A fairness-based optimization method for heterogeneous emergency resource scheduling

Abstract

The present invention discloses a method for optimizing the scheduling of heterogeneous emergency resources with consideration of fairness, which belongs to the field of emergency resource scheduling optimization. For closely cooperating heterogeneous resources, dual-dimensional modeling of time and satisfaction rate is adopted, and a hybrid coding and decoding method is adopted according to the characteristics of the problem to express the emergency resource scheduling plan in mathematical form; for the objectives and constraints, a random rule with priority is adopted to ensure the quality of the initial population; by adopting a crossover operator combining shuffling crossover and partial matching crossover, the diversity and stability of the population in the iterative process are ensured; an adaptive crossover mutation probability is adopted to maintain the diversity of the population and improve the efficiency of the algorithm; an elite retention strategy with a minimum congestion threshold is adopted to increase the diversity of the population and prevent the population from maturing prematurely. The present invention is applicable to the scheduling optimization of closely cooperating heterogeneous resources under the condition of supply and demand in the early stage of a disaster, and provides a new approach to solving the problem of heterogeneous resources in emergency resource scheduling.

Description

Technical Field

[0001] The present invention belongs to the field of emergency resource scheduling optimization and relates to a fairness-considered heterogeneous emergency resource scheduling optimization method. Background Art

[0002] Emergency resource dispatch is a special activity that relies on real-time monitoring and planning systems to quickly, reasonably and efficiently configure and allocate various emergency resources such as manpower, materials, equipment and funds when emergencies or disasters occur, so as to meet rescue needs in a timely manner and ensure the effective implementation of emergency operations. It ensures that when resources are limited, the needs of key tasks are met first and casualties and property losses are minimized. The scenario of emergency resource dispatch usually includes multiple rescue points and disaster-stricken points. For multiple emergency resources, vehicles depart from the warehouse, arrive at the disaster-stricken point, supply the disaster-stricken point with materials, and then return to the rescue point to replenish emergency resources. The sources of emergency resources at each rescue point are diverse. At the same time, due to the diversity of specifications and compatibility, decentralized departmental management and ledgers, mismatched maintenance or shelf life, inventory space and cost trade-offs, etc., it is difficult to ensure that each emergency resource is stored in an appropriate proportion at each rescue point. In the early stages of a disaster, emergency resources are often in short supply, and existing resources cannot meet the needs of all disaster-stricken points. Existing emergency resource dispatch methods mostly aim to minimize time, fairness, and cost. By studying the optimization methods of emergency resources, reasonable and effective path plans can be obtained to improve operational efficiency, reduce disaster losses, and reduce the negative impact caused by fairness.

[0003] In the paper (Long Y, Sun P, Xu G. Dynamic heterogeneous resource allocationin post-disaster relief operation considering fairness[J]. AdvancedEngineering Informatics, 2024, 62: 102858.), Long et al. pioneered the consideration of closely coordinated heterogeneous resources in the field of emergency resource scheduling. They minimized the total scheduling reward, set a satisfaction ratio threshold for the disaster-stricken points to maintain fairness, and used the Gini coefficient of the satisfaction rate to measure the fairness of the allocation in each time period. However, this paper only considered the situation of one rescue point, while the actual situation is more complicated. In the literature (Su Bingkang. Research on emergency resource scheduling for urban flood disasters based on multiple fairness dimensions [D]. Xi'an University of Architecture and Technology, 2023. DOI: 10.27393 / d.cnki.gxazu.2023.001171.): Su Bingkang established a post-disaster emergency resource scheduling optimization model, and set time, fairness, and cost as indicators respectively, established a multi-objective optimization model for goods, and used the NSGA-II algorithm for solution. However, while weighing fairness, the model ignored the waste of emergency resources at the rescue point, resulting in a large amount of emergency resources remaining after scheduling. Although fairness was maintained, the satisfaction level of the disaster-stricken point itself was not considered. In the literature (Zhang Xia, Wang Huichao, Li Yongtun, et al. Research on emergency resource scheduling considering demand under sudden flood disasters [J]. China Safety Science and Technology, 2023, 19(12): 187-192.), Zhang Xia et al. considered the maintenance risk of vehicles in the process of emergency resource scheduling, established a multi-objective optimization model considering the total satisfaction rate, cost, and allocation risk of the disaster point, and used the NSGA-II algorithm to solve it; however, this literature uses the traditional algorithm to solve it, without considering the impact of the algorithm performance on the results; and does not consider the fairness in emergency resource allocation.

[0004] Emergency resource scheduling problems are characterized by complex scenarios, diverse material types, numerous considerations, and high data flexibility. These problems place high demands on scenario construction and solution results during optimization. However, existing technologies often consider simplified scenarios and use traditional heuristic algorithms to solve the problem. These methods struggle to effectively address complex scenarios and often produce poor results. Summary of the Invention

[0005] In order to solve the above problems, the present invention provides a method for optimizing the scheduling of heterogeneous emergency resources taking fairness into consideration, wherein heterogeneous emergency resources refer to a variety of emergency resources that can only play a role in a specific disaster scenario by cooperating with each other in different proportions. In order to solve the problem of multi-rescue point allocation of heterogeneous emergency resources, first, an emergency resource scheduling model for multiple rescue points and multiple disaster points of heterogeneous resources is established, and a hybrid coding method is adopted to set the number of chromosomes of individuals according to the type of emergency resources. Each chromosome is composed of the disaster point number, resource scheduling amount, and disaster point scheduling level; for the objective function and optimization goal, a random method with priority is used to generate a group of excellent individuals in the feasible domain to ensure the feasibility of the population and improve the computational performance of the algorithm; a gene repair operator based on random repair and rescue point allocation is designed to ensure that the population obtained after the crossover mutation operation is in the feasible domain, while maintaining the diversity of the population, the evolution speed of the population is improved; combined with the encoding and decoding method of the present invention, By designing a hybrid crossover method that combines shuffling crossover with partial matching crossover, and a mutation method based on random perturbation, the search power of the population during the iteration process is ensured. Secondly, to address the problems of the traditional NSGA-II algorithm, such as poor solution performance and easy trapping in local optimality, the present invention provides an improved NSGA-II algorithm, which adopts an adaptively adjusted crossover mutation probability and adopts different crossover mutation probabilities according to the characteristics of the population during the evolutionary process. At the same time, the minimum crowding threshold method is used to improve the elite retention strategy, which can not only increase the crowding degree and diversity of the population, but also indirectly introduce individual individuals with high non-dominated levels to prevent the population from maturing prematurely. The results show that the improved method can effectively address the shortcomings of the traditional NSGA-II algorithm.

[0006] The purpose of the present invention is achieved through the following technologies:

[0007] A fairness-considered heterogeneous emergency resource scheduling optimization method includes the following steps:

[0008] Step 1: Establish a multi-objective, constrained, and fairness-considered heterogeneous emergency resource scheduling optimization model:

[0009] Assume that when a disaster occurs, the supply and demand of rescue and disaster-stricken points can be obtained in real time. The vehicles at the rescue points depart at the same time. It is assumed that the rescue points have enough rescue vehicles. Each rescue point is responsible for the rescue mission of multiple disaster-stricken points, and each disaster-stricken point can only be rescued by one rescue point. There is no coordinated transportation mechanism for materials between the rescue points and the disaster-stricken points. For the disaster-stricken points, only when the unit emergency resources arrive at the disaster-stricken points in a heterogeneous ratio can they play a role. For each type of emergency resource in each warehouse, the materials are transported to the disaster-stricken point at one time by the rescue convoy and then returned to the rescue point. During the rescue mission, the rescue vehicles are subject to a maximum transportation distance constraint, and the rescue points have a time window constraint on the emergency resources.

