installation cost For binary decision variables; For the disaster-stricken area The unit penalty cost for wounded people who cannot receive rescue services; In the formula, represents the number of injured people trapped in the disaster area; This indicates all allocated to the disaster-stricken areas. Candidate sites for emergency communication monitoring stations The probability of all failures; As a binary decision variable, if the candidate point of the emergency communication monitoring station For the disaster-stricken area Providing monitoring services ,otherwise ; The objective function for the expected total rescue time is as follows: in, The expected total rescue time; The time that rescue vehicles remain in the disaster area for search and rescue operations; The total expected travel time between the various disaster-stricken areas visited; The search and rescue time that the rescue vehicles spend in the disaster area is expressed as follows: in, For the disaster-stricken area To the candidate site of the emergency communication monitoring station The distance; This is a correction factor; As a binary decision variable, if the candidate point of the emergency communication monitoring station For the disaster-stricken area Providing monitoring services ,otherwise ; For the disaster-stricken area The monitoring accuracy is a dimensionless indicator that reflects the overall signal strength. This indicates the ideal accuracy conditions in the disaster area. The minimum rescue time, The quantity required for the disaster-stricken area, The rescue time for a single demand quantity under ideal accuracy conditions; Indicates the time increment coefficient; Indicates the decay rate; This indicates the probability that the disaster-stricken area will be visited by rescue vehicles; This indicates the failure probability of each candidate emergency communication monitoring station. The total expected travel time between the visited disaster-stricken areas. It is divided into three parts: the expected travel time from the shelter to the first disaster-stricken area visited. Expected travel time from one disaster-stricken area to the next. And the expected travel time from the last visited disaster area back to the shelter. : Let the order in which the path visits the disaster-stricken area be: , Represents the first in this path Similarly, for each of the disaster-stricken areas visited, Represents the first in this path Given a disaster-stricken area that is visited, and v > u; the expression is as follows: in, It also indicates the disaster-stricken area being visited; Indicates the disaster-stricken area Being served This indicates that all disaster-stricken areas listed ahead of it have not been served. This indicates the distance from shelter 0 to the disaster-stricken area. Travel time; in, Indicates the disaster-stricken area and Being served Indicates all the affected areas between them. arrive None of them were served. Indicates from the disaster area arrive Travel time; in, Indicates the disaster-stricken area Being served This indicates that all disaster-stricken areas listed after it have not been served. Indicates from the disaster area Travel time back to Vault 0; The dual objectives include minimizing the total cost of system rescue and minimizing the expected total rescue time; The bi-objective mixed integer nonlinear programming model is solved using a non-dominated sorting genetic algorithm, and the optimal solution set is output to obtain the optimal decision for the location of the emergency communication monitoring station and the rescue route.

2. The collaborative optimization method for monitoring station site selection and rescue route planning as described in claim 1, characterized in that, In the aforementioned communication and rescue information, the node set includes a set of disaster-stricken areas and shelters.

3. The collaborative optimization method for monitoring station site selection and rescue route planning as described in claim 1, characterized in that, The process of solving the bi-objective mixed integer nonlinear programming model using a non-dominated sorting genetic algorithm includes: Step 1: Chromosome Encoding and Population Initialization Design a chromosome with a two-layer coding structure, including: a length of | The binary encoding and length of | are | | is an integer permutation encoding; during initialization, an initial population is generated randomly; Step 2: Non-dominated sorting and crowding calculation: For each individual in the population, calculate two objective function values: the total cost of system rescue and the expected total rescue time; use a fast non-dominated sorting strategy to divide the population into several non-dominated levels; calculate the crowding distance of individuals in each non-dominated level to measure the distribution density of the solution in the objective space; Step 3: Select Operation: A binary tournament selection mechanism is adopted, in which two individuals are randomly selected each time, and the individual with the higher non-dominant level is selected; if the levels are the same, the individual with the larger crowding distance is selected; the selection operation is repeated to form a parent population for crossover and mutation. Step 4: Crossover and mutation operations: For the crossover operation, a hybrid operation of simulated binary crossover and uniform crossover is used for the address selection substring and the service allocation substring; for the mutation operation, multinomial mutation is used for the binary encoded substring, and the mutation amplitude is controlled by adjusting the distribution exponent; the crossover and mutation probabilities remain fixed during the algorithm operation. Step 5: Reorganization and Iteration Termination The offspring population after crossover and mutation is merged with the parent population, and non-dominated sorting and crowding calculation are performed again. The top N elite individuals are selected to form a new generation population. The maximum number of iterations is set as the termination condition, and the optimal solution set is finally output.

4. A collaborative optimization system for monitoring station site selection and rescue route planning, implemented by the collaborative optimization method for monitoring station site selection and rescue route planning as described in claim 1, characterized in that, include: The information acquisition module is configured to acquire communication rescue information, including the set of candidate locations for emergency communication monitoring stations, the set of nodes, and the required quantity of disaster-stricken areas. The model building module is configured to: construct a dual-objective mixed-integer nonlinear programming model using communication rescue information, wherein the dual objectives include minimizing the total system rescue cost and minimizing the expected total rescue time; The model solving module is configured to use a non-dominated sorting genetic algorithm to solve the bi-objective mixed integer nonlinear programming model, output the optimal solution set, and obtain the optimal decision for the location of the emergency communication monitoring station and the rescue route.

5. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the collaborative optimization method for monitoring station site selection and rescue route planning as described in any one of claims 1-3.

6. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the collaborative optimization method for monitoring station site selection and rescue route planning as described in any one of claims 1-3.

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