Steel coil warehouse-in loading method and system based on differential evolution algorithm

Abstract

The invention discloses a steel coil warehouse-in loading method and system based on a differential evolution algorithm, and belongs to the technical field of warehouse management. Basic information of the steel coils is collected, and a customer concentration ratio model for minimizing the storage range of the steel coils of the same customer is established; establishing a shortest loading and unloading path model based on a loading and unloading path optimization principle; based on the warehouse storage capacity, establishing a maximum loading capacity model; constructing a multi-objective optimization model by combining optimization objectives of customer concentration ratio, loading and unloading path minimization and loading capacity maximization, and setting model constraint conditions; and solving the multi-objective optimization model by using a differential evolution algorithm, and processing a warehousing loading scheme of the steel coil based on population initialization operation, mutation operation, crossover operation and selection operation to obtain an optimal loading result. While the loading safety is guaranteed, the storage space utilization rate is increased, the steel coil storage layout is optimized, and the warehouse-in and warehouse-out operation time and the management cost are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of warehouse management, and particularly to a steel coil inbound loading method and system based on differential evolution algorithm. Background Art

[0002] Steel coils are one of the important raw materials in steel production and are widely used in industries such as construction, automotive, and household appliances. Steel coils need to be stored and managed through warehouses during the production and circulation processes. One of the core tasks of warehouse management is to ensure that the storage locations of steel coils in the warehouse are properly arranged, so as to improve the utilization rate of warehouse space, reduce picking and handling costs, and optimize inventory management efficiency. Especially in the environment of large-scale production and efficient warehousing, how to reasonably plan and optimize the storage location arrangement of steel coils has become a very challenging problem.

[0003] Traditional steel coil storage location generation methods face the following problems when dealing with large-scale, high-dimensional, and complex warehousing scenarios: 1) In traditional warehouse management, the storage location allocation of steel coils often relies on the experience of warehouse administrators and manual adjustment, lacking systematicness and being difficult to cope with the dynamic changes of inventory demands and warehouse layout adjustments. In addition, manual intervention may also lead to uneven storage location allocation, reducing the space utilization efficiency of the warehouse and affecting the time and efficiency of picking. 2) Traditional inventory management methods usually assume that inventory is static, that is, the storage location arrangement and inventory situation do not change drastically. However, in the actual warehousing environment, the inventory quantity, inbound and outbound speed, inventory types, etc. will change over time. Especially during the storage process of steel coils with large weights and diverse shapes, as different types of steel coils are inbound and outbound, the storage location arrangement must be flexible and adjustable to adapt to the fluctuations of inventory and the changes of different storage demands. 4) Low utilization rate of warehouse space: Due to the limitations of traditional methods, there is waste in the utilization rate of many warehouses, especially during the storage process of steel coils. Due to unreasonable storage location allocation, there are often phenomena where some areas are overstocked while other areas are vacant. This inefficient space use not only wastes valuable storage space but also increases the complexity of inventory management. Summary of the Invention

[0004] The purpose of the present invention is to provide a steel coil inbound loading method and system based on differential evolution algorithm to solve the problems raised in the above background art.

[0005] To solve the above technical problems, the present invention provides the following technical solutions:

[0006] A method for loading steel coils into a warehouse based on a differential evolution algorithm, the method comprising the following steps: Step S1: Collect the basic information of the steel coils and establish a customer concentration model that minimizes the storage range of steel coils of the same customer, where the basic information includes the specifications, weights, customer requirements, and warehouse location distribution of the steel coils; Step S2: Based on the principle of optimizing the loading and unloading path, establish a shortest loading and unloading path model to optimize the outbound order of the steel coils and reduce the additional moving distance generated during the handling of the steel coils; Step S3: Based on the storage capacity of the warehouse, establish a maximum loading capacity model to optimize the arrangement of the steel coils in the storage locations and improve the storage density of the steel coils; Step S4: Combine the optimization objectives of customer concentration, shortest loading and unloading path, and maximum loading capacity, construct a multi-objective optimization model, and set the model constraints to ensure the feasibility of the loading plan; Step S5: Use the differential evolution algorithm to solve the multi-objective optimization model, and process the inbound loading plan of the steel coils based on population initialization operation, mutation operation, crossover operation, and selection operation to obtain the optimal loading result.

