Steel coil storage location distribution method based on improved whale optimization algorithm

Abstract

The invention discloses a steel coil storage location distribution method based on an improved whale optimization algorithm, and belongs to the technical field of intelligent storage and scheduling. Steel coil attributes, storage location parameters, crown block operation data and historical order data are collected, and an optimization model for reducing steel coil scheduling time is established; the categories of the warehouse steel coils are extracted, and an identity model is established; establishing a model hard constraint condition and a dynamic constraint condition according to an actual storage location, and establishing a multi-target storage location allocation optimization model; and taking an empty storage location as a solution space, carrying out weighting processing on the model according to an analytic hierarchy process, and solving the optimization model through an improved whale optimization algorithm to obtain an optimal allocation scheme. According to the method, the multi-target storage location optimization model is constructed by introducing elements such as multi-dimensional storage location attributes, crown block path time, steel coil turnover weight and the like, the population search capability and the global solution stability are enhanced through the improved whale optimization algorithm, and the distribution efficiency and the scheduling rationality are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent warehousing and scheduling, and particularly to a coil storage location allocation method based on an improved whale optimization algorithm. Background Technique

[0002] In the modern steel logistics management system, coil warehousing, as an important link connecting production and sales, the efficiency of its storage location allocation and the level of intelligence have a key impact on the response speed and operating costs of the entire supply chain. With the continuous increase in steel production and the promotion of customized production, problems such as high coil inbound frequency, fast outbound rhythm, complex categories, and limited space have become increasingly prominent, making it difficult for traditional rule-based or simple heuristic strategy-based storage location allocation methods to meet the requirements of efficient, accurate, and dynamic management. Currently, some studies have attempted to introduce intelligent optimization algorithms (such as genetic algorithms, particle swarm algorithms, ant colony algorithms, etc.) into storage location allocation in order to achieve multi-objective optimization. However, these methods often have problems such as the local optimal trap of the algorithm, slow convergence speed, or insufficient flexibility of the model, and it is difficult to cope with the combined optimization requirements of complex scheduling relationships, multiple constraint conditions, and dynamic environmental variables in actual scenarios.

[0003] The existing technologies mainly have the following deficiencies in the intelligent allocation of coil storage locations: First, there is a lack of comprehensive modeling of the physical characteristics of coils and the storage space structure, making it difficult to effectively coordinate multiple objectives such as coil turnover rate, concentration of similar materials, and storage safety; second, the data patterns of historical orders and the running paths of overhead cranes are not fully considered in the scheduling strategy, resulting in an unreasonable overall scheduling path and increasing scheduling time and energy consumption; third, at the solution level, traditional optimization algorithms are prone to falling into local optima in multi-objective problems with large search spaces and complex constraints, and it is difficult to obtain the global optimal solution; fourth, some existing improved algorithms still do not form a structural optimization mechanism with strong pertinence and sufficient theoretical support, especially in aspects such as population initialization, convergence control, and search strategy, there are problems such as weak generalization and single iteration process. Summary of the Invention

[0004] The purpose of the present invention is to provide a coil storage location allocation method based on an improved whale optimization algorithm to solve the problems raised in the above background technique.

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

[0006] A coil storage location allocation method based on an improved whale optimization algorithm, the method comprising the following steps: Step S1: Collect coil attributes, storage location parameters, crane operation data, and historical order data, aiming to establish an optimization model for reducing coil scheduling time; Step S2: Extract the categories of the coils in the warehouse and establish an identity model to improve the allocation efficiency; Step S3: According to the actual storage locations, establish hard constraints and dynamic constraints for the model, and establish a multi-objective storage location allocation optimization model; Step S4: Use the empty storage locations as the solution space, weight the model according to the analytic hierarchy process, transform the multi-objective problem into a single-objective problem, and solve the optimization model through the improved whale optimization algorithm to obtain the optimal allocation plan.

[0007] As a preferred embodiment of the coil storage location allocation method based on an improved whale optimization algorithm described in the present invention, the optimization model for reducing coil scheduling time is specifically as follows:

[0008]

[0009] Wherein, f1 represents the optimization model for reducing coil scheduling time, and x ij represents whether coil c i is allocated to storage location j, i represents the coil number, j represents the storage location number, and x ij ∈{0, 1} represents whether coil c i is allocated to storage location j, w i represents the turnover weight of coil c i , and t in,j is the time from the inbound port to storage location j, t j,out is the time from storage location j to the outbound port, N is the number of coils to be allocated, M is the number of available storage locations, ρ i represents the turnover rate of coil c i , and ρ k represents the turnover rate of coil c k .