[0010] Step 1.1: Establish the objective function of a multi-objective, fairness-constrained, and heterogeneous emergency resource scheduling optimization model:

[0011] The objective function of the fairness-considered heterogeneous emergency resource scheduling optimization model is to minimize the total scheduling time. , Minimize the fairness of the satisfaction of the arrival time of disaster-stricken materials and minimize the total dispatch cost composition:

[0012]

[0013]

[0014]

[0015] The variables involved in the objective function are defined as follows:

[0016] - Collection of rescue points;

[0017] - Collection of disaster-affected points;

[0018] - the set of all nodes, ;

[0019] - Collection of vehicles;

[0020] - A collection of emergency resources;

[0021] -node To Node transportation time, ;

[0022] - decision variables, Indicates vehicle Requires slave nodes Transport emergency resources r to the node , otherwise 0; ;

[0023] - Gini coefficient weight of rescue time progress, ;

[0024] -Gini coefficient of the time schedule for the arrival of supplies at the disaster site;

[0025] -Gini coefficient of material satisfaction rate in disaster-affected areas;

[0026] -vehicle The transportation cost per ton of cargo per kilometer for transporting emergency resources, ;

[0027] - the distance that vehicle k needs to travel to transport emergency resource r to disaster site j, ;

[0028] - decision variables, The size of the vehicle Need to go from rescue point Transport emergency resources to disaster sites the number of ;

[0029] -node To Node transportation distance, ;

[0030] node To Node Shipping time as follows:

[0031] ;

[0032] in, - The speed of the rescue vehicle;

[0033] disaster-stricken areas The importance is:

[0034]

[0035] in, - Disaster-affected areas Emergency Resources material needs, ; - Disaster-affected areas the importance of ;

[0036] The distance that vehicle k needs to travel to deliver emergency resources r to disaster site j as follows:

[0037]

[0038] in, - indicates a vehicle Whether to use the slave node Transport emergency resources to disaster sites , ; - indicates the previous node Arrived at the disaster site distance, ; - indicates that vehicle k transports emergency resource r to the previous node The distance to be traveled, ,in ;

[0039] Vehicle K will be emergency resources Delivered to the disaster site Time as follows:

[0040]

[0041] in, - indicates the previous node Arrived at the disaster site transportation time, ; - indicates a vehicle Transport emergency resources r to the previous node time, ,in ;

[0042] disaster-stricken areas Percentage time progress as follows:

[0043] ;

[0044] in, - Disaster-affected areas Effective rescue time, ;

[0045] Gini coefficient of the arrival time of materials at the disaster site as follows:

[0046] ;

[0047]

[0048] in, and Indicates the disaster site and Percentage time progress, ; and Indicates the disaster site and the importance of -The weighted average of the time schedule for the arrival of supplies at the disaster site is used as the denominator of the weighted Gini coefficient;

[0049] disaster-stricken areas Satisfaction rate as follows:

[0050] ;

[0051] Gini coefficient of material satisfaction rate in disaster-affected areas as follows:

[0052] ;

[0053]

[0054] in, and - Indicates the affected area and The satisfaction rate, ; -The weighted average of the satisfaction rates of the affected sites is used as the denominator of the weighted Gini coefficient. - Indicates emergency resources The synergy ratio, It means that the emergency resources 1 of two units and the emergency resources 2 of one unit jointly exert the rescue effect of the emergency resources of one unit.

[0055] Step 1.2: Set the constraints of the fairness-considered heterogeneous emergency resource scheduling optimization model:

[0056] (1) Maximum waiting time constraint: emergency resources must be transported to the disaster site within the effective rescue time. :

[0057]

[0058] (2) Return constraint: vehicle k transporting emergency resource r starts from rescue point i and must return to the same rescue point:

[0059]

[0060] (3) Road connectivity constraint: vehicles arriving at disaster site j must leave from the disaster site:

[0061] ,in

[0062] (4) Cargo flow balance constraint, which is used to calculate the relationship between the node flow and the actual cargo volume at the disaster site:

[0063]

[0064] (5) The maximum driving distance of the vehicle is limited. The vehicle can only transport emergency resources under the premise of ensuring round trip distance:

[0065]

[0066] (6) Vehicle capacity constraints: Vehicles can only carry emergency resources whose weight is less than or equal to the load capacity:

[0067]

[0068] (7) Emergency resource allocation constraints: To avoid waste of materials and ensure that all emergency resources are distributed:

[0069]

[0070]

[0071] (8) Emergency resource constraints at the disaster site: the amount of goods received by the disaster site must be less than or equal to its own needs:

[0072]

[0073] (9) Constraints on the multi-rescue and multi-disaster dispatching model, where the materials r required by each disaster site can only be delivered by one rescue site, and each rescue site can visit more than one disaster site:

[0074]

[0075]

[0076]

[0077] in, Indicates that the part in the brackets is true. Indicates that the part within the brackets is false.

[0078] (10) Relationship constraints between decision variables:

[0079]

[0080]

[0081]

[0082]

[0083] The variables involved in the model constraints are defined as follows:

[0084] - decision variables, The size of vehicle k indicates that the vehicle k is at the node To Node Carry on the path from the rescue point The amount of emergency resources r shipped out; .

[0085] -The maximum driving distance of rescue vehicle k with full fuel, ;

[0086] -The maximum weight of emergency resources loaded on vehicle k when fully loaded, ;

[0087] -Rescue Point Supplies The amount of reserves, ;

[0088] -Demand points Supplies demand, ;

[0089] Step 2: Construct the encoding and decoding method of the scheduling optimization model in step 1:

[0090] Since the problem in the scheduling optimization model belongs to a multi-objective mixed integer linear programming problem, a mixed encoding method of natural numbers and continuous numbers is adopted, and each chromosome is set to three rows, and the number of columns is the number of disaster-stricken points J + the number of rescue points I-1: there are I rescue points storing R types of emergency resources, and vehicles are dispatched to J disaster-stricken points. For each emergency resource, 1~J is the disaster-stricken point number, and the number of split points is the number of rescue points I-1, which is the first row of the chromosome. The amount of emergency resources dispatched to each disaster-stricken point is the second row, and the third row sets a scheduling level for each disaster-stricken point. Disaster-stricken points at the same scheduling level are dispatched in order of priority. The emergency resources are transported by the same fleet; one chromosome represents a method of deploying emergency resources; based on the constraints of step 1.2 and the types of emergency resources, R chromosomes that meet the constraints are generated; when decoding each chromosome, the 0 column of the chromosome is first split, and the multiple segments obtained by the segmentation are the disaster-stricken points that are responsible for rescue by the rescue points corresponding to the sequence numbers. For each chromosome segment after segmentation, according to the dispatch level of the third row of the chromosome, the disaster-stricken points with the same dispatch level are transported in sequence by the same fleet, and the deployment method and quantity represented by each emergency resource are obtained, that is, the value of the decision variable.

