An emergency disposal multi-target decision method for accidents

Abstract

The application belongs to the technical field of accident emergency disposal methods, and particularly relates to an accident emergency disposal multi-target decision method. The method comprises the following steps: converting an accident emergency action preliminary scheme into a CPM network plan chart, establishing a mathematical model corresponding to the CPM network plan chart, establishing a multi-target decision model fusing the CPM-GA method, outputting an optimal target decision scheme, drawing a Gantt chart or a CPM network plan chart according to output data, and forming an action scheme under the decision preference. The accident emergency disposal multi-target decision method of the application obtains emergency decision schemes under different scenarios by constructing a multi-target decision fitness function, setting a fitness function weight factor omega value, and provides auxiliary decision for emergency commanders. In view of the problem of multi-target simulation stagnation of the genetic algorithm, the application proposes a genetic algorithm optimization method based on priority coding, and combines CPM key path optimization, so as to improve the convergence speed and provide support for efficient multi-target decision of accident emergency.

Description

Technical Field

[0001] This invention belongs to the technical field of emergency response methods, and in particular relates to a multi-objective decision-making method for emergency response. Background Technology

[0002] Emergency response primarily targets sudden events, employing scientific methods for analysis and developing mathematical models to aid decision-makers in understanding the situation. With continuous theoretical development, methods including game theory, path planning, and neural networks have been applied to emergency response decision-making, providing diverse approaches. However, all these theories have limitations; there is no universal solution that can address all problems. Given the uncertainty and severity of accidents, comprehensively weighing multiple objectives such as risk, time, and cost to select the most effective emergency response plan is a crucial consideration in current emergency response practices. Furthermore, for some special accidents, not only is rapid decision-making required, but the decision-making process often involves the coordinated allocation of substantial operational resources. Focusing solely on time efficiency is often idealistic, and the resulting emergency response plan may fail to achieve the actual objectives of emergency response. Summary of the Invention

[0003] The purpose of this invention is to propose a priority-based genetic algorithm optimization method, combined with CPM critical path optimization to improve convergence speed, based on the current situation. This provides support for efficient multi-objective decision-making in emergency response, offers decision support for emergency command, and provides a basis for evaluating the effectiveness of emergency drills.

[0004] To achieve the above objectives, the present invention adopts the following technical solution;

[0005] A multi-objective decision-making method for emergency response includes the following steps:

[0006] Step A: Convert the preliminary emergency response plan into a CPM network plan diagram, which is defined as the action plan implemented to achieve the task objectives and the resources required to execute the task. Draw the operational tasks and prerequisites of each link and work in the emergency response plan into a CPM network plan diagram according to their internal relationships.

[0007] Step B: Establish a mathematical model corresponding to the CPM network plan diagram, including the CPM node parameter model and the CPM task parameter model; the CPM node parameter model is established based on the task time of the CPM node, the earliest completion time of the node, the latest completion time of the node, and the node time difference; the CPM task parameter model is established based on the earliest start time of the task, the latest start time of the task, the earliest end time of the task, the latest end time of the task, the single task time difference, and the total task time difference.

[0008] Step C: Establish a multi-objective decision-making model that integrates the CPM-GA method.

[0009] C1. Chromosome coding design creates priority variables to assign priority values ​​to each task in the emergency mission. Chromosome storage stores a sequence of randomly generated priorities.

[0010] C2. Chromosome decoding design: The decoding process restores the priority sequence to a valid job scheduling sequence.

[0011] C3. Establish the fitness function and objective function, including the time objective function, the resource load rate objective function, and the resource balance objective function;

[0012] C4. Complete CPM-GA simulation and output. Based on the CPM graph generated from the initial action plan, load the CPM task parameters; generate the initial population based on the priority-based chromosome encoding scheme; decode the chromosomes to obtain the initial task sequence, solve the objective function and fitness function, evaluate the chromosome fitness, and perform genetic mutation operations; at the end of the iteration, output the optimal chromosome to obtain the optimal objective decision scheme, and draw a Gantt chart or CPM network plan diagram based on the output data to form the action plan under this decision preference.

[0013] A further improvement or preferred implementation of the aforementioned multi-objective decision-making method for emergency response, specifically step A, converting the preliminary emergency response plan into a CPM network plan diagram, includes:

[0014] A1, defined as the action plan implemented to achieve the task objective, represented as a set:

[0015] Where N represents the number of operations required for emergency response, and T i This represents the i-th task; for example, pollution suppression is a task within an emergency response mission.

[0016] A2. Define the resources required to execute the task, represented as a set:

[0017] Where M represents the quantity of resources, P j This represents the j-th resource; for example, in an emergency response mission, the decontamination and cleaning team is an operational resource.

[0018] A3. Draw a CPM network diagram showing the operational tasks and prerequisites of each stage and task in the emergency response plan, according to their inherent relationships; use arrows (→) to correspond to a task in task set T. The number below it indicates the duration of the operation. Circles (○) represent nodes, which are the connections between tasks.

[0019] A further improvement or preferred implementation of the aforementioned multi-objective decision-making method for emergency response, specifically step B, establishing a mathematical model corresponding to the CPM network plan diagram, includes:

[0020] B1. Establish a CPM node parameter model, whereby the node parameters include: job time, earliest node completion time, latest node completion time, and node time difference. The corresponding parameter model is as follows:

[0021] (1) Operation time model , refers to homework The duration is calculated using the three-time estimation method and is expressed as: Where a is the most optimistic time, b is the most pessimistic time, and c is the most likely time;

[0022] (2) Earliest Node Implementation Time Model , refers to the maximum earliest completion time of a job ending at node j, denoted as . ;in, for The earliest implementation time of all immediate predecessor nodes;

[0023] (3) Latest Node Implementation Time Model This refers to the latest time that node i must be completed without affecting the task's duration, calculated backwards from the immediately following node j, and is expressed as: ;in, for The latest implementation time of all successor nodes. Duration of the task;

[0024] (4) Node time difference model The meaning is the node's maneuver time, expressed as ;

[0025] B2, CPM job parameter model, wherein the job parameters include the earliest start time of the job, the latest start time of the job, the earliest end time of the job, the latest end time of the job, the single job float, and the total job float, and the corresponding parameter model is as follows;

[0026] (1) Earliest start time model for tasks This refers to the earliest time when all preceding operations of this task have completed, expressed as... ;

[0027] (2) Latest start time model for assignments This refers to the latest completion time of the end node minus the job duration, expressed as:

[0028] (3) Earliest End Time Model for Tasks It refers to the earliest start time plus the duration of the task, expressed as: ;

[0029] (4) Model of the latest completion time of the task This refers to the latest time that can be achieved no later than the end node, expressed as... ;

[0030] (5) Time difference model of work order This refers to the slack time that a task has without affecting the earliest start time of its successor tasks, and is expressed as: ;

[0031] (6) Total Float Model This refers to the maximum available slack time for the task, expressed as... .