[0007] As a preferred embodiment of the method for loading steel coils into a warehouse based on a differential evolution algorithm of the present invention, the method for establishing the customer concentration model is specifically as follows:

[0008]

[0009] Among them, F1 represents the objective function value of the customer concentration model (used to measure the concentration degree of the storage range of steel coils of the same customer, and the steel coils of the same customer are stored as concentrated as possible by minimizing F1), and respectively represent the maximum row number and the minimum row number where the steel coils of the kth customer are located, and K represents the total number of customers.

[0010] As a preferred embodiment of the method for loading steel coils into a warehouse based on a differential evolution algorithm of the present invention, the method for establishing the shortest loading and unloading path model is specifically as follows:

[0011]

[0012] Among them, F2 represents the objective function value of the shortest loading and unloading path model, and H cc ' represents the distance between steel coil c and steel coil c′ in the steel coil warehouse. is a variable of [0 - 1], when it means that steel coil c and c′ are consecutive in the outbound order, and the loading and unloading path is optimized by minimizing L to improve the outbound efficiency, and C represents the set of steel coils.

[0013] As a preferred embodiment of the method for loading steel coils into a warehouse based on a differential evolution algorithm of the present invention, the method for establishing the maximum loading capacity model is specifically as follows:

[0014]

[0015] Among them, F3 represents the objective function value of the maximum loading capacity model, r represents the row number, and R max represents the maximum number of rows allowed in the coil storage, t represents the layer number, and T max represents the upper limit of the number of layers of coil stacking, s represents the position number, and S max represents the maximum number of positions that can accommodate coils on each layer, represents whether coil c is placed at the r-th row, t-th layer, and s-th position in the warehouse; if it is 1, it means that coil c is loaded at the (r, t, s) position in the coil storage, otherwise coil c is not loaded at this position. By making the best use of each effective position in the coil storage, the loading quantity of coils is maximized.

[0016] As a preferred solution of the coil storage loading method based on the differential evolution algorithm described in the present invention, the multi-objective optimization model needs to satisfy the single position constraint condition, the storage capacity constraint condition, the coil stacking stability constraint condition, and the layer constraint condition;

[0017] The single position constraint condition means that each coil can only be placed in a unique warehouse position, specifically as follows:

[0018]

[0019] For any coil c, among all the combinations of rows, layers, and positions, only one position is selected for placement, that is, the sum of all variables is less than or equal to 1;

[0020] The storage capacity constraint condition means that each storage location can store at most one coil:

[0021]

[0022] The coil stacking stability constraint condition means that when the coil is stored on the second layer and above, there must be sufficient support below it:

[0023]

[0024] The layer constraint condition means that the number of coils in the upper layer shall not exceed the number of coils in the lower layer:

[0025]

[0026] Among them, represents whether coil c is placed at the r-th row, (t - 1)-th layer, and s-th position in the warehouse, represents whether coil c is placed at the r-th row, (t - 1)-th layer, and (s + 1)-th position in the warehouse.

[0027] As a preferred solution of the steel coil storage loading method based on the differential evolution algorithm described in the present invention, the solution steps of the differential evolution algorithm include:

[0028] When the problem dimension is D and the population size is N, the g-th generation population can be expressed as where represents the i-th individual, and there is The j-th dimension component of the i-th individual in the initial population is obtained as follows:

[0029]

[0030] where, and are the upper and lower limits of the j-th variable, and rand(0,1) is a uniformly distributed random number.

