Heterogeneous emergency resource scheduling optimization method considering fairness

Abstract

The invention discloses a heterogeneous emergency resource scheduling optimization method considering fairness, and belongs to the field of emergency resource scheduling optimization. For close cooperation type heterogeneous resources, time and satisfaction rate dual-dimension modeling is adopted, a hybrid coding and decoding mode is adopted according to problem features, and an emergency resource scheduling scheme is expressed in a mathematical form; aiming at a target and a constraint condition, adopting a random rule with priority to ensure the quality of an initial population; by adopting a crossover operator combining shuffling crossover and partial matching crossover, the diversity and stability of the population in the iteration process are ensured; by adopting the adaptive crossover mutation probability, the diversity of the population is maintained, and the efficiency of the algorithm is improved; and an elitism strategy with a lowest crowding degree threshold is adopted, population diversity is increased, and premature maturity of the population is prevented. The method is suitable for scheduling optimization of close cooperation type heterogeneous resources under the condition of short supply in the early stage of disasters, and a new thought is provided for solving the problem of emergency resource scheduling of the heterogeneous resources.

Description

Technical Field

[0001] The present invention belongs to the field of emergency resource scheduling optimization, and relates to an optimization method for heterogeneous emergency resource scheduling considering fairness. Background Art

[0002] Emergency resource scheduling is a special activity that, in the event of an emergency or disaster, relies on real-time monitoring and a pre-plan system to quickly, reasonably, and efficiently allocate and dispatch various emergency resources such as manpower, materials, equipment, and funds to meet rescue needs in a timely manner and ensure the effective implementation of emergency operations. It ensures that, in the case of limited resources, the needs of critical tasks are prioritized to minimize casualties and property losses. The scenarios of emergency resource scheduling usually include multiple rescue points and disaster-stricken points. For various emergency resources, vehicles depart from the warehouse, reach the disaster-stricken points, replenish the materials at the disaster-stricken points, and then return to the rescue points to replenish the emergency resources; the sources of emergency resources at each rescue point are diverse, and at the same time, it is difficult to ensure that each type of emergency resource is stored in an appropriate proportion at each rescue point due to reasons such as diverse specifications and compatibility, scattered department management and account books, mismatched maintenance or shelf life, and trade-off between inventory space and cost; in the initial stage of the disaster, emergency resources are often in short supply, and existing resources cannot meet the needs of all disaster-stricken points. Existing emergency resource scheduling methods mostly aim at minimizing time, fairness, and cost. By studying the optimization methods of emergency resources, reasonable and effective path plans are obtained to improve the operation efficiency, reduce disaster losses, and reduce the negative impacts caused by fairness.

[0003] In the literature (Long Y, Sun P, Xu G. Dynamic heterogeneous resource allocation in post-disaster relief operation considering fairness[J]. Advanced Engineering Informatics, 2024, 62: 102858.): Long et al. pioneered the consideration of closely collaborative heterogeneous resources in the field of emergency resource scheduling. To minimize the total scheduling reward, they set the satisfaction ratio threshold of disaster-stricken points to maintain fairness and used the Gini coefficient of the satisfaction rate to measure the fairness after allocation in each period. However, this literature only considered the situation of one rescue point, while the actual situation is more complex. In the literature (Su B K. Research on urban flood disaster emergency resource scheduling based on multiple fairness dimensions[D]. Xi'an University of Architecture and Technology, 2023. DOI: 10.27393 / d.cnki.gxazu.2023.001171.): Su Binkang established an optimization model for post-disaster emergency resource scheduling, set time, fairness, and cost as indicators respectively, established a multi-objective optimization model for one kind of goods, and used the NSGA-II algorithm for solution. However, while weighing fairness, this model ignored the waste of emergency resources at rescue points, resulting in a large amount of emergency resources remaining after scheduling. Although fairness was maintained, the satisfaction degree of the disaster-stricken points themselves was not considered. In the literature (Zhang X, Wang H C, Li Y T, et al. Research on emergency resource scheduling considering demand under sudden flood disasters[J]. Journal of 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 of disaster points, cost, and allocation risk, and used the NSGA-II algorithm for solution. However, this literature used traditional algorithms for solution, did not consider the impact of algorithm performance on the results, and did not consider fairness in emergency resource allocation.

[0004] The emergency resource scheduling problem has characteristics such as complex scenarios, diverse material types, many considerations, and strong data flexibility, and has high requirements for the construction of scenarios and the results of solutions in optimization. However, most of the existing technologies construct simplified scenarios and use traditional heuristic algorithms to solve problems, making it difficult to effectively solve problems in complex scenarios and resulting in poor solution effects. Summary of the Invention

[0005] To solve the above problems, the present invention provides an optimization method for heterogeneous emergency resource scheduling considering fairness. Among them, heterogeneous emergency resources refer to various emergency resources that can play a role in specific disaster scenarios only by cooperating with each other in different proportions. For the problem of allocating heterogeneous emergency resources to multiple rescue points, first, an emergency resource scheduling model for multiple rescue points and multiple disaster-affected points for heterogeneous resources is established. A hybrid coding method is adopted, and the number of chromosomes of an individual is set according to the types of emergency resources. Each chromosome is composed of the number of the disaster-affected point, the amount of resource scheduling, and the scheduling level of the disaster-affected point. For the objective function and optimization objective, a random method with priorities is used to generate a group of excellent individuals within the feasible region, ensuring the feasibility of the population and improving 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 crossover and mutation operations is within the feasible region, while maintaining the diversity of the population and improving the evolution speed of the population. Combining the coding and decoding methods of the present invention, a hybrid crossover method combining the shuffle crossover method and the partially matched crossover method and a mutation method based on random perturbation are designed to ensure the search power of the population during the iteration process. Secondly, aiming at the problems such as poor solution effect and easy to fall into local optimum of the traditional NSGA-II algorithm, the present invention provides an improved NSGA-II algorithm, which adopts an adaptive adjustment of the crossover and mutation probabilities and takes different crossover and mutation probabilities according to the characteristics of the population during the evolution process. At the same time, the elitist retention strategy is improved by using the method of the minimum crowding degree threshold, which can not only improve the crowding degree of the population and increase the diversity, but also indirectly introduce individual individuals with a high non-dominated rank to prevent the population from premature maturity. The results prove that the improved method can effectively solve the deficiencies of the traditional NSGA-II algorithm.