[0032] In a further improvement or preferred implementation of the aforementioned multi-objective decision-making method for emergency response, step C1, chromosome coding design, specifically refers to: creating a priority variable Priority for each task T in the emergency mission. i Assign a priority value; chromosome x stores a sequence x with a randomly generated priority. Where N is the number of operations required for emergency response, and Pi is the priority variable of operation Ti;

[0033] The C2 chromosome decoding design step specifically refers to:

[0034] S1. Within each loop cycle, extract the sequence of tasks to be executed. , judge task Whether to carry out:

[0035] Condition 1: If the task has already been initiated, then proceed with the next task in sequence.

[0036] Condition 2: If not carried out, check whether the prerequisite tasks have been completed;

[0037] S2, if task If the preceding tasks are not completed, the next task is extracted sequentially from the sequence of tasks to be executed; if the tasks are already completed, further judgment is made on the task. Are the required resources available?

[0038] S3, if task If the required resources are available, then the task will be... Add the task to the sequence of tasks to be executed; if the task is not idle, extract the next task from the sequence of tasks to be executed in order.

[0039] S4. Repeat S1~S3 until all pending tasks that meet the resource idle condition are added to the sequence of tasks to be executed.

[0040] S5. Sort the sequence of tasks to be executed according to their priority values ​​from largest to smallest, and execute the tasks with higher priority first.

[0041] A further improvement or preferred implementation of the aforementioned multi-objective decision-making method for emergency response, specifically step C3, establishing the fitness function and the objective function, includes:

[0042] S1. Fitness Function: Introducing the weight factor ω, designing the fitness function. as follows:

[0043] Where is the time objective function, is the resource load objective function, is the resource balance objective function, and is the weight of the objective function.

[0044] S2, Time Objective Function

[0045] in, The total actual time to complete the task corresponds to the earliest finish time in the CPM parameter model. , This refers to the latest completion time of the task, corresponding to the latest end time in the CPM parameter model. ;

[0046] S3, the resource load rate objective function, divides the total project duration (Time) into m consecutive time slices. Δt is the smallest time granularity; resources The single resource load rate is:

[0047] in, For resources Actual effective working time slices refers to resources The total amount of resources, For all tasks currently being executed within the k-th time slice, the resources... Resource intensity;

[0048] The objective function for the overall resource load factor is:

[0049] Among them, M still represents the quantity of emergency response resources;

[0050] S4, Objective function for resource balance

[0051] The coefficient of variation is used to measure the stationarity of resource consumption; resource P j The coefficient of variation is:

[0052] in, For resources Average consumption; For resources Standard deviation of resource consumption;

[0053] The objective function for resource balance is: .

[0054] Further improvements or preferred implementations of the aforementioned multi-objective decision-making method for emergency response include the following specific steps in step C4: completing CPM-GA simulation and output:

[0055] S1. Based on the CPM diagram generated from the initial action plan, load the CPM operation parameters, including: operation code T(i), operation resources Res(i), preceding operation Pre(i), operation time t(i), and total resources Q(i);

[0056] S2. Generate the initial population. Where M is the population size; according to step C1, based on the priority-based chromosome coding scheme, each chromosome can be represented as: x i ;

[0057] S3. Decode the chromosome to obtain M initial task sequences T, each sequence representing a possible solution; as defined in step A1, the task set... It can be seen that each group of tasks after decoding still consists of N jobs;

[0058] S4. Solve the objective function , , and fitness function ;

[0059] S5. Assess the fitness of each chromosome, retain 10% of the elite population, and generate offspring through crossover, using the crossover probability... Produce offspring, based on mutation probability Introducing new features;

[0060] S6. Determine whether one of the following iteration termination conditions is met:

[0061] Condition 1: The maximum number of iterations G = 200 is reached;

[0062] Condition 2: The optimal solution has not improved for 50 consecutive generations; The conditions have reached the set target value.

[0063] If none of the conditions are met, return to S4 and continue iterating; if the conditions are met, output the optimal chromosome.

[0064] S7. Obtain the current weight ( , , The optimal objective decision scheme under the given conditions includes:

[0065] Data 1 (Job Information): Job code T(i), earliest start time ES(i), earliest end time EF(i), job duration t(i), whether it is a critical job CP(i);

[0066] Data 2 (Comparison Indicators between Schemes): Total Work Time Resource balance Resource load factor Resource balance Average resource usage Standard deviation Coefficient of variation Indicators such as;

[0067] Based on the output data, a Gantt chart or CPM network plan can be drawn to form an action plan under this decision preference.

[0068] In a further improvement or preferred implementation of the aforementioned multi-objective decision-making method for emergency response, in step C1, the CPM method is used to identify critical paths and assign higher priority values ​​to critical tasks, so that high-quality genes can obtain more selection opportunities in the initial population.

[0069] In a further improved or preferred implementation of the aforementioned multi-objective decision-making method for emergency response, the decoding is performed cyclically with the smallest time granularity Δt as the unit.

