Emergency logistics vehicle path optimization method based on AHP-TOPSIS and genetic algorithm

Abstract

The application discloses an emergency logistics vehicle path optimization method based on AHP-TOPSIS and a genetic algorithm, and specifically comprises the following steps: firstly, a disaster point material service urgency evaluation system is constructed, and an AHP-TOPSIS evaluation method is used for solving; secondly, an emergency material distribution scheme based on service urgency is provided; and thirdly, an emergency logistics vehicle path optimization model considering vehicle load limitation and having a time window is constructed, and a genetic algorithm is used for solving the model. The application constructs an emergency logistics vehicle path optimization method under an uncertain environment, reduces the conditions of vehicle detour transportation and counterflow transportation, and effectively improves the emergency logistics vehicle operation efficiency.

Description

Technical Field

[0001] This invention relates to the field of emergency logistics vehicle route optimization technology, and more specifically, to an emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithms. Background Technology

[0002] With rapid economic development, natural disasters and public health emergencies are becoming increasingly frequent, severely impacting the lives and property of people in affected areas. In the context of natural disasters and public health emergencies, especially when demand is uncertain, general route optimization methods, such as the VRP (Vehicle Routing Problem), are no longer applicable when dealing with emergency logistics and supplies. Therefore, efficiently planning emergency logistics vehicle routes during disasters, while ensuring timely delivery and equitable distribution of emergency supplies to various disaster areas, is a crucial task in emergency logistics and a primary issue to address in responding to disasters.

[0003] An analysis of the current development of emergency logistics vehicle transportation reveals the following problems:

[0004] (1) Overemphasis on minimizing distribution costs. The urgency of emergency supplies needs at disaster sites was not considered during the distribution of emergency supplies, which to some extent affected the efficiency of rescue efforts at disaster sites;

[0005] (2) Emergency supplies routes lack reasonable planning. In actual emergency supplies delivery, the route is mainly determined by the driver's familiarity with the local road conditions, which can easily lead to problems such as detours and back-flow transportation during the delivery process;

[0006] (3) Frequent logistics activities and large amount of information in the short term. Disasters are generally sudden, so the demand for emergency logistics and materials increases sharply in the short term, and the amount of related information that needs to be processed also increases dramatically.

[0007] Current research largely focuses on model building, and the demand at disaster-stricken areas is already known. However, due to limited emergency supplies and vehicle capacity, the urgency of demand for various emergency supplies is not comprehensively considered when distributing them during disasters, resulting in inadequate and unreasonable evaluation systems. This invention addresses this issue by constructing an emergency supply evaluation system for disaster-stricken areas, a supply allocation plan, a vehicle routing model for uncertain environments, and a genetic algorithm to optimize vehicle routes, all while considering service urgency in an environment of uncertain demand. Summary of the Invention

[0008] Research on emergency logistics vehicle route optimization in the event of a sudden disaster has revealed problems such as unfair distribution and timely delivery of emergency supplies, as well as excessively high vehicle transportation costs. To address these issues, this invention provides an emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithms. When the demand in disaster-stricken areas is uncertain, this method quantifies the urgency of the demand for various supplies in disaster-stricken areas, considers vehicle penalty costs and transportation expenses, and assists in constructing an emergency logistics vehicle route optimization model to cope with disaster outbreaks, thereby achieving efficient allocation of emergency supplies.

[0009] This invention provides an emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm, comprising the following steps:

[0010] S1: Obtain information on the basic situation, material reserves, and emergency material shortages of each disaster site, and assess the specific needs of each disaster site for various types of emergency materials.

[0011] S2: Emergency Supply Service Urgency Analysis at Disaster-Stricken Areas. This involves constructing an emergency supply service urgency system to rank disaster-stricken areas based on their urgency, prioritizing the delivery of emergency supplies to areas with high urgency. Details are as follows:

[0012] S2-1: Organize the factors affecting the urgency of emergency supplies services at disaster-stricken areas;

[0013] S2-2: Establish an evaluation system for the urgency of emergency supplies services at disaster-stricken areas;

[0014] S2-3: Based on the emergency material service urgency evaluation system for disaster-stricken areas, establish a hierarchical model and select appropriate scales to construct a judgment matrix; through expert analysis of each indicator at each level, construct the judgment matrix A = (a... ij ) m×n , A = (a ij ) m×n Indicates that factors i and j are relative to each other. A = (a ij ) m×n The importance value, the judgment matrix has the following property: a ij >0; a ij =1 / a ji (i≠j); a ii =1 (i = 1, 2, ..., n; j = 1, 2, ..., m); The scaling criteria are shown in Table 1:

[0015] Table 1 Scale Standards

[0016] Scale meaning 1 Indicator i is as important as indicator j 3 Indicator i is slightly more important than indicator j. 5 Indicator i is significantly more important than indicator j. 1 / 3 Indicator i is less important than indicator j 1 / 5 Indicator i is less important than indicator j

[0017] S2-4: Calculate the weight values ​​of each component in the judgment matrix, standardize the column vectors, and obtain the initial matrix W. i Then, the matrix is ​​subjected to row summation, and finally, the weights of each indicator are determined through standardization.

[0018] S2-5: Consistency check, calculate the largest eigenvalue corresponding to the judgment matrix Ci. Calculate the consistency index CI, CI = (λ) max -n) / (n-1); To test the consistency of the weights of each indicator in the emergency material service urgency evaluation system for disaster-stricken areas, calculate CR = CI / RI. If CR < 0.1, the judgment matrix is ​​considered to meet the consistency test. If not, it is necessary to re-solicit expert opinions to form a new judgment matrix before recalculating. RI is the average consistency index, which is obtained by looking up the number of factors in the judgment matrix, as shown in Table 2.

