A logistics network optimization method, device, medium and equipment based on a fractional-order hybrid grey wolf optimizer algorithm

Abstract

The application discloses a logistics network optimization method and device based on a fractional-order hybrid grey wolf optimizer algorithm, a medium and equipment, and belongs to the technical field of logistics and intelligent optimization. The method comprises the following steps: modeling a logistics environment, generating a logistics network model and a road section feasibility matrix; initializing a fractional-order hybrid grey wolf optimizer algorithm population through a chaotic mapping strategy, generating an initial vehicle path and a warehouse configuration scheme in a double-layer coding mode, and constructing a multi-objective weighted total cost function; performing hybrid fractional-order grey wolf optimizer algorithm iteration updating and stage regulation; terminating the cycle when the number of iterations reaches a threshold value, and outputting an optimized logistics network scheduling scheme. The logistics network optimization method based on the hybrid fractional-order grey wolf optimizer algorithm in the post-epidemic and post-disaster recovery period utilizes the memory characteristics of a fractional-order operator and the probability search ability of an odor matrix, cooperatively optimizes warehouse continuous variables and vehicle path discrete variables, and constructs a hybrid optimization model for a two-stage logistics network.

Description

Technical Field

[0001] This invention relates to a logistics network optimization method, apparatus, medium, and equipment based on a fractional-order hybrid gray wolf optimizer algorithm, belonging to the field of logistics and intelligent optimization technology. Background Technology

[0002] Precise optimization of logistics networks during the post-pandemic and post-disaster recovery period is a core technology for ensuring the basic living needs of disaster-stricken people. However, the logistics network optimization problem inherently involves a mixed optimization challenge of continuous and discrete variables. Traditional gray wolf optimizers, when handling such problems, typically need to convert discrete variables to continuous variables or use simple encoding, which destroys the essential structure of the problem and leads to low search efficiency. Later, fractional calculus and the scent matrix mechanism were added, which can enhance the memory of continuous algorithms and effectively guide the search of discrete variables, respectively, but existing algorithms have not achieved a deep integration of the two. Therefore, how to construct a hybrid optimization method that can efficiently handle both types of variables simultaneously has become a core challenge. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a logistics network optimization method, apparatus, medium and equipment based on the fractional-order hybrid gray wolf optimizer algorithm.

[0004] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution.

[0005] In a first aspect, this invention discloses a logistics network optimization method based on a fractional-order hybrid gray wolf optimizer algorithm, comprising:

[0006] Model the logistics environment of the target area to generate a logistics network model and a route feasibility matrix;

[0007] The fractional-order hybrid gray wolf optimizer algorithm population is initialized by a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, a two-layer coding method is used to generate the initial vehicle route and warehouse configuration scheme. A multi-objective weighted total cost function is constructed based on the initial vehicle route and warehouse configuration scheme.

[0008] Based on the initialized fractional-order hybrid gray wolf optimizer algorithm population and the multi-objective weighted total cost function, the hybrid fractional-order gray wolf optimizer algorithm is iteratively updated and staged, including: based on the multi-objective weighted total cost function, the fractional-order gray wolf optimization algorithm is used to process the warehouse continuous variable, and the odor matrix gray wolf optimization algorithm is used to process the vehicle path discrete variable, to determine the global dominant wolf for this round; based on the global dominant wolf for this round, the parameters of the hybrid fractional-order gray wolf optimizer algorithm are updated through a dual-algorithm collaboration of the dominant wolf communication mechanism and the differential update mechanism.

[0009] The loop terminates when the number of iterations reaches a threshold, and the optimized logistics network scheduling scheme is output.

[0010] Furthermore, the process of modeling the logistics environment of the target area to generate a logistics network model and a route feasibility matrix includes:

[0011] Basic data on the logistics background of the target area are collected through satellite remote sensing monitoring, drone reconnaissance or on-site survey. The basic data includes: coordinates of factory supply points, set of alternative warehouse nodes, set of end customer demand points, material demand of each customer point and average road traffic speed; the target area refers to the area in the post-epidemic or post-disaster recovery period.

[0012] Abnormal data is removed from the basic data to obtain normal data. Based on the normal data, a logistics environment road segment feasibility matrix Z is constructed. ij And the actual transport distance C of the feasible route ij Z ij ∈{0,1},Z ij =1 indicates that the road segment is feasible, Z ij =0 indicates that the road segment is not feasible; based on the actual transport distance C of the feasible road segment. ij Determine the transportation time T ij T ij =C ij / S, where S represents the average speed of vehicles on the roads after the disaster;

[0013] Based on the urgency of the acquired supplies, time window constraint levels are divided, and an early arrival penalty coefficient α is determined. i And the lateness penalty coefficient β i .

[0014] Furthermore, the fractional-order hybrid gray wolf optimizer algorithm population is initialized using a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, a two-layer encoding method is used to generate initial vehicle routes and warehouse configuration schemes. A multi-objective weighted total cost function is constructed based on the initial vehicle routes and warehouse configuration schemes, including:

[0015] Two subpopulations of the fractional-order hybrid gray wolf optimizer algorithm are initialized using chaotic mapping. The two subpopulations consist of two groups of size N. c Fractional order gray wolf optimizer population P c and of size N d Scent matrix gray wolf optimizer population P d , where N c >N d ;

[0016] The logistics network scheme is initialized using a two-level coding method, where the first level of coding is the continuous variable N of warehouse storage quantity. cThe second layer of encoding assigns discrete variables X to the vehicle path. ijk X ijk ∈{0,1};

[0017] Constructing the total cost function for post-pandemic and post-disaster logistics networks:

[0018] ;

[0019] In the formula, min represents taking the minimum value, and C total The total cost of the logistics network after the pandemic and disaster is represented by C1, C2, C3, and C4.

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] In the formula, Assign discrete variables to the vehicle path of the k-th vehicle between the i1-th warehouse and the j2-th customer. Let i be the actual transport distance of the feasible route between the i1th warehouse and the j2th customer. Let i be the transportation time between the i1th warehouse and the j2th customer. Let be the actual transport distance of the feasible road segment between the i2th factory and the j1st warehouse. Let K be the transportation time between the i2th factory and the j1st warehouse; K be the vehicle set, F be the factory set, M be the customer set, and N be the warehouse set; E be the transportation time between the i2th factory and the j1st warehouse. V E represents the cost per use of a vehicle. D E is the cost per unit distance. S E is the cost per unit of time. W V represents the unit construction cost of the warehouse, and V represents the maximum load capacity of the vehicle. Let J be the material transfer volume of the j1th warehouse.

[0025] Set the constraints for the total cost function of the post-pandemic / post-disaster logistics network:

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] In the formula, For customer J2's material requirements, To determine the feasibility of the route between the i1th warehouse and the j2th customer, , Let be a discrete variable representing the vehicle path assignment for the k-th vehicle between the i2-th factory and the j1-th warehouse. To determine the feasibility of the road segment between the i2th factory and the j1st warehouse, .

[0032] Furthermore, based on the multi-objective weighted total cost function, the fractional-order gray wolf optimization algorithm is used to process the continuous variables of the warehouse, and the odor matrix gray wolf optimization algorithm is used to process the discrete variables of the vehicle path, to determine the globally dominant wolf in this round, including:

[0033] Initialize the fractional-order gray wolf optimizer algorithm population and the odor matrix gray wolf optimizer algorithm population, which are used to optimize continuous and discrete variables in the logistics network, respectively.