[0070] Its beneficial effects are as follows:

[0071] The multi-objective decision-making method for emergency response in this application constructs a multi-objective decision fitness function. By setting the fitness function weight factor ω, emergency decision-making schemes under different scenarios are obtained, providing auxiliary decision-making for emergency commanders. In view of the problem of simulation stagnation in multi-objective simulation of genetic algorithms, this application proposes a genetic algorithm optimization method based on priority encoding, and combines it with CPM critical path optimization to improve the convergence speed and provide support for efficient multi-objective decision-making in accident emergency response. Attached Figure Description

[0073] Figure 1 This is an example of using the CPM method to generate emergency decision-making solutions;

[0074] Figure 2 It is a diagram showing the relationship between the operation parameters;

[0075] Figure 3 Comparison of convergence curves between CPM critical path optimization simulation and conventional simulation;

[0076] Figure 4 Schematic diagram of chromosome decoding scheme;

[0077] Figure 5 Chromosome decoding results;

[0078] Figure 6 This is a schematic diagram of the CPM-GA simulation process;

[0079] Figure 7 This is the Gantt chart for Option A;

[0080] Figure 8 This is the network diagram for scheme A;

[0081] Figure 9 This is the Gantt chart for Option B;

[0082] Figure 10 This is the network diagram for Option B;

[0083] Figure 11 This is the Gantt chart for scheme C;

[0084] Figure 12 This is the network diagram for scheme C;

[0085] Figure 13 This is a matrix chart comparing the total time spent on assignments;

[0086] Figure 14 It is a simulation convergence curve;

[0087] Figure 15 This is a comparison matrix of workload rates;

[0088] Figure 16 It is a graph showing the change in workload rate over time;

[0089] Figure 17 This is a matrix chart comparing the total time spent on assignments;

[0090] Figure 18 It is a graph showing how the work balance changes over time. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0093] Emergency response decision-making is a process under high time pressure, uncertainty, and significant risk, often facing numerous difficulties in practice. To rapidly mitigate accident damage and prevent escalation of consequences, time is typically prioritized, but this also exposes problems such as imbalanced resource allocation and insufficient multi-task coordination. Addressing the issue of low overall effectiveness of current solutions, this application proposes a multi-objective decision-making method for emergency response, constructing a fitness function... By changing The medium weighting factor ω value provides a multi-objective decision-making scheme, addressing the problem of idealized single-objective decision-making. To address the challenge of high chromosome invalidity rates in multi-objective decision-making, which leads to convergence stagnation in genetic algorithms, this application proposes a priority-based encoding solution. Chromosome encoding employs a priority-based encoding method, implementing legality detection during decoding. A legal scheduling sequence is dynamically generated through topological sorting, and the CPM method is combined to identify critical paths, accelerating the convergence speed of the genetic algorithm and effectively solving the problem of high chromosome invalidity rates. After 20 repeated simulations, the results all met expectations, verifying the accuracy of the proposed method.

[0094] The following provides a detailed explanation of each step in conjunction with the specific implementation:

[0095] Step A: Convert the emergency response plan into a CPM network plan diagram.

[0096] Network planning techniques are a general term for various network planning methods, commonly used in task planning. By establishing mathematical models, they uncover inherent logical relationships and numerical characteristics, helping commanders see beyond the surface of a problem to its essence. The Critical Path Method (CPM) includes two methods: single-symbol network diagrams and double-symbol network diagrams. In a single-symbol network diagram, nodes represent tasks, and paths only indicate the connection relationships between nodes. In a double-symbol network diagram, paths represent tasks, and nodes only represent the start and end points of tasks. Single-symbol network diagrams are only suitable for simple, small-scale task flows. Since emergency response task flows are relatively complex, this application uses double-symbol network diagrams.

[0097] After receiving a mission, the commander needs to analyze the mission objectives, make a decision, and clarify the intentions and effects to be achieved in carrying out the mission.

[0098] Define task resources as the preconditions for executing a task, represented as... , , This represents the i-th precondition; for example, in an emergency response mission, the decontamination and cleaning team is a task resource unit.

[0099] Defined as a set of action plans implemented to achieve a task objective. , , This indicates the m-th task; for example, pollution suppression is a task action within an emergency response mission.

[0100] The CPM method often uses circles, arrows and other graphics and symbols to create a network-like diagram of the various links and work items of the plan according to their internal connections and the commander's ideas

[19] . Figure 1 An example of converting an accident emergency response plan into a dual-code CPM diagram;

[0101] Figure 1 In the diagram, the arrow (→) corresponds to a task in task set T. The number below the slash indicates the task. The required time, for example, T3 / 15 in the diagram represents the operation of drone monitoring (T3), lasting 15 minutes; circles (○) represent nodes, which are the connecting points between operations. Nodes do not represent actual significance, especially in terms of prevention and resource allocation. The nodes are only used when calculating CPM graph parameters to avoid confusion.

[0102] Step B: Convert CPM into a computable mathematical model

[0103] Converting an emergency response plan into a CPM network diagram is only the first step in the application of the program. It is also necessary to convert the CPM into a calculable mathematical model in order to achieve scientific optimization of the action plan. By calculating the parameters in the mathematical model, the critical path of the CPM is determined, thereby determining the earliest and latest start and end times of the emergency response action, judging the work order float and total float, and providing a basis for the optimization design of the plan. The CPM mathematical model mainly includes two types: node parameter model and work parameter model.

[0104] B1. Node Parameter Model

[0105] This includes the earliest node implementation time, the latest node implementation time, and the node time difference;

[0106] (1) Earliest implementation time of the node

[0107] The earliest completion time of a node is equal to the earliest completion time of all its immediate predecessor jobs, that is, the maximum value among the earliest completion times of jobs ending at that node, expressed as:

[0108] ;

[0109] in, for The earliest implementation time of all immediate predecessor nodes. The duration of the operation can be determined using one-time estimation, three-time estimation, and statistical methods.

