An Optimization Method for Emergency Resource Scheduling

Abstract

This invention discloses an optimization method for emergency resource scheduling, belonging to the field of emergency resource scheduling. The invention transforms the emergency resource scheduling problem into a problem that can be handled by an optimization method through natural number encoding and decoding. For the optimization objective, nearest neighbor rules and time rules are used to ensure the diversity of the initial population and expand the search space of the optimization method. By improving global and local mutation operators, the diversity of the population during the search process is guaranteed. Based on the changing characteristics of the population's demand for global and local search capabilities during evolution, the population evolution process is divided into three stages, employing an adaptive parameter adjustment strategy. In each stage, a crossover rate and mutation rate more consistent with evolutionary characteristics are used to improve the search efficiency and convergence of the optimization method. This invention is applicable to the field of emergency resource scheduling, improving the efficiency and reliability of emergency resource scheduling.

Description

Technical Field

[0001] This invention relates to an optimization method for emergency resource scheduling, belonging to the field of emergency resource scheduling. Background Technology

[0002] Emergency resource dispatch refers to a special logistics activity that provides emergency support for the needs of materials, personnel, and funds in response to sudden events such as severe natural disasters, public health emergencies, public safety incidents, and military conflicts. It is characterized by high difficulty, high cost, and high timeliness. Emergency resource dispatch typically involves several warehouses and incident points. Transport vehicles depart from the warehouses to replenish supplies to the incident points. This replenishment can be unidirectional (replenishing only one incident point at a time) or non-unidirectional (replenishing multiple incident points simultaneously). Existing methods mostly aim to minimize time and cost. Researching optimization methods for emergency resource dispatch aims to obtain reasonable and efficient route schemes, thereby improving the operational efficiency of emergency logistics and reducing losses caused by disasters and other events.

[0003] Patent document CN201710052109.3 provides an emergency resource scheduling method, constructing a model with the objectives of earliest accident end time and minimum emergency rescue cost. However, this document uses traditional mathematical methods for solution, resulting in low efficiency. Patent document CN202011138157.2, based on the background of earthquake disasters, proposes an emergency resource scheduling method based on ant colony optimization algorithm and multi-objective function model, constructing a model with the objectives of minimizing time efficiency and path cost, and using ant colony optimization algorithm for solution. This document converts the multi-objective problem into a single-objective problem instead of directly solving the multi-objective problem, leading to subjective results. Patent document CN201711172799.2 proposes a modular emergency material scheduling method based on an improved NSGA-II algorithm. In generating the parent population, it uses the calculation of chromosome neighborhood sets and introduces an elimination mechanism, maintaining population diversity to some extent. However, there is still room for improvement in model solution efficiency.

[0004] Emergency resource scheduling problems are characterized by large amounts of data, high computational complexity, and diverse objectives, placing high demands on computational efficiency and solution results during optimization. However, existing technologies mostly employ traditional mathematical methods or single-objective evolutionary algorithms to solve these problems, resulting in long optimization times and poor solution results in complex situations. Summary of the Invention

[0005] To address the problems of long optimization time and poor solution results in existing technologies for emergency resource scheduling, the main objective of this invention is to provide an optimization method for emergency resource scheduling that transforms the emergency resource scheduling problem into one that can be handled by the optimization method. For the optimization objective, nearest neighbor rules and time rules are employed to ensure the diversity of the initial population and expand the search space of the optimization method. By improving global and local mutation operators, the diversity of the population during the search process is guaranteed. Based on the changing characteristics of the population's demand for global and local search capabilities during evolution, the population evolution process is divided into three stages. An adaptive parameter adjustment strategy is adopted, using crossover and mutation rates that better conform to evolutionary characteristics in each stage, thereby improving the search efficiency and convergence of the optimization method, and ultimately improving the efficiency and reliability of emergency resource scheduling.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses an emergency resource scheduling optimization method. It employs a natural number encoding and decoding method for the emergency resource scheduling problem. The encoding of individuals in the population is composed of accident point numbers arranged in sequence. Combined with the constraints of emergency resource scheduling, the population individuals are decoded to obtain each sub-path scheme for emergency resource scheduling, transforming the emergency resource scheduling problem into a problem that the optimization method can handle. Based on the optimization objective, nearest neighbor rules and time rules are used to generate some superior individuals during population initialization, ensuring the diversity of the initial population and expanding the search space of the optimization method. Combining the encoding and decoding method of the emergency resource scheduling problem, an improved mutation operator is used, including a global mutation operator and a local mutation operator. The global mutation operator randomly exchanges genes in different sub-paths, while the local mutation operator randomly exchanges genes in the same sub-path, ensuring the diversity of the population during the search process. Based on the changing characteristics of the population's demand for global and local search capabilities during evolution, the population evolution process is divided into three stages. An adaptive parameter adjustment strategy is adopted, and parameter formulas for crossover and mutation rates are designed. At each stage, crossover and mutation rates that better conform to evolutionary characteristics are used to improve the search efficiency and convergence of the optimization method.