[0019] Table 2 Consistency Index RI

[0020] n 1 2 3 4 5 6 7 8 9 10 11 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51

[0021] S2-6: Determine the emergency supplies allocation plan. This invention proposes a basic supplies allocation model and a supplies allocation model based on service urgency. Calculate the emergency supplies allocation for each disaster-stricken area. Let the total quantity of emergency supplies be Q, the service urgency of each disaster-stricken area be F, the proportion of the basic allocation quantity for each disaster-stricken area to the emergency supplies quantity of the emergency distribution center be a, and the basic allocation of supplies for each disaster-stricken area be β1. The allocation of supplies to each disaster-stricken area based on the urgency of their needs is β2. The total amount of supplies allocated to each disaster-stricken area is β, where β = β1 + β2.

[0022] S3: TOPSIS evaluation analyzes data from each assessment objective to determine the relative distances between objectives, thereby assessing the merits of each objective. Its basic steps are as follows:

[0023] S3-1: Indicator Standardization. Because the TOPSIS method uses distance to measure the quality of disaster-affected areas, the first step in applying the TOPSIS method is to standardize each indicator.

[0024] S3-2: Standardized initial decision matrix evaluation. Make index j of evaluation objective i denoted as x. ij (i = 1, 2, ..., n; j = 1, 2, ..., m) The matrix consisting of the indicators of n evaluation objectives is called the initial matrix. Standardize X to obtain the decision matrix. in,

[0025] S3-3: Construct a weighted decision matrix. Multiply the decision matrix C by the weights W of each influencing factor to construct the weighted decision matrix. Where R ij =c ij w j (i=1,2,…,n; j=1,2,…,m);

[0026] S3-4: Determine the positive and negative ideal solutions. Positive ideal solution R + , Negative ideal solution R - ,

[0027]

[0028] S3-5: Calculate the distance from the evaluation target to the positive and negative ideal solutions:

[0029] S3-6: Calculate the distance between each evaluation objective and the ideal solution. Sort them from largest to smallest.

[0030] S4: Taking the total operating cost of vehicles as the objective and considering the fairness of material supply to various disaster-stricken areas, this invention sets a penalty cost. If rescue vehicles fail to arrive at the disaster-stricken area within the stipulated time, a corresponding penalty cost will be incurred. t i The latest service time for disaster-affected site i; Let i be the time required to receive emergency supplies. An emergency logistics vehicle route optimization model is constructed under uncertain conditions, considering penalty costs, and constraints such as vehicle capacity, emergency supply flow, and time windows are determined. The specific model is as follows:

[0031] The objective function for minimizing the total operating cost of the vehicle is:

[0032]

[0033] Where N = {1, 2, ..., n}; K is the set of transport vehicles, K = {1, 2, ..., k}; x kij Vehicle k travels from disaster site i to disaster site j; d ij The distance from disaster point i to disaster point j; β represents the amount of supplies allocated to the disaster-stricken areas; c represents the penalty coefficient for delayed aid. f Fixed operating costs for the vehicle; a i This indicates whether there is a delay in rescue efforts at disaster site i. If there is a delay in rescue efforts, the value is 1; otherwise, the value is 0.

[0034] The objective function for minimizing the total vehicle operating cost consists of three terms: the first is the vehicle routing cost, the second is the penalty cost for rescue delays, and the third is the fixed usage cost of the vehicle. Minimizing the total vehicle operating cost includes minimizing both the vehicle routing cost and the penalty cost for rescue delays.

[0035] The constraints of the emergency logistics vehicle route optimization model under uncertain conditions considering penalty costs include:

[0036] For vehicle load constraints;

[0037] The total demand for supplies at disaster-stricken areas should not exceed the total demand of emergency distribution centers.

[0038] Access restrictions for disaster-stricken areas;

[0039] Access restrictions for emergency delivery centers;

[0040] Uniqueness constraint for access to disaster-stricken areas;

[0041] Vehicles are required to leave the disaster area;

[0042] Restrictions on vehicle access to disaster-stricken areas;

[0043] Limit the number of times a vehicle can visit the emergency delivery center;

[0044] Constraints on node access time windows;

[0045] Constraints are for non-negative variables;

[0046] Constraints are for non-negative variables;

[0047] α1>0, α2>0, β>0, are non-negative variable constraints;

[0048] Binary variable constraints.

[0049] Where M is the set of emergency distribution centers, M = 1; N = {1, 2, ..., n}; K is the set of transport vehicles, K = {1, 2, ..., k}; θ m x represents the maximum number of available vehicles in the emergency logistics center m; kij Vehicle k travels from disaster site i to disaster site j; kj Vehicle k will serve the disaster-stricken area i; The amount of supplies allocated to disaster-stricken areas; α1 is the penalty coefficient for oversupply; α2 is the penalty coefficient for undersupply; β is the penalty coefficient for delayed aid; c f Fixed operating costs for the vehicle; t i The latest service time for disaster-affected site i; The time for receiving emergency supplies at disaster site i; a i This indicates whether there is a delay in rescue efforts at disaster site i. If there is a delay in rescue efforts, the value is 1; otherwise, the value is 0.