[0091] Step 3: Design a chromosome gene repair and rescue point allocation operator based on the characteristics of the model's emergency resource allocation constraints:

[0092] Design an operator for random repair and rescue point allocation to prevent individuals generated by chromosomes from falling into the infeasible region after the crossover mutation step, thereby increasing computation time and convergence difficulty and reducing algorithm performance.

[0093] When designing a specific random repair and rescue point allocation operator: by scanning the second row of the chromosome step by step, when the cumulative sum exceeds the emergency resource reserve of the rescue point corresponding to the sequence number for the first time, record the disaster point number as the edge point, and its scheduling amount is the edge value; divide the edge value into two parts: the first part is to make the sum of the scheduling amount of the scanned disaster point equal to the emergency resource reserve of the rescue point corresponding to the sequence number, and the second part is obtained by subtracting the edge value from the first part; use the ratio of the first part of the edge value to the edge value as the probability of the random repair method, generate a random number from 0 to 1, and select the allocation method according to the size of the random number and the probability: (1) When the random number is less than the probability of the random repair method: take the edge point as the disaster point that the current rescue point is responsible for scheduling, and in the absence of Under the premise of violating the constraints of the disaster-stricken point, the redundant values of the cargo volume dispatched by the current rescue point are randomly deleted internally, and then the deleted values are randomly added to the emergency resources dispatched by other disaster-stricken points in the future to meet the quantity balance, and the edge point is used as the split point; (2) When the random number is greater than the probability of the random repair method: the edge point is used as the disaster-stricken point that the next rescue point is responsible for dispatching, and under the premise of not violating the constraints of the disaster-stricken point, the generated vacancy value is randomly added to the dispatched cargo volume of the disaster-stricken point that the current rescue point is responsible for, and the emergency resources dispatched by the subsequent disaster-stricken points are randomly deleted to meet the quantity balance, and the edge point is used as the split point; the location of each split point is recorded during the repair process so that the split point for dividing the rescue points can be inserted in the subsequent steps.

[0094] Insert 0 into the position of each split point so that the second row of the chromosome meets the emergency resource allocation constraints of each rescue point and ensures that all emergency resources are distributed.

[0095] Apply the gene repair and rescue point allocation operators designed in step 3 to step 2, and repair the chromosome to a feasible solution that meets the constraints after encoding; improve the split point position in the encoding method, which is also the prerequisite for the decoding step.

[0096] Step 4: Obtain emergency resource scheduling related data:

[0097] When solving the scheduling optimization model, we must first obtain the relevant data required by the model, including the road transportation distance between the rescue point and the disaster-stricken point in the road network, the supply and demand of each resource, the collaboration ratio of heterogeneous resources, the time window information of the disaster-stricken point, the load capacity of the transportation vehicle, the maximum driving distance, the driving speed, the transportation cost per kilometer per ton of goods, etc.

[0098] Step 5: Initialize the population using a random rule with priority:

[0099] The population initialized by the prioritized random rule is within the feasible domain and has individuals with better objectives, which can optimize the quality of the initial individuals and thus promote the improvement of the overall model performance;

[0100] Among the random rules with priorities, the dynamic programming counting and random sampling method is used as the first random rule to allocate the number of emergency resources to each disaster site. Then, based on the results of the first random rule, the second random rule is used to allocate disaster sites to rescue sites using the priority allocation based on the shortest transportation distance between rescue sites and disaster sites.

[0101] The first random rule focuses on total cargo volume constraints and fairness objectives. To ensure basic supplies for each disaster site, a minimum acceptable supply quantity is first allocated. Then, a set of feasible supply allocation plans is generated using dynamic programming counting and random sampling. Specifically, for a given type of emergency resource, the total supply quantity for that site is subtracted from the sum of the minimum supply quantities for all disaster sites to obtain the quantity to be allocated. Simultaneously, the maximum acceptable additional allocation for each disaster site is calculated: that is, the site's maximum demand minus its minimum supply quantity. Then, a dynamic programming counting method is used: a state table is constructed, starting with the last disaster site and counting the number of feasible allocation plans given the remaining cargo quantity. For each row (corresponding to a disaster site), all possible allocation shares are enumerated. The number of solutions for subsequent disaster sites given the remaining cargo quantity corresponding to each allocation quantity is taken and added together to obtain the total number of solutions in the current state. To speed up the summation process, the prefix sum method can be used to optimize the cumulative calculation efficiency. Then, the random sampling phase begins: After the statistics are completed, starting from the first disaster-stricken point, its optional additional allocation quantities are enumerated, and the number of subsequent state solutions is used as the sampling weight for random selection. After each selection, the remaining supply quantity is updated, and the process is repeated in sequence until the last disaster-stricken point, ultimately obtaining a set of feasible supply allocation solutions that meet all upper and lower constraints on supplies.

[0102] The second random rule focuses on the time target. First, for each disaster-stricken point, the total distance from the disaster-stricken point to all rescue points is used as the denominator, and the distance from the disaster-stricken point to a certain rescue point is used as the numerator as a proper fraction. The difference between 1 and the proper fraction is used as the probability of the disaster-stricken point selecting a certain rescue point for allocation. The disaster point is allocated until the dispatched amount of emergency resources reaches the critical value of the emergency resources reserved by the rescue point, and then the next rescue point is allocated. The allocation is carried out in accordance with the encoding method in step 2: each rescue point corresponds to a chromosome fragment of the disaster point, and then the chromosome gene repair operator in step 3 is used to integrate and repair the obtained chromosome fragments to form the first and second rows of chromosomes with a length of the number of disaster-stricken points + the number of rescue points - 1.

[0103] Step 6: Set the algorithm improvement strategy and optimization method parameters; use the improved NSGA-II algorithm to solve the mathematical optimization model established in step 1 and obtain a set of Pareto frontier solution sets.

[0104] Since the problem of the present invention belongs to a multi-objective optimization model, the present invention uses the NSGA-II multi-objective optimization method with low computational complexity as the basis for solving the model; based on the defects of the traditional NSGA-II algorithm that the convergence speed is slow and it is easy to fall into the local optimum, an adaptive crossover and mutation probability operator is designed to ensure the power of the population iteration process, expand the search range of the population, and prevent the population from falling into the local optimum; adopt an elite retention strategy based on the crowding threshold, which is conducive to making the solution set evenly cover the entire Pareto front, while indirectly introducing individuals with higher non-dominated levels, improving the diversity of the population in the iteration process, and preventing premature maturity; setting parameters in the scheduling optimization model, including the population size P of the improved NSGA-II algorithm, the maximum number of iterations Mgen, the maximum and minimum values of the crossover rate, the maximum and minimum values of the mutation rate, and the maximum and minimum values of the crowding threshold percentage.

[0105] Step 6.1. After initializing the population, based on the scheduling optimization model established in step 1, the objective function is used as the fitness function. Each individual contains R chromosomes of emergency resources. The fitness function value of each individual in the population pop is calculated separately. During the calculation process, the impact of the constraints on the fitness function is taken into account by imposing penalty values on individuals that violate the constraints, and the fitness function is used as the basis for the calculation of step 6.2.