[0008] This invention discloses an emergency resource scheduling optimization method, comprising the following steps:

[0009] Step 1: Construct a multi-objective, constrained emergency resource scheduling model;

[0010] The transport vehicle performs non-unidirectional resupply with a return route. That is, it departs from the warehouse, resupplys multiple incident points at once, and returns to the warehouse after all incident points along the sub-path have been resupplyed. During the resupply process, incident points have time windows and priority constraints on the supplies.

[0011] Step 1.1: Establish the objective function of the multi-objective constrained emergency resource scheduling model;

[0012] The objective function of the emergency resource scheduling model consists of minimizing the timeout penalty F1 and minimizing the transportation cost F2.

[0013]

[0014]

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

[0016] N - The number of transport vehicles in the warehouse;

[0017] M - Number of accident sites;

[0018] c - Unit transportation cost of the means of transport;

[0019] x kij - Decision variable, x kij =1 indicates that the transport vehicle k needs to be resupplyed from accident point i to accident point j; otherwise, it is 0.

[0020] x ksi - Decision variable, x ksi =1 indicates that the means of transport k departs from warehouse s and arrives at the accident point i; otherwise, it is 0.

[0021] x kjs - Decision variable, x kjs =1 indicates that the means of transport k returns to the warehouse s from the accident point j; otherwise, it is 0.

[0022] d ij —The Euclidean distance from accident point i to accident point j;

[0023] d si —The Euclidean distance from warehouse s to accident point i;

[0024] d js —The Euclidean distance from accident point j to warehouse s.

[0025] Timeout penalty tl ki As shown below:

[0026]

[0027] Where, p i The priority of materials at accident point i is defined by the time window. t ki This represents the actual time it takes for transport vehicle k to arrive at accident point i. The time penalty takes into account the impact of priority; the higher the priority, the greater the impact of the timeout penalty on the target, and vice versa.

[0028] The actual time t for vehicle k to reach accident point i ki for:

[0029]

[0030] Among them, t kj This refers to the actual time when transport vehicle k arrives at accident point j, which is the start time of transport vehicle k's service at the previous accident point j. t represents the lower limit of the time window at accident point j. kji The travel time from accident point j to accident point i is denoted as .

[0031] The travel time t of vehicle k from accident point j to accident point i kji As shown below:

[0032]

[0033] Where, d ji Let be the Euclidean distance from accident point j to accident point i. The speed of the transport vehicle.

[0034] Step 1.2: Set the constraints for the multi-objective constrained emergency resource scheduling model;

[0035] (1) Closed-loop constraint: the transportation vehicle departs from the warehouse and needs to return to the warehouse;

[0036]

[0037] (2) Emergency point resupply constraint: each emergency point is resupplyed only once;

[0038]

[0039] (3) Constraints on the number of transport vehicles: the number of departing transport vehicles cannot exceed the total number of transport vehicles in the warehouse;

[0040]

[0041] (4) The load capacity constraint of the transport vehicle, that is, the total supply of a sub-route shall not exceed the load capacity W of the transport vehicle;

[0042]

[0043] (5) Value constraints of decision variables.

[0044]

[0045]

[0046] The variables involved in the model constraints are defined as follows:

[0047] N - The number of transport vehicles in the warehouse;

[0048] M - Number of accident sites;

[0049] x ksi - Decision variable, x ksi =1 indicates that the means of transport k departs from warehouse s and arrives at the accident point i; otherwise, it is 0.

[0050] x kjs - Decision variable, x kjs =1 indicates that the means of transport k returns to the warehouse s from the accident point j; otherwise, it is 0.

[0051] x kij - Decision variable, x kij =1 indicates that the transport vehicle k needs to be resupplyed from accident point i to accident point j; otherwise, it is 0.

[0052] y ki - Decision variable, y ki =1 indicates that the means of transport k needs to supply the accident point i; otherwise, it is 0.

[0053] D i - The amount of supplies required at accident point i;

[0054] W - Load capacity of the transport vehicle.

[0055] Step 2: Construct the natural number encoding and decoding method for the emergency resource scheduling optimization method;

[0056] Since emergency resource scheduling is a multidimensional discrete problem, a natural number encoding method is adopted. The warehouse has N transport vehicles, and the number of accident points is M. Numbers 1 to M represent the accident point numbers. Based on the population initialization method, an encoded sequence of length M individuals can be obtained, representing one solution. According to the constraints in step 1.2, the encoded accident point sequence is decoded to generate multiple sub-paths. For each sub-path, the transport vehicle departs from the warehouse, and returns to the warehouse after all accident points along the sub-path have been resupplyed.

[0057] Step 3: Obtain relevant data on emergency resource scheduling and set optimization method parameters;

[0058] When optimizing the solution for emergency resource scheduling, it is first necessary to obtain relevant data on the emergency resource scheduling problem, mainly including the locations of warehouses and accident sites, the number and carrying capacity of transportation vehicles, the demand at accident sites, and the time windows and priorities of accident sites; then, the parameters in the optimization method are set, including the population size Sc, the number of iterations gen, and the initial crossover rate P of the NSGA-II algorithm. c and the rate of variation P m .