[0006] The object of the present invention is achieved by the following technology:

[0007] An optimization method for heterogeneous emergency resource scheduling considering fairness, comprising the following steps:

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

[0009] It is assumed that the supply and demand of rescue points and disaster-affected points can be obtained in real time when a disaster occurs. The vehicles at the rescue points set out at the same time, and it is considered that there are enough rescue vehicles at the rescue points. Each rescue point is responsible for the rescue tasks of multiple disaster-affected points, while each disaster-affected point can only be rescued by one rescue point. There is no coordination and transfer mechanism for materials between the rescue points and the disaster-affected points. For the disaster-affected points, only the unit emergency resources can play a role when they reach the disaster-affected points according to the heterogeneous ratio. For each type of emergency resource in each warehouse, the materials are transported to the disaster-affected points in one go by the rescue fleet and then returned to the rescue point. In the rescue task, there is a maximum transportation mileage constraint for the rescue vehicles, and there is a time window constraint for the emergency resources at the rescue points;

[0010] Step 1.1. Establish the objective function of the heterogeneous type emergency resource scheduling optimization model with multi-objectives considering fairness:

[0011] The objective function of the heterogeneous type emergency resource scheduling optimization model considering fairness consists of minimizing the total scheduling time , the fairness of the satisfaction degree of the material arrival time at the disaster points and minimizing the total scheduling cost :

[0012]

[0013]

[0014]

[0015] The variable definitions involved in the objective function are as follows:

[0016] - The set of rescue points;

[0017] - The set of disaster-affected points;

[0018] - The set of all nodes, ;

[0019] - The set of vehicles;

[0020] - The set of types of emergency resources;

[0021] - Node to node transportation time, ;

[0022] - Decision variable, indicating that vehicle needs to transport emergency resource r from node to node , otherwise 0; ;

[0023] - The Gini coefficient weight of the rescue time schedule, ;

[0024] - The Gini coefficient of the material arrival time schedule at the disaster-affected points;

[0025] - Gini coefficient of the satisfaction rate of materials at the disaster-stricken points;

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

[0027] - The distance that vehicle k needs to travel to reach the disaster-stricken point j when transporting emergency resource r, ;

[0028] - Decision variable, The magnitude of which represents the number of vehicles that need to transport emergency resource r from the rescue point to the disaster-stricken point ; ;

[0029] - The transportation distance from node to node is as follows: ;

[0030] Node to node The transportation time is as follows:

[0031] ;

[0032] Among them, - The driving speed of the rescue vehicle;

[0033] The importance level of the disaster-stricken point is:

[0034]

[0035] Among them, - The material demand of the disaster-stricken point for the emergency resource is ; - The importance level of the disaster-stricken point is ;

[0036] The distance that vehicle k needs to travel to deliver the emergency resource r to the disaster-stricken point j is as follows:

[0037]

[0038] Among them, - Indicates whether vehicle starts from node Transport emergency resource r to the disaster-stricken point , ; - represents the previous node arriving at this disaster-stricken point distance, ; - represents the distance that vehicle k needs to travel to transport emergency resource r to the previous node , where ; ;

[0039] The time when vehicle k delivers the emergency resource to the disaster-stricken point is as follows:

[0040]

[0041] Among them, - represents the transportation time of the previous node arriving at this disaster-stricken point , ; - represents the time when vehicle transports emergency resource r to the previous node , where ;

[0042] The percentage time progress of the disaster-stricken point is as follows:

[0043] ;

[0044] Among them, - the effective rescue time of the disaster-stricken point , ;

[0045] The Gini coefficient of the arrival time progress of materials at the disaster-stricken point is as follows:

[0046] ;

[0047]

[0048] Among them, and represent the percentage time progress of the disaster-stricken points and , ; and represent the disaster-stricken points and Degree of importance; - The weighted average of the arrival time progress of materials at the disaster-affected points, which serves as the denominator of the weighted Gini coefficient;

[0049] Disaster-affected point Satisfaction rate As follows:

[0050] ;

[0051] Gini coefficient of the material satisfaction rate at the disaster-affected points As follows:

[0052] ;

[0053]

[0054] Among them, and - Represent the satisfaction rate of the disaster-affected point and ; ; - The weighted average of the satisfaction rate of the disaster-affected points, which serves as the denominator of the weighted Gini coefficient. - Represent the coordination ratio of emergency resources ; It means that two units of emergency resource 1 and one unit of emergency resource 2 jointly play the rescue effect of one unit of emergency resource.

[0055] Step 1.2. Set the constraint conditions of the heterogeneous type emergency resource scheduling optimization model considering fairness:

[0056] (1) Maximum waiting time constraint. The emergency resources must transport the emergency resources to the disaster point within the effective rescue time :

[0057]

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

[0059]

[0060] (3) Road connectivity constraint. The vehicle arriving at the disaster-affected point j must leave from this disaster-affected point:

[0061] , where

[0062] (4) Freight flow balance constraint, which is used to calculate the relationship between the node flow and the actual freight volume at the disaster-affected point:

[0063]

[0064] (5) Maximum driving distance constraint of the vehicle: The vehicle can only transport emergency resources on the premise of ensuring a round trip.

[0065]

[0066] (6) Vehicle capacity constraint: The vehicle can only load emergency resources whose weight is less than or equal to the load capacity.

[0067]

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

[0069]

[0070]

[0071] (8) Emergency resource constraint at the disaster-stricken point: The goods received at the disaster-stricken point must be less than or equal to its own demand.

[0072]

[0073] (9) Scheduling mode constraint for multiple rescue points and multiple disaster-stricken points: Among them, the required materials r at each disaster-stricken point can only be transported by one rescue point, and each rescue point can access more than one disaster-stricken point.

[0074]

[0075]

[0076]

[0077] Among them, indicates that the part in the parentheses is true, indicates that the part in the parentheses is false.

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

[0079]

[0080]

[0081]

[0082]

[0083] Among them, the variable definitions involved in the model constraints are as follows:

[0084] - Decision variable, The magnitude of represents the quantity of emergency resource r transported from the rescue point to node by vehicle k on the path from node ; .