[0050] S5: Based on the priority of emergency supplies at disaster sites, a genetic algorithm is used to optimize the route selection. The specific steps are as follows:

[0051] S5-1: Algorithm Design: In the process of biological evolution, the survival of the fittest is mainly achieved through natural selection, gene recombination, and gene mutation. Genetic algorithms, based on this process, have developed a set of self-searching optimization methods. During operation, they mainly involve operations such as selection, crossover, and mutation. Their basic steps are as follows: Figure 2 As shown.

[0052] Step 1: Input the relevant parameters of the algorithm, combine them with the characteristics of the solution to the problem to be solved, generate an initial population according to certain encoding rules, and appropriately control the population size;

[0053] Step 2: Obtain the fitness value of each individual to determine the quality of individuals in the population;

[0054] Step 3: Select the better individuals from the population according to the established selection strategy;

[0055] Step 4: Use the crossover operator to perform crossover operations on the selected individuals to improve the search ability of the algorithm and increase the diversity of the population;

[0056] Step 5: Use mutation operators to mutate the crossover individuals to improve the algorithm's local search capability;

[0057] Step 6: Determine if the termination condition (maximum number of iterations) is met. If it is met, output the final result; otherwise, return to Step 2 and repeat Step 2 to Step 5 until the final result is output.

[0058] Based on the emergency logistics vehicle route optimization model constructed in this chapter, a genetic algorithm is specifically designed:

[0059] S5-2: Encoding. Common encoding forms for genetic algorithms include binary encoding, Gray code encoding, and floating-point encoding. In the emergency logistics vehicle route optimization model constructed in this invention under uncertain environments, factors such as the service urgency of disaster-stricken points and vehicle load limitations are considered. Based on these characteristics, natural number encoding is used for the encoding design. Assuming there are k emergency delivery vehicles delivering emergency supplies to n disaster-stricken points, where 0 represents a distribution center and 1, 2, ..., n represents a disaster-stricken point, to form k delivery routes, k-1 separators need to be inserted into the sequence of disaster-stricken points 1, 2, ..., n. Therefore, k-1 virtual distribution centers are set.

[0060] S5-3: Determining the Initial Population. Randomly generate a permutation of L+K-1 unique natural numbers from 1 to L+K-1, forming one individual. Let the population size be N; then, by randomly generating N such individuals, the initial population is formed.

[0061] S5-4: Fitness Function. The fitness function needs to be adjusted according to the objective function of the problem to be solved. In the model constructed in this invention, the optimization objective is to minimize the total delivery cost. When setting the fitness function, it should be ensured that the fitness is higher when the total delivery cost is lower. Therefore, the reciprocal of the total delivery cost is used as the fitness function. Considering the load limit of delivery vehicles involved in the optimization problem, during iteration, some individuals may have delivery routes where the sum of the delivered goods exceeds their own load limit. These individuals do not meet the constraints and their fitness should be as poor as possible to prevent them from being selected for the next generation. Therefore, a maximum penalty is set. The specific fitness function formula is shown below:

[0062]

[0063] S5-5: Selection for Replication. This invention employs a roulette wheel selection method. First, the sum of the fitness of all individuals in the previous generation population is calculated. Then, the proportion of fitness of each individual is calculated. The probability of each individual being selected is proportional to its fitness value. The higher the fitness value, the higher the probability of being selected to enter the next generation for crossover and mutation. This selection method can ensure that the best individual survives to the next generation and that individuals with higher fitness have a greater chance of entering the next generation.

[0064] S5-6: Crossover Method. This invention employs an improved crossover method, specifically as follows: Following the maximum retention crossover method and replacing genes according to the mapping relationship, 0s are reinserted according to the emergency vehicle capacity constraint, maintaining the vehicle order within the original individuals. The fitness function value of the new individual is then calculated and compared with the parent generation. If the new individual is superior to the parent, it is accepted; otherwise, the parent's chromosome is allowed to enter the next generation. In other words, for the new population generated through selection and replication, besides the top-ranked optimal individual, the other N-1 individuals are crossovered according to probability P. c Perform pairwise cross-recombination;

[0065] S5-7: Mutation method, with probability P m Once a mutation occurs, the number of swaps J is generated randomly, and the genes of the individual to be mutated are swapped J times (the positions of the swapped genes are also randomly generated).

[0066] S6: Using the genetic algorithm described above, generate the path with the lowest delivery cost as the optimal emergency logistics vehicle route optimization scheme.

[0067] The present invention has the following beneficial effects:

[0068] This invention provides an emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm.

[0069] The emergency supplies service urgency evaluation system constructed by this invention can scientifically reflect the urgency of the material needs at disaster-stricken areas. Based on this, the vehicle route planning can reduce the situation of vehicle detour transportation and convection transportation, and effectively improve the efficiency of emergency logistics.

[0070] This invention takes into account the limitations of emergency supplies and vehicle capacity, effectively quantifies the urgency of the demand for various supplies at each disaster site, and effectively addresses the allocation of emergency supplies during disasters, reducing the waste of vehicle transportation resources.

[0071] This invention constructs a mathematical model adapted to the corresponding problem, which can serve as a tool for formulating vehicle route optimization schemes in the event of a sudden disaster. This improves the efficiency of emergency logistics and provides strong assistance for rescuing lives and property in the first instance.

[0072] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0073] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0074] Figure 1 The flowchart of the optimization method provided by the present invention.

[0075] Figure 2 This is a basic flowchart of the genetic algorithm of this invention.

[0076] Figure 3 A diagram illustrating the emergency supplies urgency evaluation index system provided by this invention.