[0059] Step 4: Initialize the population Pop based on random methods and specific rules;

[0060] This invention is based on the NSGA-II algorithm, therefore, it requires initializing the population as input to the optimization method. First, a portion of the population is initialized using a random method. Then, a specific rule-based method is introduced to initialize another portion of the population based on the objective function. The population initialized using the specific rule-based method contains some relatively optimal solutions, which can expand the algorithm's search space. Finally, the two are combined to form a population Pop of size Sc.

[0061] In the specific rule initialization method, it mainly focuses on a certain objective function of the model and selectively initializes some individuals that fit the objective function. In the emergency resource scheduling problem, the objective function is often the minimum time and distance, so the nearest neighbor rule and the time rule are used. The nearest neighbor rule generates individuals based on the nearest distance between points. First, an initial accident point is randomly selected; then, the accident point closest to the previous accident point is selected as the next point to be served; and so on, generating the initial population of individuals according to the encoding method in step 2. The time rule includes the start time of replenishment, the average time of replenishment, and the end time of replenishment. The start time, average time of replenishment, and end time of the accident points are arranged in ascending order to generate the population of individuals.

[0062] Step 5: Based on the multi-objective constrained emergency resource scheduling model established in Step 1, calculate the objective function value of the population; after initializing the population, based on the multi-objective emergency resource scheduling model established in Step 1.1, calculate the objective function value of the population Pop, taking into account the influence of the constraints described in Step 1.2 on the solution of the objective function during the calculation.

[0063] Step 6: Perform fast non-dominated sorting and crowding distance calculation on the population Pop; The emergency resource scheduling problem is a multi-objective model. Based on the NSGA-II multi-objective optimization method, during the optimization process, based on the obtained objective function value, fast non-dominated sorting is performed on the population Pop to reduce computational complexity, and the crowding distance at each level is calculated so that individuals can expand to the entire Pareto domain and be evenly distributed, thus maintaining the diversity of the population.

[0064] Step 7: Select, crossover, and perform improved mutation operations on the population Pop to generate the offspring population OPop. Based on the results of fast non-dominated sorting and crowding distance calculation, select, crossover, and perform improved mutation operations on the population Pop to ensure the diversity of the population during the evolutionary process, generating an offspring population OPop of size Sc. In this process, an adaptive parameter adjustment strategy is adopted to dynamically change the crossover rate and mutation rate to meet the requirements of different stages of evolution for global and local search capabilities, thereby improving the search efficiency of the optimization method.

[0065] Step 7.1: An improved mutation method combining global and local mutation operators is adopted;

[0066] Traditional mutations are random and cannot adequately guarantee diversity during population evolution. Based on the encoding method described in step 2, each individual in the population contains multiple sub-paths. This invention employs an improved mutation method combining global and local mutation operators. The global mutation operator involves randomly exchanging genes on different sub-paths. The local mutation operator involves randomly exchanging two genes on the same sub-path.

[0067] Step 7.2: Construct an adaptive parameter adjustment strategy to dynamically change the crossover rate and mutation rate of the optimization method;

[0068] Traditional crossover and mutation rates are typically determined based on subjective experience, easily overlooking population characteristics during evolution. In swarm intelligence optimization methods, the cooperation and competition between crossover and mutation enable the algorithm to achieve global and local equilibrium search capabilities. Based on the changing characteristics of global and local search capabilities at each evolutionary stage, an adaptive parameter adjustment strategy is constructed to dynamically change the crossover and mutation rates during the iteration process. The adjustment scheme for crossover and mutation rates is as follows, employing a piecewise function: parameter values ​​decrease in the first stage, remain unchanged in the second stage, and decrease again in the third stage.

[0069]

[0070]

[0071] Among them, P c1 P c2 and P c3 These are the initial crossover rates, P, for the three stages. m1 P m2 and P m3 These represent the initial mutation rates for the three stages. The total number of iterations is gen, and parameters β1 and β2 are defined. The number of iterations for each stage is calculated as follows:

[0072] gen1 = gen × β1

[0073] gen2 = gen × β2

[0074] gen3 = gen - (gen1 + gen2)

[0075] Step 8: Merge the parent population Pop and the offspring population OPop, and use an elite selection strategy to generate a new population Pop; merge the parent population Pop and the offspring population OPop to generate a merged population IPop of size 2Sc; then perform fast non-dominated sorting on the merged population IPop and calculate the crowding distance at each level; finally, use an elite selection strategy to select Sc individuals from the merged population IPop to form a new population Pop.

[0076] Step 9: Iterate and solve the problem. Determine if the termination condition is met. If not, return to step 5 and continue execution. If the condition is met, output the population Pop. Combine the decoding method from step 2 to decode and obtain the emergency resource scheduling result.

[0077] It also includes step 10: Based on the emergency resource scheduling results obtained in step 9, scheduling guidance is provided for emergency resources with time windows and priorities to improve the efficiency and reliability of emergency resource scheduling and solve practical engineering problems.