[0010] As a preferred embodiment of the coil storage location allocation method based on an improved whale optimization algorithm described in the present invention, the establishment of the identity model includes the following steps:

[0011] Define the set of coil types and map them to numerical values, specifically: Wherein, t i represents the type of coil c i ; represent the three-dimensional coordinates of storage location j as (x j , y j , z j ), and represent the vector after allocating coil i to storage location j as (x j , y j , z j , ti ), where x j represents the horizontal position of storage location j, y j represents the vertical position of storage location j, and z j represents the vertical position of storage location j;

[0012] Calculate the type similarity between coil c i and coil c k , and the calculation formula is: where δ(t i , t k ) represents the type similarity between coil c i and coil c k , t k represents the type of coil c k ;

[0013] Calculate the Manhattan distance between storage location j and storage location m according to the storage locations, and the calculation formula is as follows:

[0014] d jm = |x j - x m | + |y j - y m | + |z j - z m |;

[0015] where d jm represents the Manhattan distance between storage location j and storage location m, and x m , y m and z m represent the horizontal position, vertical position and vertical position of storage location m respectively.

[0016] As a preferred solution of the coil storage location allocation method based on the improved whale optimization algorithm described in the present invention, the establishment of the identity model further includes the following steps:

[0017] Based on the Manhattan distance d jm between storage location j and storage location m, calculate the similarity between storage location j and storage location m, and the calculation formula is: where s jm represents the similarity between storage location j and storage location m, and d max is the Manhattan distance between the two storage locations farthest apart in the warehouse;

[0018] Based on the similarity s jm and the type similarity δ(t i , t k ), construct the identity model, specifically as follows:

[0019]

[0020] Among them, f2 represents the aggregation degree of steel coils with similar types, N is the number of steel coils to be allocated, M is the number of available storage positions, and x ij represents whether the steel coil c i is allocated to the storage position j, and x km represents whether the steel coil c k is allocated to the storage position m.

[0021] As a preferred solution of the steel coil storage position allocation method based on the improved whale optimization algorithm described in the present invention, the constraint conditions include uniqueness constraint, capacity constraint, stacking layer limit, and safety distance constraint;

[0022] The uniqueness constraint is specifically as follows:

[0023]

[0024] The capacity constraint is specifically as follows:

[0025]

[0026] Among them, S j represents the maximum storage position capacity;

[0027] The stacking layer limit is specifically as follows:

[0028]

[0029] Among them, h j represents the maximum stacking layer number;

[0030] The safety distance constraint is specifically as follows:

[0031] Satisfy d jm <d s ;

[0032] Among them, d s represents the maximum safety distance.

[0033] As a preferred solution of the steel coil storage position allocation method based on the improved whale optimization algorithm described in the present invention, based on the scheduling time and identity of the steel coils, the analytic hierarchy process is used to obtain the allocation weights σ1 and σ2, and σ1 + σ2 = 1, and the multi-objective model is weighted to obtain the weighted model:

[0034] min F = α1f1 + α2f2;

[0035] Among them, F represents the weighted single-objective function, and α1 and α2 represent the objective function weights;

[0036] The steps of the improved whale optimization algorithm are as follows:

[0037] Initialize the parameters, set the population size N and the maximum number of iterations t max , and initialize the positions of the whales;

[0038] Calculate the fitness of the whale population, find and retain the optimal fitness. The calculation formula of the fitness is as follows:

[0039] f n (t) = B · [X * (t) - X(t)];

[0040]

[0041] Among them, f n (t) represents the degree of difference between the current whale individual position X(t) and the optimal whale position X * (t) at the t-th iteration. X * (t) represents the optimal whale position at the t-th iteration, X(t) represents the position of the whale at the t-th iteration, B represents the fitness coefficient, and t max represents the maximum number of iterations;

[0042] Update the positions of the whale population through the mechanism of whales surrounding prey, spiral predation mechanism and interactive search mechanism, and update the positions by comparing the fitness of the old and new positions. The calculation formula for updating the positions is as follows:

[0043] X(t + 1) = |X(t) + f n (t)|;

[0044] Among them, X(t) represents the position of the whale at the t-th iteration, f n (t) represents the degree of difference between the current whale individual position X(t) and the optimal whale position X * (t) at the t-th iteration. X(t + 1) represents the position of the whale at the (t + 1)-th iteration;

[0045] If the maximum number of iterations is not reached, jump to the step of updating the positions of the whale population to continue the iteration, otherwise output the optimal solution.