[0106] Step 6.2: Calculate the fast non-dominated sorting and crowding distance of the population;

[0107] During the calculation process of each individual, the population is quickly non-dominated and sorted based on the multiple fitness function values of the individuals in the population to obtain non-dominated layers of different levels. The crowding distance of each individual in each non-dominated layer is calculated, and the individuals are assigned two attributes, namely non-dominated level and crowding degree, so that individuals can be evenly selected in the subsequent evolution process, maintaining the diversity and stability of the population.

[0108] Step 6.3: Perform selection, crossover, and mutation operations on the population pop to generate the offspring population. Based on the calculation results of the fast non-dominated sort and crowding distance in step 6.2, the binary tournament operator is used in the selection operator to perform the selection operation on the pop population: randomly pick two individuals in the population, first compare the non-dominated rank attributes of each individual, select the individual with the lower non-dominated rank, and when the non-dominated ranks are the same, select the individual with the larger crowding distance; design a crossover operator that combines the shuffle crossover operator and the partial matching crossover operator (PMX), perform crossover and mutation operations on each chromosome in the individual, and generate a descendant population of size P In this process, dynamically adjusted crossover rate and mutation rate are set to meet the exploration ability and convergence efficiency of the population at different stages, thereby improving the efficiency of the overall optimization method. The specific steps are as follows:

[0109] Step 6.3.1: Use a crossover operator that combines the shuffle crossover operator and the partial matching crossover operator (PMX), and introduce a random perturbation as a mutation operator;

[0110] Based on the encoding method in step 2, each chromosome in the population contains information about the number of each disaster-stricken point, the corresponding dispatched resources, and the corresponding rescue point. For the crossover operator, a combination of a shuffle crossover operator and a partial matching crossover operator (PMX) is used: the shuffle crossover operator first uses the two-point crossover method to select the crossover fragments, randomly shuffles the crossover fragments, and then uses the conflict detection function of the partial matching crossover to operate on the offspring chromosomes, ensuring that the genes in each chromosome appear only once. For the mutation operator, the dispatch amount of each disaster-stricken point in the second row of the chromosome is multiplied by a random perturbation, and it is ensured that the mutated number does not exceed the feasible range. At the same time, for the third row of the chromosome, in order to prevent the introduction of an excessively large dispatch level after the crossover, a descending process is first performed so that all dispatch levels are no greater than the total number of disaster-stricken points that the rescue point is responsible for rescuing. Then a single-point random mutation is performed: that is, a random number no greater than the total number of disaster-stricken points is generated as the new dispatch level.

[0111] Step 6.3.2: Adopt an adaptive crossover and mutation adjustment strategy to dynamically change the crossover and mutation probabilities:

[0112] Traditional fixed crossover mutation will make the algorithm unable to adopt appropriate probabilities according to its own iteration, and it is easy to ignore the characteristics of the population, causing the population to mature prematurely or difficult to converge; therefore, adopting a crossover mutation probability that can change in real time according to the characteristics of the population can not only improve the efficiency of the algorithm, but also obtain a better Pareto frontier solution; in the early stages of population evolution, a higher mutation rate will produce more diverse individuals, explore more combinations of material allocation quantities, and help maintain the diversity of the population; in the later stages of population evolution, a higher crossover rate can help prevent the population from falling into local optimality, explore more allocation methods, and increase the evolutionary power of the population. A lower mutation rate can accelerate the convergence of the population, thereby improving the efficiency of the algorithm; the crossover rate and mutation rate The adjustment strategy is as follows:

[0113]

[0114] in, and Respectively represent the crossover rate and mutation rate of the gen generation, and represent the minimum crossover rate and the maximum crossover rate, respectively; and They represent the minimum mutation rate and the maximum mutation rate respectively; gen represents the current number of iterations, and Mgen represents the maximum number of iterations.

[0115] Step 6.4: Merge the parent population pop and the offspring population spop generated in step 6.3, and use the elite selection strategy with the lowest crowding threshold to generate a new population pop;

[0116] The parent and child populations are merged to generate a new population of size 2P. The new population is then subjected to a fast non-dominated sort and the crowding distance of each layer is calculated. An elite retention strategy is adopted according to the crowding distance threshold, and individuals with a crowding degree greater than the threshold are selected from the non-dominated level in descending order, and the selection is gradually carried out until the number of individuals fills the population pool.

[0117] In the elite retention strategy unique to the NSGA-II algorithm, since all non-dominated layers with low non-dominated levels are selected, the population crowding distance will decrease and the diversity will be reduced. However, setting a crowding threshold in the elite retention strategy can not only increase the crowding and diversity of the population, but also indirectly introduce individual individuals with high non-dominated levels to prevent the population from maturing prematurely.

[0118] In the specific implementation process, a crowding threshold percentage is set, and each non-dominated layer is traversed from small to large according to the non-dominated level. The crowding threshold is calculated based on the product of the number of individuals in the non-dominated layer and the crowding threshold percentage, and individuals with a crowding distance greater than or equal to the crowding threshold are retained. If the retention percentage is too small, resulting in the population pool still not being filled after traversing all non-dominated layers, the crowding threshold is appropriately reduced, and the remaining individuals are preferentially selected from the non-dominated layers with small non-dominated levels until the population pool is filled. The dynamic change of the crowding threshold with the number of iterations is as follows:

[0119]

[0120] in, Indicates the crowding threshold percentage of the gen generation, and They represent the minimum and maximum congestion threshold percentages, respectively.

[0121] Step 6.5: Iterate and solve to determine whether the termination condition is met. If so, output the Pareto frontier solution set. According to the decoding rules of step 2, output multiple specific scheduling schemes that meet the constraints and are optimal at multiple fitness values. At this time, the fitness function is equal to the objective function. If not, return to step 6.1 to continue.

[0122] Step 7: Based on the emergency resource scheduling results obtained in step 6, for the specific situation of the decision maker at the time of the disaster, and based on the relevant preferences such as timeliness, fairness, and economy, select the emergency resource scheduling plan with prominent preference characteristics: (1) When timeliness is the main consideration, select the objective function The smallest scheduling solution; (2) When fairness is the main consideration, select the objective function Minimum scheduling solution; (3) When considering economy, select the objective function Minimal scheduling solution.

[0123] Beneficial effects of the present invention:

[0124] 1. The present invention considers the problem of multiple rescue point allocation with closely cooperating heterogeneous resources stored in non-heterogeneous proportions. In the early stage of a disaster, due to various reasons, it is difficult for heterogeneous resources in multiple rescue points to be stored according to the exact heterogeneous proportion. In order to increase the post-disaster emergency response speed, the allocation rate of emergency resources, the fairness of allocation among various disaster-stricken points, and reduce the allocation cost of emergency resources, the present invention establishes a multi-objective, multi-constraint mathematical optimization model that considers timeliness, fairness, and cost based on the characteristics of closely cooperating heterogeneous resources. While introducing closely cooperating heterogeneous resources, the present invention innovatively considers the situation where heterogeneous resources cannot be stored in an accurate proportion in multiple warehouses.