[0078] Beneficial effects:

[0079] 1. This invention discloses an emergency resource scheduling optimization method. Based on the characteristic of the emergency resource scheduling problem as a multidimensional discrete problem, it uses accident point numbers arranged according to a population initialization method to form the encoding of individual populations. Combined with the constraints of emergency resource scheduling, the population individuals are decoded to obtain each sub-path scheme of emergency resource scheduling. This natural number encoding and decoding method, as the input and output of the optimization method, conforms to the background of emergency resource scheduling and can simply and effectively transform the emergency resource scheduling problem into a problem that the optimization method can handle.

[0080] 2. The emergency resource scheduling optimization method disclosed in this invention initializes the population using specific rule methods of nearest neighbor rules and time rules according to the optimization objective. This can generate some better individuals that fit the objective during initialization. Furthermore, by combining specific rule methods with random methods, the diversity of the population is ensured, and the search space of the optimization method is expanded, which is more conducive to solving a reasonable and feasible emergency resource scheduling scheme.

[0081] 3. This invention discloses an emergency resource scheduling optimization method. An individual in the population represents a solution composed of multiple sub-paths. A global mutation operator randomly swaps genes in different sub-paths, while a local mutation operator randomly swaps genes in the same sub-path. Through global and local mutation operators, the diversity of the population during evolution can be maintained, preventing the optimization method from getting trapped in local optima during the search process. This facilitates the search for the optimal solution for emergency resource scheduling and improves the convergence of the optimization method.

[0082] 4. The emergency resource scheduling optimization method disclosed in this invention divides the population evolution process into three stages and adopts an adaptive parameter adjustment strategy. By adjusting the crossover rate and mutation rate parameters as the number of iterations increases according to the adaptive strategy, each stage has a crossover rate and mutation rate that are more in line with the evolutionary characteristics. This enables the optimization method to adjust its global search capability and local search capability during the evolution process, thereby improving the search efficiency and convergence of the optimization method, reducing the computation time of the emergency resource scheduling problem, and improving the solution results. Attached Figure Description

[0083] Figure 1 This is a flowchart of an emergency resource scheduling optimization method disclosed in this invention;

[0084] Figure 2 A schematic diagram illustrating the encoding and decoding methods for emergency resource allocation issues;

[0085] Figure 3 A schematic diagram of the global mutation operator for improving the mutation method;

[0086] Figure 4 A schematic diagram of a local mutation operator for improving mutation methods;

[0087] Figure 5 The Pareto optimal frontier obtained by solving the emergency resource scheduling optimization method;

[0088] Figure 6 This is a schematic diagram of the supply path obtained by selecting an optimal solution. Detailed Implementation

[0089] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0090] There is a warehouse at coordinates [40, 50]. The warehouse has 10 transport vehicles, each with a load capacity of 100, and 25 accident points. Transport vehicles perform non-unidirectional resupply with a return route; that is, they depart from the warehouse, resupply multiple accident points at a time, and return to the warehouse once all accident points along that sub-path have been resupplyed. During resupply, the unit transport cost for each vehicle is 15, and the travel speed is 60 km / h. Accident points have time windows and priority constraints on supplies, with five priority levels; the higher the level, the more severe the accident. Examples of some accident point information are shown below:

[0091] Table 1 Information on Partial Accident Locations

[0092] serial number coordinates X / km coordinates Y / km Demand Time window Priority 1 45 68 10 [912,967] 1 2 45 70 30 [825,870] 1 3 42 66 10 [65,146] 5 4 42 68 10 [727,782] 2 5 42 65 10 [15,67] 5 6 40 69 20 [621,702] 2 7 40 66 20 [170,225] 4 8 38 68 20 [255,324] 4 9 38 70 10 [534,605] 2 10 35 66 10 [357,410] 3

[0093] An emergency resource scheduling optimization method disclosed in this embodiment is used for emergency resource scheduling, such as... Figure 1 As shown, it includes the following steps:

[0094] Step 1: Construct a multi-objective constrained emergency resource scheduling model;

[0095] Step 1.1: Establish the objective function of the multi-objective constrained emergency resource scheduling model;

[0096] The objective function of the emergency resource scheduling model consists of minimizing the timeout penalty F1 and minimizing the transportation cost F2.

[0097]

[0098]

[0099] The variables involved in the objective function are defined as follows:

[0100] N—Number of transport vehicles in the warehouse;

[0101] M—Number of accident sites;

[0102] c—Unit transportation cost of the means of transport;

[0103] x kij —Decision variable, x kij =1 indicates that the transport vehicle k needs to be resupplyed from accident point i to accident point j; otherwise, it is 0.

[0104] x ksi —Decision variable, x ksi =1 indicates that the means of transport k departs from warehouse s and arrives at the accident point i; otherwise, it is 0.

[0105] x kjs —Decision variable, x kjs =1 indicates that the means of transport k returns to the warehouse s from the accident point j; otherwise, it is 0.