[0031] A new mutation vector (candidate solution) v is generated through the difference between population individuals i . To improve the adaptability of the algorithm, the improved differential evolution algorithm introduces an adaptive strategy based on fitness to dynamically adjust the mutation method. First, a fitness threshold is set, and different mutation strategies are determined according to the difference between the fitness of the current optimal solution and the target fitness.

[0032] When the fitness value is poor: At this time, it is far from the dissociation optimal solution, and a more aggressive mutation strategy should be adopted for extensive search, exploring the solution space, increasing the diversity of the population, and avoiding falling into local optima;

[0033] Randomly select three different individuals for mutation to generate a mutation vector:

[0034]

[0035] where, represents the i-th mutated individual in the g-th generation population, and represent three different individuals randomly selected from the g-th generation population, and F represents the mutation scaling factor;

[0036] When the fitness value is close to the optimum: At this time, the solution is close to the optimal solution, and the mutation amplitude should be reduced, and a more conservative mutation strategy should be adopted for refined search to further improve the quality of the solution.

[0037]

[0038] where, is the optimal individual in the current population, are two different individuals randomly selected from the population

[0039] Generating test individuals through binomial crossover:

[0040]

[0041] wherein, represents the j-th dimensional component of the i-th test individual in the g-th generation population, represents the j-th dimensional component of the i-th mutated individual in the g-th generation population, represents the j-th dimensional component of the i-th individual in the g-th generation population, CR is the crossover probability, and CR ∈ (0, 1), jrand represents the randomly selected dimension, ensuring that at least one dimension comes from the mutated vector;

[0042] Comparing the fitness of the test individual and the current individual, and retaining the better individual:

[0043]

[0044] wherein, represents the i-th individual in the (g + 1)-th generation population, represents the i-th test individual in the g-th generation population, represents the i-th individual in the g-th generation population, and f() represents the fitness function value;

[0045] Repeat the above content until the maximum number of iterations or the convergence condition is reached.

[0046] As a preferred scheme of the steel coil storage loading method based on the differential evolution algorithm described in the present invention, the differential evolution algorithm improves the search efficiency by dynamically adjusting the mutation scaling factor F and the crossover probability CR, specifically as follows:

[0047] F = F min +(F max -F min )·e -t / T

[0048] CR = CR min +(CR max -CR min )·(1 - e -t / T )

[0049] wherein, t represents the current number of iterations, T represents the maximum number of iterations, F min represents the minimum mutation scaling factor, F max represents the maximum mutation scaling factor, CR min and CR max respectively represent the minimum and maximum values of the crossover probability.

[0050] As a preferred solution of the steel coil warehousing loading method based on the differential evolution algorithm according to the present invention, the differential evolution algorithm adopts an adaptive differential evolution strategy, and adjusts the mutation strategy through the change of fitness.

[0051] A steel coil warehousing loading system based on the differential evolution algorithm, the system includes: a steel coil information collection and customer concentration modeling module, which is used to collect the basic information of the steel coil and establish a customer concentration model that minimizes the storage range of steel coils of the same customer. The basic information includes the specifications, weights, customer requirements and warehouse location distribution of the steel coils; a loading and unloading path optimization modeling module, which is used to establish a shortest loading and unloading path model based on the loading and unloading path optimization principle; a warehouse loading capacity optimization modeling module, which is used to establish a maximum loading capacity model based on the warehouse storage capacity; a multi-objective optimization model construction module, which is used to combine the optimization objectives of customer concentration, shortest loading and unloading path, and maximum loading capacity, construct a multi-objective optimization model, and set model constraint conditions; a multi-objective model solving and loading plan optimization module, which is used to solve the multi-objective optimization model by using the differential evolution algorithm, and process the warehousing loading plan of the steel coil based on population initialization operation, mutation operation, crossover operation and selection operation to obtain the optimal loading result.