[0125] 2. In order to quickly solve the mathematical model proposed in the present invention, improve the operating efficiency of the algorithm, and obtain high-quality frontier solutions, the present invention adopts: (1) a hybrid coding method that combines the disaster-affected points with the number of scheduling resources and the scheduling level, and sets a number of chromosomes equal to the number of resources for each individual, which respectively represents the allocation method of each emergency resource; (2) according to the optimization objectives and constraints, the population is initialized using a random rule with priority, which can ensure that the initialized population is within the feasible domain and has individuals with better targets, and can optimize the quality of the initial individuals; (3) according to the characteristics of hybrid coding for each chromosome of the population individual, a crossover operator combining shuffle crossover and partial matching crossover and a mutation operator of random perturbation are used.

[0126] 3. Based on the defects of the traditional NSGA-II algorithm, which has a slow convergence speed and is prone to falling into local optimality; in the crossover and mutation part: the present invention adopts an adaptive crossover and mutation probability, by setting the crossover rate to increase with the increase of the number of iterations, and the mutation rate to decrease with the increase of the number of iterations. In terms of the elite retention strategy: an elite retention strategy based on the crowding threshold is adopted: individuals with a crowding degree greater than the threshold are selected, and gradually selected until the number of individuals fills the population pool; this improved method can not only improve the efficiency of the algorithm and maintain the diversity of the population, but also obtain a better Pareto frontier solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] Figure 1 This is a flow chart of a fairness-considered heterogeneous emergency resource scheduling optimization method of the present invention;

[0128] Figure 2 Schematic diagram of the encoding and decoding methods of the present invention;

[0129] Figure 3 Schematic diagram of the improved crossover method;

[0130] Figure 4 Schematic diagram of the Pareto optimal frontier obtained by the heterogeneous emergency resource scheduling optimization method considering fairness. DETAILED DESCRIPTION

[0131] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0132] In this example, it is assumed that there are 3 rescue points and 16 disaster-affected points; the cooperation ratio of heterogeneous emergency resources is 2:1, that is, only when 2 units of emergency resource A and 1 unit of emergency resource B arrive together can they play a role; each vehicle has a load capacity of , driving speed , transportation costs , maximum driving distance The information of rescue points and disaster-affected points are shown in Table 1 and Table 2 below:

[0133] Table 1 Rescue point related information

[0134]

[0135] Table 2 Related information of disaster-affected areas

[0136]

[0137] The length of the road sections from the three emergency resource reserves to each emergency event is shown in Table 3 below.

[0138] Table 3 Distance from rescue point to disaster site

[0139]

[0140] The present invention discloses a fairness-considered heterogeneous emergency resource scheduling optimization method to perform emergency resource scheduling. The process is as follows: Figure 1 As shown, all steps are the same as those in the invention content, and the steps that require special explanation are described in detail:

[0141] Step 1: Construct an emergency resource scheduling model that includes multiple objectives, constraints, and heterogeneous resource characteristics, including fairness;

[0142] Step 2: Construct chromosome encoding and decoding methods for emergency resource scheduling optimization method: Each individual in the population is designed with 2 chromosomes according to the resource type. A mixed encoding method is adopted according to the model characteristics, for example Figure 2 As shown, each chromosome is equal to the number of disaster sites + the number of rescue sites - 1, with three rows in total. The first row represents the disaster site number, the second row represents the amount of resources dispatched, and the third row represents the dispatch level for each disaster site. During decoding, the sequence is divided into three sub-chromosomes based on the position of 0 in the chromosome. The order of each sub-chromosome represents the sequence of the rescue sites. The first row of each sub-chromosome represents the disaster site number that the current rescue site is responsible for rescuing, the second row represents the amount of supplies dispatched to that disaster site by the current rescue site, and the third row represents the transportation level for the disaster sites that the same rescue site is responsible for dispatching. For emergency resource A, a vehicle departing from rescue site A first arrives at disaster site 5, unloads 35 tons of supplies, then arrives at disaster site 13, unloads 15 tons of supplies, and returns to rescue site A, dispatching 22 tons of supplies to disaster site 7. Rescue site B dispatches 34 tons of supplies to disaster site 2 and 21 tons to disaster site 1, and so on.

[0143] Step 3: Design relevant chromosome repair operators based on the optimization model characteristics;

[0144] Step 4: Obtain relevant data on emergency resource scheduling and set optimization method parameters; when solving the model of the present invention, it is first necessary to obtain relevant data according to step 1, mainly including the road transportation distance between the rescue point and the disaster-stricken point in the road network, the supply and demand of each resource, the collaboration ratio of heterogeneous resources, the time window information of the disaster-stricken point, the load capacity of the transportation tool, the maximum driving distance, the driving speed, the unit freight rate per unit cargo, etc., as shown in Table 1, Table 2, and Table 3 above; then set the relevant parameters of the optimization method.

[0145] Step 5: Design a population pop initialization method that satisfies random characteristics;

[0146] Step 6: Set the algorithm improvement strategy and optimization method parameters; use the improved NSGA-II algorithm to solve the mathematical optimization model established in step 1 and obtain a set of Pareto frontier solutions.

[0147] Step 6.1, calculate the fitness function of the population based on the multi-objective constrained mathematical optimization model established in step 1;

[0148] Since the method used in this invention is the improved NSGA-II algorithm, the parameters include population size P=260, maximum number of iterations Mgen=800, maximum and minimum crossover rates respectively. =0.8, =0.4, the maximum and minimum mutation rates =0.3, =0.15, the maximum and minimum congestion threshold percentages are =1, =0.5, and adjust the weight according to the specific situation Set to 0.5.

[0149] Step 6.2: Calculate the fast non-dominated sorting and crowding distance of the population;

[0150] Step 6.3: Perform selection, crossover, and mutation operations on the population pop to generate a child population spop. Based on the calculation results of the fast non-dominated sorting and crowding distance of the NSGA-II algorithm, use the binary tournament operator to perform selection, crossover, and mutation operations on the pop population to generate a child population spop of size P. In this process, dynamically adjust the crossover rate and mutation rate to meet the exploration ability and convergence efficiency of the population at different times, thereby improving the efficiency of the overall optimization method.

[0151] Step 6.3.1: In this embodiment, a crossover operator combining a shuffle crossover operator and a partial match crossover operator (PMX) is used;

[0152] The shuffle crossover operator first uses the two-point crossover method to select the crossover segments, randomly shuffles the crossover segments, and then uses the conflict detection function of partial matching crossover to operate on the offspring chromosomes, ensuring that the genes in each chromosome appear only once; Figure 3 As shown, first delete the 0 split point, use the two-point method to select the intersection points of the parent generation, which are 1-4-5-3 and 6-4-1-3 respectively, and then perform a shuffling operation to randomly disrupt the order, and perform a conflict detection and repair operation on the other parent generation. Find the repetition of 5 and the non-intersection segment of the other parent generation in the first child segment, and use 6 to replace the 5 in the non-intersection segment of the other parent generation according to the corresponding sequence rules. Then use the first child generation to replace the intersection segment of the other parent generation as a whole to complete the crossover of the first child generation; the crossover operation of the second child generation is the same.