[0106] d ij —The Euclidean distance from accident point i to accident point j;

[0107] d si —The Euclidean distance from warehouse s to accident point i;

[0108] d js —The Euclidean distance from accident point j to warehouse s.

[0109] Timeout penalty tl ki As shown below:

[0110]

[0111] Where, p i The priority of materials at accident point i is defined by the time window. t ki This represents the actual time it takes for transport vehicle k to arrive at accident point i. The time penalty takes into account the impact of priority; the higher the priority, the greater the impact of the timeout penalty on the target, and vice versa.

[0112] The actual time t for vehicle k to reach accident point i ki for:

[0113]

[0114] Among them, t kj This refers to the actual time when transport vehicle k arrives at accident point j, which is the start time of transport vehicle k's service at the previous accident point j. t represents the lower limit of the time window at accident point j. kji The travel time from accident point j to accident point i is denoted as .

[0115] The travel time t of vehicle k from accident point j to accident point i kji As shown below:

[0116]

[0117] Where, d ji Let be the Euclidean distance from accident point j to accident point i. The speed of the transport vehicle.

[0118] Step 1.2: Set the constraints for the multi-objective constrained emergency resource scheduling model;

[0119] (1) Closed-loop constraint: the transportation vehicle departs from the warehouse and needs to return to the warehouse;

[0120]

[0121] (2) Emergency point resupply constraint: each emergency point is resupplyed only once;

[0122]

[0123] (3) Constraints on the number of transport vehicles: the number of departing transport vehicles cannot exceed the total number of transport vehicles in the warehouse;

[0124]

[0125] (4) The load capacity constraint of the transport vehicle, that is, the total supply of a sub-route shall not exceed the load capacity W of the transport vehicle;

[0126]

[0127] (5) Value constraints of decision variables.

[0128]

[0129]

[0130] The variables involved in the model constraints are defined as follows:

[0131] N—Number of transport vehicles in the warehouse;

[0132] M—Number of accident sites;

[0133] x ksi —Decision variable, x ksi =1 indicates that the means of transport k departs from warehouse s and arrives at the accident point i; otherwise, it is 0.

[0134] x kjs —Decision variable, x kjs =1 indicates that the means of transport k returns to the warehouse s from the accident point j; otherwise, it is 0.

[0135] x kij —Decision variable, x kij =1 indicates that the transport vehicle k needs to be resupplyed from accident point i to accident point j; otherwise, it is 0.

[0136] y ki —Decision variable, y ki =1 indicates that the means of transport k needs to supply the accident point i; otherwise, it is 0.

[0137] D i —The amount of supplies needed at accident site i;

[0138] W—The load capacity of the transport vehicle.

[0139] Step 2: Construct the natural number encoding and decoding method for the emergency resource scheduling optimization method; since emergency resource scheduling is a multidimensional discrete problem, a natural number encoding method is adopted, such as... Figure 2 As shown. During encoding, M accident points are encoded into a sequence, serving as an individual in the population of the optimization method. During decoding, the sequence is divided into n sub-paths based on constraints such as the number and capacity of transport vehicles. Sub-path 1 refers to transport vehicle 1 starting from the warehouse, passing through accident points 4, 10, and 6, and returning to the warehouse. Sub-path 2 refers to transport vehicle 2 starting from the warehouse, passing through accident points 7, 5, and 8, and returning to the warehouse. Sub-path n refers to transport vehicle n starting from the warehouse, passing through several accident points, and returning to the warehouse.

[0140] Step 3: Obtain relevant data on emergency resource scheduling and set optimization method parameters. When optimizing emergency resource scheduling, it is first necessary to obtain relevant data on the emergency resource scheduling problem based on Step 1. This mainly includes the locations of warehouses and accident sites, the number and carrying capacity of transportation vehicles, the demand at accident sites, and the time windows and priorities of accident sites. Then, set the relevant parameters for the optimization method. Since the optimization method of this invention is based on the NSGA-II algorithm, the parameters include population size Sc = 300, number of iterations gen = 100, and initial crossover rate P. c1 =0.9, P c2 =0.7, P c3 =0.5, initial mutation rate P m1 =0.1, P m2 =0.05, P m3 =0.01, parameters β1=0.3, β2=0.7.

[0141] Step 4: Initialize the population Pop based on a random method and specific rules. This embodiment is based on the NSGA-II algorithm, so it is necessary to initialize the population as input for the optimization method. First, a portion of the population is initialized using a random method. Then, a specific rule method is introduced to initialize another portion of the population based on the objective function. The population initialized by the specific rule method contains some better solutions, which can expand the search space of the algorithm. Finally, the two are combined to form a population Pop of size Sc.

[0142] In the specific rule initialization method, it mainly focuses on a specific objective function of the model, selectively initializing individuals that fit the objective function. In the emergency resource scheduling problem, the objective function is often to minimize time and distance; therefore, nearest neighbor rules and time rules are designed. The nearest neighbor rule generates individuals based on the shortest distance between points. First, an initial accident point is randomly selected; then, the accident point closest to the previous accident point is selected as the next point to be served; and so on, generating the initial population of individuals according to the encoding method in step 2. The time rules include start supply time, average supply time, and end supply time. The start supply time, average supply time, and end supply time of the accident points are arranged in ascending order to generate the population of individuals.