[0110] The work time is estimated using the three-time estimation method, which is expressed as follows:

[0111] ;

[0112] Where a is the most optimistic time, b is the most pessimistic time, and c is the most likely time;

[0113] (2) Latest implementation time of the node

[0114] The latest completion time of a node is the latest time that a node must be completed without affecting the task's duration. It is the minimum of the earliest completion times for jobs ending at that node, expressed as:

[0115] ;

[0116] in, for The latest implementation time of all successor nodes. Given the job duration, we can see the latest completion time of each node. From the immediate successor node It was deduced by reverse reasoning;

[0117] (3) Node time difference

[0118] Node slack refers to the slack time of a node without affecting the timely completion of the task; it is the difference between the latest completion time and the earliest completion time of the node, expressed as: ;

[0119] B2, CPM Operation Parameter Model

[0120] Node parameters are the foundation of job parameters. For double-symbol CPM, the job parameter model is the key to solving the problem. There are six job parameters: earliest start time, latest start time, earliest finish time, latest finish time, single float, and total float. The relationships between these job parameters are as follows: Figure 2 As shown;

[0121] (1) Earliest start time of the assignment

[0122] The earliest start time of a task is the earliest time when all its immediate predecessor tasks have finished, expressed as:

[0123] ;

[0124] (2) Latest start time of the assignment

[0125] To ensure the task is completed on schedule, the latest start time of the task's completion node cannot be affected. This can be expressed as the latest completion time of the task's completion node minus the task's duration.

[0126] ;

[0127] (3) Earliest completion time of the task

[0128] To ensure the task is completed on schedule, the latest start time of this task cannot affect the end node. This is calculated by adding the earliest start time of the task to its duration, expressed as:

[0129] ;

[0130] (4) Latest end time of the assignment

[0131] To ensure the task is completed on schedule, this operation must be completed no later than the latest completion time of the end node. , is represented as:

[0132] ;

[0133] (5) Time difference of work order

[0134] Job slack refers to the slack time that a job has without affecting the earliest start time of its successor jobs. It is expressed as... ;

[0135] (6) Total Float of Operations —

[0136] Any job can only start at its earliest time. and latest end time The schedule is arranged within this time period, excluding the duration of the operation. This is the total float of the operation. , represented as ;

[0137] from Figure 2 As can be seen, single float is part of total float. When planning tasks, single float can be used first without considering the start of subsequent tasks. Only when single float is insufficient should total float be used, but this will delay subsequent tasks.

[0138] Step C: Establish a multi-objective decision-making model that integrates the CPM-GA method.

[0139] In emergency response, if only the optimization of work time is considered, it can be directly solved using the CPM work parameter model. However, multi-objective decision-making needs to consider resource constraints. To meet the multi-objective constraints of time and resources, this application designs a multi-objective decision-making model that integrates the CPM-GA method. The genetic algorithm (GA) simulates the biological evolution process, and its genetic crossover and mutation operations have good matching with the CPM work parameter model. Furthermore, computer-aided design can be used to improve the versatility of the scenario.

[0140] C1. Chromosome coding design

[0141] Its genetic crossover and mutation operations match well with the CPM job parameter model, and computer-aided design can be used to improve the versatility of the scenario. Chromosome encoding and decoding design is the foundation of the CPM-GA method and the basis for initial population generation. Traditional genetic algorithms encode task sequences as chromosomes. Due to the existence of various constraints in multi-objective decision-making, these constraints are easily violated during the initialization and simulation iteration of the genetic algorithm, resulting in a large number of illegal individuals and causing the genetic algorithm to stagnate. To address this, this application proposes a priority-based encoding approach, which implements legality detection during the decoding process, dynamically generates legal scheduling sequences through topological sorting, and combines it with the CPM method to identify critical paths, thereby accelerating the convergence speed of the genetic algorithm.

[0142] Emergency response decision-making typically employs two approaches to encode chromosome X:

[0143] (1) Based on the job set, a single chromosome is an N-dimensional row vector: Where N is the number of tasks;

[0144] (2) Based on the resource set, a single chromosome is an M-dimensional row vector: Where M represents the quantity of emergency response resources;

[0145] However, due to the unique nature of emergency response tasks, constraints exist within operational resources and timeframes. Genes in set X are not independent individuals but rather exhibit partial order relationships. Under this inherent partial order constraint, randomly generated chromosomes during initialization have a high probability of being invalid. Even if a valid scheduling sequence is generated initially, this partial order relationship can easily be disrupted after multiple crossover and mutation iterations, leading to the generation of a large number of invalid chromosomes in the next generation. These issues often cause genetic algorithms to stall during simulation calculations, which is the main reason why genetic algorithms cannot be applied in emergency decision-making.

[0146] Therefore, this application proposes a genetic algorithm optimization method based on priority encoding. The core of this method is to design a "Priority" variable, assigning a priority value to each task. The chromosome does not directly store the task sequence, but rather stores the sequence that generates priorities, represented as: Where N is still the number of assignments. This represents the priority value of the nth task.

[0147] Priority-encoded chromosomes, whether generated during initialization or genetic mutation, remain a set of priority sequences, requiring no correction of validity. The core idea of ​​this method is to remove the partial order constraint from the chromosome and place it into the decoder for processing. During decoding, the scheduling validity is determined based on the job parameters, and individuals with higher priority values ​​are selected preferentially.

[0148] Emergency response tasks typically involve a large number of operations. As the number of operations increases, the simulation complexity grows exponentially. To improve the iterative efficiency of genetic algorithms, this application proposes a genetic algorithm initialization strategy combining the CPM method with priority encoding. The CPM method identifies critical operations on the critical path and assigns them higher priority values, thereby increasing their selection opportunities during the genetic process and improving convergence speed. This optimization method shows significant effectiveness in optimizing large-scale models. Figure 3 To compare the simulation results of a task containing 28 tasks with and without the CPM method.

[0149] The results show that the average number of generations for CPM convergence was reduced from 19.1 to 16.3, and the convergence speed was improved by 14.7%. Furthermore, CPM initialization significantly improved the quality of the first generation population, effectively guiding the search direction of the algorithm and reducing invalid explorations.

[0150] C2, Chromosome Decoding Design

[0151] A priority-based genetic algorithm transfers the validity check to the decoding process. This application designs, as follows: Figure 4 The logical judgment mechanism shown addresses the issue of job serialization in the initial coding through loop judgment. Multiple tasks without dependencies and resource conflicts are scheduled for parallel execution on the actual timeline. Based on this, further judgment is made to select the job with the highest "Priority".