[0034] The fitness of the population in the fractional-order gray wolf optimizer algorithm is calculated. Higher fitness indicates a better logistics network scheduling scheme. Then, based on the fitness ranking, the gray wolves are classified into three levels, identifying the three best wolves in the population as α, β, and δ wolves. The positions of α, β, and δ wolves are updated using fractional-order memory. Finally, the remaining wolves in the pack update their positions based on the updated positions of α, β, and δ wolves. The fitness calculation includes: in each iteration, calculating the total cost of each individual in the population based on a multi-objective weighted total cost function. Based on the total cost of each individual Calculate fitness , ;

[0035] For the gray wolf optimizer algorithm population, an odor probability matrix M1 is constructed. The matrix elements in M1 are updated according to the path information of the corresponding individuals in the population to obtain the updated odor probability matrix. Except for the top three fitness wolves α, β and δ, the remaining individuals are selected node by node using the roulette wheel selection strategy based on the updated odor probability matrix to construct new candidate solutions. Among them, the path information of α, β and δ wolves are used to update the odor probability matrix and guide their search direction, but they do not participate in the roulette wheel-based path reconstruction process.

[0036] After each iteration of the wolf pack, the fitness of α wolves in the fractional-order gray wolf optimizer algorithm population and the scent matrix gray wolf optimizer algorithm population are compared. The best wolf in both algorithm populations is determined as the globally dominant wolf for this round, with probability p. ex The key solution structure information of the global advantage wolf is injected into individuals with lower fitness rankings in another algorithm population; wherein, the key solution structure information includes decision variables in path node sequences or continuous variable vectors, and the injection method is to replace or embed corresponding variables or path segments.

[0037] Furthermore, the position updates for α wolf, β wolf, and δ wolf using fractional-order memory are expressed as follows:

[0038] ;

[0039] in, and Let be the position vectors of wolf γ in generation t and generation t+1, respectively, and let Dγ be the distance vector between the wolf and the current individual, calculated using the following formula: A1 and C1 are coefficient vectors controlling the search behavior, X t This represents the position vector of the current individual in generation t, where q is the fractional order and L is the memory length. Here, Γ(·) is the historical index variable, and Γ(·) is the gamma function. For the γ wolf in the first The position vector of the generation, where, , .

[0040] Furthermore, the global dominant wolf algorithm based on this round updates the parameters of the hybrid fractional gray wolf optimizer algorithm through a dual-algorithm collaboration of the dominant wolf communication mechanism and the differential update mechanism, including:

[0041] A differential update mechanism is adopted. For individuals with lower fitness ranking in the fractional gray wolf optimizer algorithm population, a guiding term from α wolves in the odor matrix gray wolf optimizer population is introduced during the position update process.

[0042] The guiding term is the difference vector between the continuous space reference vector constructed based on the path solution of the α wolf in the gray wolf optimizer population of the odor matrix and the current individual position vector. It is used to correct the position update direction of the current individual, thereby realizing the mapping and guidance of discrete path optimization information to the continuous variable space.

[0043] When the global optimal solution has not been updated for a consecutive number of times ε t At times <5D, the wolf pack is in the global search phase, ε tThe value of the counter for the number of consecutive updates is given, where D is the problem dimension. The fractional order q of the fractional-order gray wolf optimizer algorithm population is set to a smaller value to enhance the algorithm's global exploration capability.

[0044] When 5D≤ε t When the value is less than 10D, the local fine search phase is entered, the fractional order q of the fractional gray wolf optimizer algorithm population is increased, and the odor matrix of the gray wolf optimizer population is updated by reinforcement learning.

[0045] When ε t When the number of individuals reaches ≥10D, the wolf pack diversity reset phase begins. The current α wolf is retained, and the remaining individuals in both populations are placed in the neighborhood of the current global optimum. The search space is randomly reset;

[0046] The neighborhood Defined as:

[0047] ;

[0048] Reset the region to a neighborhood Supplement The radius r is adaptively determined based on the search space range or population distribution. X Let represent any feasible solution in the solution space. X best This represents the currently found optimal solution.

[0049] Furthermore, the reinforcement learning update of the odor matrix of the gray wolf optimizer population includes:

[0050] In each iteration, based on the path sequences corresponding to α, β, and δ wolves, the transition probabilities of the corresponding path edges in the odor matrix are enhanced, while the probabilities of unselected path edges are decayed. The update method is as follows:

[0051] ;

[0052] in, Let represent the updated transition probability from node i to node j. Let represent the transition probability from node i to node j in generation t. To update the coefficients; After the update, the matrix is ​​normalized row by row so that the sum of the elements in each row is 1.

[0053] Secondly, this invention also discloses a logistics network optimization device based on a fractional-order hybrid gray wolf optimizer algorithm, comprising:

[0054] The modeling module is used to model the logistics environment of the target area and generate a logistics network model and a route feasibility matrix.

[0055] The initialization module is used to initialize the fractional-order hybrid gray wolf optimizer algorithm population through a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, it generates the initial vehicle route and warehouse configuration scheme using a two-layer encoding method. Based on the initial vehicle route and warehouse configuration scheme, it constructs a multi-objective weighted total cost function.

[0056] The update module is used to iteratively update and stage-based control of the hybrid fractional-order gray wolf optimizer algorithm based on the initialized fractional-order hybrid gray wolf optimizer algorithm population and multi-objective weighted total cost function. This includes: using the fractional-order gray wolf optimization algorithm to process continuous variables related to the warehouse and the odor matrix gray wolf optimization algorithm to process discrete variables related to vehicle paths, based on the multi-objective weighted total cost function, to determine the global dominant wolf for the current round; and updating the parameters of the hybrid fractional-order gray wolf optimizer algorithm based on the global dominant wolf for the current round through a dual-algorithm collaborative process using a dominant wolf communication mechanism and a differential update mechanism.

[0057] The output module is used to terminate the loop when the number of iterations reaches a threshold and output the optimized logistics network scheduling scheme.

[0058] Thirdly, the present invention also discloses a computer-readable storage medium storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform the method described in the first aspect.

[0059] Fourthly, the present invention also discloses a computer device, comprising,

[0060] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing the method of the first aspect.

[0061] The beneficial effects achieved by this invention are as follows:

[0062] This invention presents a post-pandemic / disaster recovery logistics network optimization method based on a hybrid fractional-order gray wolf optimizer algorithm. It leverages the memory property of fractional-order operators and the probabilistic search capability of the odor matrix to collaboratively optimize continuous warehouse variables and discrete vehicle path variables, constructing a hybrid optimization model for two-stage logistics networks. Specifically, the memory property of fractional-order operators incorporates historical multi-generational individual information into current position updates, enabling the algorithm to retain effective search trajectories and reduce ineffective oscillations, thereby improving solution stability and convergence efficiency. The probabilistic search mechanism of the odor matrix, through adaptive updates of the transition probabilities between path nodes, continuously strengthens high-quality paths during iteration while retaining a certain degree of randomness to maintain population diversity, thus improving the search capability in the discrete path space. These two mechanisms, through dual-population collaboration and information interaction, achieve joint optimization of continuous and discrete variables, avoiding the problem of insufficient search capability of a single algorithm in different variable spaces. Furthermore, by introducing information sharing of advantageous individuals and a phased search strategy during iteration, the algorithm achieves a dynamic balance between global search and local exploitation, further reducing the risk of getting trapped in local optima. Compared with traditional methods, this invention can effectively reduce the total logistics cost and accelerate the iteration convergence speed while ensuring the solution accuracy. Attached Figure Description

[0063] Figure 1 This is a flowchart of the logistics network optimization method for post-pandemic and post-disaster recovery based on the hybrid fractional gray wolf optimizer algorithm of the present invention;

[0064] Figure 2 This is a schematic diagram illustrating the collaborative optimization principle of the hybrid fractional-order gray wolf optimizer algorithm of this invention.