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

[0086] - The maximum weight of emergency resources loaded by vehicle k in a fully - loaded state, ;

[0087] - The reserve quantity of materials at rescue point , ; ;

[0088] - The demand quantity of materials at demand point , ; ;

[0089] Step 2. Construct the encoding and decoding methods 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. Each chromosome is set to three rows, and the number of columns is the number of disaster - affected points J plus the number of rescue points I - 1: There are I rescue points storing R kinds of emergency resources, which are dispatched by vehicles to J disaster - affected points. For each kind of emergency resource, 1~J are the numbers of disaster - affected points, and the number of split points is the number of rescue points I - 1, which is the first row of the chromosome. The quantity of emergency resources dispatched to each disaster - affected point is the second row, and the third row sets a scheduling level for each disaster - affected point. Disaster - affected points in the same scheduling level are transported with emergency resources by the same batch of vehicle fleets according to the order; A chromosome represents a deployment method of an emergency resource; According to the constraint conditions in Step 1.2 and the types of emergency resources, R chromosomes that meet the constraint conditions are generated; When decoding each chromosome, first split the 0th column of the chromosome. The multiple segments obtained by splitting are the disaster - affected points responsible for rescue by the rescue points corresponding to the sequence numbers. For each chromosome segment after splitting, according to the scheduling level in the third row of the chromosome, disaster - affected points with the same scheduling level are transported in sequence by the same batch of vehicle fleets according to the order, and the deployment method and quantity represented by each kind of emergency resource, that is, the value of the decision variable, are obtained.

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

[0092] Design an operator for random repair and rescue point allocation to prevent individuals generated after the chromosome undergoes the crossover and mutation steps from falling into the non-feasible region, thereby increasing the calculation time and convergence difficulty and reducing the performance of the algorithm.

[0093] When designing the specific operator for random repair and rescue point allocation: By gradually scanning the second row of the chromosome, when the cumulative sum first exceeds the emergency resource reserve of the rescue point corresponding to the sequence number, record the disaster point number as the edge point, and its scheduling volume is the edge value; Divide the edge value into two parts: The first part is such that the sum of its scheduling volume with the scanned disaster points is equal to the emergency resource reserve of the rescue point corresponding to the sequence number, and the second part is obtained by subtracting the first part from the edge value; 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 responsible for scheduling by the current rescue point. Without violating the constraints of the disaster point, randomly delete the excess value of the cargo volume responsible for scheduling by the current rescue point internally, and then randomly add the deleted value to the emergency resources scheduled by subsequent other disaster points to make it meet the quantity balance, and use the point after the edge point as the splitting point; (2) When the random number is greater than the probability of the random repair method: Take the edge point as the disaster point responsible for scheduling by the next rescue point. Without violating the constraints of the disaster point, randomly add the generated vacancy value to the scheduling cargo volume of the disaster point responsible for by the current rescue point, and randomly delete the emergency resources scheduled by subsequent disaster points to meet the quantity balance, and use the point before the edge point as the splitting point; Record the position of each splitting point during the repair process for inserting the splitting points for dividing the rescue points in subsequent steps.

[0094] Insert 0 at the position of each splitting point to make the second row of the chromosome meet the emergency resource allocation constraints of each rescue point and ensure that all emergency resources are distributed.

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

[0096] Step 4: Obtain relevant data for emergency resource scheduling:

[0097] When solving the scheduling optimization model, the relevant data required by the model must be obtained first, including the road transportation distances between rescue points and disaster-stricken points in the road network, the supply and demand quantities of each type of resource, the cooperation ratio of heterogeneous resources, the time window information of disaster-stricken points, the load capacity of transportation vehicles, 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 priorities:

[0099] The population initialized using a random rule with priorities is within the feasible region and has individuals with relatively optimal objectives, which can optimize the quality of the initial individuals, thereby promoting the improvement of the overall model performance.

[0100] In the random rule with priorities, first use the methods of dynamic programming counting and random sampling as the first random rule to allocate the quantity of emergency resources for each disaster-stricken point; then, combined with the results of the first random rule, use the priority allocation of the small transportation distance between the rescue point and the disaster-stricken point as the second random rule to allocate the disaster-stricken points to the rescue points.

[0101] The first random rule focuses on the total quantity of goods constraint and the fairness objective. To ensure the basic material guarantee for each disaster-stricken point, first allocate a minimum acceptable quantity of materials to it, and then use the methods of dynamic programming counting and random sampling to generate a set of feasible material allocation plans. The specific steps are as follows: For a certain type of emergency resource, first subtract the sum of the minimum guarantee quantities of all disaster-stricken points from the total quantity of materials at the rescue point to obtain the quantity of materials to be allocated. At the same time, calculate the maximum acceptable additional allocation quantity for each disaster-stricken point, that is, the maximum demand at that point minus its minimum guarantee quantity. Then use the dynamic programming counting method: construct a state table, starting from the last disaster-stricken point, and calculate the "number of feasible allocation plans under the given remaining quantity of goods" sequentially forward. For each row (corresponding to a disaster-stricken point), enumerate all possible shares that can be allocated, and add up the "number of plans for the subsequent disaster-stricken points under the remaining quantity of goods" corresponding to each allocation quantity to obtain the total number of plans in the current state. To speed up the summation process, the prefix sum method can be used to optimize the cumulative calculation efficiency; then enter the random sampling stage: after the statistics are completed, starting from the first disaster-stricken point, enumerate the optional additional allocation quantities, and use the number of plans in the subsequent state as the sampling weight for random extraction. After each selection, update the remaining quantity of materials, and execute this process sequentially until the last disaster-stricken point, finally obtaining a set of feasible material allocation plans that meet all the upper and lower limit constraints of the materials.

[0102] The second random rule focuses on time targets. First, for each disaster-stricken point, using the total distance from the disaster-stricken point to all rescue points as the denominator and the distance from the disaster-stricken point to a certain rescue point as the numerator to form a proper fraction, the difference between 1 and this proper fraction is used as the probability for the disaster-stricken point to select a certain rescue point for the allocation of disaster-stricken points until the dispatching volume of emergency resources reaches the critical value of the emergency resources reserved at the rescue point, and then the allocation of the next rescue point is carried out; the obtained is in line with the coding method in step 2: the chromosome segments of the disaster-stricken points corresponding to each rescue point, and then the chromosome gene repair operator in step 3 is used to integrate and repair the obtained chromosome segments to form the first and second rows of the chromosome 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 set the parameters of the optimization method; use the improved NSGA-II algorithm to solve the mathematical optimization model established in step 1 and obtain a set of Pareto front 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 relatively low computational complexity as the basis to solve the model; based on the defects of the traditional NSGA-II algorithm with slow convergence speed and easy to fall into local optimum, by designing an adaptive crossover and mutation probability operator to ensure the power in the population iteration process, expand the search range of the population, and prevent the population from falling into local optimum; adopt an elite retention strategy based on the crowding degree threshold, which is beneficial to making the solution set evenly cover the entire Pareto front, and indirectly introduce individuals with higher non-dominated ranks at the same time to improve the diversity of the population in the iteration process and prevent premature convergence; set the 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, and the maximum and minimum values of the mutation rate, and the maximum and minimum values of the crowding degree threshold percentage.