[0077] Figure 4 This is a diagram illustrating the genetic algorithm optimization process in an embodiment of the present invention. Detailed Implementation

[0078] The following specific examples illustrate the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. The technical solution of the present invention will be further described below in conjunction with specific embodiments and accompanying drawings.

[0079] This invention proposes an emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithms. Please refer to [link / reference]. Figure 1 The flowchart shown is illustrated below, and the specific methods are explained in detail:

[0080] Step 1: Obtain basic information, material reserves, and the degree of emergency material shortage at each disaster site, and assess the specific needs of each disaster site for various types of emergency materials. Due to the rapid and continuous nature of disasters, information acquisition is difficult. Data acquisition channels are relatively scarce regarding the degree of emergency material shortage, and data processing is somewhat subjective. However, this does not affect the effectiveness and practical significance of the subsequent vehicle route problem.

[0081] Step 2: Analyze the urgency of emergency supplies services at disaster-stricken areas. By constructing an emergency supplies service urgency system, disaster-stricken areas are ranked according to their priority. Emergency supplies are prioritized for disaster-stricken areas with high service urgency, as detailed below:

[0082] Step 2-1: Organize the factors affecting the urgency of emergency supplies services at disaster sites. After sorting out the factors, personnel, material reserves, and infrastructure are identified as the main influencing factors.

[0083] Step 2-2: Establish an evaluation system for the urgency of emergency supplies services at disaster-stricken areas. Based on Step 2-1, using the main impacts as the primary indicator, construct an evaluation system for the urgency of emergency supplies services at disaster-stricken areas. (See...) Figure 3 ;

[0084] Steps 2-3: Based on the emergency material service urgency evaluation system for disaster-stricken areas, establish a hierarchical model and select appropriate scales to construct a judgment matrix; through expert analysis of each indicator at each level, construct the judgment matrix A = (a... ij ) m×n , A = (a ij ) m×n Indicates that factors i and j are relative to each other. A = (a ij ) m×n The importance value, the judgment matrix has the following property: a ij >0; a ij =1 / a ji (i≠j); a ii =1 (i = 1, 2, ..., n; j = 1, 2, ..., m), and the scaling criteria are shown in Table 3:

[0085] Table 3 Scale Standards

[0086] Scale meaning 1 Indicator i is as important as indicator j 3 Indicator i is slightly more important than indicator j. 5 Indicator i is significantly more important than indicator j. 1 / 3 Indicator i is less important than indicator j 1 / 5 Indicator i is less important than indicator j

[0087] Steps 2-4: Calculate the weight values ​​of each component in the judgment matrix, standardize the column vectors, and obtain the initial matrix W. i Then, the matrix is ​​subjected to row summation, and finally, the weights of each indicator are determined through standardization.

[0088] Steps 2-5: Consistency check, calculate the largest eigenvalue corresponding to the judgment matrix Ci. Calculate the consistency index CI, CI = (λ) max -n) / (n-1); To test the consistency of the weights of each indicator in the emergency material service urgency evaluation system for disaster-stricken areas, calculate CR = CI / RI. If CR < 0.1, the judgment matrix is ​​considered to meet the consistency test. If not, it is necessary to re-solicit expert opinions to form a new judgment matrix before recalculating. RI is the average consistency index, which is obtained by looking up the number of factors in the judgment matrix, as shown in Table 4.

[0089] Table 4 Consistency Index RI

[0090] n 1 2 3 4 5 6 7 8 9 10 11 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51

[0091] Steps 2-6: Determine the emergency supplies allocation plan. This invention proposes a basic supplies allocation model and a supplies allocation model based on service urgency. This model not only reduces problems such as the algorithm's inability to update in a timely manner, but also allows for the formulation of a relatively reasonable supplies allocation plan for each disaster-stricken point based on service urgency. Calculate the emergency supplies allocation for each disaster-stricken point. Let the total quantity of emergency supplies be Q, the service urgency of each disaster-stricken point be F, the proportion of the basic allocation quantity of each disaster-stricken point to the emergency supplies quantity of the emergency distribution center be a, and the basic allocated supplies for each disaster-stricken point be β1. The allocation of supplies to each disaster-stricken area based on the urgency of their needs is β2. The total amount of supplies allocated to each disaster-stricken area is β, where β = β1 + β2;

[0092] Step 3: TOPSIS evaluation. This involves analyzing the data for each evaluation objective to determine the relative distances between objectives, thereby identifying the strengths and weaknesses of each objective. The basic steps are as follows:

[0093] Step 3-1: Indicator Standardization. Because the TOPSIS method uses distance to measure the quality of disaster-affected areas, the first step in applying the TOPSIS method is to standardize each indicator.

[0094] Step 3-2: Standardize the initial decision matrix for evaluation. Make index j of evaluation target i equal to x. ij (i = 1, 2, ..., n; j = 1, 2, ..., m) The matrix consisting of the indicators of n evaluation objectives is called the initial matrix. Standardize X to obtain the decision matrix. in,

[0095] Step 3-3: Construct a weighted decision matrix. Multiply the decision matrix C by the weights W of each influencing factor to construct the weighted decision matrix. Where R ij =c ij w j (i=1,2,…,n; j=1,2,…,m);

[0096] Steps 3-4: Determine the positive and negative ideal solutions. Positive ideal solution R + , Negative ideal solution R - ,

[0097] Steps 3-5: Calculate the distance from the evaluation target to the positive and negative ideal solutions:

[0098]

[0099] Steps 3-6: Calculate the distance between each evaluation objective and the ideal solution. Sort them from largest to smallest.