[0065] Figure 3 This is a schematic diagram of the optimal route setting for the post-epidemic and post-disaster logistics network in an embodiment of the present invention;

[0066] Figure 4 A schematic diagram illustrating the optimal route setting for post-pandemic and post-disaster logistics networks, comparing the DE+GA2 algorithm. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0068] Example 1, as Figure 1 As shown in the figure, this embodiment introduces a logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm, including:

[0069] Model the logistics environment of the target area to generate a logistics network model and a route feasibility matrix;

[0070] The fractional-order hybrid gray wolf optimizer algorithm population is initialized by a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, a two-layer coding method is used to generate the initial vehicle route and warehouse configuration scheme. A multi-objective weighted total cost function is constructed based on the initial vehicle route and warehouse configuration scheme.

[0071] Based on the initialized fractional-order hybrid gray wolf optimizer algorithm population and the multi-objective weighted total cost function, the hybrid fractional-order gray wolf optimizer algorithm is iteratively updated and staged, including: based on the multi-objective weighted total cost function, the fractional-order gray wolf optimization algorithm is used to process the warehouse continuous variable, and the odor matrix gray wolf optimization algorithm is used to process the vehicle path discrete variable, to determine the global dominant wolf for this round; based on the global dominant wolf for this round, the parameters of the hybrid fractional-order gray wolf optimizer algorithm are updated through a dual-algorithm collaboration of the dominant wolf communication mechanism and the differential update mechanism.

[0072] The loop terminates when the number of iterations reaches a threshold, and the optimized logistics network scheduling scheme is output.

[0073] In this embodiment, the step of modeling the logistics environment of the target area and generating a logistics network model and a route feasibility matrix includes:

[0074] Basic data on the logistics background of the target area are collected through satellite remote sensing monitoring, drone reconnaissance or on-site survey. The basic data includes: coordinates of factory supply points, set of alternative warehouse nodes, set of end customer demand points, material demand of each customer point and average road traffic speed; the target area refers to the area in the post-epidemic or post-disaster recovery period.

[0075] Abnormal data is removed from the basic data to obtain normal data. Based on the normal data, a logistics environment road segment feasibility matrix Z is constructed. ij And the actual transport distance C of the feasible route ij Z ij ∈{0,1},Z ij =1 indicates that the road segment is feasible, Z ij =0 indicates that the road segment is not feasible; based on the actual transport distance C of the feasible road segment. ij Determine the transportation time T ij T ij =C ij / S, where S represents the average speed of vehicles on the roads after the disaster;

[0076] Based on the urgency of the acquired supplies, time window constraint levels are divided, and an early arrival penalty coefficient α is determined. i And the lateness penalty coefficient β i .

[0077] In this embodiment, the initialization of the fractional-order hybrid gray wolf optimizer algorithm population through a chaotic mapping strategy, the generation of initial vehicle routes and warehouse configuration schemes using a two-layer encoding method based on the logistics network model and the road segment feasibility matrix, and the construction of a multi-objective weighted total cost function based on the initial vehicle routes and warehouse configuration schemes include:

[0078] Two subpopulations of the fractional-order hybrid gray wolf optimizer algorithm are initialized using chaotic mapping. The two subpopulations consist of two groups of size N. c Fractional order gray wolf optimizer population P c and of size N d Scent matrix gray wolf optimizer population P d , where N c >N d ;

[0079] The logistics network scheme is initialized using a two-level coding method, where the first level of coding is the continuous variable N of warehouse storage quantity. c The second layer of encoding assigns discrete variables X to the vehicle path. ijk X ijk ∈{0,1};

[0080] Constructing the total cost function for post-pandemic and post-disaster logistics networks:

[0081] ;

[0082] In the formula, min represents taking the minimum value, and C total The total cost of the logistics network after the pandemic and disaster is represented by C1, C2, C3, and C4.

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] In the formula, Assign discrete variables to the vehicle path of the k-th vehicle between the i1-th warehouse and the j2-th customer. Let i be the actual transport distance of the feasible route between the i1th warehouse and the j2th customer. Let i be the transportation time between the i1th warehouse and the j2th customer. Let be the actual transport distance of the feasible road segment between the i2th factory and the j1st warehouse. Let K be the transportation time between the i2th factory and the j1st warehouse; K be the vehicle set, F be the factory set, M be the customer set, and N be the warehouse set; E be the transportation time between the i2th factory and the j1st warehouse. V E represents the cost per use of a vehicle. D E is the cost per unit distance. S E is the cost per unit of time. W V represents the unit construction cost of the warehouse, and V represents the maximum load capacity of the vehicle. Let J be the material transfer volume of the j1th warehouse.

[0088] Set the constraints for the total cost function of the post-pandemic / post-disaster logistics network:

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] In the formula, For customer J2's material requirements, To determine the feasibility of the route between the i1th warehouse and the j2th customer, , Let be a discrete variable representing the vehicle path assignment for the k-th vehicle between the i2-th factory and the j1-th warehouse. To determine the feasibility of the road segment between the i2th factory and the j1st warehouse, .

[0095] In this embodiment, the step of determining the globally dominant wolf for the current round based on the multi-objective weighted total cost function, using the fractional gray wolf optimization algorithm to process the continuous variables of the warehouse and the odor matrix gray wolf optimization algorithm to process the discrete variables of the vehicle path, includes:

[0096] Initialize the fractional-order gray wolf optimizer algorithm population and the odor matrix gray wolf optimizer algorithm population, which are used to optimize continuous and discrete variables in the logistics network, respectively.

[0097] The fitness of the population in the fractional-order gray wolf optimizer algorithm is calculated. Higher fitness indicates a better logistics network scheduling scheme. Then, based on the fitness ranking, the gray wolves are classified into three levels, identifying the three best wolves in the population as α, β, and δ wolves. The positions of α, β, and δ wolves are updated using fractional-order memory. Finally, the remaining wolves in the pack update their positions based on the updated positions of α, β, and δ wolves. The fitness calculation includes: in each iteration, calculating the total cost of each individual in the population based on a multi-objective weighted total cost function. Based on the total cost of each individual Calculate fitness , ;

[0098] For the gray wolf optimizer algorithm population, an odor probability matrix M1 is constructed. The matrix elements in M1 are updated according to the path information of the corresponding individuals in the population to obtain the updated odor probability matrix. Except for the top three fitness wolves α, β and δ, the remaining individuals are selected node by node using the roulette wheel selection strategy based on the updated odor probability matrix to construct new candidate solutions. Among them, the path information of α, β and δ wolves are used to update the odor probability matrix and guide their search direction, but they do not participate in the roulette wheel-based path reconstruction process.