[0052] Compared with the prior art, the beneficial effects achieved by the present invention are: in the steel coil warehousing loading method and system based on the differential evolution algorithm provided by the present invention, by optimizing the loading method during the warehousing of steel coils, the utilization rate of the warehouse space is improved, the loading and unloading path is reduced, and the warehousing and outbound efficiency is improved. First, collect the basic information of the steel coil, including the steel coil specifications, customer requirements and warehouse location distribution, and establish a customer concentration model that minimizes the storage range of steel coils of the same customer; secondly, based on the optimization principle of the outbound order, construct a shortest loading and unloading path model to reduce the distance and time cost during the handling of steel coils; then, consider the warehouse storage capacity and establish a maximum loading capacity model to improve the storage density of steel coils. Combining the above three objectives, a multi-objective optimization model is constructed and adjusted based on the constraint conditions to ensure the feasibility of the loading plan. Finally, the differential evolution algorithm (DE) is used to solve the optimization model, and through operations such as population initialization, mutation, crossover and selection, the warehousing loading plan of the steel coil is gradually optimized. Compared with the traditional manual scheduling and heuristic algorithms, the method of the present invention improves the utilization rate of the warehousing space, optimizes the storage layout of the steel coil, and reduces the warehousing and outbound operation time and management cost while ensuring the loading safety. Description of the Drawings

[0053] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention.

[0054] Figure 1Flowchart of the storage location allocation method for the steel coil warehouse in the embodiments of the present invention;

[0055] Figure 2 It is the flowchart of the differential evolution algorithm in the embodiments of the present invention. Detailed implementation manners

[0056] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0057] Please refer to Figure 1 , in the first embodiment: A steel coil inbound loading method based on the differential evolution algorithm is provided, and the method includes the following steps:

[0058] Step S1: Collect the basic information of the steel coils and establish a customer concentration model that minimizes the storage range of steel coils of the same customer. The basic information includes the specifications, weights, customer demands, and warehouse storage location distributions of the steel coils.

[0059] The specific method for establishing the customer concentration model is as follows:

[0060]

[0061] Among them, F1 represents the objective function value of the customer concentration model (used to measure the concentration degree of the storage range of steel coils of the same customer, and minimizing F1 realizes the as-concentrated-as-possible storage of steel coils of the same customer), and respectively represent the maximum row number and the minimum row number where the steel coils of the k-th customer are located, and K represents the total number of customers.

[0062] Step S2: Based on the principle of optimizing the handling path, establish a shortest handling path model to optimize the outbound order of the steel coils and reduce the extra moving distance generated during the handling process of the steel coils.

[0063] The specific method for establishing the shortest handling path model is as follows:

[0064]

[0065] Among them, F2 represents the objective function value of the shortest handling path model, and H cc ' represents the distance between the steel coil c and the steel coil c′ in the steel coil warehouse. is a variable of [0-1]. When When it indicates that coils c and c′ are consecutive in the outbound sequence, the loading and unloading path is optimized by minimizing L to improve the outbound efficiency, and C represents the set of coils.

[0066] Step S3: Based on the warehouse storage capacity, establish a maximum loading capacity model to optimize the arrangement of coils in the storage positions and improve the storage density of coils.

[0067] The specific method for establishing the maximum loading capacity model is as follows:

[0068]

[0069] Among them, F3 represents the objective function value of the maximum loading capacity model, r represents the row number, R max represents the maximum number of rows allowed in the coil warehouse, t represents the layer number, T max represents the upper limit of the number of layers for coil stacking, s represents the position number, S max represents the maximum number of positions that can accommodate coils on each layer, indicates whether coil c is placed at the r-th row, t-th layer, and s-th position in the warehouse.

[0070] Step S4: Combine the optimization objectives of customer concentration, shortest loading and unloading path, and maximum loading capacity to construct a multi-objective optimization model and set the model constraint conditions to ensure the feasibility of the loading plan.