[0153] Step 6.3.2: Adopt an adaptive crossover and mutation adjustment strategy to dynamically change the crossover and mutation probabilities of the algorithm:

[0154] Traditional fixed crossover mutation will make the algorithm unable to adopt appropriate probabilities according to its own iteration, and it is easy to ignore the characteristics of the population, causing the population to mature prematurely or difficult to converge; therefore, adopting a crossover mutation probability that can change in real time according to the characteristics of the population can not only improve the efficiency of the algorithm, but also obtain a better Pareto frontier solution; in the early stages of population evolution, a higher mutation rate will produce more diverse individuals, explore more combinations of material allocation quantities, and help maintain the diversity of the population; in the later stages of population evolution, a higher crossover rate can help prevent the population from falling into local optimality, explore more allocation methods, and increase the evolutionary power of the population. A lower mutation rate can accelerate the convergence of the population, thereby improving the efficiency of the algorithm; the crossover rate and mutation rate The adjustment strategy is as follows:

[0155]

[0156] in, and Respectively represent the crossover rate and mutation rate of the gen generation, and represent the minimum crossover rate and the maximum crossover rate, respectively; and They represent the minimum mutation rate and the maximum mutation rate respectively; gen represents the current number of iterations, and Mgen represents the maximum number of iterations.

[0157] Step 6.4: Merge the parent population pop and the offspring population generated in step 6.3 , using the elite selection strategy with the lowest crowding threshold to generate a new population pop.

[0158] Step 6.5: Iterate and solve to determine whether the termination condition is met. If so, output the Pareto frontier solution set. According to the decoding rules of step 2, output multiple specific scheduling schemes that meet the constraints and are optimal at multiple fitness values. At this time, the fitness function is equal to the objective function. If not, return to step 6.1 to continue.

[0159] It also includes step 7: Based on the emergency resource scheduling results obtained in step 6, the decision maker selects an emergency resource scheduling scheme with prominent preference characteristics according to the specific situation when the disaster occurs and the relevant preferences such as timeliness, fairness, and economy: (1) When timeliness is the main consideration, select the objective function The smallest scheduling solution; (2) When fairness is the main consideration, select the objective function Minimum scheduling solution; (3) When considering economy, select the objective function Minimal scheduling solution.

[0160] Among them, when solving the emergency resource scheduling optimization problem, the fairness-considered heterogeneous emergency resource scheduling optimization method disclosed in the present invention performs well; compared with the solution using the traditional NSGA-II model, the population calculated by the method disclosed in the present invention is more diverse and has stronger convergence;

[0161] The Pareto frontier solutions obtained by the two methods are as follows Figure 4 As shown in the figure, it can be seen that the method proposed in the present invention performs better than the frontier solution obtained by the traditional NSGA-II algorithm in multiple objectives and has better convergence. It can provide a new solution for the scheduling and allocation of closely coordinated heterogeneous resources in the early stage of disasters.

[0162] For multi-objective optimization problems, multiple optimal solutions can be obtained. Since too many frontier solutions are obtained and it is impossible to analyze them all, the optimal individuals on each objective are selected for analysis. The optimal values of different algorithms on each objective are shown in Table 4 below. Among them, Option 1 is optimal in Objective 1 (timeliness), Option 2 is optimal in Objective 2 (fairness), and Option 3 is optimal in Objective 3 (economy). The optimal scheduling calculation results of each option are shown in Table 5 below. After verification, each scheduling result meets the constraints of the mathematical model.

[0163] Table 4 Objective function values of the single-objective optimization in different algorithms

[0164]

[0165] Table 5 Example of improved algorithm scheduling calculation results

[0166]

[0167] In Table 4, Scheme 1 represents the solution with the optimal scheduling time; Scheme 2 represents the solution with the optimal scheduling fairness; and Scheme 3 represents the solution with the optimal scheduling cost. It can be seen that the solution with the optimal value for a single objective calculated using the improved NSGA-II algorithm is the best for the corresponding objective compared to the solution obtained using the traditional NSGA-II algorithm, further verifying the superiority of the improved algorithm.

[0168] Table 4 further shows that for the optimal solution obtained by the improved algorithm of the present invention, compared with Scheme 2, Scheme 1 has a scheduling time (objective function 1) reduced by 10.2%, and unfairness (objective function 2) increased by 15.11%. Compared with Scheme 3, Scheme 1 has a scheduling time (objective function 1) reduced by 3.25%, and a scheduling cost (objective function 3) increased by 0.75%. Compared with Scheme 3, Scheme 2 has a scheduling unfairness (objective function 2) reduced by 15.11%, and a scheduling cost (objective function 3) increased by 10.43%. Compared with Scheme 2, Scheme 1 reduces scheduling time but introduces more unfairness. Compared with Scheme 3, Scheme 1 increases scheduling cost but has a more significant optimization effect on scheduling time. Compared with Scheme 3, Scheme 2 increases scheduling cost but has a more significant reduction in unfairness.

[0169] As can be seen from Table 5, there are differences in the material storage at different rescue points according to the needs of the disaster-stricken points. Therefore, in order to meet the heterogeneous resource needs of the disaster-stricken points, the heterogeneous resources of the same disaster-stricken point will be dispatched from different rescue points respectively, and it is difficult to allocate resources to the disaster-stricken points with an absolute heterogeneous ratio.

[0170] Therefore, in real situations, managers can make preferences for time, fairness, and cost goals based on the actual situation and choose a decision-making plan that is more suitable for the disaster situation.