[0099] After each iteration of the wolf pack, the fitness of α wolves in the fractional-order gray wolf optimizer algorithm population and the scent matrix gray wolf optimizer algorithm population are compared. The best wolf in both algorithm populations is determined as the globally dominant wolf for this round, with probability p. ex The key solution structure information of the global advantage wolf is injected into individuals with lower fitness rankings in another algorithm population; wherein, the key solution structure information includes decision variables in path node sequences or continuous variable vectors, and the injection method is to replace or embed corresponding variables or path segments.

[0100] In this embodiment, the position update of α wolf, β wolf, and δ wolf using fractional-order memory is expressed as follows:

[0101] ;

[0102] in, and Let be the position vectors of wolf γ in generation t and generation t+1, respectively, and let Dγ be the distance vector between the wolf and the current individual, calculated using the following formula: A1 and C1 are coefficient vectors controlling the search behavior, X t This represents the position vector of the current individual in generation t, where q is the fractional order and L is the memory length. Here, Γ(·) is the historical index variable, and Γ(·) is the gamma function. For the γ wolf in the first The position vector of the generation, where, , .

[0103] In this embodiment, the global dominant wolf algorithm based on the current round updates the parameters of the hybrid fractional gray wolf optimizer algorithm through a dual-algorithm collaboration of the dominant wolf communication mechanism and the differential update mechanism, including:

[0104] A differential update mechanism is adopted. For individuals with lower fitness ranking in the fractional gray wolf optimizer algorithm population, a guiding term from α wolves in the odor matrix gray wolf optimizer population is introduced during the position update process.

[0105] The guiding term is the difference vector between the continuous space reference vector constructed based on the path solution of the α wolf in the gray wolf optimizer population of the odor matrix and the current individual position vector. It is used to correct the position update direction of the current individual, thereby realizing the mapping and guidance of discrete path optimization information to the continuous variable space.

[0106] When the global optimal solution has not been updated for a consecutive number of times ε t At times <5D, the wolf pack is in the global search phase, ε t The value of the counter for the number of consecutive updates is given, where D is the problem dimension. The fractional order q of the fractional-order gray wolf optimizer algorithm population is set to a smaller value to enhance the algorithm's global exploration capability.

[0107] When 5D≤ε t When the value is less than 10D, the local fine search phase is entered, the fractional order q of the fractional gray wolf optimizer algorithm population is increased, and the odor matrix of the gray wolf optimizer population is updated by reinforcement learning.

[0108] When ε t When the number of individuals reaches ≥10D, the wolf pack diversity reset phase begins. The current α wolf is retained, and the remaining individuals in both populations are placed in the neighborhood of the current global optimum. The search space is randomly reset;

[0109] The neighborhood Defined as:

[0110] ;

[0111] Reset the region to a neighborhood Supplement The radius r is adaptively determined based on the search space range or population distribution. X Let represent any feasible solution in the solution space. X best This represents the currently found optimal solution.

[0112] In this embodiment, the reinforcement learning update of the odor matrix of the gray wolf optimizer population includes:

[0113] In each iteration, based on the path sequences corresponding to α, β, and δ wolves, the transition probabilities of the corresponding path edges in the odor matrix are enhanced, while the probabilities of unselected path edges are decayed. The update method is as follows:

[0114] ;

[0115] in, Let represent the updated transition probability from node i to node j. Let represent the transition probability from node i to node j in generation t. To update the coefficients, the matrix is ​​then normalized row by row so that the sum of the elements in each row is 1.

[0116] Example 2, based on the same inventive concept as Example 1, introduces a logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm, specifically implemented according to the following steps:

[0117] Step 1: Model and quantify the logistics environment during the recovery period after a disaster;

[0118] Step 2: Initialize the fractional-order hybrid gray wolf optimizer algorithm and the logistics network, and construct the multi-objective weighted total cost function;

[0119] Step 3: Iterate and adjust the fractional-order hybrid gray wolf optimizer algorithm in stages;

[0120] Step 4: After the termination conditions are met, output the optimal logistics network scheduling scheme and the overall total cost.

[0121] The specific process of step 1 is as follows:

[0122] Step 1.1: Collect basic data on the logistics background during the post-disaster recovery period through satellite remote sensing monitoring, drone reconnaissance or on-site surveys, including the coordinates of factory supply points, the set of alternative warehouse nodes, the set of end customer demand points, the material demand of each customer point, and the average road traffic speed, etc.

[0123] Step 1.2: Remove outlier data and construct a logistics environment road segment feasibility matrix Z based on road damage information. ij ∈{0,1},Z ij =1 indicates that the road segment is feasible, and the actual transport distance C of the feasible road segment is... ij Transportation time T ij =C ij / S;

[0124] Step 1.3: Divide the time window constraint levels according to the urgency of post-disaster material supply, and determine the early arrival penalty coefficient α. i And the lateness penalty coefficient β i .

[0125] The specific process of step 2 is as follows:

[0126] Step 2.1: Initialize two subpopulations of the fractional-order hybrid gray wolf optimizer algorithm using chaotic mapping: fractional-order gray wolf optimizer population P. c Scale N c =60, Scent Matrix, Gray Wolf Optimizer, Population P d Scale N d =40;

[0127] Step 2.2: Initialize the logistics network scheme using a two-layer coding method: The first layer of coding is the continuous variable N of warehouse storage quantity. c The second layer of encoding assigns discrete variables X to the vehicle path. ijk ∈{0,1};

[0128] Step 2.3, construct the total cost function of the post-pandemic / post-disaster logistics network:

[0129] ;

[0130] C1 represents the vehicle usage cost:

[0131] ;

[0132] C2 represents the distance consumption cost:

[0133] ;

[0134] C3 represents time cost:

[0135] ;

[0136] C4 represents the warehouse construction cost:

[0137] ;

[0138] In the above equation, K is the set of vehicles, F is the set of factories, M is the set of customers, N is the set of warehouses, and E is the set of... V E represents the cost per use of a vehicle. D E is the cost per unit distance. S E is the cost per unit of time. W Where V is the unit construction cost of the warehouse, DN is the maximum load capacity of the vehicle, and DN is the maximum load capacity of the vehicle. j Let J be the material transfer volume of warehouse j;

[0139] Step 2.4, Define constraints:

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] .

[0145] The specific process of step 3 is as follows:

[0146] Step 3.1: Initialize the fractional-order gray wolf optimizer population and the odor matrix gray wolf optimizer population, which are used to optimize continuous and discrete variables in the logistics network, respectively.

[0147] Step 3.2: For the fractional-order gray wolf optimizer population, classify the individual gray wolves into ranks based on fitness, determine the α, β, δ wolves and the remaining wolf pack, and update the positions of the α, β, and δ wolves using fractional-order memory.

[0148] ;

[0149] in, A1 and C1 are coefficient vectors, q is the fractional order, K is the memory length, and Γ is the gamma function;

[0150] Step 3.3: Construct an odor probability matrix M for the gray wolf optimizer population, with matrix elements m. ij This matrix represents the transition probability of path node i connecting to node j. Other individuals use this matrix to perform a roulette wheel selection to generate a new solution.

[0151] Step 3.4 introduces a dominant wolf communication mechanism. After each iteration, the fitness of the α wolves in the two populations is compared, and the globally optimal wolf is established as the "dominant wolf" with probability p. ex Inject some of its information into individuals ranked lower in another algorithm population;

[0152] Step 3.5: Using a differential update mechanism, when updating the position of individuals with poor fitness in the fractional gray wolf optimizer population, a guiding term from the α wolf in the odor matrix gray wolf optimizer population is introduced.