[0071] The multi-objective optimization model needs to satisfy the single-position constraint condition, the storage position capacity constraint condition, the coil stacking stability constraint condition, and the layer constraint condition;

[0072] The single-position constraint condition means that each coil can only be placed in a unique warehouse position, and specifically as follows:

[0073]

[0074] For any coil c, among all the combinations of rows, layers, and positions, only one position is selected for placement, that is, the sum of all variables is less than or equal to 1;

[0075] The storage position capacity constraint condition means that each storage position can store at most one coil:

[0076]

[0077] The coil stacking stability constraint condition means that when the coil is stored on the second layer and above, there must be sufficient support below it:

[0078]

[0079] The hierarchical constraint condition indicates that the number of coils in the upper layer shall not exceed the number of coils in the lower layer:

[0080]

[0081] where indicates whether coil c is placed at the s-th position on the (t - 1)-th layer in the r-th row of the warehouse, and

[0082] Step S5: Solve the multi-objective optimization model using the differential evolution algorithm. Based on the population initialization operation, mutation operation, crossover operation, and selection operation, process the inbound loading plan of the coils to obtain the optimal loading result.

[0083] When the problem dimension is D and the population size is N, the g-th generation population can be expressed as where represents the i-th individual, and there is The j-th dimensional component of the i-th individual in the initial population is obtained as follows:

[0084]

[0085] where and are the upper and lower limits of the j-th variable, and rand(0, 1) is a uniformly distributed random number.

[0086] Generate a new mutation vector (candidate solution) v through the difference between population individuals i . To improve the adaptability of the algorithm, the improved differential evolution algorithm introduces an adaptive strategy based on fitness to dynamically adjust the mutation method. First, set a fitness threshold, and determine when to adopt different mutation strategies according to the difference between the fitness of the current optimal solution and the target fitness.

[0087] When the fitness value is poor: At this time, it is far from the dissociation optimal solution, and a more radical mutation strategy should be adopted for extensive search, exploring the solution space, increasing the diversity of the population, and avoiding falling into local optima;

[0088] Randomly select three different individuals for mutation to generate a mutation vector:

[0089]

[0090] where represents the i-th mutated individual in the g-th generation population, and represent three different individuals randomly selected from the g-th generation population, and F represents the mutation scaling factor;

[0091] When the fitness value is close to the optimum: At this time, the solution is close to the optimal solution, and the mutation amplitude should be reduced. A more conservative mutation strategy should be adopted for refined search to further improve the quality of the solution.

[0092]

[0093] Among them, is the optimal individual in the current population, are two different individuals randomly selected from the population

[0094] Generate trial individuals through binomial crossover:

[0095]

[0096] Among them, represents the j-th dimension component of the i-th trial individual in the g-th generation population, represents the j-th dimension component of the i-th mutated individual in the g-th generation population, represents the j-th dimension component of the i-th individual in the g-th generation population, CR is the crossover probability, and CR ∈ (0, 1). jrand represents the randomly selected dimension to ensure that at least one dimension comes from the mutation vector;

[0097] Compare the fitness of the trial individual with the current individual and retain the better individual:

[0098]

[0099] Among them, represents the i-th individual in the (g + 1)-th generation population, represents the i-th trial individual in the g-th generation population, represents the i-th individual in the g-th generation population, and f() represents the fitness function value;

[0100] Repeat the above content until the maximum number of iterations or the convergence condition is reached.

[0101] The differential evolution algorithm improves the search efficiency by dynamically adjusting the mutation scaling factor F and the crossover probability CR, specifically as follows:

[0102] F = F min +(F max -F min )·e -t / T

[0103] CR = CR min +(CR max -CR min )·(1 - e -t / T )

[0104] where \(t\) represents the current iteration number, \(T\) represents the maximum iteration number, \(F\) min represents the minimum mutation scaling factor, \(F\) max represents the maximum mutation scaling factor, \(CR\) min and \(CR\) max represent the minimum and maximum values of the crossover probability, respectively.