[0105] 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 of emergency resources. Calculate the fitness function values of each individual in the population pop respectively. During the calculation process, the influence of the constraint conditions on the fitness function is taken into account by imposing a penalty value on the individuals that violate the constraints, and the fitness function is used as the calculation basis for step 6.2.

[0106] Step 6.2. Perform fast non-dominated sorting and calculation of crowding distance on the population.

[0107] In the calculation process of each individual, based on multiple fitness function values of the population individuals, a fast non-dominated sorting is performed on the population to obtain non-dominated layers of different levels, and the crowding distance of each individual is calculated in each non-dominated layer. Two attributes, non-dominated rank and crowding degree, are assigned to the individuals, so that the individuals can be evenly selected during 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 an offspring population ; Based on the calculation results of the fast non-dominated sorting and crowding distance in Step 6.2, a binary tournament operator is used in the selection operator to perform a selection operation on the pop population: randomly select two individuals from the population, first compare the non-dominated rank attributes of each individual, and select the individual with a lower non-dominated rank. In the case of the same non-dominated rank, select the individual with a larger crowding distance; design a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator (PMX), and perform crossover and mutation operations on each chromosome in the individual to generate an offspring population of size P And in this process, dynamically adjusted crossover and mutation rates are set to meet the exploration ability and convergence efficiency of the population at different times, improving the efficiency of the overall optimization method. The specific steps are as follows:

[0109] Step 6.3.1: Adopt a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator (PMX), and introduce a random perturbation as a mutation operator;

[0110] Based on the coding method in Step 2, each chromosome in the population contains the number of each disaster-stricken point, the corresponding amount of dispatched resources, and the information of the corresponding rescue point; for the crossover operator, a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator (PMX) is adopted: the shuffle crossover operator means first using the two-point crossover method to select the crossover segment, randomly shuffling the crossover segment, and then using the conflict detection function of the partially matched crossover to operate on the offspring chromosome, ensuring that each gene in each chromosome appears only once; for the mutation operator, multiply the dispatching amount of each disaster-stricken point in the second row of the chromosome by a random perturbation, and ensure 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 an overly large dispatching level from being introduced after crossover, first perform a descending order process so that all dispatching levels are not greater than the total number of disaster-stricken points responsible for rescue by this rescue point, and then perform a single-point random mutation: that is, generate a random number not greater than the total number of disaster-stricken points as the new dispatching 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 and mutation will prevent the algorithm from adopting appropriate probabilities according to its own iteration situation, easily ignoring the characteristics of the population, resulting in premature maturation or difficult convergence of the population. Therefore, adopting a crossover and 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 front solution. In the initial stage of population evolution, a higher mutation rate will generate more diverse individuals, explore more combinations of material allocation quantities, and help maintain the diversity of the population. In the later stage of population evolution, a higher crossover rate helps prevent the population from falling into local optima, explore more allocation methods, increase the evolutionary power of the population, and a lower mutation rate can accelerate the convergence of the population, thereby improving the efficiency of the algorithm; the crossover rate and the mutation rate are adjusted as follows:

[0113]

[0114] Among them, and represent the crossover rate and mutation rate of the gen-th generation respectively, and represent the minimum crossover rate and the maximum crossover rate respectively; and represent the minimum mutation rate and the maximum mutation rate respectively; gen represents the current iteration number, and Mgen represents the maximum iteration number.

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

[0116] Merge the parent and offspring populations to generate a new population with a population size of 2P. Subsequently, perform a fast non-dominated sorting on this new population and calculate the crowding degree distance of each layer. According to the crowding degree distance threshold, adopt an elite retention strategy, and select individuals with a crowding degree greater than the threshold in the order from the lowest non-dominated rank to the highest, and gradually select until the individual quantity fills the population pool.

[0117] In the elite retention strategy unique to the NSGA-II algorithm, since all non-dominated layers with a lower non-dominated rank are selected, it will lead to a decrease in the crowding degree distance of the population and a reduction in diversity. By setting a crowding degree threshold, in the elite retention strategy, it can not only improve the crowding degree of the population and increase diversity, but also indirectly introduce individual individuals with a high non-dominated rank to prevent the population from maturing prematurely.

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

[0119]

[0120] Among them, represents the crowding degree threshold percentage of the gen-th generation, and respectively represent the minimum crowding degree threshold percentage and the maximum crowding degree threshold percentage.

[0121] Step 6.5: Iteratively solve and determine whether the termination condition is met. If it is met, the Pareto front solution set is output, and multiple specific scheduling plans that meet the constraint conditions and are respectively optimal in multiple fitness values are output according to the decoding rule in Step 2. At this time, the fitness function is equal to the objective function. If it is not met, return to Step 6.1 to continue.

[0122] Step 7: According to the emergency resource scheduling result obtained in Step 6, for the specific situation of the decision maker during the disaster, and based on relevant preferences such as timeliness, fairness, and economy, select an emergency resource scheduling plan with prominent preference characteristics: (1) When mainly considering timeliness, select the scheduling plan with the minimum objective function ; (2) When mainly considering fairness, select the scheduling plan with the minimum objective function ; (3) When mainly considering economy, select the scheduling plan with the minimum objective function .

[0123] Advantages of the present invention:

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

[0125] 2. In order to quickly solve the mathematical model proposed by the present invention, improve the operation efficiency of the algorithm, and obtain high-quality frontier solutions, the present invention adopts the following methods: (1) A hybrid coding method combining the number of disaster-stricken points, the number of dispatching resources, and the dispatching level, and setting the number of chromosomes equal to the number of resources for each individual, respectively representing the allocation methods of each type of emergency resource; (2) According to the optimization objectives and constraint conditions, a random rule with priorities is used to initialize the population, which can ensure that the initialized population is within the feasible region and has individuals with better objectives, and can optimize the quality of the initial individuals; (3) According to the characteristics of hybrid coding for each chromosome of the population individuals, a crossover operator combining shuffle crossover and partially matched crossover and a mutation operator with random perturbation are adopted.