[0153] Step 3.6, when the global optimal solution has not been updated for ε consecutive times t At 5D, the wolf pack is in the global search phase;

[0154] Step 3.7, when 5D≤ε tWhen the value is less than 10D, the local fine search phase is entered, the fractional order α of the fractional gray wolf optimizer population is increased, and the odor matrix of the gray wolf optimizer population is updated by reinforcement learning.

[0155] Step 3.8, when ε t When the value is ≥10D, the wolf pack diversity reset phase begins. The current α wolf is retained, and the remaining individuals in the two populations are randomly reset in areas that avoid the current optimal solution.

[0156] In step 4, when the number of function evaluations NFES = D * 1000, the algorithm ends and outputs the optimal logistics network scheduling scheme and the overall total cost.

[0157] Example 3, based on the same inventive concept as other examples, introduces a logistics network optimization method based on a fractional-order hybrid gray wolf optimizer algorithm, including:

[0158] Step 1: Model and quantify the logistics environment during the post-pandemic and post-disaster recovery period.

[0159] In optimizing the logistics network during the post-pandemic and post-disaster recovery period, the first step is to complete the collection of basic logistics environment data. This involves using satellite remote sensing, drone reconnaissance, or on-site surveys to collect fundamental logistics data for the recovery period, including the coordinates of factory supply points, sets of alternative warehouse locations, sets of end-customer demand points, the material demand at each customer point, the extent of road damage after the disaster, and average traffic speed. This data will then form the basis for a comprehensive logistics environment analysis data support system.

[0160] Secondly, the raw data collected is inevitably affected by factors such as sensor fluctuations and limitations of on-site survey conditions, resulting in quality defects and data gaps. Direct use of this data will lead to analytical distortion. Therefore, data optimization processing is necessary to remove outlier data and construct a road segment feasibility matrix Z based on road damage information. ij Z ij =1 indicates that the road segment is feasible, Z ij =0 indicates that the road segment is impassable, and the actual transport distance C of the feasible road segment is calculated simultaneously. ij and transportation time T ij =C ij / S.

[0161] Finally, time window constraint levels were divided according to the urgency of post-disaster material supply, and early arrival penalty coefficients and late arrival penalty coefficients corresponding to each level were determined to provide parameter basis for subsequent cost calculation.

[0162] Step 2: Initialize the hybrid fractional-order gray wolf optimizer algorithm and the logistics network scheme, and generate a multi-objective weighted total cost function.

[0163] First, the two subpopulations of the fractional-order hybrid gray wolf optimizer algorithm are initialized using a chaotic mapping strategy. The population size of the fractional-order gray wolf optimizer is set to 60, and the population size of the scent matrix gray wolf optimizer is set to 40. This method achieves a random distribution of the initial population in the solution space, avoiding premature convergence caused by an overly concentrated initial state.

[0164] Secondly, a two-layer coding method is used to initialize the logistics network scheme. The first layer of coding is the continuous variable N of warehouse storage quantity. C The first layer represents the actual storage capacity of each candidate warehouse; the second layer of encoding assigns discrete variables X to vehicle routes. ijk ∈{0,1}, X ijk =1 indicates that vehicle k is assigned to transport goods from location i to location j.

[0165] Finally, a total cost function for the post-pandemic and post-disaster logistics network is constructed, aiming to minimize the total cost of material allocation within the logistics system. This function comprises four parts: vehicle usage cost C1, distance consumption cost C2, time cost C3, and warehouse construction cost C4. Simultaneously, a series of constraints must be satisfied to ensure the feasibility of the solution: full coverage of customer demand, vehicle transportation task constraints, vehicle load constraints, and route feasibility constraints.

[0166] Step 3: Iterative update and stage control of the mixed fractional-order gray wolf optimizer algorithm.

[0167] The principle of collaborative optimization in this step is as follows: Figure 2 As shown.

[0168] The fractional-order gray wolf optimizer grouping follows the social hierarchy of the gray wolf optimizer, naming the three best individuals in the population as α, β, and δ wolves. During the prey-encircling phase, individuals are updated based on the positions of α, β, and δ wolves. The key difference between this and the traditional gray wolf optimizer lies in the fact that this invention introduces a fractional-order differential operator for updating the positions of α, β, and δ wolves, utilizing past position information for a memory-based smooth search to calculate the current position. This mechanism makes the movement trajectory of the dominant wolves smoother and more memory-based, better adapting to the dynamic changes in the post-disaster logistics environment.

[0169] The odor matrix gray wolf optimizer also follows the social hierarchy of gray wolves, but its core search mechanism is based on the odor probability matrix M1. An odor probability matrix is ​​constructed for the population of the odor matrix gray wolf optimizer algorithm. Where D is the total number of path nodes, and the matrix elements are... This represents the transition probability from path node i to path node j. The odor matrix is ​​updated based on the path information of all individuals in the population. For the nth wolf, if its path contains a connection from node i to node j, the matrix elements are incrementally updated according to the following formula:

[0170] ;

[0171] in, This is a temporary scent matrix, where N is the population size and n is the wolf's index in the fitness ranking. This represents the wolf's fitness value. This represents the current average fitness value of the population.

[0172] For the three alpha wolves with the best fitness in the population ( (Wolf), giving it additional update weight. When When there is a connection from node i to node j in the wolf's path, the matrix elements are strengthened and updated according to the following formula:

[0173] ;

[0174] in, They represent The fitness value of wolves The fitness value is the optimal α wolf.

[0175] A fractional-order memory-based update strategy is introduced to smoothly update the odor matrix, unifying the information of the updated matrix in the current generation with that in the historical generations, resulting in the final odor matrix:

[0176] ;

[0177] in, Let t be the fractional order of memory, and t be the current iteration algebra.

[0178] After completing the construction of the odor probability matrix, except for the top three in fitness... For the individuals other than the wolves, based on the updated scent probability matrix M1, a roulette wheel selection strategy is used to generate path sequences node by node, thereby constructing new candidate solutions. As superior individuals, wolves use their path information to update the scent probability matrix and guide their search direction, rather than participating in the roulette-based path reconstruction process.

[0179] After each iteration, the fitness values ​​of the fractional-order gray wolf optimizer α wolf and the odor matrix gray wolf optimizer α wolf are compared, and the wolf with the better fitness is established as the globally dominant wolf for this round. The communication probability is adaptively adjusted based on the current iteration number, and the local feature information of the dominant wolf is directly injected into the corresponding parts of the lower-ranked individuals in the other algorithm population. For the poorly performing individuals in the fractional-order gray wolf optimizer population (ranked in the bottom 30% of fitness), after they complete the standard fractional-order position update, an additional discrete-guided differential correction term is added. This correction term fine-tunes their current position towards the continuous spatial reference point mapped by the discrete sequence of the odor matrix gray wolf optimizer α wolf.

[0180] Define counter ε t ε is used to record the number of iterations in which the global optimum has not been improved. Its update rule is: if the current optimal solution is better than the historical global optimum, then ε... t Clear to zero; otherwise ε t Add 1. When ε t When the number of paths is less than 5D, the system enters the global wide-area search phase. The fractional-order gray wolf optimizer uses a relatively small fractional-order α=0.3, making the position update of the dominant wolf more dependent on current information, thus highlighting the wolf pack's exploration ability. The scent matrix gray wolf optimizer has a high update rate setting, enabling it to quickly learn various possible path structures.