Claims

1. A fairness-based optimization method for heterogeneous emergency resource scheduling, characterized in that: The steps include: Step 1: Establish a multi-objective, constrained, and fairness-considered heterogeneous emergency resource scheduling optimization model: Step 1.1: Establish the objective function of a multi-objective, fairness-constrained, and heterogeneous emergency resource scheduling optimization model: The objective function of the fairness-considered heterogeneous emergency resource scheduling optimization model is to minimize the total scheduling time. , Minimize the fairness of the satisfaction of the arrival time of disaster-stricken materials and minimize the total dispatch cost composition: ， ， ， The variables involved in the objective function are defined as follows: - Collection of rescue points; - Collection of disaster-affected points; - the set of all nodes, ; - Collection of vehicles; - A collection of emergency resources; -node To Node transportation time, ; - decision variables, Indicates vehicle Requires slave nodes Transport emergency resources r to the node , otherwise 0; ; - Gini coefficient weight of rescue time progress, ; -Gini coefficient of the time schedule for the arrival of supplies at the disaster site; -Gini coefficient of material satisfaction rate in disaster-affected areas; -vehicle The transportation cost per ton of cargo per kilometer for transporting emergency resources, ; - the distance that vehicle k needs to travel to transport emergency resource r to disaster site j, ; - decision variables, The size of the vehicle Need to go from rescue point Transport emergency resources to disaster sites the number of ; -node To Node transportation distance, ; node To Node Shipping time as follows: ； in, - The speed of the rescue vehicle; disaster-stricken areas The importance is: ,in, - Disaster-affected areas Emergency Resources material needs, ; - Disaster-affected areas the importance of ; The distance that vehicle k needs to travel to deliver emergency resources r to disaster site j as follows: ,in, - indicates a vehicle Whether to use the slave node Transport emergency resources to disaster sites , ; - indicates the previous node Arrived at the disaster site distance, ; - indicates that vehicle k transports emergency resource r to the previous node The distance to be traveled, ,in ; Vehicle K will be emergency resources Delivered to the disaster site Time as follows: ,in, - indicates the previous node Arrived at the disaster site transportation time, ; - indicates a vehicle Transport emergency resources r to the previous node time, ,in ; disaster-stricken areas Percentage time progress as follows: ;in, - Disaster-affected areas Effective rescue time, ; Gini coefficient of the time schedule for the arrival of materials at the disaster site as follows: ； ,in, and Indicates the disaster site and Percentage time progress, ; and Indicates the disaster site and the importance of -The weighted average of the time schedule for the arrival of supplies at the disaster site is used as the denominator of the weighted Gini coefficient; disaster-stricken areas Satisfaction rate as follows: ； Gini coefficient of material satisfaction rate in disaster-affected areas as follows: ； ,in, and - Indicates the affected area and The satisfaction rate, ; -The weighted average of the satisfaction rates of the affected sites is used as the denominator of the weighted Gini coefficient; - Indicates emergency resources The synergy ratio, It means that the emergency resources 1 of two units and the emergency resources 2 of one unit can jointly exert the rescue effect of the emergency resources of one unit; Step 1.2: Set the constraints of the fairness-considered heterogeneous emergency resource scheduling optimization model: (1) Maximum waiting time constraint: emergency resources must be transported to the disaster site within the effective rescue time. : ,(2) Return constraint, the vehicle k transporting emergency resource r starts from the rescue point i and must return to the same rescue point: , (3) Road connectivity constraint, vehicles arriving at disaster site j must leave from the disaster site: ,in ,(4) Cargo flow balance constraint, which is used to calculate the relationship between the node flow and the actual cargo volume at the disaster site: (5) The maximum driving distance of the vehicle is limited. The vehicle can only transport emergency resources under the premise of ensuring round trip: ,(6) Vehicle capacity constraint, a vehicle can only carry emergency resources whose weight is less than or equal to its load capacity: ,(7) Emergency resource allocation constraints, in order to avoid waste of materials and ensure that all emergency resources are distributed: , , (8) Emergency resource constraints at the disaster site: the goods received by the disaster site must be less than or equal to its own demand: ,(9) Multi-rescue and multi-disaster point scheduling mode constraints, where the materials r required by each disaster-affected point can only be delivered by one rescue point, and each rescue point can visit more than one disaster-affected point: , , ,in, Indicates that the part in the brackets is true. Indicates that the part in the brackets is false; (10) Relationship constraints between decision variables: , , , , where the variables involved in the model constraints are defined as follows: - decision variables, The size of vehicle k indicates that the vehicle k is at the node To Node Carry on the path from the rescue point The amount of emergency resources r shipped out; ; -The maximum driving distance of rescue vehicle k with full fuel, ; -The maximum weight of emergency resources loaded on vehicle k when fully loaded, ; -Rescue Point Supplies The amount of reserves, ; -Demand points Supplies demand, ; Step 2: Construct the encoding and decoding method of the scheduling optimization model in step 1: A mixed coding method of natural numbers and continuous numbers is used, and each chromosome is set to three rows, with the number of columns being the number of disaster-stricken points J + the number of rescue points I-1: there are I rescue points storing R types of emergency resources, which are dispatched to J disaster-stricken points by vehicles. For each emergency resource, 1 to J are the disaster-stricken point numbers, and the number of split points is the number of rescue points I-1, which is the first row of the chromosome. The amount of emergency resources dispatched to each disaster-stricken point is the second row, and the third row sets a dispatch level for each disaster-stricken point. Disaster-stricken points at the same dispatch level are transported emergency resources by the same fleet in order of priority. Each chromosome represents a method for deploying emergency resources. Based on the constraints in step 1.2 and the types of emergency resources, R chromosomes that meet the constraints are generated. When decoding each chromosome, the 0 column of the chromosome is first segmented. The multiple segments obtained by segmentation are the disaster-stricken points that are responsible for rescue by the rescue point corresponding to the sequence number. For each segmented chromosome segment, according to the dispatch level in the third row of the chromosome, the disaster-stricken points with the same dispatch level are transported in sequence by the same fleet. This results in the deployment method and quantity represented by each emergency resource, that is, the value of the decision variable. Step 3: Design a chromosome gene repair and rescue point allocation operator based on the characteristics of the model's emergency resource allocation constraints: By scanning the second row of the chromosome step by step, when the accumulated sum exceeds the emergency resource reserve of the rescue point corresponding to the sequence number for the first time, the disaster point number is recorded as the edge point, and its scheduling amount is the edge value; the edge value is divided into two parts: the first part is to make the sum of the scheduling amount of the scanned disaster point equal to the emergency resource reserve of the rescue point corresponding to the sequence number, and the second part is obtained by subtracting the edge value from the first part; the ratio of the first part of the edge value to the edge value is used as the probability of the random repair method, and a random number from 0 to 1 is generated. The allocation method is selected according to the size of the random number and the probability: (1) When the random number is less than the probability of the random repair method: the edge point is regarded as the disaster point that the current rescue point is responsible for scheduling, without violating the constraints of the disaster point. , randomly delete the redundant values of the cargo volume that the current rescue point is responsible for dispatching, and then randomly add the deleted values to the emergency resources dispatched by other disaster-stricken points in the future to meet the quantity balance, and use the edge point as the split point; (2) When the random number is greater than the probability of the random repair method: use the edge point as the disaster-stricken point that the next rescue point is responsible for dispatching, and under the premise of not violating the constraints of the disaster-stricken point, randomly add the generated vacancy value to the dispatched cargo volume of the disaster-stricken point that the current rescue point is responsible for, and randomly delete the emergency resources dispatched by subsequent disaster-stricken points to meet the quantity balance, and use the edge point as the split point; record the location of each split point during the repair process so that the split point that divides the rescue point can be inserted in the subsequent steps; Insert 0 into the position of each split point so that the second row of the chromosome meets the emergency resource allocation constraints of each rescue point and ensures that all emergency resources are distributed; Step 4: Obtain emergency resource scheduling related data: Obtain relevant data required by the model, including the road transportation distance between rescue points and disaster-stricken points in the road network, the supply and demand of each resource, the coordination ratio of heterogeneous resources, the time window information of the disaster-stricken point, the load capacity of the transportation vehicle, the maximum driving distance, the driving speed, and the transportation cost per kilometer per ton of goods; Step 5: Initialize the population using a random rule with priority: Among the random rules with priorities, the dynamic programming counting and random sampling method is used as the first random rule to allocate the number of emergency resources to each disaster site. Then, based on the results of the first random rule, the second random rule is used to allocate disaster sites to rescue sites using the priority allocation based on the shortest transportation distance between rescue sites and disaster sites. Step 6: Set the algorithm improvement strategy and optimization method parameters; use the improved NSGA-II algorithm to solve the mathematical optimization model established in step 1 and obtain a set of Pareto frontier solutions; Step 6.1: After initializing the population, based on the scheduling optimization model established in step 1, use the objective function as the fitness function. Each individual contains R chromosomes, which are the number of emergency resources. Calculate the fitness function value of each individual in the population pop. During the calculation process, penalty values are imposed on individuals that violate the constraints to take into account the impact of the constraints on the fitness function. The fitness function is used as the basis for the calculation in step 6.