[0126] 3. Based on the defects of the traditional NSGA-II algorithm, such as slow convergence speed and easy to fall into local optimum; 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 the elite retention strategy: an elite retention strategy based on the crowding degree threshold is adopted: selecting individuals with a crowding degree greater than the threshold, and gradually selecting until the number of individuals fills the population pool; this improved method can not only improve the efficiency of the algorithm, maintain the diversity of the population, but also obtain better Pareto frontier solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] Figure 1 is a flowchart of an optimization method for heterogeneous emergency resource dispatching considering fairness according to the present invention;

[0128] Figure 2 is a schematic diagram of the coding method and decoding method according to the present invention;

[0129] Figure 3 is a schematic diagram of the improved crossover method;

[0130] Figure 4 is a schematic diagram of the Pareto optimal frontier obtained by the optimization method for heterogeneous emergency resource dispatching considering fairness. DETAILED DESCRIPTION OF THE INVENTION

[0131] The following further describes the specific implementation manners of the present invention in conjunction with the drawings and technical solutions.

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

[0133] Table 1 Relevant Information of Rescue Points

[0134]

[0135] Table 2 Relevant Information of Disaster-Stricken Points

[0136]

[0137] The information of the road lengths from three emergency resource reserve warehouses to each emergency event is shown in Table 3 as follows.

[0138] Table 3 Distances from Rescue Points to Disaster-Stricken Points

[0139]

[0140] Adopt an optimization method for heterogeneous type emergency resource scheduling considering fairness disclosed in the present invention to conduct emergency resource scheduling. The process is as Figure 1 shown, where all steps are the same as the invention content, and the steps that need special explanation are expanded as follows:

[0141] Step 1: Construct an emergency resource scheduling model that includes multi-objectives with fairness, has constraint conditions, and covers the characteristics of heterogeneous resources;

[0142] Step 2: Construct the chromosome encoding and decoding methods of the emergency resource scheduling optimization method: Each individual in the population designs 2 chromosomes according to the resource types. Adopt a hybrid encoding method according to the model characteristics. For example, as Figure 2 shown, the length of each chromosome is the number of disaster-stricken points + the number of rescue points - 1, with a total of three rows; the first row represents the disaster-stricken point number, the second row represents the quantity of resources scheduled, and the third row represents the scheduling level of each disaster-stricken point. When decoding, according to the position of 0 in the chromosome, the sequence is divided into 3 sub-chromosomes. The order of each sub-chromosome represents the serial number of the rescue point. The first row of each sub-chromosome represents the disaster-stricken point number responsible for rescue by the current rescue point, the second row represents the quantity of materials dispatched by the current rescue point to this disaster-stricken point, and the third row represents the transportation level of the disaster-stricken points responsible for scheduling by the same rescue point. For emergency resource A, after the vehicle departs from rescue point A, it first arrives at disaster-stricken point 5, unloads 35 tons of materials, then arrives at disaster-stricken point 13, unloads 15 tons of materials and returns to rescue point A, and at the same time dispatches 22 tons of materials to disaster-stricken point 7, etc.; Rescue point B is responsible for dispatching 34 tons of materials to disaster-stricken point 2 and 21 tons of materials to disaster-stricken point 1 at the same time; and so on.

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

[0144] Step 4: Obtain relevant data for emergency resource scheduling and set parameters of the optimization method; When solving the model of the present invention, relevant data need to be obtained according to Step 1 first, mainly including the road transportation distances between rescue points and disaster-stricken points in the road network, the supply and demand quantities of each type of resource, the cooperation ratio of heterogeneous resources, the time window information of disaster-stricken points, the load capacity, maximum driving distance, driving speed, and unit freight rate of unit goods of transportation vehicles, as shown in Table 1, Table 2, and Table 3 above; Then set relevant parameters of the optimization method.

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

[0146] Step 6: Set the algorithm improvement strategy and set parameters of the optimization method; Use the improved NSGA-II algorithm to solve the mathematical optimization model established in Step 1 and obtain a set of Pareto front solution sets

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

[0148] Since the method used in the present 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 are respectively = 0.8, = 0.4, the maximum and minimum mutation rates are = 0.3, = 0.15, the maximum and minimum crowding degree threshold percentages are respectively = 1, = 0.5, and the weight is set to 0.5 according to specific circumstances.

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

[0150] Step 6.3: Perform selection operation, crossover, and mutation operations on the population pop to generate the offspring population spop; Based on the calculation results of 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 an offspring population spop with a size of P, and in this process, set dynamically adjusted crossover rate and mutation rate to meet the exploration ability and convergence efficiency of the population at different times and improve the efficiency of the overall optimization method.

[0151] Step 6.3.1: In this embodiment, a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator (PMX) is adopted;

[0152] The shuffle crossover operator first selects the crossover segment using the two-point crossover method, randomly shuffles the crossover segment, and then operates on the offspring chromosomes using the conflict detection function of the partially matched crossover, ensuring that each gene in each chromosome appears only once; as Figure 3 shown, first delete the 0 split point, use the two-point method to select the crossover points of the parent generation, which are 1-4-5-3 and 6-4-1-3 respectively, then perform the shuffle operation, randomly shuffle the order, perform the conflict detection and repair operation on the other parent generation, find that 5 in the first offspring segment repeats with the non-crossover segment of the other parent generation, according to the corresponding order rule, use 6 to replace 5 in the non-crossover segment of the other parent generation, and then use the first offspring as a whole to replace the crossover segment of the other parent generation to complete the crossover of the first offspring; the crossover operation of the second offspring 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 and mutation will make the algorithm unable to adopt suitable probabilities according to its own iteration situation, easily ignore the characteristics of the population, resulting in premature maturity or difficult convergence of the population; therefore, adopting crossover and mutation probabilities that can change in real time according to the population characteristics can not only improve the efficiency of the algorithm, but also obtain a better Pareto front solution; in the initial stage of population evolution, a higher mutation rate will generate more diverse individuals, explore more combinations of material allocation quantities, and help maintain the diversity of the population; in the later stage of population evolution, a higher crossover rate helps prevent the population from falling into local optima, explore more allocation methods, increase the evolutionary power of the population, and a lower mutation rate can accelerate the convergence of the population, thereby improving the efficiency of the algorithm; the crossover rate and the mutation rate are adjusted as follows:

[0155]

[0156] Among them, and represent the crossover rate and mutation rate of the gen-th generation respectively, and represent the minimum crossover rate and the maximum crossover rate respectively; and represent the minimum mutation rate and the maximum mutation rate respectively; gen represents the current iteration number, and Mgen represents the maximum iteration number.