[0181] When 5D≤ε t When the value is less than 10D, the local fine-grained search phase begins. The fractional-order gray wolf optimizer's fractional-order α is adaptively increased to 0.7 to enhance the utilization of historical information; the scent matrix gray wolf optimizer undergoes reinforcement learning-based updates, focusing on excellent patterns.

[0182] When ε t When the number of individuals reaches ≥10D, the wolf pack diversity reset phase begins. This phase retains the α wolves of the current fractional-order gray wolf optimizer and the scent matrix gray wolf optimizer, while reinitializing the positions or sequences of all other individuals in both populations. After the reset, the counter ε... t Reset to zero.

[0183] Repeat the above update, communication, difference, and adjustment process until the function evaluation count (NFES) reaches the preset maximum value.

[0184] Step 4: Output the optimal logistics network scheduling scheme after the termination conditions are met.

[0185] The algorithm stops iterating when the function evaluation count (NFES) reaches the preset maximum value (NFES = D * 1000). The output is a logistics network scheduling scheme determined by the continuous variables of the final fractional-order gray wolf optimizer α and the discrete variables of the odor matrix gray wolf optimizer α, and the overall total cost C is calculated and output. total .

[0186] The effects of this invention can be specifically illustrated through simulation experiments:

[0187] Experimental conditions:

[0188] All experiments were run on a personal computer configured with an 11th Gen Intel(R) Core(TM) i7-11800H CPU 2.30GHz and 16GB RAM. The software environment was a Matlab R2024a simulation platform running Windows 11.

[0189] Experimental Design:

[0190] Logistics Environment Setup: Six standard MDVRP-DD (Multi-Warehouse Vehicle Routing Problem - Dynamic Demand) test problems were selected as experimental subjects, and the parameter settings are shown in Table 1. In Table 1, the values ​​in the "Customers" column represent the number of customers, the values ​​in the "Warehouses" column represent the maximum number of warehouses, the number of "Transfer Warehouses" is considered the minimum number to meet customer demand to accommodate most algorithms, and the values ​​in the "Vehicles" column represent the maximum number of vehicles available for transportation in each warehouse, i.e., the number of routes that each warehouse can operate. For all problems, the number of vehicles per warehouse is set to 3 to prevent uneven distribution between customers and warehouses during the optimization process.

[0191] Table 1 MDVRP-DD Test Problem Parameters

[0192] Test issues client storehouse vehicle MTPDVRP1 50 2 3 MTPDVRP2 50 2 3 MTPDVRP3 100 3 3 MTPDVRP4 100 3 3 MTPDVRP5 200 5 3 MTPDVRP6 300 7 3

[0193] The cost parameters are set as follows: Vehicle single-use cost E V =200 yuan, unit distance cost E D =5 yuan / km, unit time cost E S =50 yuan / hour, warehouse unit construction cost E W =10000 yuan. The factory location is uniformly set to the origin (0,0).

[0194] Algorithm and Parameter Settings Comparison: Considering various solutions to the hybrid problem, four different comparison algorithms were selected: JAYA algorithm, Differential Evolution algorithm, Firefly algorithm, and Differential Evolution-Genetic Hybrid algorithm. Differential Evolution is a highly representative algorithm among continuous algorithms, while Genetic Algorithms have excellent applications in combinatorial optimization problems such as discrete problems and vehicle routing problems. Therefore, the Differential Evolution-Genetic Hybrid algorithm was adopted for the hybrid optimization problem. In practice, it was found that the Differential Evolution-Genetic Hybrid algorithm requires a high number of convergence iterations. To ensure the reasonableness of the experimental results, a second experiment was conducted, represented in Table 2 as DE+GA2. In this experiment, the number of iterations was increased from 1000 to a value sufficient for the algorithm to converge, specifically set to the number of vehicles multiplied by 1000.

[0195] The total population size for all algorithms is uniformly set to 100. For the specific parameter settings of each algorithm, please refer to Table 2.

[0196] Table 2 Comparison of Algorithm Parameters

[0197] Comparison Algorithm Year of proposal Parameter settings Differential Evolution Algorithm 1997 N=100; F=0.5; CR=0.9 Firefly Algorithm 2005 N=100; α=0.2; β=1.0; γ=1.0 JAYA Algorithm 2016 N=100 Differential Evolution-Genetic Hybrid Algorithm 2005 <![CDATA[N=100; F=0.5; CR=0.8; p c =0.8; p m =0.02]]> Differential Evolution-Genetic Hybrid Algorithm 2 —— <![CDATA[N=100; F=0.5; CR=0.8; p c =0.8; p m =0.02; Iter=number of vehicles×1000]]> Method of the present invention —— <![CDATA[N c =60; N d =40; a 初 =0.3; p ex初 =0.4; K=5]]>

[0198] Each test problem is run independently 11 times, with the mean and standard deviation used as evaluation criteria to measure the accuracy and stability of different models, and the mean ranking of the 11 runs is calculated. The algorithm termination condition is set at 1000 iterations, and for DE+GA2 it is set to the number of vehicles × 1000 iterations to ensure complete convergence.

[0199] Experimental Results and Analysis: Table 3 shows the comparison of optimization results of each algorithm on 6 MDVRP-DD test problems.

[0200] Table 3 Results of Logistics Network Optimization

[0201]

[0202] In Table 3, DE represents Differential Evolutionary Algorithm; JAYA represents JAYA Optimization Algorithm; Firefly represents Firefly Algorithm; DE+GA represents a hybrid algorithm of Differential Evolutionary and Genetic Algorithm; DE+GA 2 represents another improved hybrid strategy of Differential Evolutionary and Genetic Algorithm; HFOGWO represents Hybrid Fractional Gray Wolf Optimization Algorithm. 50C1, 50C2, 100C1, 100C2, etc., represent test problems of different scales and scenarios, where: numbers (such as 50, 100, 200, 300) represent the problem scale (such as the number of nodes or the number of customers); the letter C represents different instance categories under the same scale; C1 and C2 represent different test scenarios or data instances under this scale.

[0203] As shown in Table 3, the HFOGWO algorithm ranked first in all test problems, demonstrating superior optimization performance. Ordinary optimization algorithms are simply unable to effectively handle the MDVRP-DD problem proposed in this paper, while combinatorial optimization methods such as DE+GA can handle simpler problems like 50C1 and 50C2. However, when the number of clients exceeds 100, the difference in optimization results becomes extremely significant. For example, in the 300C problem, the mean of HFOGWO is 1.33e+04, while the mean of DE+GA2 is 2.58e+04. Furthermore, DE+GA2 was tested under the condition of complete convergence, further confirming the excellent performance of HFOGWO in mixed optimization problems.