[0105] In the process of solving, the differential evolution algorithm adopts an adaptive differential evolution strategy, adjusts the mutation strategy through the change of fitness, so that the algorithm has stronger global search ability in the initial stage, faster convergence speed in the later stage, and improves the optimization effect.

[0106] This embodiment also provides a coil-inwarehouse loading system based on the differential evolution algorithm. The system includes: a coil information acquisition and customer concentration modeling module, which is used to collect the basic information of the coils and establish a customer concentration model for minimizing the storage range of coils of the same customer. The basic information includes the specifications, weights, customer demands and warehouse location distributions of the coils; a handling path optimization modeling module, which is used to establish a shortest handling path model based on the handling path optimization principle; a warehouse loading capacity optimization modeling module, which is used to establish a maximum loading capacity model based on the warehouse storage capacity; a multi-objective optimization model construction module, which is used to combine the optimization objectives of customer concentration, shortest handling path and maximum loading capacity, construct a multi-objective optimization model, and set the model constraint conditions; a multi-objective model solving and loading plan optimization module, which is used to use the differential evolution algorithm to solve the multi-objective optimization model, and process the coil-inwarehouse loading plan based on population initialization operation, mutation operation, crossover operation and selection operation to obtain the optimal loading result.

[0107] In the second embodiment: A coil-inwarehouse planning method based on the differential evolution algorithm is proposed. In order to facilitate the establishment and solution of the mathematical model in the present invention, based on the actual operation situation among the main bodies of the coil warehouse, the following assumptions are made for the mathematical model:

[0108] The maximum number of rows in the coil warehouse is \(R\) max ;

[0109] The maximum stacking layers in the coil warehouse is \(T\) max ;

[0110] The maximum number of positions in the coil warehouse is \(S\) max ;

[0111] \(C\) represents the set of coils \(c\in C\);

[0112] \(H\) cc ' represents the distance between coil \(c\) and coil \(c'\) in the coil warehouse;

[0113] Indicates whether coil c is next to coil c′ in the outbound order (0-1 variable). If it is 1, it means coils c and c are consecutive in the outbound order; otherwise, it means they are not consecutive.

[0114] Indicates whether coil c is loaded at the rth row, tth layer, sth position. If it is 1, it means coil c is loaded at the (r, t, s) position of the coil warehouse, otherwise coil c is not loaded at this position;

[0115] Step 1: First, obtain a customer list based on the list of steel coils to be loaded, and then count which customers belong to each row of goods in the warehouse. The maximum row number minus the minimum row number of the customer is the customer concentration. This method is used to calculate the customer concentration of each customer in the customer list. Finally, the overall customer concentration in the steel coil warehouse is the sum of the customer concentrations. The customer concentration mathematical model is as follows:

[0116]

[0117] Step 2: Minimize the distance for taking goods out of the warehouse, that is, the time used is the least and the efficiency is the highest. Existing steel enterprises have fixed loading points in the finished steel warehouse. The overhead crane that transports finished steel will start from the loading point and take away the goods in the order of steel coils entering the warehouse. Therefore, after each steel coil is placed in a warehouse, it will generate a distance for picking up goods in its own warehouse. It is only necessary to sum up the distance for picking up goods in each warehouse in the order of the goods entering the warehouse, which is the distance for taking goods out of the warehouse. The shortest loading and unloading path model is as follows:

[0118]

[0119] Step 3: Under the premise of ensuring the safety of all operations in the steel coil warehouse, maximize the storage quantity of steel coils by making full use of every effective position in the steel coil warehouse. The maximum loading capacity model is as follows:

[0120]

[0121] Step 4: Use the actual steel coil warehouse location generation rules (as shown in Table 1) to further constrain the steel coil allocation model:

[0122]

[0123] Table 1 Storage location generation rules

[0124]

[0125]

[0126] Step 5: Solve the models obtained in Steps 1, 2, and 3 through the differential evolution algorithm to obtain the optimal storage location plan.