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

[0158] Step 6.5: Iteratively solve and determine whether the termination condition is met. If it is met, output the Pareto front solution set, and according to the decoding rule in Step 2, output multiple specific scheduling plans that meet the constraint conditions and are respectively optimal in multiple fitness values. At this time, the fitness function is equal to the objective function. If it is not met, return to Step 6.1 and continue.

[0159] It further includes Step 7: According to the emergency resource scheduling result obtained in Step 6, considering the specific situation of the decision-maker during the disaster, and based on relevant preferences such as timeliness, fairness, and economy, select an emergency resource scheduling plan with prominent preference characteristics: (1) When mainly considering timeliness, select the scheduling plan with the smallest objective function; (2) When mainly considering fairness, select the scheduling plan with the smallest objective function; (3) When mainly considering economy, select the scheduling plan with the smallest objective function.

[0160] Among them, when solving the emergency resource scheduling optimization problem, the heterogeneous type emergency resource scheduling optimization method considering fairness disclosed in the present invention performs excellently; compared with solving 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 front solutions obtained by the two methods are as Figure 4 shown. It can be seen that the method proposed in the present invention has better performance in multiple objectives than the front solutions obtained by the traditional NSGA-II algorithm, has better convergence, and can provide a new solution for the scheduling and allocation of closely cooperative heterogeneous resources in the initial stage of the disaster.

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

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

[0164]

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

[0166]

[0167] The first solution in Table 4 represents the solution with the optimal scheduling time; the second solution represents the solution with the optimal scheduling fairness; the third solution represents the solution with the optimal scheduling cost. It can be seen that the solution with the optimal value on a single objective obtained by using the improved NSGA-II algorithm is superior to the solution obtained by the traditional NSGA-II algorithm on the corresponding objective, further verifying the superiority of the improved algorithm.

[0168] Regarding the optimal solution obtained by the improved algorithm of the present invention, it can be further seen from Table 4 that: compared with the second solution, for the first solution, the scheduling time (objective function 1) has decreased by 10.2%, and the unfairness (objective function 2) has increased by 15.11%; compared with the third solution, the scheduling time (objective function 1) has decreased by 3.25%, and the scheduling cost (objective function 3) has increased by 0.75%; compared with the third solution, for the second solution, the unfairness (objective function 2) has decreased by 15.11%, and the scheduling cost (objective function 3) has increased by 10.43%; compared with the second solution, although the first solution reduces the scheduling time, it brings more unfairness; compared with the third solution, although the first solution increases some scheduling costs, the optimization effect on the scheduling time is more remarkable; compared with the third solution, although the second solution increases some scheduling costs, the reduction in unfairness is more remarkable.

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

[0170] Therefore, in the actual situation, the manager can make preference selections for the time, fairness, and cost objectives according to the different situations of the disaster occurrence and the actual situation, and select a decision-making scheme that is more suitable for the disaster occurrence situation.

Claims

1. An optimization method for heterogeneous type emergency resource scheduling considering fairness, characterized in that It includes the following steps: Step 1. Establish a heterogeneous type emergency resource scheduling optimization model with multi-objective constraints considering fairness: Step 1.

1. Establish the objective function of the heterogeneous type emergency resource scheduling optimization model with multi-objective constraints considering fairness: The objective function of the heterogeneous type emergency resource scheduling optimization model considering fairness consists of minimizing the total scheduling time , minimizing the fairness of the satisfaction degree of the arrival time of materials at disaster points , and minimizing the total scheduling cost : ， ， ， The variable definitions involved in the objective function are as follows: - Set of rescue points; - Set of disaster-affected points; - The set of all nodes, ; - A set of vehicles; - Set of types of emergency resources; - Node Transportation time to the node , ; - Decision variable, indicating that vehicle needs to transport emergency resource r from node to node , otherwise it is 0; ; - Gini coefficient weight of rescue time progress, ; - Gini coefficient of the arrival time progress of materials at the disaster-stricken points; - Gini coefficient of the satisfaction rate of materials at the disaster-stricken points; - Vehicle The transportation cost per kilometer per ton of goods for transporting emergency resources, ; - The distance that the vehicle k needs to travel to transport the emergency resource r to the disaster area j, ; - Decision variable, The magnitude of represents the number of vehicles required to transport emergency resource r from the rescue point to the disaster area; ; - Node To Node transportation distance ; Node To the node Transportation time Is as follows: ； Among them, - The traveling speed of the rescue vehicle; Disaster-affected point The importance level is: , among which, - disaster-stricken points the material requirements for emergency resources, ; - disaster-stricken points the importance level, ; The distance that vehicle k needs to travel to deliver emergency resource r to the disaster-stricken point j is as follows: , where - indicates whether the vehicle transports the emergency resource r to the disaster area from node , ; - indicates the distance from the previous node to this disaster area, ; - indicates the distance that vehicle k needs to travel to transport the emergency resource r to the previous node , where , ; Vehicle k will deliver emergency resources to the disaster-stricken area at the following time as follows: , where - represents the transportation time for the previous node to reach this disaster - affected point . ; - represents the time for the vehicle to transport the emergency resource r to the previous node . , where ; Disaster-stricken point Percentage time progress is as follows: ; wherein, - disaster-stricken point effective rescue time, ; Gini coefficient of the arrival time progress of materials at the disaster-stricken point is as follows: ； , where and represent the percentage time progress of the disaster-stricken points and ; ; and represent the importance levels of the disaster-stricken points and ; - The weighted average of the arrival time progress of materials at the disaster-stricken points, serving as the denominator of the weighted Gini coefficient. Disaster-stricken point Satisfaction rate Is as follows: ； Gini coefficient of the satisfaction rate of materials at the disaster-stricken points As follows: ； , where and - represents the disaster - affected point and satisfaction rate, ; - The weighted average of the disaster - affected point satisfaction rates serves as the denominator of the weighted Gini coefficient; - represents the collaborative ratio of emergency resources , indicating that one unit of the rescue effect of emergency resource 2 is jointly exerted by two units of emergency resource 1 of two units; Step 1.