[0152] The specific steps are as follows:

[0153] S1. In each loop cycle, extract the first task from the sequence of tasks to be executed. , judge task Expand if necessary; if expanded, retrieve the next task sequentially from the sequence of pending tasks; if the task... If not expanded, then the detection task... Have the preliminary tasks been completed?

[0154] S2, if task If the preceding tasks are not completed, the next task is extracted sequentially from the sequence of tasks to be executed; if the tasks are already completed, further judgment is made on the task. Are the required resources available?

[0155] S3, if task If the required resources are available, then the task will be... Add the task to the sequence of tasks to be executed. If the task is not idle, extract the next task from the sequence of tasks to be executed in order.

[0156] S4. Repeat S1~S3 until all pending job tasks with available resources have been added to the job task sequence to be executed.

[0157] S5. Sort the tasks in the sequence of tasks to be executed according to their priority values ​​from largest to smallest, and select the task with the highest priority value to execute.

[0158] Taking an emergency response task as an example, the genetic algorithm decoding process will be explained in detail. This task has four jobs, and the parameters of each job are shown in Table 1.

[0159] Table 1 Examples of Chromosome Decoding

[0160]

[0161] For example, based on emergency response practices, the cyclic judgment is based on a unit time of 0.5 hours, that is, the smallest time granularity Δt is 0.5 hours. Assuming a certain group of chromosomes X is [T1, T2, T3, T4], the decoding process is as follows:

[0162] Time 0: Job T1 is scanned, resource P1 is idle, no preceding job, priority is 0.33; Job T2 is scanned, preceding job T1 exists; Job T3 is scanned, no preceding job, priority is 0.90; Job T4 is scanned, no preceding job, priority is 0.12. Although jobs T3 and T4 have no preceding jobs, according to priority ranking, job T3 has priority, so T3 is scheduled first, proceeding from time 0 to time 1. Job T1, since there is no resource conflict, is carried out synchronously with job T3, proceeding from time 0 to time 0.5. Job T4, since the total resource is 7, cannot be carried out in parallel.

[0163] Time 0.5: Job T1 completes, resource P1 is released. The list is scanned sequentially; jobs T2 and T4 are pending. Job T3 is still in progress, and resource P2 has not been released, therefore job T4 cannot proceed. Job T2's predecessor, job T1, has completed, and resource P2 is available; therefore, job T2 is scheduled, proceeding from time 0.5 to time 2.

[0164] Time 1: Job T3 is completed, and resource P2 is released. The list is scanned sequentially, and the next job to be processed is job T4. Therefore, job T4 is scheduled, and the process continues from time 1 to time 2.5.

[0165] Time 1.5: Unfinished tasks T2 and T4.

[0166] Time 2: Task T2 is completed, but task T4 is incomplete.

[0167] Time 2.5: All tasks are completed.

[0168] Finally, the task time for each task is as follows: Figure 5 As shown, the total time taken was 2.5 hours. By decoding the original chromosome and incorporating all operational parameter information, the action plan became more realistic.

[0169] C2. Establish the fitness function and objective function.

[0170] Emergency response faces the objectives of "time, cost, and risk," which are interconnected yet contradictory. Firstly, emergency response typically prioritizes time, but inevitably involves resource conflicts and prioritization, while also considering resource costs. Secondly, improving resource efficiency is crucial, but this often comes at the cost of risk, as high efficiency implies tighter resource coordination but also weaker resistance to unexpected disruptions. The fitness function design is the core of the CPM-GA method. To represent emergency plans with different decision-making preferences, this application introduces a weighting factor ω, embedded in the genetic algorithm's fitness function, thereby providing emergency response commanders with decision-making options based on their preferences.

[0171] Emergency response typically faces the objectives of "time, cost, and risk," which are interconnected yet contradictory. Firstly, emergency response usually prioritizes time, but inevitably involves resource conflicts and priorities; resources cannot be used indefinitely, and resource costs must be considered. Secondly, improving resource efficiency is necessary to reduce resource costs, but this often comes at the cost of risk. Higher efficiency means tighter resource coordination but weaker resilience to unexpected disruptions; failure of any resource can lead to mission failure. Considering these factors, this application designs a fitness function... as follows:

[0172] ;

[0173] in Let the time objective function be... Let the resource load objective function be... The objective function is the resource balance. , , Weights are allocated according to decision-making needs to satisfy... ;

[0174] (1) Time objective function

[0175] Time objective function It is the most basic objective function, aiming to achieve time priority; its solution is based on the CPM job parameter model. Since the fitness function requires a larger and better value, an inverse transformation is needed, which is expressed as:

[0176] ;

[0177] in This represents the total time actually taken by the task. Here, represents the latest completion time of the task, and represents the latest end time in the CPM parameter model. ;

[0178] (2) Resource load factor objective function

[0179] Resource load factor, or resource utilization rate, aims to minimize resource costs. Emergency response operations are discrete tasks, and resource load factor cannot be calculated using integrals of continuous functions. For example, if a task has a total duration of 10 hours, and resource j is only used during the 4-5 hour timeframe, resource j may be at 100% full load in that time unit. However, due to idle time during the operation, the average load factor is only 10%, failing to accurately reflect resource utilization efficiency. Therefore, this application introduces the concept of time slices, dividing the total project duration into m consecutive time slices, with the smallest time granularity Δt representing the time slice. ;

[0180] In this embodiment, the minimum time granularity is 0.5h, and time slices are divided based on this standard.

[0181] Resource The total amount of resources is For the k-th time slice, define all tasks currently executing within that time slice that affect resources. The resource intensity is ,resource The actual effective working time slice is Then resources Average consumption for:

[0182] ;

[0183] The above formula only considers the actual effective usage time of resources and does not consider idle time, which can fully reflect the resource's actual usage time. The actual consumption level, then the final resources Single resource load rate ;

[0184] Overall average load factor The average load of all resources is represented as a function of the load. ;

[0185] In the formula, M represents the quantity of emergency response resources;

[0186] (3) Objective function of resource balance

[0187] Resource balance is an indicator of the stability of task planning, aiming to achieve stable resource consumption and reduce operational risks; in statistics, the core indicator for measuring the relative dispersion of data is usually the coefficient of variation. ;

[0188] Among them, the standard deviation of the consumption of the j-th resource ;

[0189] Adaptive function A higher value indicates a better solution, therefore it is necessary to... Normalization and positiveization processing, average balance after processing ;

[0190] C3. Complete CPM-GA simulation and output.