[0100] Step 4: Taking the total operating cost of the vehicles as the objective and considering the fairness of material supply to various disaster-stricken areas, this invention sets a penalty cost. If rescue vehicles fail to arrive at the disaster-stricken area within the stipulated time, a corresponding penalty cost will be incurred. t i The latest service time for disaster-affected site i; Let i be the time required to receive emergency supplies. An emergency logistics vehicle route optimization model is constructed under uncertain conditions, considering penalty costs, and constraints such as vehicle capacity, emergency supply flow, and time windows are determined. The specific model is as follows:

[0101] The objective function for minimizing the total operating cost of the vehicle is:

[0102]

[0103] Where N = {1, 2, ..., n}; K is the set of transport vehicles, K = {1, 2, ..., k}; x kij Vehicle k travels from disaster site i to disaster site j; d ij The distance from disaster point i to disaster point j; β represents the amount of supplies allocated to the disaster-stricken areas; c represents the penalty coefficient for delayed aid. f Fixed operating costs for the vehicle; a i This indicates whether there is a delay in rescue efforts at disaster site i. If there is a delay in rescue efforts, the value is 1; otherwise, the value is 0.

[0104] The objective function for minimizing the total vehicle operating cost consists of three terms: the first is the vehicle routing cost, the second is the penalty cost for rescue delays, and the third is the fixed usage cost of the vehicle. Minimizing the total vehicle operating cost includes minimizing both the vehicle routing cost and the penalty cost for rescue delays.

[0105] The constraints of the emergency logistics vehicle route optimization model under uncertain conditions considering penalty costs include:

[0106] For vehicle load constraints;

[0107] The total demand for supplies at disaster-stricken areas should not exceed the total demand of emergency distribution centers.

[0108] Access restrictions for disaster-stricken areas;

[0109] Access restrictions for emergency delivery centers;

[0110] Uniqueness constraint for access to disaster-stricken areas;

[0111] Vehicles are required to leave the disaster area;

[0112] Restrictions on vehicle access to disaster-stricken areas;

[0113] Limit the number of times a vehicle can visit the emergency delivery center;

[0114] Constraints on node access time windows;

[0115] Constraints are for non-negative variables;

[0116] Constraints are for non-negative variables;

[0117] α1>0, α2>0, β>0, are non-negative variable constraints;

[0118] Binary variable constraints.

[0119] Where M is the set of emergency distribution centers, M = 1; N = {1, 2, ..., n}; K is the set of transport vehicles, K = {1, 2, ..., k}; θ m x represents the maximum number of available vehicles in the emergency logistics center m; kij Vehicle k travels from disaster site i to disaster site j; kj Vehicle k will serve the disaster-stricken area i; The amount of supplies allocated to disaster-stricken areas; α1 is the penalty coefficient for oversupply; α2 is the penalty coefficient for undersupply; β is the penalty coefficient for delayed aid; c f Fixed operating costs for the vehicle; t i The latest service time for disaster-affected site i; The time for receiving emergency supplies at disaster site i; a i This indicates whether there is a delay in rescue efforts at disaster site i. If there is a delay in rescue efforts, the value is 1; otherwise, the value is 0.

[0120] Step 5: Based on the priority of emergency supplies at the disaster site, use a genetic algorithm to optimize the route selection. The specific steps are as follows:

[0121] Step 5-1: Algorithm Design: In the process of biological evolution, the survival of the fittest is mainly achieved through natural selection, gene recombination, and gene mutation. Based on this process, genetic algorithms have developed a set of self-searching optimization methods. During operation, they mainly involve operations such as selection, crossover, and mutation. Their basic steps are as follows: Figure 2 As shown;

[0122] Based on the emergency logistics vehicle route optimization model constructed in this chapter, a genetic algorithm is specifically designed:

[0123] Step 5-2: Encoding. Common encoding forms in genetic algorithms include binary encoding, Gray code encoding, and floating-point encoding. In the emergency logistics vehicle route optimization model constructed in this invention under uncertain environments, factors such as the service urgency of disaster-stricken points and vehicle load limitations are considered. Based on these characteristics, natural number encoding is used for the encoding design. Assuming there are k emergency delivery vehicles delivering emergency supplies to n disaster-stricken points, where 0 represents a distribution center and 1, 2, ..., n represents a disaster-stricken point, to form k delivery routes, k-1 separators need to be inserted into the sequence of disaster-stricken points 1, 2, ..., n. Therefore, k-1 virtual distribution centers are set.

[0124] Step 5-3: Determining the initial population. Randomly generate a permutation of L+K-1 unique natural numbers from 1 to L+K-1, thus forming an individual. Let the population size be N; then, by randomly generating N such individuals, the initial population is formed.

[0125] Step 5-4: Fitness Function. The fitness function needs to be adjusted according to the objective function of the problem to be solved. In the model constructed in this invention, the optimization objective is to minimize the total delivery cost. When setting the fitness function, it should be ensured that the fitness is higher when the total delivery cost is lower. Therefore, the reciprocal of the total delivery cost is used as the fitness function. Considering the load limit of delivery vehicles involved in the optimization problem, during iteration, some individuals may have delivery routes where the sum of the delivered goods exceeds their own load limit. These individuals do not meet the constraints and their fitness should be as poor as possible to prevent them from being selected for the next generation. Therefore, a maximum penalty is set. The specific fitness function formula is shown below:

[0126]

[0127] Step 5-5: Selection and Replication. This invention employs a roulette wheel selection method. First, the sum of the fitness of all individuals in the previous generation is calculated. Then, the proportion of fitness of each individual is calculated. The probability of each individual being selected is proportional to its fitness value. The higher the fitness value, the higher the probability of being selected to enter the next generation for crossover and mutation. This selection method can ensure that the best individual survives to the next generation and that individuals with higher fitness have a greater chance of entering the next generation.