[0127] As Figure 2 shown, the specific algorithm steps are as follows:

[0128] 51) Population initialization: Initialize N candidate solutions (individuals) as the population, denoted as P = {x1, x2,..., x N}, and each individual represents a candidate solution.

[0129] 52) Mutation operation: Generate a new mutation vector (candidate solution) v i .

[0130] 53) Crossover operation: Combine the mutated individual v i with the individual x i in the current population to generate a trial individual u i .

[0131] 54) Selection operation: Select a better solution between the current solution x i and the trial individual u i as an individual in the next generation population.

[0132] 55) Repeat the above steps 52) to 54) until the maximum number of iterations, and output the optimal solution.

[0133] Step 6: Summarize the following table for the improvement amount of the objective value and the average calculation time of the traditional differential evolution algorithm for the improved differential evolution algorithm.

[0134] Table 2 Statistical Table of Algorithm Comparison Results

[0135]

[0136] Through the result comparison between the traditional DE and the improved DE, the average improvement amount of the improved DE for the objective value is 28.08%, and the average improvement amount of the traditional DE is 19.88%. This shows that when solving problems, the solution quality of the improved DE is better than that of the traditional DE. In terms of the solution time, as the number of steel coils increases, the solution time of the improved DE is also better than that of the traditional DE.

[0137] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variation thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device.

[0138] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent substitution on some of the technical features. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for loading steel coils into a warehouse based on a differential evolution algorithm, characterized in that, The method includes the following steps: Step S1: Collect the basic information of the steel coils and establish a customer concentration model that minimizes the storage range of steel coils of the same customer. The basic information includes the specifications, weights, customer requirements, and warehouse location distribution of the steel coils; Step S2: Based on the principle of optimizing the loading and unloading path, establish a shortest loading and unloading path model; Step S3: Based on the warehouse storage capacity, establish a maximum loading capacity model; Step S4: Combine the optimization objectives of customer concentration, shortest loading and unloading path, and maximum loading capacity to construct a multi-objective optimization model and set the model constraint conditions; Step S5: Use the differential evolution algorithm to solve the multi-objective optimization model. Based on the population initialization operation, mutation operation, crossover operation, and selection operation, process the inbound loading plan of the steel coils to obtain the optimal loading result.

2. The steel coil warehousing loading method based on the differential evolution algorithm according to claim 1, wherein The specific implementation process of step S1 includes: The method for establishing the customer concentration model is as follows: where F1 represents the objective function value of the customer concentration model, and respectively represent the maximum row number and the minimum row number where the steel coil of the k-th customer is located, and K represents the total number of customers.

3. A method for loading steel coils into a warehouse based on the differential evolution algorithm according to claim 1, characterized in that, The specific implementation process of step S2 includes: The method for establishing the shortest loading and unloading path model is as follows: Among them, F2 represents the objective function value of the shortest handling path model, H cc ' represents the distance between coil c and coil c′ in the coil warehouse, is a variable of [0-1]. When is the case, it means that coils c and c′ are consecutive in the outbound order. By minimizing L, the handling path is optimized to improve the outbound efficiency, and C represents the set of coils.

4. A method for loading steel coils into a warehouse based on a differential evolution algorithm according to claim 1, characterized in that, The specific implementation process of step S3 includes: The method for establishing the maximum loading capacity model is as follows: Among them, F3 represents the objective function value of the maximum loading capacity model, r represents the row number, and R max represents the maximum number of rows allowed in the coil library, t represents the layer number, and T max represents the upper limit of the number of layers of coil stacking, s represents the position number, and S max represents the maximum number of positions that can accommodate coils on each layer, indicates whether coil c is placed at the r-th row, t-th layer, and s-th position in the warehouse.