[0191] CPM-GA simulation is based on iterative iterations, with core constraints being "preceding constraints + resource constraints," primarily revolving around the fitness function. fitness A higher value indicates a better solution;

[0192] The CPM-GA simulation process is as follows: Figure 6 As shown, it mainly includes:

[0193] S1. First, load the CPM graph job parameters and generate the initial population: ,in For population size, chromosomes It is a population One individual in a problem corresponds to one solution to the problem; chromosome Represented as: Where N is the number of tasks, and genes It is a basic unit of chromosomes, representing a random number that indicates the job priority.

[0194] S2. Decode the chromosome to form a chromosome that can incorporate all CPM job parameters. The core information of these parameters includes the job code T. i , homework resources P j Pre-job Pre(i), Job time t, Resource intensity Total resources Priority;

[0195] S3. Evaluate the fitness of the scheme represented by each chromosome group, select excellent parents, retain 10% of the elite population, and generate offspring through crossover. The crossover probability is... Mutation introduces new characteristics, mutation probability ;

[0196] S4. Determine if the iteration termination condition is met:

[0197] Condition 1: The maximum number of iterations G is reached, typically G = 200;

[0198] Condition 2: The optimal solution has not improved for 50 consecutive generations;

[0199] Condition 3: The set target value has been achieved;

[0200] If the condition is not met, continue to evaluate the fitness of each group of chromosomes, select the optimal chromosome, and repeat the iterative loop; if the termination condition is met, output the optimal chromosome.

[0201] S5. Output the current fitness function. Weights ( , , The optimal target decision scheme under the commander's decision preference is represented by the iterative optimal solution. The output of CPM core operation parameters includes: operation code, earliest start time of operation, earliest end time of operation, operation duration, and whether it is a critical operation. Gantt charts or CPM network plans can be drawn to form the action plan under the decision preference.

[0202] Furthermore, to compare the differences between different schemes, the simulation process synchronously generates the following parameters (as shown in Table 3): total operation time, resource balance, resource load factor, and average resource usage. Standard deviation Coefficient of variation Indicators such as these.

[0203] Implementation Case:

[0204] Small breach loss-of-coolant accident is a type of accident in which a small breach occurs at the pressure boundary of the primary circuit of a passive pressurized water reactor (AP1000). It is one of the most important design basis accidents in nuclear safety analysis. Therefore, the typical emergency response process can be divided into five stages, including: breach discharge depressurization stage, natural circulation stage, automatic depressurization system discharge stage, IRWST injection stage, and long-term cooling stage. In the process of small breach loss-of-coolant accident, complex thermal-hydraulic phenomena are usually present

[24] , the on-site situation changes rapidly, and various factors are intertwined. Emergency decision-making requires the coordination of various emergency resources. The required resources mainly include: emergency command center, on-site operators, emergency maintenance personnel, radiation monitoring personnel, emergency support personnel, and joint response of safety-critical systems such as protection system, diagnostic system, passive safety system, CMT water tank, ADS system, IRWST, IRWST, and PXS. In order to accurately describe this complex relationship, 32 operations were planned, 12 resources were used, and a preliminary emergency plan was prepared as shown in Table 1. The proposed scheme needs to be optimized using the priority-based genetic algorithm described in this application.

[0205] Table 2 Preliminary Emergency Response Plan for Small Breach Accidents (Time Unit: h)

[0206]

[0207] Simulation calculation

[0208] Regarding small breach water loss incidents, this application prioritizes "time, cost, and risk," with a weighted approach. , , The values ​​are set as follows: (0.9, 0.1, 0.1), (0.1, 0.9, 0.1), and (0.1, 0.1, 0.9), respectively. The core constraints are time constraints and resource constraints. The "time constraint" must satisfy the preceding task constraints of each task in Table 1, and the "resource constraint" must satisfy the condition "resource intensity ≤ total resource amount" for each task in Table 1. The simulation is implemented using Matlab software. The complete simulation process is as follows: Figure 7 As shown, the core functions include: Data Input—LoadData, Population Initialization—InitPopulation, Decode, Fitness Calculation—CalFitness, Elite Retention—Selection, Crossover, Mutation, and OutputResult. The population size is 100, and the evolutionary generation is 100.

[0209] Around the fitness function: fitness A larger numerical value indicates a better solution. To prevent discrepancies in results, multiple simulations were performed to determine the optimal value, with a total of 20 simulations. The simulation results of the three solutions are displayed as Gantt charts and double-symbol network diagrams, as shown below. Figures 8-13 As shown.

[0210] Comparative Analysis of Simulation Results

[0211] The simulation results comparison and analysis are mainly based on the fitness function. There is no absolute superiority or inferiority among the three schemes; they only exhibit a certain degree of competition in terms of the three objectives: total operation time, resource load rate, and resource balance. To support the analysis conclusions, some key indicators were calculated during the simulation, including: total operation time, resource balance, resource load rate, and average resource usage. Standard deviation Coefficient of variation The simulation data results for each scheme are shown in Table 3, along with other indicators.

[0212] Table 3 Simulation data results for each scheme

[0213]

[0214] (1) Comparative analysis of total task time

[0215] The time-priority objective is to minimize the total task time, allowing for moderate resource overload. The only constraint is that all tasks must satisfy a prerequisite relationship. To meet the requirements of completing the emergency response task as quickly as possible, the time objective function of Option A is... weight Set the weight to 0.9, and the weights of the other two schemes... Set to 0.1. Simulation results are as follows: Figure 13 , Figure 14 As shown, the results indicate that Scheme A has a compact work schedule and a total duration of 16.0 hours. The other two schemes take 20.0 hours and 22.5 hours respectively. Scheme A has the shortest total time and meets the expected goal.