[0128] Steps 5-6: Crossover Method. This invention employs an improved crossover method, specifically as follows: Following the maximum retention crossover method and replacing genes according to the mapping relationship, 0s are reinserted according to the emergency vehicle capacity constraint, maintaining the vehicle order within the original individuals. The fitness function value of the new individual is then calculated and compared with the parent generation. If the new individual is superior to the parent, it is accepted; otherwise, the parent's chromosome is allowed to enter the next generation. In other words, for the new population generated through selection and replication, besides the top-ranked optimal individual, the other N-1 individuals are crossovered according to probability P. c Perform paired crossover recombination.

[0129] Steps 5-7: Mutation method, with probability P m Once a mutation occurs, the number of swaps J is generated randomly, and the genes of the individual to be mutated are swapped J times (the positions of the swapped genes are also randomly generated).

[0130] Step 6: Using the genetic algorithm described above, generate the path with the lowest delivery cost as the optimal emergency logistics vehicle route optimization scheme.

[0131] A preferred embodiment of the emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm is as follows:

[0132] Based on step 1, obtain basic information about the disaster-stricken areas, as shown in Table 5.

[0133] Table 5 Basic Information on Disaster-Affected Areas

[0134]

[0135] If supplies cannot be delivered to the disaster-stricken area within the specified timeframe, corresponding delay penalty costs will be incurred. Specific time window information is shown in Table 6.

[0136] Table 6 Time windows for disaster-affected areas (unit: hours)

[0137] node Left Time Window Right Time Window Loading and unloading time Disaster site 1 0 2 0.5 Disaster site 2 0 2 0.5 Disaster site 3 0 2 0.5 Disaster site 4 0 2 0.5 Disaster site 5 0 2 0.5 Disaster site 6 0 2 0.5 Disaster site 7 0 2 0.5 Disaster site 8 0 2 0.5 Disaster site 9 0 2 0.5 Disaster site 10 0 2 0.5 Disaster site 11 0 2 0.5 Disaster site 12 0 2 0.5

[0138] Based on the established data, this invention makes reasonable assumptions to derive the basic information of the distribution center. The specific basic information of this emergency distribution center is shown in Table 7 below.

[0139] Table 7 Basic Information of Emergency Distribution Center

[0140] parameter Value Existing storage capacity 10t Number of available vehicles 6-7 vehicles Vehicle rated load capacity 1.8t Vehicle speed 30km / h Unit operating cost 3.9 yuan Vehicle fixed operating costs 700 yuan Supply shortage cost 500 yuan Oversupply Costs 200 yuan Delay penalty cost 500 yuan

[0141] Based on steps 1 and 2, establish an evaluation system for the urgency of emergency supplies services at disaster-stricken areas. (See...) Figure 3 ;

[0142] The data is standardized to obtain the initial matrix A1.

[0143]

[0144] Normalize the column vectors in the initial matrix A1 to obtain the decision matrix A2;

[0145]

[0146] Then, the weights of the indicators are determined. Based on steps 2-4 and 2-5, the weights W = (0.31, 0.13, 0.36, 0.2) obtained by the analytic hierarchy process are used and pass the consistency test. The weights of each indicator are shown in Table 8.

[0147] Table 8 Weights of Each Indicator

[0148]

[0149] According to step 3-3, the weight W is multiplied by the decision matrix A2 to obtain the weighted decision matrix A3;

[0150]

[0151] Then calculate the positive and negative ideal solutions.

[0152] Positive ideal solution: R + = (0.31, 0.129, 0.36, 0.2); Negative ideal solution: R - =(0.054,0.049,0.072,0.033)

[0153] Based on steps 3-6, the urgency of emergency supplies services at disaster-stricken areas was determined, resulting in service urgency values ​​of {0.998, 0.304, 0.543, 0.814, 0.387, 0.345, 0.401, 0.252, 0.31, 0.051, 0.848, 0.455}. The ranking of service urgency at disaster-stricken areas is shown in Table 9.

[0154] Table 9 Ranking of Service Urgency at Disaster-Affected Areas

[0155] Ranking Disaster site Service urgency 1 Disaster site 1 0.998 2 Disaster site 11 0.848 3 Disaster site 4 0.814 4 Disaster site 3 0.543 5 Disaster site 12 0.455 6 Disaster site 7 0.401 7 Disaster site 5 0.387 8 Disaster site 6 0.345 9 Disaster site 9 0.31 10 Disaster site 2 0.304 11 Disaster site 8 0.252 12 Disaster site 10 0.051

[0156] Based on steps 2-6, the basic allocation β1 for each disaster-stricken site is 0.5 tons, and the allocation β2 is based on the urgency of the need. The total amount of emergency supplies allocated to the disaster-stricken sites is β, as shown in Figure 10.