2. Set the constraint conditions of the heterogeneous type emergency resource scheduling optimization model considering fairness: (1) Maximum waiting time constraint. The emergency resources must be transported to the disaster site within the effective rescue time. : , (2) Return trip constraint: The vehicle k carrying the transportation emergency resource r must return to the same rescue point i after departing from the rescue point i. , (3) Road connectivity constraint: The vehicles arriving at the disaster-stricken point j must leave from this disaster-stricken point: , among which , (4) Freight flow balance constraint, which is used to calculate the relationship between the node flow and the actual freight volume at the disaster-stricken points: , (5) Maximum driving distance constraint of the vehicle. The vehicle can only transport emergency resources on the premise of ensuring a round trip: , (6) Capacity constraint of the vehicle. The vehicle can only load emergency resources whose material weight is less than or equal to the load capacity: , (7) Emergency resource allocation constraint. To avoid waste of materials and ensure that all emergency resources are distributed: , , (8) Emergency resource constraints at the disaster-affected points, where the goods received at the disaster-affected points must be less than or equal to their own demands: , (9) Constraints for the multi-rescue-point and multi-disaster-point scheduling mode, where the materials r required by each disaster-affected point can only be transported by one rescue point, and each rescue point can access more than one disaster-affected point: , , , where, means the part in parentheses is true, means the part in parentheses is false; (10) Relationship constraints between decision variables: , , , , where the variable definitions involved in the model constraints are as follows: - Decision variable, The magnitude of which represents the quantity of emergency resource r carried by vehicle k on the path from node to node and transported out from the rescue point ; ; - The maximum driving distance of the rescue vehicle k in a full fuel state, ; - The maximum weight of the emergency resources loaded when vehicle k is fully loaded, ; - Relief point Supplies Reserve quantity of, ; - Requirement point materials demand quantity, ; Step 2. Construct the encoding and decoding methods of the scheduling optimization model in Step 1: Adopt a mixed encoding method of natural numbers and continuous numbers. Each chromosome is set to three rows, and the number of columns is the number of disaster-affected points J plus the number of rescue points I - 1. There are I rescue points storing R types of emergency resources, which are dispatched to J disaster-affected points by vehicles. For each type of emergency resource, 1 to J are the numbers of disaster-affected points, and the number of split points is the number of rescue points I - 1, which is used as the first row of the chromosome. The amount of emergency resources dispatched to each disaster-affected point is used as the second row. The third row sets a scheduling level for each disaster-affected point. Disaster-affected points at the same scheduling level are transported with emergency resources by the same batch of vehicle fleets according to the order. A chromosome represents a deployment method of an emergency resource. For the constraint conditions in Step 1.2 and the types of emergency resources, generate R chromosomes that meet the constraint conditions. When decoding each chromosome, first split the 0th column of the chromosome. The multiple segments obtained after splitting are the disaster-affected points responsible for rescue by the rescue points corresponding to the sequence numbers. For each chromosome segment after splitting, according to the scheduling level of the third row of the chromosome, disaster-affected points at the same scheduling level are transported in sequence by the same batch of vehicle fleets according to the order, and the deployment method and quantity represented by each type of emergency resource, that is, the value of the decision variable, are obtained. Step 3. Design a chromosome gene repair and rescue point allocation operator based on the characteristics of the emergency resource allocation constraints of the model By gradually scanning the second row of the chromosome, when the cumulative sum first exceeds the emergency resource reserve of the rescue point corresponding to the sequence number, record the disaster-affected point number as the edge point, and its scheduling volume is the edge value; divide the edge value into two parts: the first part is such that the sum of its scheduling volumes with the scanned disaster-affected points is equal to the emergency resource reserve of the rescue point corresponding to the sequence number, and the second part is obtained by subtracting the first part from the edge value; 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 between 0 and 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-affected point responsible for scheduling by the current rescue point. On the premise of not violating the constraints of the disaster-affected points, randomly delete the excess value of the cargo volume responsible for scheduling by the current rescue point internally, and then randomly add the deleted value to the emergency resources scheduled by other subsequent disaster-affected points to make it meet the quantity balance, and take the point after the edge point as the splitting point; (2) When the random number is greater than the probability of the random repair method: Take the edge point as the disaster-affected point responsible for scheduling by the next rescue point. On the premise of not violating the constraints of the disaster-affected points, randomly add the generated vacancy value to the cargo volume scheduled by the disaster-affected points responsible for by the current rescue point, and randomly delete the emergency resources scheduled by the subsequent disaster-affected points to meet the quantity balance, and take the point before the edge point as the splitting point; Record the position of each splitting point during the repair process for inserting the splitting points for dividing the rescue points in subsequent steps; Insert 0 at the position of each splitting point to make the second row of the chromosome meet the emergency resource allocation constraints of each rescue point and ensure that all emergency resources are distributed; Step 4: Obtain relevant data for emergency resource scheduling: Obtain relevant data required by the model, including the road transportation distances between rescue points and disaster-affected points in the road network, the supply and demand quantities of each resource, the cooperation ratio of heterogeneous resources, the time window information of disaster-affected points, the load capacity of transportation tools, the maximum driving distance, the driving speed, and the transportation cost per ton of goods per kilometer; Step 5: Initialize the population using a random rule with priorities: In the random rule with priorities, first use the methods of dynamic programming counting and random sampling as the first random rule to allocate the quantity of emergency resources for each disaster-affected point; then, combined with the results of the first random rule, use the priority allocation of the small transportation distance between the rescue point and the disaster-affected point as the second random rule to allocate disaster-affected points to the rescue point; Step 6: Set the algorithm improvement strategy and set the parameters of the optimization method; use the improved NSGA-II algorithm to solve the mathematical optimization model established in Step 1 and obtain a set of Pareto front solution sets; Step 6.1: After initializing the population, based on the scheduling optimization model established in Step 1, take the objective function as the fitness function. Each individual contains R chromosomes of emergency resources. Calculate the fitness function values of each individual in the population pop respectively. During the calculation process, impose a penalty value on the individuals that violate the constraints to take into account the influence of the constraints on the fitness function, and use the fitness function as the calculation basis for Step 6.2; Step 6.2: Perform fast non-dominated sorting and calculate the crowding distance for the population; In the calculation process of each individual, based on multiple fitness function values of the population individuals, perform fast non-dominated sorting on the population to obtain non-dominated levels of different ranks, and calculate the crowding distance of each individual in each non-dominated level, and assign the individual two attributes: non-dominated rank and crowding degree; Step 6.3: Perform selection, crossover, and mutation operations on the population pop to generate an offspring population ; Based on the calculation results of the fast non-dominated sorting and crowding distance in Step 6.2, use the binary tournament operator in the selection operator to perform selection operations on the pop population: randomly select two individuals from the population, first compare the non-dominated rank attributes of each individual, and select the individual with a lower non-dominated rank. In the case of the same non-dominated rank, select the individual with a larger crowding distance; design a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator, perform crossover and mutation operations on each chromosome among the individuals, and generate an offspring population of size P , and during this process, set dynamically adjusted crossover rates and mutation rates; Step 6.4: Merge the parent population pop and the offspring population spop generated in Step 6.3, and adopt an elite selection strategy with the lowest crowding degree threshold to generate a new population pop; Merge the parent and offspring populations to generate a new population with a population size of 2P. Subsequently, perform fast non-dominated sorting on this new population and calculate the crowding distance of each layer; According to the crowding distance threshold, adopt an elite retention strategy, select individuals with a crowding degree greater than the threshold in ascending order of non-dominated rank, and gradually select until the number of individuals fills the population pool; Step 6.5: Iteratively solve, and determine whether the termination condition is met. If it is met, output the Pareto front solution set, and output multiple specific scheduling plans that meet the constraint conditions and are respectively optimal in multiple fitness values according to the decoding rule in Step 2. At this time, the fitness function is equal to the objective function; If not, return to Step 6.1 and continue; Step 7: According to the emergency resource scheduling result obtained in Step 6, for the specific situation of the decision maker during a disaster, and based on relevant preferences such as timeliness, fairness, and economy, select an emergency resource scheduling plan with prominent preference characteristics: (1) When mainly considering timeliness, select the scheduling plan with the minimum objective function ; (2) When mainly considering fairness, select the scheduling plan with the minimum objective function ; (3) When mainly considering economy, select the scheduling plan with the minimum objective function .