[0143] Step 5: Based on the multi-objective constrained emergency resource scheduling model established in Step 1, calculate the objective function value of the population; after initializing the population, based on the multi-objective emergency resource scheduling model established in Step 1.1, calculate the objective function value of the population Pop, taking into account the influence of the constraints described in Step 1.2 on the solution of the objective function during the calculation.

[0144] Step 6: Perform fast non-dominated sorting and crowding distance calculation on the population Pop; The emergency resource scheduling problem is a multi-objective model. This invention is based on the NSGA-II multi-objective optimization method. During the optimization process, based on the obtained objective function value, the population Pop is fast non-dominated sorted to reduce computational complexity, and the crowding distance of each level is calculated so that individuals can expand to the entire Pareto domain and be evenly distributed, thus maintaining the diversity of the population.

[0145] Step 7: Select, crossover, and perform improved mutation operations on the population Pop to generate the offspring population OPop. Based on the results of fast non-dominated sorting and crowding distance calculation, select, crossover, and perform improved mutation operations on the population Pop to ensure the diversity of the population during the evolutionary process, generating an offspring population OPop of size Sc. In this process, an adaptive parameter adjustment strategy is adopted to dynamically change the crossover rate and mutation rate to meet the requirements of different stages of evolution for global and local search capabilities, thereby improving the search efficiency of the optimization method.

[0146] Step 7.1: In this embodiment, an improved mutation method combining global and local mutation operators is employed. Traditional mutations are random and cannot adequately guarantee diversity during population evolution. Based on the encoding method of this invention, the population contains multiple sub-paths, and an improved mutation operator is used, including global and local mutation operators. The global mutation operator refers to randomly exchanging genes on different sub-paths, see [link to relevant documentation]. Figure 3 Before mutation, 1-2-3-4 is one sub-path, and 5-6-7-8 is another. The accident points 2 and 6 in these two sub-paths are swapped to achieve mutation between the sub-paths. The local mutation operator refers to randomly swapping two genes on the same sub-path. See [link to relevant documentation]. Figure 4 1-2-3-4 is a sub-path. The order of accident points 2 and 3 in the sub-path is swapped to achieve mutation within the sub-path.

[0147] Step 7.2: Construct an adaptive parameter adjustment strategy to dynamically change the crossover rate and mutation rate of the optimization method; the traditional values ​​of crossover rate and mutation rate mostly depend on subjective experience, which can easily ignore the characteristics of the population during the evolution process.

[0148] In swarm intelligence optimization methods, the algorithm achieves global and local balanced search capabilities through cooperation and competition between crossover and mutation. Therefore, based on the changing characteristics of global and local search capabilities at different evolutionary stages, an adaptive parameter adjustment strategy is adopted to dynamically change the crossover and mutation rates during the iteration process. The population evolution process is divided into three stages: In the early stage, excellent solutions are far from the Pareto optimal front; to ensure population participation and improve global search capabilities, a larger crossover and mutation rate is used, gradually decreasing. In the middle stage, it is necessary to balance global and local search capabilities, improving search speed while avoiding getting trapped in local optima; therefore, a fixed crossover and mutation rate is used. In the late stage, approaching the neighborhood of the optimal solution, the local search capability of the mutation operator can accelerate convergence to the optimal solution, but the crossover and mutation rates should be small and decreasing; otherwise, the population structure may be disrupted. Therefore, a decreasing crossover and mutation probability is adopted.

[0149] The adjustment formulas for crossover rate and mutation rate are as follows, using a piecewise function form: the parameter values ​​decrease in the first stage, remain unchanged in the second stage, and decrease again in the third stage.

[0150]

[0151]

[0152] Among them, P c1 P c2 and P c3 These are the initial crossover rates, P, for the three stages. m1 P m2 and P m3 These represent the initial mutation rates for the three stages. The total number of iterations is gen, and parameters β1 and β2 are defined. The number of iterations for each stage is calculated as follows:

[0153] gen1 = gen × β1

[0154] gen2 = gen × β2

[0155] gen3 = gen - (gen1 + gen2)

[0156] Step 8: Merge the parent population Pop and the offspring population OPop, and use an elite selection strategy to generate a new population Pop. In a specific embodiment, merge the parent population Pop and the offspring population OPop to generate a merged population IPop of size 2Sc. Then, perform fast non-dominated sorting on the merged population IPop and calculate the crowding distance at each level. Finally, use an elite selection strategy to select Sc individuals from the merged population IPop to form a new population Pop.

[0157] Step 9: Iterate and solve the problem. Determine if the termination condition is met. If not, return to step 5 and continue execution. If the condition is met, output the population Pop. Combine the decoding method from step 2 to decode and obtain the emergency resource scheduling result.

[0158] It also includes step 10: Based on the emergency resource scheduling results obtained in step 9, it can provide guidance for emergency resource scheduling with time windows and priorities, improve the efficiency and reliability of emergency resource scheduling, and solve practical engineering problems.