[0157] Table 10 Distribution of Emergency Supplies in Disaster-Stricken Areas

[0158] Disaster site Demand urgency allocation in tons Total amount of emergency supplies allocated to disaster-stricken areas (tons) Disaster site 1 0.7 1.2 Disaster site 2 0.21 0.71 Disaster site 3 0.38 0.88 Disaster site 4 0.57 1.07 Disaster site 5 0.27 0.77 Disaster site 6 0.24 0.74 Disaster site 7 0.28 0.78 Disaster site 8 0.18 0.68 Disaster site 9 0.22 0.72 Disaster site 10 0.03 0.53 Disaster site 11 0.6 1.1 Disaster site 12 0.32 0.82

[0159] Based on steps 4 and 5, an emergency logistics vehicle route optimization model under uncertain conditions is established, along with the design of the solution algorithm. First, the algorithm's parameters are set, combining the urgency analysis of emergency material services and the analysis of the emergency logistics vehicle route model under uncertain conditions. The algorithm is then run using MATLAB software. During the solution process, the basic parameters of the genetic algorithm need to be set, as shown in Table 11.

[0160] Table 11 Genetic Algorithm Parameters

[0161] parameter symbol Value Crossover probability <![CDATA[P c ]]> 0.9 Mutation probability <![CDATA[P m ]]> 0.1 Number of iterations N 300

[0162] Then, the calculation results were analyzed. The emergency logistics vehicle routing problem at disaster-stricken areas was solved and optimized using MATLAB software. As the number of iterations increased, the number of vehicles decreased and remained stable, and the objective function gradually reached its minimum, outputting the final optimization result. The final delivery transportation route was then determined, and the optimization process is as follows: Figure 4 As shown.

[0163] This led to the generation of the optimal driving routes for vehicles to travel to disaster-stricken areas.

[0164] Number of vehicles used: 6; Total cost: 5182.7857 yuan; Delivery route 1: 0→1→10→0; Load capacity: 1.73t; Delivery route 2: 0→11→8→0; Load capacity: 1.78t; Delivery route 3: 0→2→4→0; Load capacity: 1.78t; Delivery route 4: 0→3→7→0; Load capacity: 1.66t; Delivery route 5: 0→5→9→0; Load capacity: 1.49t; Delivery route 6: 0→12→6→0; Load capacity: 1.56t.

Claims

1. An emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm, characterized in that, The method specifically includes the following steps: S1: Obtain information on the basic situation, material reserves, and emergency material shortages of each disaster site, and assess the specific needs of each disaster site for various types of emergency materials. S2: Analysis of the urgency of emergency supplies services at disaster-stricken areas. By constructing an emergency supplies service urgency system at disaster-stricken areas, the areas are ranked according to their priority, and emergency supplies are given priority to disaster-stricken areas with high service urgency. S3: TOPSIS evaluation, which analyzes the data of each evaluation target to determine the relative distance between targets, thereby determining the merits of each target; S4: Construct an emergency logistics vehicle route optimization model under uncertain conditions that considers penalty costs, and determine constraints such as vehicle capacity constraints, emergency material flow and time window; S5: Based on the priority of emergency supplies at disaster sites and the characteristics of the solution to the problem, a genetic algorithm is used to optimize the path selection. S6: Using the genetic algorithm described above, generate the path with the lowest delivery cost as the optimal emergency logistics vehicle route optimization scheme.

2. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, In step S1, the basic situation, material reserves, and degree of emergency material shortage of each disaster point are obtained, and the specific needs of each disaster point for various types of emergency materials are assessed. Due to the rapid and continuous nature of disasters, information is difficult to obtain. In terms of the degree of emergency material shortage, the data acquisition channels are relatively scarce, and the data processing is somewhat subjective. However, this does not affect the effectiveness and practical significance of the subsequent vehicle route problem.

3. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, To establish an emergency material service urgency system for disaster-stricken areas, information on the number of affected people, the availability and shortage of rescue equipment, and the shortage of emergency supplies is collected. Disaster-stricken areas are then prioritized, and emergency supplies are distributed to those with high service urgency.

4. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, Based on the emergency material service urgency evaluation system for disaster-stricken areas, a hierarchical structure model was established, and a judgment matrix was constructed by selecting an appropriate scale. Through expert analysis of each indicator at each level, the weight values ​​of each indicator in the judgment matrix were calculated, the column vectors were standardized, and a consistency check was performed to determine the weight of each indicator.

5. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, This invention proposes a basic material allocation model and a material allocation model based on service urgency to determine emergency material allocation schemes. This model not only reduces problems such as the inability to update algorithms in a timely manner, but also formulates a relatively reasonable material allocation plan for each disaster-stricken point based on service urgency. The emergency material allocation for each disaster-stricken point is calculated, with the total quantity of emergency materials denoted as Q, the service urgency of each disaster-stricken point as F, the basic allocation quantity for each disaster-stricken point as the proportion of the emergency materials quantity in the emergency distribution center as a, and the basic allocation materials for each disaster-stricken point as β1. The allocation of supplies to each disaster-stricken area based on the urgency of their needs is β2. The total amount of supplies allocated to each disaster-stricken area is β, where β = β1 + β2.

6. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, By analyzing the data of each assessment target, the relative distances between targets are calculated to determine the merits of each target. The first step is to standardize the indicators. Because the TOPSIS method uses distance to measure the merits of disaster-stricken points, standardization of the indicators is necessary before applying the TOPSIS method, resulting in a standardized initial decision matrix evaluation. This allows the j-th indicator of assessment target i to be x. ij (i = 1, 2, ..., n; j = 1, 2, ..., m) The matrix consisting of the indicators of n evaluation objectives is called the initial matrix. Standardize X to obtain the decision matrix. in, Based on the weights of each indicator obtained from AHP, a weighted decision matrix is ​​established. The decision matrix C is then multiplied by the weights W of each influencing factor to construct the weighted decision matrix. Where R ij =c ij w j (i = 1, 2, ..., n; j = 1, 2, ..., m); determine the positive and negative ideal solutions. Positive ideal solution R + , Negative ideal solution R - , Then calculate the distance from the evaluation target to the positive and negative ideal solutions: Finally, the distances between each evaluation objective and the ideal solution are calculated. Sort them from largest to smallest to determine the quality of the disaster-stricken areas.

7. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, This invention incorporates a penalty cost, targeting the total operating cost of vehicles and considering the fairness of material supply to various disaster-stricken areas. If a rescue vehicle fails to arrive at the disaster-stricken area within the stipulated time, a corresponding penalty cost will be incurred. t i The latest service time for disaster-affected site i; Let i be the time required to receive emergency supplies. An emergency logistics vehicle route optimization model is constructed under uncertain conditions, considering penalty costs, and constraints such as vehicle capacity, emergency supply flow, and time windows are determined. The specific model is as follows: The objective function for minimizing the total operating cost of the vehicle is: Where N = {1, 2, ..., n}; K is the set of transport vehicles, K = {1, 2, ..., k}; x kij Vehicle k travels from disaster site i to disaster site j; d ij The distance from disaster point i to disaster point j; β represents the amount of supplies allocated to the disaster-stricken areas; c represents the penalty coefficient for delayed aid. f Fixed operating costs for the vehicle; a i This indicates whether there is a delay in rescue efforts at disaster site i. If there is a delay in rescue efforts, the value is 1; otherwise, the value is 0. The constraints of the emergency logistics vehicle route optimization model under uncertain conditions considering penalty costs include: For vehicle load constraints; The total demand for supplies at disaster-stricken areas should not exceed the total demand of emergency distribution centers. Access restrictions for disaster-stricken areas; Access restrictions for emergency delivery centers; Uniqueness constraint for access to disaster-stricken areas; Vehicles are required to leave the disaster area; Restrictions on vehicle access to disaster-stricken areas; Limit the number of times a vehicle can visit the emergency delivery center; Constraints on node access time windows; Constraints are for non-negative variables; Constraints are for non-negative variables; α1>0, α2>0, β>0, are non-negative variable constraints; Binary variable constraints; Where M is the set of emergency distribution centers, M = 1; N = {1, 2, ..., n}; K is the set of transport vehicles, K = {1, 2, ..., k}; θ m x represents the maximum number of available vehicles in the emergency logistics center m; kij Vehicle k travels from disaster site i to disaster site j; kj Vehicle k will serve the disaster-stricken area i; The amount of supplies allocated to disaster-stricken areas; α1 is the penalty coefficient for oversupply; α2 is the penalty coefficient for undersupply; β is the penalty coefficient for delayed aid; c f Fixed operating costs for the vehicle; t i The latest service time for disaster-affected site i; The time for receiving emergency supplies at disaster site i; a i This indicates whether there is a delay in rescue efforts at disaster site i. If there is a delay in rescue efforts, the value is 1; otherwise, the value is 0.

8. The emergency logistics vehicle route optimization method based on AHP-TOPSIS and genetic algorithm according to claim 1, characterized in that, Based on the emergency logistics vehicle route optimization model constructed in this chapter under uncertain environments, a genetic algorithm is specifically designed, including: ① Encoding and Decoding. The emergency logistics vehicle route optimization model for uncertain environments constructed in this invention involves factors such as the service urgency of disaster-stricken points and vehicle load limitations. Based on these characteristics, a natural number encoding method is used for the encoding design. Assuming there are k emergency delivery vehicles delivering emergency supplies to n disaster-stricken points, where 0 represents a distribution center and 1, 2, ..., n represents a disaster-stricken point, to form k delivery routes, k-1 separators need to be inserted into the sequence of disaster-stricken points 1, 2, ..., n. Therefore, k-1 virtual distribution centers are set. ② Determining the initial population. Randomly generate a permutation of L+K-1 unique natural numbers from 1 to L+K-1, thus forming an individual. Let the population size be N; then, by randomly generating N such individuals, the initial population is formed. ③ Fitness Function Construction. In the model constructed in this invention, the optimization objective is to minimize the total delivery cost. When setting the fitness function, it should be ensured that the lower the total delivery cost, the higher the fitness. Therefore, the reciprocal of the total delivery cost is used as the fitness function. Simultaneously, considering the load limits of delivery vehicles involved in the optimization problem, during iteration, some individuals may have delivery routes where the sum of the delivered goods exceeds their own load limit. These individuals do not meet the constraints, and their fitness should be minimized to prevent them from being selected for the next generation. Therefore, a maximum penalty is set. The specific fitness function formula is shown below: ④ Selection of replication operation. This invention adopts the roulette wheel selection method. First, the sum of the fitness of all individuals in the previous generation population is calculated. Then, the proportion of fitness of each individual is calculated. The probability of each individual being selected is proportional to its fitness value. The higher the fitness value, the higher the probability of being selected to enter the next generation for crossover and mutation. This selection method can ensure that the best individual survives to the next generation and that individuals with higher fitness have a greater chance of entering the next generation. ⑤ Crossover operation. This invention employs an improved crossover method, specifically as follows: In the new population generated through replication, excluding the top-ranked individual, the other N-1 individuals are crossovered according to probability P. c Perform pairwise cross-recombination; ⑥ Mutation operation, with probability P m Once a mutation occurs, the number of swaps H is generated randomly, and the genes of the individual to be mutated are swapped H times, where the positions of the swapped genes are also randomly generated.

Images