5. A method for loading steel coils into a warehouse based on a differential evolution algorithm according to claim 1, characterized in that, The specific implementation process of step S4 includes: The multi-objective optimization model needs to satisfy the single location constraint condition, warehouse location capacity constraint condition, steel coil stacking stability constraint condition, and hierarchical constraint condition; The single location constraint condition means that each steel coil can only be placed in a unique warehouse location, specifically as follows: For any steel coil c, among all row, layer, and position combinations, only one position is selected for placement, i.e., the sum of all variables is less than or equal to 1; The warehouse location capacity constraint condition means that each warehouse location can store at most one steel coil: The steel coil stacking stability constraint condition means that when the steel coil is stored on the second layer or above, there must be sufficient support below it: The hierarchical constraint condition means that the number of steel coils in the upper layer shall not exceed the number of steel coils in the lower layer: Among them, indicates whether the steel coil c is placed at the s-th position on the (t - 1)-th layer in the r-th row of the warehouse, indicates whether the steel coil c is placed at the (s + 1)-th position on the (t - 1)-th layer in the r-th row of the warehouse.

6. The steel coil storage loading method based on the differential evolution algorithm according to claim 1, characterized in that The specific implementation process of step S5 includes; The solution steps of the differential evolution algorithm include: Set the population size N and initialize the individual solutions; Randomly select three different individuals for mutation to generate a mutation vector: Among them, represents the i-th mutated individual in the g-th generation population, and represent three different individuals randomly selected from the g-th generation population, and F represents the mutation scaling factor; Generate trial individuals through binomial crossover: Among them, represents the j-th dimension component of the i-th test individual in the g-th generation population, represents the j-th dimension component of the i-th mutant individual in the g-th generation population, represents the j-th dimension component of the i-th individual in the g-th generation population, CR is the crossover probability, and jrand represents the randomly selected dimension; Compare the fitness of the trial individuals with the current individuals and retain the better individuals: Among them, represents the i-th individual in the (g + 1)-th generation population, represents the i-th test individual in the g-th generation population, represents the i-th individual in the g-th generation population, and f() represents the fitness function value; Repeat the above until the maximum number of iterations or the convergence condition is reached.

7. A method for loading steel coils into a warehouse based on a differential evolution algorithm according to claim 6, characterized in that, The differential evolution algorithm improves the search efficiency by dynamically adjusting the mutation scaling factor F and the crossover probability CR, specifically as follows: F = F min +(F max -F min )·e -t / T CR = CR min +(CR max -CR min )·(1 - e -t / T ) Among them, t represents the current iteration number, T represents the maximum iteration number, F min represents the minimum mutation scaling factor, F max represents the maximum mutation scaling factor, CR min and CR max represent the minimum and maximum values of the crossover probability, respectively.

8. A method for loading steel coils into a warehouse based on a differential evolution algorithm according to claim 7, characterized in that The differential evolution algorithm adopts an adaptive differential evolution strategy and adjusts the mutation strategy according to the change of fitness.

9. A steel coil warehousing and loading system based on the differential evolution algorithm, which executes a steel coil warehousing and loading method based on the differential evolution algorithm according to any one of claims 1-8, characterized in that, The system includes: A steel coil information collection and customer concentration modeling module, which is used to collect the basic information of the steel coils and establish a customer concentration model that minimizes the storage range of steel coils of the same customer. The basic information includes the specifications, weights, customer requirements, and warehouse location distribution of the steel coils; A loading and unloading path optimization modeling module, which is used to establish a shortest loading and unloading path model based on the principle of optimizing the loading and unloading path; A warehouse loading capacity optimization modeling module, which is used to establish a maximum loading capacity model based on the warehouse storage capacity; A multi-objective optimization model construction module, which is used to combine the optimization objectives of customer concentration, shortest loading and unloading path, and maximum loading capacity to construct a multi-objective optimization model and set the model constraint conditions; The multi-objective model solving and loading scheme optimization module is used to solve the multi-objective optimization model by using the differential evolution algorithm, and process the inbound loading scheme of the steel coils based on population initialization operation, mutation operation, crossover operation and selection operation to obtain the optimal loading result.

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