[0216] from Figure 14 It can be seen that the convergence curve of Scheme A converges rapidly, achieving the optimal solution in the 5th generation, and showing no improvement in the subsequent 100 generations. Combining the data in Table 3, after 20 simulations, the average duration and fluctuation (Mean±Std) of Scheme A are 16.0±0.0, with identical results, indicating that the total operation time target is relatively easy to achieve in emergency decision-making.

[0217] (2) Comparative analysis of work resource load rate

[0218] The resource priority objective is to achieve the optimal resource utilization rate and, without exceeding resource limits, shorten the project duration as much as possible. Option B resource utilization rate. weight Set the weight to 0.9, and the weights of the other two schemes... Set to 0.1. Simulation results are as follows: Figure 15 , Figure 16 As shown, simulation results indicate that Scheme B achieves the best resource load rate, at 87.48%, while the other two schemes have time consumption rates of 80.21% and 73.05%, respectively, which meets expectations and verifies the accuracy of the multi-objective decision-making method proposed in this application. However, the differences among the three schemes are not significant, mainly because the emergency resource margin in the case is insufficient, leaving little room for decision optimization. This also suggests that resource load rate is not a primary consideration in emergency response.

[0219] (3) Comparative analysis of the balance of work resources

[0220] The equilibrium priority objective is to achieve balanced resource utilization, with the goal of minimizing resource fluctuations. Option C represents the resource equilibrium level. weight Set the weight to 0.9, and the weights of the other two schemes... Set to 0.1. Simulation results are as follows: Figure 17 , Figure 18 As shown, simulation results indicate that Scheme C has the highest resource balance, with a balance of 1.88, while the other two schemes have balances of 1.43 and 1.21, respectively, meeting the expected goals. Scheme C aims for balanced resource utilization, minimizing resource fluctuations and reducing the risk of task completion. However, this scheme comes at the cost of sacrificing total task time; therefore, Scheme C has the longest total task time of 22.5 hours.

[0221] In summary, it is recommended to choose Option C as the preferred option when time permits. This option has the strongest risk resistance and is particularly suitable for emergency response missions where the situation on-site is unclear, the availability of emergency resources is uncertain, and the mission risk is high. Option A is suitable for emergency rescue missions with urgent situations, and its time advantage is more obvious. In emergency response, time is life, and Option A is the best choice if rapid rescue is the priority. However, Option A has a smaller resource margin, and to ensure the smooth execution of the mission, the commander needs to coordinate resources in a comprehensive manner, especially ensuring that critical resources are redundantly configured and reserved in advance. Option B prioritizes efficient resource operation and is a viable option in scenarios that do not involve saving lives or controlling the development of the accident. However, this option focuses on resource utilization, with critical resources running at full capacity for extended periods. Simulation results show that the load rate advantage of this option is not significant, therefore it should not be considered as the primary option.

[0222] The results of the examples show that the time-priority scheme focuses on rapid rescue, but has a small resource margin and a high risk of mission completion; the resource-priority scheme strictly adheres to resource constraints and shortens the construction period as much as possible, but key resources operate at full capacity for a long time, and the mission risk is moderate; the balanced priority scheme has strong risk resistance, but the mission takes a long time and is not suitable for emergency rescue missions with urgent situations.

[0223] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A multi-objective decision-making method for emergency response to accidents, characterized in that, The steps include the following: Step A: Convert the preliminary emergency response plan into a CPM network plan diagram, which is defined as the action plan implemented to achieve the task objectives and the resources required to execute the task. Draw the operational tasks and prerequisites of each link and work in the emergency response plan into a CPM network plan diagram according to their internal relationships. Step B: Establish a mathematical model corresponding to the CPM network plan diagram, including the CPM node parameter model and the CPM task parameter model; the CPM node parameter model is established based on the task time of the CPM node, the earliest completion time of the node, the latest completion time of the node, and the node time difference; the CPM task parameter model is established based on the earliest start time of the task, the latest start time of the task, the earliest end time of the task, the latest end time of the task, the single task time difference, and the total task time difference. Step C: Establish a multi-objective decision-making model that integrates the CPM-GA method. C1. Chromosome coding design creates priority variables to assign priority values ​​to each task in the emergency mission. Chromosome storage stores a sequence of randomly generated priorities. C2. Chromosome decoding design: The decoding process restores the priority sequence to a valid job scheduling sequence. C3. Establish the fitness function and objective function, including the time objective function, the resource load rate objective function, and the resource balance objective function; C4. Complete CPM-GA simulation and output, and load CPM operation parameters based on the CPM diagram generated from the initial action plan; An initial population is generated based on a priority-based chromosome coding scheme; The chromosome is decoded to obtain the initial task sequence, the objective function and fitness function are solved, the fitness of the chromosome is evaluated, and genetic mutation is performed. After the iteration ends, the optimal chromosome is output to obtain the optimal objective decision scheme. Based on the output data, a Gantt chart or CPM network plan diagram is drawn to form the action plan under the decision preference.

2. The multi-objective decision-making method for emergency response according to claim 1, characterized in that, Step A, converting the preliminary emergency response plan into a CPM network plan diagram, specifically includes: A1, defined as the action plan implemented to achieve the task objective, represented as a set: Where N represents the number of operations required for emergency response, and T i This represents the i-th task; for example, pollution suppression is a task within an emergency response mission. A2. Define the resources required to execute the task, represented as a set: Where M represents the quantity of resources, P j This represents the j-th resource; for example, in an emergency response mission, the decontamination and cleaning team is an operational resource. A3. Draw a CPM network diagram showing the operational tasks and prerequisites of each stage and task in the emergency response plan, according to their inherent relationships; use arrows (→) to correspond to a task in task set T. The number below it indicates the duration of the operation. Circles (○) represent nodes, which are the connections between tasks.