2. The optimization method for heterogeneous type emergency resource scheduling considering fairness according to claim 1, characterized in that The random rule in Step 5 is as follows: The first random rule: First, allocate a minimum acceptable amount of materials to it, and then use the method of dynamic programming counting and random sampling to generate a set of feasible material allocation plans, specifically as follows: For a certain type of emergency resource, first subtract the sum of the minimum guarantee amounts of all disaster-stricken points from the total amount of materials at the rescue point to obtain the amount of materials to be allocated; At the same time, calculate the maximum acceptable additional allocation amount for each disaster-stricken point, that is, the maximum demand at this point minus its minimum guarantee amount; Then use the dynamic programming counting method: construct a state table, starting from the last disaster-stricken point, calculate the "number of feasible allocation plans under the given remaining quantity of goods" in turn; For each row corresponding to a disaster-stricken point, enumerate all possible shares that can be allocated, and add up the "number of plans for subsequent disaster-stricken points under the remaining quantity of goods" corresponding to each allocation amount to obtain the total number of plans in the current state; Subsequently, enter the random sampling stage: After the statistics are completed, starting from the first disaster-stricken point, enumerate the optional additional allocation amounts, and use the number of plans in the subsequent state as the sampling weight for random extraction; After each selection, update the remaining amount of materials, and execute this process in turn until the last disaster-stricken point, and finally obtain a set of feasible material allocation plans that meet all the upper and lower limit constraints of the materials; The second random rule: First, for each disaster-stricken point, use the total distance from this disaster-stricken point to all rescue points as the denominator, and the distance from this disaster-stricken point to a certain rescue point as the numerator to form a proper fraction. Use the difference between 1 and this proper fraction as the probability for this disaster-stricken point to select a certain rescue point for the distribution of disaster-stricken points until the dispatching volume of emergency resources reaches the critical value of the emergency resources reserved at the rescue point, and then proceed with the distribution of the next rescue point; the distribution results in chromosome segments corresponding to disaster-stricken points for each rescue point in accordance with the coding method in step 2, and then use the chromosome gene repair operator in step 3 to integrate and repair the obtained chromosome segments to form the first and second rows of a chromosome with a length of the number of disaster-stricken points + the number of rescue points - 1.

3. An optimization method for heterogeneous type emergency resource scheduling considering fairness according to claim 1, characterized in that, The specific content of step 6.3 is as follows: Step 6.3.1: Adopt a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator, and introduce a random perturbation as a mutation operator; Based on the coding method in step 2, each chromosome in the population respectively contains the information of each disaster-stricken point number, the corresponding dispatched resource volume, and the corresponding rescue point; for the crossover operator, adopt a crossover operator that combines a shuffle crossover operator and a partially matched crossover operator: the shuffle crossover operator means first using the two-point crossover method to select the crossover segment, randomly shuffling the crossover segment, and then using the conflict detection function of the partially matched crossover to operate on the offspring chromosomes to ensure that each gene in each chromosome appears only once; for the mutation operator, multiply the dispatching volume of each disaster-stricken point in the second row of the chromosome by a random perturbation, and ensure 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 an overly large dispatching level from being introduced after crossover, first perform a descending order process so that all dispatching levels are not greater than the total number of disaster-stricken points responsible for rescue by this rescue point, and then perform single-point random mutation: that is, generate a random number not greater than the total number of disaster-stricken points 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 are adjusted as follows: , , where and represent the crossover rate and mutation rate of the gen-th generation respectively, and represent the minimum crossover rate and the maximum crossover rate respectively; and represent the minimum mutation rate and the maximum mutation rate respectively; gen represents the current iteration number, and Mgen represents the maximum iteration number.

4. A fairness - considered optimization method for heterogeneous - type emergency resource scheduling according to claim 1, characterized in that The specific content of step 6.4 is as follows: Set a crowding degree threshold percentage, traverse each non-dominated layer from small to large according to the non-dominated rank, and calculate the crowding degree threshold according to the product of the number of individuals in the non-dominated layer and the crowding degree threshold percentage, and retain the individuals whose crowding degree distance is greater than or equal to the crowding degree threshold; If the retention percentage is too small, resulting in the population pool not being filled after traversing all non-dominated layers, appropriately reduce the crowding degree threshold, and preferentially select the remaining individuals from the non-dominated layers with a small non-dominated rank until the population pool is filled. The dynamic change of the crowding degree threshold with the number of iterations is as follows: , where represents the crowding threshold percentage of the gen-th generation, and represent the minimum crowding threshold percentage and the maximum crowding threshold percentage, respectively.

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