[0204] Path scheme analysis:

[0205] Figure 3 and Figure 4 Schematic diagrams of the optimal routes generated by HFOGWO and DE+GA2 are given respectively. Figure 3 and Figure 4 In (a), (b), (c), (d), (e), and (f), the yellow dots represent factory locations, uniformly set to the origin (0,0); the orange dots represent transit warehouse locations, which are determined by algorithm optimization, so the locations are different in each image; the hollow circles represent customer locations, which are the same in the same problem; different colors represent different routes for providing services to customers; and gray lines connect factories and warehouses. Figure 3 (a), (b), (c), (d), (e), and (f) in the table correspond to the optimal routes of HFOGWO's post-epidemic and post-disaster logistics network in scenarios of 50C1, 50C2, 100C1, 100C2, 200C, and 300C, respectively. Figure 4 (a), (b), (c), (d), (e), and (f) in the diagram correspond to the optimal routes of the post-epidemic and post-disaster logistics network of DE+GA 2 under scenarios of 50C1, 50C2, 100C1, 100C2, 200C, and 300C, respectively.

[0206] from Figure 3 and Figure 4 As can be seen, in problems 50C1 and 50C2, the performance of the DE+GA2 algorithm is similar to that of the HFOGWO algorithm; both algorithms can connect customers through appropriate paths. However, as the complexity of the problem increases, the routes planned by DE+GA2 gradually become chaotic and unreasonable, only ensuring that vehicles are not overloaded. In contrast, HFOGWO can effectively determine the location of the transit warehouse, rationally plan customer service routes, and allocate vehicle transportation tasks.

[0207] for Figure 3For route planning in problems 100C1 and 100C2, especially for problem 100C2, HFOGWO identified three transit warehouses located between the vertical coordinates 60 and 70. Furthermore, using the horizontal coordinate as a reference, the area was divided into three zones based on the customer's spatial location, ensuring that the transit warehouses could provide customers with more efficient and faster cargo transportation services. In contrast, Figure 4 The optimization results of DE+GA2 on problems 100C1 and 100C2 show a significant performance gap compared to HFOGWO.

[0208] Conclusion: This embodiment verifies the effectiveness and superiority of the method of the present invention through simulation experiments on six standard MDVRP-DD test problems. The experimental results show that the method of the present invention achieves optimal performance on test problems of different scales, with a standard deviation one order of magnitude lower than the comparative algorithm, demonstrating high accuracy and strong robustness.

[0209] Example 4, based on the same inventive concept as other examples, introduces a logistics network optimization device based on a fractional-order hybrid gray wolf optimizer algorithm, comprising:

[0210] The modeling module is used to model the logistics environment of the target area and generate a logistics network model and a route feasibility matrix.

[0211] The initialization module is used to initialize the fractional-order hybrid gray wolf optimizer algorithm population through a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, it generates the initial vehicle route and warehouse configuration scheme using a two-layer encoding method. Based on the initial vehicle route and warehouse configuration scheme, it constructs a multi-objective weighted total cost function.

[0212] The update module is used to iteratively update and stage-based control of the hybrid fractional-order gray wolf optimizer algorithm based on the initialized fractional-order hybrid gray wolf optimizer algorithm population and multi-objective weighted total cost function. This includes: using the fractional-order gray wolf optimization algorithm to process continuous variables related to the warehouse and the odor matrix gray wolf optimization algorithm to process discrete variables related to vehicle paths, based on the multi-objective weighted total cost function, to determine the global dominant wolf for the current round; and updating the parameters of the hybrid fractional-order gray wolf optimizer algorithm based on the global dominant wolf for the current round through a dual-algorithm collaborative process using a dominant wolf communication mechanism and a differential update mechanism.

[0213] The output module is used to terminate the loop when the number of iterations reaches a threshold and output the optimized logistics network scheduling scheme.

[0214] Example 5, based on the same inventive concept as other examples, describes a computer-readable storage medium storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any of the methods described in Example 1.

[0215] Example 6, based on the same inventive concept as other examples, describes a computer device, including,

[0216] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for performing any of the methods described in Embodiment 2.

[0217] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0218] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0219] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0220] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0221] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A logistics network optimization method based on a fractional-order hybrid gray wolf optimizer algorithm, characterized in that, include: Model the logistics environment of the target area to generate a logistics network model and a route feasibility matrix; The fractional-order hybrid gray wolf optimizer algorithm population is initialized by a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, a two-layer coding method is used to generate the initial vehicle route and warehouse configuration scheme. A multi-objective weighted total cost function is constructed based on the initial vehicle route and warehouse configuration scheme. Based on the initialized fractional-order hybrid gray wolf optimizer algorithm population and the multi-objective weighted total cost function, the hybrid fractional-order gray wolf optimizer algorithm is iteratively updated and staged, including: based on the multi-objective weighted total cost function, the fractional-order gray wolf optimization algorithm is used to process the warehouse continuous variable, and the odor matrix gray wolf optimization algorithm is used to process the vehicle path discrete variable, to determine the global dominant wolf for this round; based on the global dominant wolf for this round, the parameters of the hybrid fractional-order gray wolf optimizer algorithm are updated through a dual-algorithm collaboration of the dominant wolf communication mechanism and the differential update mechanism. The loop terminates when the number of iterations reaches a threshold, and the optimized logistics network scheduling scheme is output.

2. The logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm according to claim 1, characterized in that, The process of modeling the logistics environment of the target area to generate a logistics network model and a route feasibility matrix includes: Basic data on the logistics background of the target area are collected through satellite remote sensing monitoring, drone reconnaissance or on-site survey. The basic data includes: coordinates of factory supply points, set of alternative warehouse nodes, set of end customer demand points, material demand of each customer point and average road traffic speed; the target area refers to the area in the post-epidemic or post-disaster recovery period. Abnormal data is removed from the basic data to obtain normal data. Based on the normal data, a logistics environment road segment feasibility matrix Z is constructed. ij And the actual transport distance C of the feasible route ij Z ij ∈{0,1},Z ij =1 indicates that the road segment is feasible, Z ij =0 indicates that the road segment is not feasible; based on the actual transport distance C of the feasible road segment. ij Determine the transportation time T ij T ij =C ij / S, where S represents the average speed of vehicles on the roads after the disaster; Based on the urgency of the acquired supplies, time window constraint levels are divided, and an early arrival penalty coefficient α is determined. i And the lateness penalty coefficient β i .

3. The logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm according to claim 2, characterized in that, The fractional-order hybrid gray wolf optimizer algorithm population is initialized using a chaotic mapping strategy. Based on the logistics network model and road segment feasibility matrix, a two-layer encoding method is used to generate initial vehicle routes and warehouse configuration schemes. A multi-objective weighted total cost function is constructed based on the initial vehicle routes and warehouse configuration schemes, including: Two subpopulations of the fractional-order hybrid gray wolf optimizer algorithm are initialized using chaotic mapping. The two subpopulations consist of two groups of size N. c Fractional order gray wolf optimizer population P c and of size N d Scent matrix gray wolf optimizer population P d , where N c >N d ; The logistics network scheme is initialized using a two-level coding method, where the first level of coding is the continuous variable N of warehouse storage quantity. c The second layer of encoding assigns discrete variables X to the vehicle path. ijk X ijk ∈{0,1}; Constructing the total cost function for post-pandemic and post-disaster logistics networks: ； In the formula, min represents taking the minimum value, and C total The total cost of the logistics network after the pandemic and disaster is represented by C1, C2, C3, and C4. ； ； ； ； In the formula, Assign discrete variables to the vehicle path of the k-th vehicle between the i1-th warehouse and the j2-th customer. Let i be the actual transport distance of the feasible route between the i1th warehouse and the j2th customer. Let i be the transportation time between the i1th warehouse and the j2th customer. Let be the actual transport distance of the feasible road segment between the i2th factory and the j1st warehouse. Let K be the transportation time between the i2th factory and the j1st warehouse; K be the vehicle set, F be the factory set, M be the customer set, and N be the warehouse set; E be the transportation time between the i2th factory and the j1st warehouse. V E represents the cost per use of a vehicle. D E is the cost per unit distance. S E is the cost per unit of time. W V represents the unit construction cost of the warehouse, and V represents the maximum load capacity of the vehicle. Let J be the material transfer volume of the j1th warehouse. Set the constraints for the total cost function of the post-pandemic / post-disaster logistics network: ； ； ； ； ； In the formula, For customer J2's material requirements, To determine the feasibility of the route between the i1th warehouse and the j2th customer, , Let be a discrete variable representing the vehicle path assignment for the k-th vehicle between the i2-th factory and the j1-th warehouse. To determine the feasibility of the road segment between the i2th factory and the j1st warehouse, .