3. The multi-objective decision-making method for emergency response to accidents according to claim 2, characterized in that, Step B, establishing the mathematical model corresponding to the CPM network plan diagram, specifically includes: B1. Establish a CPM node parameter model, whereby the node parameters include: job time, earliest node completion time, latest node completion time, and node time difference. The corresponding parameter model is as follows: (1) Operation time model , refers to homework The duration is calculated using the three-time estimation method and is expressed as: Where a is the most optimistic time, b is the most pessimistic time, and c is the most likely time; (2) Earliest Node Implementation Time Model , refers to the maximum earliest completion time of a job ending at node j, denoted as . ;in, for The earliest implementation time of all immediate predecessor nodes; (3) Latest Node Implementation Time Model This refers to the latest time that node i must be completed without affecting the task's duration, calculated backwards from the immediately following node j, and is expressed as: ;in, for The latest implementation time of all successor nodes. Duration of the task; (4) Node time difference model The meaning is the node's maneuver time, expressed as ; B2, CPM job parameter model, wherein the job parameters include the earliest start time of the job, the latest start time of the job, the earliest end time of the job, the latest end time of the job, the single job float, and the total job float, and the corresponding parameter model is as follows; (1) Earliest start time model for tasks This refers to the earliest time when all preceding operations of this task have completed, expressed as... ; (2) Latest start time model for assignments This refers to the latest completion time of the end node minus the job duration, expressed as: (3) Earliest End Time Model for Tasks It refers to the earliest start time plus the duration of the task, expressed as: ; (4) Model of the latest completion time of the task This refers to the latest time that can be achieved no later than the end node, expressed as... ; (5) Time difference model of work order This refers to the slack time that a task has without affecting the earliest start time of its successor tasks, and is expressed as: ; (6) Total Float Model This refers to the maximum available slack time for the task, expressed as... .

4. The multi-objective decision-making method for emergency response to accidents according to claim 3, characterized in that, Step C1, chromosome coding design, specifically refers to: creating a priority variable Priority for each task T in the emergency task. i Assign a priority value; chromosome x stores a sequence x with a randomly generated priority. Where N is the number of operations required for emergency response, and Pi is the priority variable of operation Ti; The C2 chromosome decoding design step specifically refers to: S1. Within each loop cycle, extract the sequence of tasks to be executed. , judge task Whether to carry out: Condition 1: If the task has already been initiated, then proceed with the next task in sequence. Condition 2: If not carried out, check whether the prerequisite tasks have been completed; S2, if task If the preceding tasks are not completed, the next task is extracted sequentially from the sequence of tasks to be executed; if the tasks are already completed, further judgment is made on the task. Are the required resources available? S3, if task If the required resources are available, then the task will be... Add the task to the sequence of tasks to be executed; if the task is not idle, extract the next task from the sequence of tasks to be executed in order. S4. Repeat S1~S3 until all pending tasks that meet the resource idle condition are added to the sequence of tasks to be executed. S5. Sort the sequence of tasks to be executed according to their priority values ​​from largest to smallest, and execute the tasks with higher priority first.

5. The multi-objective decision-making method for emergency response to accidents according to claim 4, characterized in that, Step C3, establishing the fitness function and objective function, specifically includes: S1. Fitness Function: Introducing the weight factor ω, designing the fitness function. as follows: in, Let the time objective function be... Let the resource load objective function be... The objective function is the resource balance. , , The weights of the objective function, ; S2, Time Objective Function in, The total actual time to complete the task corresponds to the earliest finish time in the CPM parameter model. , This refers to the latest completion time of the task, corresponding to the latest end time in the CPM parameter model. ; S3, the resource load rate objective function, divides the total project duration (Time) into m consecutive time slices. Δt is the smallest time granularity; resources The single resource load rate is: in, For resources Actual effective working time slices refers to resources The total amount of resources, For all tasks currently being executed within the k-th time slice, the resources... Resource intensity; The objective function for the overall resource load factor is: Among them, M still represents the quantity of emergency response resources; S4, Objective function for resource balance The coefficient of variation is used to measure the stationarity of resource consumption; resource P j The coefficient of variation is: in, For resources Average consumption; For resources Standard deviation of resource consumption; The objective function for resource balance is: .

6. The multi-objective decision-making method for emergency response to accidents according to claim 5, characterized in that, Step C4, completing the CPM-GA simulation and output, includes the following specific steps: S1. Based on the CPM diagram generated from the initial action plan, load the CPM operation parameters, including: operation code T(i), operation resources Res(i), preceding operation Pre(i), operation time t(i), and total resources Q(i); S2. Generate the initial population. Where M is the population size; according to step C1, based on the priority-based chromosome coding scheme, each chromosome can be represented as: x i ; S3. Decode the chromosome to obtain M initial task sequences T, each sequence representing a possible solution; as defined in step A1, the task set... It can be seen that each group of tasks after decoding still consists of N jobs; S4. Solve the objective function , , and fitness function ; S5. Assess the fitness of each chromosome, retain 10% of the elite population, and generate offspring through crossover, using the crossover probability... Produce offspring, based on mutation probability Introducing new features; S6. Determine whether one of the following iteration termination conditions is met: Condition 1: The maximum number of iterations G = 200 is reached; Condition 2: The optimal solution has not improved for 50 consecutive generations; Condition 3: The set target value has been achieved; If none of the conditions are met, return to S4 and continue iterating; if the conditions are met, output the optimal chromosome. S7. Obtain the current weight ( , , The optimal objective decision scheme under the given conditions includes: Data 1 (Job Information): Job code T(i), earliest start time ES(i), earliest end time EF(i), job duration t(i), whether it is a critical job CP(i); Data 2 (Comparison Indicators between Schemes): Total Work Time Resource balance Resource load factor Resource balance Average resource usage Standard deviation Coefficient of variation Indicators such as; Based on the output data, draw a Gantt chart or CPM network plan diagram to form an action plan under this decision preference.

7. The multi-objective decision-making method for emergency response to accidents according to claim 6, characterized in that, In step C1, the CPM method is used to identify critical paths and assign higher priority values ​​to critical tasks, so that high-quality genes can have more selection opportunities in the initial population.

8. The multi-objective decision-making method for emergency response to accidents according to claim 1, characterized in that, The decoding is performed cyclically in units of the smallest time granularity Δt.

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