[0159] In solving the emergency resource scheduling problem, the computation time of the emergency resource scheduling optimization method disclosed in this invention is 10.43s, while the computation time of the traditional NSGA-II optimization method is 12.50s. The Pareto fronts obtained by the two methods are as follows: Figure 5 As shown, compared with the traditional NSGA-II optimization method, the emergency resource scheduling optimization method proposed in this invention has higher computational efficiency and better convergence, which can improve the efficiency and reliability of emergency resource scheduling.

[0160] Since this is a multi-objective optimization problem, multiple optimal solutions are obtained through optimization. One of these optimal solutions is selected for explanation. The planned supply routes are shown in Table 2. As can be seen, there are a total of 6 sub-paths. Each sub-path starts from warehouse 1, passes through several accident points, and returns to the warehouse when the transport vehicle's carrying capacity is insufficient to supply the next accident point. Verification shows that each sub-path satisfies the model's constraints.

[0161] Table 2 Example of scheduling results

[0162] serial number Specific path 1 1→6→4→8→5→3→2→1 2 1→9→7→10→12→11→24→22→1 3 1→21→25→26→23→1 4 1→14→18→19→20→1 5 1→16→17→15→1 6 1→13→1

[0163] Figure 6 This is a schematic diagram of the supply results, in which the pentagram represents the warehouse and the circle represents the accident point. Through the schematic diagram, one can have an intuitive and clear understanding of the results obtained by solving the emergency resource scheduling method disclosed in this invention.

[0164] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is merely a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An emergency resource scheduling optimization method, characterized in that: Includes the following steps, Step 1: Construct a multi-objective, constrained emergency resource scheduling model; Step 2: Construct the natural number encoding and decoding method for the emergency resource scheduling optimization method; The implementation method for step 2 is as follows: Since emergency resource allocation is a multidimensional discrete problem, a natural number encoding method is adopted; the warehouse has There are [number] vehicles and [number] accident sites. Numbering the accident sites, the population length can be obtained based on the population initialization method. The encoded sequence represents a solution; according to the constraints, the encoded sequence of accident points is decoded to generate multiple sub-paths; for each sub-path, the transport vehicle departs from the warehouse, and returns to the warehouse after all accident points in the sub-path have been resupplied. Step 3: Obtain relevant data on emergency resource scheduling and set optimization method parameters; Step 4: Initialize the population based on random methods and specific rules ; Step 5: Based on the multi-objective constrained emergency resource scheduling model established in Step 1, calculate the objective function value of the population; after initializing the population, calculate the population objective function value based on the multi-objective emergency resource scheduling model established in Step 1. The objective function value is calculated while taking into account the influence of the constraints described in step 1 on the solution of the objective function. Step 6: Population Fast non-dominated sorting and crowding distance calculation are performed; the emergency resource scheduling problem is a multi-objective model, based on the NSGA-II multi-objective optimization method. During the optimization process, the population is optimized based on the obtained objective function value. We perform a fast non-dominated sort to reduce computational complexity and calculate the crowding distance at each level, enabling individuals to expand across the entire Pareto domain and be evenly distributed, thus maintaining population diversity. Step 7: Population Select, crossover, and improved mutation operations are performed to generate offspring populations. Based on the results of fast non-dominated sorting and crowding distance calculation, the population is analyzed. Selection, crossover, and improved mutation operations are performed to ensure the diversity of the population during the evolutionary process, generating a population of a certain size. offspring population In this process, an adaptive parameter adjustment strategy is adopted to dynamically change the crossover rate and mutation rate to meet the requirements of different stages of evolution for global and local search capabilities, thereby improving the search efficiency of the optimization method. Step 8: Merge parent populations and offspring population A new population is generated by employing an elite selection strategy. ; Merging parent populations and offspring population The generated scale is Merged population Then merge the populations. A fast non-dominated sorting process is performed, and the crowding distance at each level is calculated. Finally, an elite selection strategy is employed to merge populations. Select Individuals form a new population. ; Step 9: Iterate through the solution and determine if the termination condition is met. If not, return to step 5 and continue execution. If the condition is met, output the population. Combining the decoding method in step 2, the emergency resource scheduling result is obtained through decoding.

2. The emergency resource scheduling optimization method as described in claim 1, characterized in that: It also includes step 10, which, based on the emergency resource scheduling results obtained in step 9, provides scheduling guidance for emergency resources with time windows and priorities, thereby improving the efficiency and reliability of emergency resource scheduling and solving practical engineering problems.