2. Step 6.2: Calculate the fast non-dominated sorting and crowding distance of the population; In the calculation process of each individual, based on the multiple fitness function values of the individuals in the population, the population is quickly non-dominated sorted to obtain non-dominated layers of different levels. The crowding distance of each individual in each non-dominated layer is calculated, and the individuals are assigned two attributes: non-dominated level and crowding degree. Step 6.3: Perform selection, crossover, and mutation operations on the population pop to generate the offspring population. Based on the calculation results of the fast non-dominated sort and crowding distance in step 6.2, the binary tournament operator is used in the selection operator to perform the selection operation on the pop population: randomly pick two individuals in the population, first compare the non-dominated rank attributes of each individual, select the individual with the lower non-dominated rank, and when the non-dominated ranks are the same, select the individual with the larger crowding distance; design a crossover operator that combines the shuffle crossover operator and the partial match crossover operator, perform crossover and mutation operations on each chromosome in the individual, and generate a descendant population of size P , and in this process, set the dynamically adjusted crossover rate and mutation rate; Step 6.4: Merge the parent population pop and the offspring population spop generated in step 6.3, and use the elite selection strategy with the lowest crowding threshold to generate a new population pop; Merge the parent and offspring populations to generate a new population of size 2P. Then perform a fast non-dominated sort on the new population and calculate the crowding distance of each layer. Adopt an elite retention strategy based on the crowding distance threshold, and select individuals with crowding greater than the threshold from the non-dominated level from low to high, step by step until the number of individuals fills the population pool. Step 6.5: Iterate and solve to determine whether the termination condition is met. If so, output the Pareto frontier solution set. According to the decoding rule in step 2, output multiple specific scheduling solutions that meet the constraints and are optimal at multiple fitness values. At this time, the fitness function is equal to the objective function. If not, return to step 6.1 to continue. Step 7: Based on the emergency resource scheduling results obtained in step 6, for the specific situation of the decision maker at the time of the disaster, and based on the relevant preferences such as timeliness, fairness, and economy, select the emergency resource scheduling plan with prominent preference characteristics: (1) When timeliness is the main consideration, select the objective function The smallest scheduling solution; (2) When fairness is the main consideration, select the objective function Minimum scheduling solution; (3) When considering economy, select the objective function Minimal scheduling solution.

2. A fairness-based heterogeneous emergency resource scheduling optimization method according to claim 1, characterized in that: The random rules in step 5 are as follows: The first random rule: first allocate a minimum acceptable amount of supplies, and then use dynamic programming counting and random sampling methods to generate a set of feasible material distribution plans. Specifically, for a certain type of emergency resources, first subtract the total amount of supplies at the rescue point from the sum of the minimum guaranteed amounts of all disaster-stricken points to obtain the amount of supplies to be distributed; at the same time, calculate the maximum acceptable additional allocation for each disaster-stricken point, that is, the maximum demand at the point minus its minimum guaranteed amount; then use the dynamic programming counting method: construct a state table, starting from the last disaster-stricken point, and sequentially calculate the "feasible distribution under a given remaining amount" "Number of allocation plans"; for each row corresponding to a disaster-stricken point, all possible allocation shares are enumerated, and the "number of options for subsequent disaster-stricken points under the remaining cargo volume" corresponding to each allocation amount is taken out and added to obtain the total number of options in the current state; then enter the random sampling stage: after the statistics are completed, starting from the first disaster-stricken point, its optional additional allocation amounts are enumerated, and the number of options in the subsequent state is used as the sampling weight for random sampling; after each selection, the remaining material volume is updated, and this process is executed in sequence to the last disaster-stricken point, and finally a set of feasible material allocation plans that meet all material upper and lower limit constraints are obtained; The second random rule: First, for each disaster-stricken point, the total distance from the disaster-stricken point to all rescue points is used as the denominator, and the distance from the disaster-stricken point to a certain rescue point is used as the numerator as a proper fraction. The difference between 1 and the proper fraction is used as the probability of the disaster-stricken point selecting a certain rescue point to allocate the disaster-stricken point until the dispatched amount of emergency resources reaches the critical value of the emergency resources reserved by the rescue point, and then the next rescue point is allocated; the allocation is carried out in accordance with the encoding method in step 2: each rescue point corresponds to a chromosome fragment of the disaster-stricken point, and then the chromosome gene repair operator in step 3 is used to integrate and repair the obtained chromosome fragments to form the first and second rows of chromosomes with a length of the number of disaster-stricken points + the number of rescue points - 1.

3. The fairness-based heterogeneous emergency resource scheduling optimization method according to claim 1, characterized in that: The step 6.3 is as follows: Step 6.3.1: Use a crossover operator that combines the shuffle crossover operator and the partial match crossover operator, and introduce a random perturbation as a mutation operator. Based on the encoding method of step 2, each chromosome in the population contains the information of each disaster-stricken point number, the corresponding dispatching resource amount, and the corresponding rescue point; for the crossover operator, a crossover operator combining a shuffle crossover operator and a partial matching crossover operator is adopted: the shuffle crossover operator refers to first using the two-point crossover method to select the crossover fragments, randomly shuffling the crossover fragments, and then using the conflict detection function of the partial matching crossover to operate the offspring chromosomes, ensuring that the genes in each chromosome appear only once; for the mutation operator, the dispatching amount of each disaster-stricken point in the second row of the chromosome is multiplied by a random disturbance, and it is ensured that the mutated number does not exceed the feasible range; at the same time, for the third row of the chromosome, in order to prevent the introduction of an excessively large dispatching level after the crossover, a descending process is first performed so that all dispatching levels are no greater than the total number of disaster-stricken points that the rescue point is responsible for rescuing, and then a single-point random mutation is performed: that is, a random number no greater than the total number of disaster-stricken points is generated as the new dispatching level; Step 6.3.2: Adopt an adaptive crossover and mutation adjustment strategy to dynamically change the crossover and mutation probabilities: Crossover rate and mutation rate The adjustment strategy is as follows: , ,in, and Respectively represent the crossover rate and mutation rate of the gen generation, and represent the minimum crossover rate and the maximum crossover rate, respectively; and They represent the minimum mutation rate and the maximum mutation rate respectively; gen represents the current number of iterations, and Mgen represents the maximum number of iterations.

4. The fairness-based heterogeneous emergency resource scheduling optimization method according to claim 1, characterized in that: The steps 6.4 are as follows: Set a crowding threshold percentage, traverse each non-dominated layer from small to large according to the non-dominated level, and calculate the crowding threshold according to the product of the number of individuals in the non-dominated layer and the crowding threshold percentage, and retain individuals whose crowding distance is greater than or equal to the crowding threshold; If the retention percentage is too small, resulting in the population pool still not being filled after traversing all non-dominated layers, the crowding threshold is appropriately reduced, and the remaining individuals are preferentially selected from the non-dominated layers with small non-dominated levels until the population pool is filled. The dynamic change of the crowding threshold with the number of iterations is as follows: ,in, Indicates the crowding threshold percentage of the gen generation, and They represent the minimum and maximum congestion threshold percentages, respectively.

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