4. The logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm according to claim 1, characterized in that, Based on the multi-objective weighted total cost function, the fractional-order gray wolf optimization algorithm is used to process the continuous variables of the warehouse, and the odor matrix gray wolf optimization algorithm is used to process the discrete variables of the vehicle path, to determine the globally dominant wolf for this round, including: Initialize the fractional-order gray wolf optimizer algorithm population and the odor matrix gray wolf optimizer algorithm population, which are used to optimize continuous and discrete variables in the logistics network, respectively. The fitness of the population in the fractional-order gray wolf optimizer algorithm is calculated. Higher fitness indicates a better logistics network scheduling scheme. Then, based on the fitness ranking, the gray wolves are classified into three levels, identifying the three best wolves in the population as α, β, and δ wolves. The positions of α, β, and δ wolves are updated using fractional-order memory. Finally, the remaining wolves in the pack are updated based on the updated positions of α, β, and δ wolves. The fitness calculation includes: in each iteration, calculating the total cost of each individual in the population based on a multi-objective weighted total cost function. Based on the total cost of each individual Calculate fitness , ; For the gray wolf optimizer algorithm population, an odor probability matrix M1 is constructed. The matrix elements in M1 are updated according to the path information of the corresponding individuals in the population to obtain the updated odor probability matrix. Except for the top three fitness wolves α, β and δ, the remaining individuals are selected node by node using the roulette wheel selection strategy based on the updated odor probability matrix to construct new candidate solutions. Among them, the path information of α, β and δ wolves are used to update the odor probability matrix and guide their search direction, but they do not participate in the roulette wheel-based path reconstruction process. After each iteration of the wolf pack, the fitness of α wolves in the fractional-order gray wolf optimizer algorithm population and the scent matrix gray wolf optimizer algorithm population are compared. The best wolf in both algorithm populations is determined as the globally dominant wolf for this round, with probability p. ex The key solution structure information of the global advantage wolf is injected into individuals with lower fitness rankings in another algorithm population; wherein, the key solution structure information includes decision variables in path node sequences or continuous variable vectors, and the injection method is to replace or embed corresponding variables or path segments.

5. The logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm according to claim 4, characterized in that, The positions of α wolf, β wolf, and δ wolf are updated using fractional-order memory, as follows: ； in, and Let be the position vectors of wolf γ in generation t and generation t+1, respectively, and let Dγ be the distance vector between the wolf and the current individual, calculated using the following formula: A1 and C1 are coefficient vectors controlling the search behavior, X t This represents the position vector of the current individual in generation t, where q is the fractional order and L is the memory length. Here, Γ(·) is the historical index variable, and Γ(·) is the gamma function. For the γ wolf in the first The position vector of the generation, where, , .

6. The logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm according to claim 5, characterized in that, The global dominant wolf algorithm based on this round updates the parameters of the hybrid fractional gray wolf optimizer algorithm through a dual-algorithm collaboration of the dominant wolf communication mechanism and the differential update mechanism, including: A differential update mechanism is adopted. For individuals with lower fitness ranking in the fractional gray wolf optimizer algorithm population, a guiding term from α wolves in the odor matrix gray wolf optimizer population is introduced during the position update process. The guiding term is the difference vector between the continuous spatial reference vector constructed based on the path solution of the α wolf in the gray wolf optimizer population of the odor matrix and the current individual position vector, which is used to correct the position update direction of the current individual; When the global optimal solution has not been updated for a consecutive number of times ε t At times <5D, the wolf pack is in the global search phase, ε t The value of the continuously updated counter is D, where D is the problem dimension; When 5D≤ε t When the value is less than 10D, the local fine search phase is entered, the fractional order q of the fractional gray wolf optimizer algorithm population is increased, and the odor matrix of the gray wolf optimizer population is updated by reinforcement learning. When ε t When the number of individuals reaches ≥10D, the wolf pack diversity reset phase begins. The current α wolf is retained, and the remaining individuals in both populations are placed in the neighborhood of the current global optimum. The search space is randomly reset; The neighborhood Defined as: ； Reset the region to a neighborhood Supplement The radius r is adaptively determined based on the search space range or population distribution. X Let represent any feasible solution in the solution space. X best This represents the currently found optimal solution.

7. The logistics network optimization method based on the fractional-order hybrid gray wolf optimizer algorithm according to claim 6, characterized in that, The reinforcement learning update of the odor matrix of the gray wolf optimizer population includes: In each iteration, based on the path sequences corresponding to α, β, and δ wolves, the transition probabilities of the corresponding path edges in the odor matrix are enhanced, while the probabilities of unselected path edges are decayed. The update method is as follows: ； in, Let represent the updated transition probability from node i to node j. Let represent the transition probability from node i to node j in generation t. To update the coefficients; After the update, the matrix is ​​normalized row by row so that the sum of the elements in each row is 1.

8. A logistics network optimization device based on a fractional-order hybrid gray wolf optimizer algorithm, characterized in that, include: The modeling module is used to model the logistics environment of the target area and generate a logistics network model and a route feasibility matrix. The initialization module is used to initialize the fractional-order hybrid gray wolf optimizer algorithm population through a chaotic mapping strategy. Based on the logistics network model and the road segment feasibility matrix, it generates the initial vehicle route and warehouse configuration scheme using a two-layer encoding method. Based on the initial vehicle route and warehouse configuration scheme, it constructs a multi-objective weighted total cost function. The update module is used to iteratively update and stage-based control of the hybrid fractional-order gray wolf optimizer algorithm based on the initialized fractional-order hybrid gray wolf optimizer algorithm population and multi-objective weighted total cost function. This includes: using the fractional-order gray wolf optimization algorithm to process continuous variables related to the warehouse and the odor matrix gray wolf optimization algorithm to process discrete variables related to vehicle paths, based on the multi-objective weighted total cost function, to determine the global dominant wolf for the current round; and updating the parameters of the hybrid fractional-order gray wolf optimizer algorithm based on the global dominant wolf for the current round through a dual-algorithm collaborative process using a dominant wolf communication mechanism and a differential update mechanism. The output module is used to terminate the loop when the number of iterations reaches a threshold and output the optimized logistics network scheduling scheme.

9. A computer-readable storage medium for storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any of the methods of claims 1 to 7.

10. A computer device, characterized in that, include, One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing the method of any of claims 1 to 7.

Images