3. An emergency resource scheduling optimization method as described in claim 1 or 2, characterized in that: The implementation method for step 1 is as follows: The transportation vehicle conducts non-unidirectional resupply with return routes, that is, it departs from the warehouse, resupplyes multiple accident points at once, and returns to the warehouse after all accident points on the sub-path have been resupplyed; during the resupply process, the accident points have time windows and priority constraints on the materials. Step 1.1: Establish the objective function of the multi-objective constrained emergency resource scheduling model; The objective function of the emergency resource scheduling model is to minimize the timeout penalty. and minimize transportation costs composition; , The variables involved in the objective function are defined as follows: —Number of transport vehicles in the warehouse; — Number of accident points; —Unit transportation cost of the means of transport; —Decision variables, Means of transport It is necessary to start from the accident site to the accident site Replenish supplies if necessary, otherwise return 0. —Decision variables, Means of transport From warehouse Departure to the accident site Otherwise, it is 0; —Decision variables, Means of transport From the accident site Return to warehouse Otherwise, it is 0; —Accident point to the accident site Euclidean distance; -storehouse to the accident site Euclidean distance; —Accident point To the warehouse Euclidean distance; Timeout penalty As shown below: in, Accident point Prioritization of supplies, with a time window of [timeframe missing]. , Means of transport Arrival at the accident site The actual time; the impact of priority is taken into account in the time penalty. The higher the priority, the greater the impact of the timeout penalty on the target, and vice versa. transportation Arrival at the accident site The actual time of the point for: in, For transportation Arrival at the accident site The actual time, i.e., the means of transport At the previous accident site The start time of service, Indicates the accident point The lower limit of the time window, Accident point to the accident site Travel time; transportation From the accident site to the accident site travel time As shown below: in, Accident point to the accident site Euclidean distance, The speed of the transport vehicle; Step 1.2: Set the constraints for the multi-objective constrained emergency resource scheduling model; (1) Closed-loop constraint: the transport vehicle departs from the warehouse and needs to return to the warehouse; (2) Supply constraint at accident sites: each accident site is supplied only once; ； (3) Constraints on the number of means of transport: the number of means of transport departing shall not exceed the total number of means of transport in the warehouse; ； (4) Load capacity constraint of transport vehicles, that is, the total supply volume of a sub-route shall not exceed the load capacity of the transport vehicles. ; ； (5) Value constraints on decision variables; ， ； The variables involved in the model constraints are defined as follows: —Decision variables, Means of transport The accident site needs to be given. Replenish supplies if necessary, otherwise return 0. —Accident point Demand for supplies; —The load capacity of the transport vehicle.

4. The emergency resource scheduling optimization method as described in claim 3, characterized in that: The implementation method for step 3 is as follows: When optimizing emergency resource scheduling, it is first necessary to obtain relevant data on the emergency resource scheduling problem, including the locations of warehouses and accident sites, the number and carrying capacity of transportation vehicles, the demand at accident sites, and the time windows and priorities of accident sites; then, the parameters in the optimization method are set, including the population size of the NSGA-II algorithm. Number of iterations Initial cross rate and variability .

5. The emergency resource scheduling optimization method as described in claim 4, characterized in that: The implementation method for step 4 is as follows: A portion of the population is initialized using a random method, and then a further portion is initialized based on a specific rule-based method according to the objective function. The population initialized using the specific rule-based method contains some better solutions, which expands the search space of the algorithm. Finally, the two methods are combined to form a population of size [size missing]. population ; In the specific rule initialization method, it focuses on a certain objective function of the model and initializes some individuals that fit the objective function in a targeted manner; In emergency resource allocation problems, the objective function is often to minimize time and distance, so the nearest neighbor rule and the time rule are adopted. The nearest neighbor rule generates individuals based on the closest distance between points. First, an initial incident point is randomly selected. Then, the incident point closest to the previous incident point is selected as the next point to be served. This process is repeated to generate the initial population of individuals according to the encoding method in step 2. The time rules include the start time of resupply, the average time of resupply, and the end time of resupply. The start time, average time, and end time of resupply at the accident site are arranged in ascending order to generate population individuals.

6. The emergency resource scheduling optimization method as described in claim 5, characterized in that: The implementation method for step 7 is as follows: Step 7.1: An improved mutation method combining global and local mutation operators is adopted; Based on the encoding method described in step 2, the population contains multiple sub-paths. An improved mutation method combining global mutation operators and local mutation operators is adopted. The global mutation operator refers to randomly exchanging genes on different sub-paths. The local mutation operator refers to randomly exchanging two genes on the same sub-path. Step 7.2: Construct an adaptive parameter adjustment strategy to dynamically change the crossover rate and mutation rate of the optimization method; Traditional crossover and mutation rates are generally determined based on subjective experience, which can easily overlook the characteristics of the population during the evolutionary process. In swarm intelligence optimization methods, the algorithm achieves global and local equilibrium search capabilities through cooperation and competition between crossover and mutation. Based on the changing characteristics of global and local search capabilities during evolutionary stages, an adaptive parameter adjustment strategy is constructed to dynamically change the crossover and mutation rates during the iteration process. The adjustment scheme for the crossover and mutation rates is as follows, using a piecewise function: the parameter values ​​decrease in the first stage, remain unchanged in the second stage, and decrease again in the third stage. , in, , and These are the initial crossover rates for the three stages. , and These are the initial mutation rates for the three stages; the total number of iterations is... Define parameters and The number of iterations in each stage is calculated as follows: ， ， 。

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