[0046] As a preferred solution of the steel coil storage location allocation method based on the improved whale optimization algorithm of the present invention, the improved whale optimization algorithm includes the following improvement steps:

[0047] Initialize the positions of the whale population using Logistic-Tent chaotic mapping. The calculation formula is as follows:

[0048]

[0049] Among them, x nrepresents the value of the iterative variable at the nth iteration in the Logistic-Tent chaotic map, x n+1 represents the value of the iterative variable at the (n + 1)th iteration in the Logistic-Tent chaotic map, r represents the control parameter of the chaotic map, and r ∈ (0, 4);

[0050] Introduce a non-linear convergence factor dynamic adjustment algorithm to explore and develop capabilities. The calculation formula of the non-linear convergence factor is as follows:

[0051]

[0052] where, a represents the non-linear convergence factor, μ represents the coefficient controlling the change of the convergence factor, t represents the current iteration number, t max represents the maximum iteration number.

[0053] As a preferred scheme of the steel coil storage location allocation method based on the improved whale optimization algorithm of the present invention, the improved whale optimization algorithm further includes: introducing an interactive search strategy in the global search mechanism to enhance information exchange between populations. The calculation formula of the interactive search strategy is as follows:

[0054] X(t + 1) = X(t) + φ(X(t) - X k ) + φ(X randp - X(t));

[0055] where, X(t) represents the position of the whale individual at the tth iteration, X(t + 1) represents the position of the whale individual at the (t + 1)th iteration, φ and φ are weight coefficients controlling the interaction intensity, and φ ∈ (0, 2), φ ∈ (0, 1), X k is a random individual, X randp is an external random individual.

[0056] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: In a coil storage location allocation method based on an improved whale optimization algorithm provided by the present invention, through the establishment of a coil type identity model and multi-objective optimization constraints, intelligent clustering storage of the same type of coils is realized. Using Manhattan distance mapping and similarity measurement, the same type of coils are allocated to adjacent storage locations, reducing redundant spacing, effectively improving the storage density of the stereoscopic warehouse, and effectively alleviating the "warehouse capacity anxiety" that the iron and steel enterprises have faced for a long time. Compared with the traditional manual planning mode, the present invention fully exploits the potential of the three-dimensional space through algorithm-driven precise storage location matching, reducing storage costs; aiming at the defect that the traditional whale optimization algorithm is prone to fall into local optimum, a Logistic-Tent chaotic mapping initialization strategy is proposed to enhance population diversity and avoid premature convergence; a non-linear convergence factor is introduced, dynamically adjusted based on the cosine function, balancing the exploration and exploitation capabilities of the algorithm, improving the convergence speed, and being able to find a suitable solution in a short time; an interaction strategy is introduced to enhance the information exchange between populations, strengthen the global search ability, and be able to effectively handle multi-peak problems, providing an effective way to solve practical problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention.

[0058] Figure 1 is a schematic diagram of the steps of a coil storage location allocation method based on an improved whale optimization algorithm of the present invention;

[0059] Figure 2 is an iteration diagram of the proposed non-linear convergence factor;

[0060] Figure 3 Flow chart of the improved whale optimization algorithm in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the 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 of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative work shall fall within the protection scope of the present invention.

[0062] For the convenience of establishing and solving the mathematical model in the present invention, there are several assumptions about the mathematical model: The coils all meet the standards and there will be no storage locations that cannot be allocated; The crane moves at a constant speed in the X, Y, and Z axes; The position of the storage location is represented by a coordinate point.

[0063] Please refer to Figures 1-3, in the first embodiment: A method for allocating storage locations of steel coils based on an improved whale optimization algorithm is provided, and the method includes the following steps:

[0064] Step S1: Collect steel coil attributes, storage location parameters, overhead crane operation data, and historical order data, and establish an optimization model for reducing steel coil scheduling time.

[0065] Specifically, the optimization model for reducing steel coil scheduling time is as follows:

[0066]

[0067] Among them, f1 represents the optimization model for reducing steel coil scheduling time, and x ij represents whether steel coil c i is allocated to storage location j, i represents the steel coil number, j represents the storage location number, w i represents the turnover weight of steel coil c i , and t in,j is the time from the inbound port to storage location j, t j,out is the time from storage location j to the outbound port, N is the number of steel coils to be allocated, M is the number of available storage locations, ρ i represents the turnover rate of steel coil c i , and ρ k represents the turnover rate of steel coil c k .

[0068] Step S2: Extract the categories of the steel coils in the warehouse and establish an identity model.

[0069] Specifically, the establishment of the identity model includes the following steps:

[0070] Define the set of steel coil types and map them to numerical values, specifically: Among them, t i represents the type of steel coil c i ; represent the three-dimensional coordinates of storage location j as (x j , y j , z j ), and represent the vector after allocating steel coil i to storage location j as (x j , y j , z j , t i ), where x j represents the horizontal position of storage location j, y j represents the longitudinal position of storage location j, and z j represents the vertical position of storage location j;

[0071] Calculate the type similarity between steel coil c i and steel coil c k , and the calculation formula is: Among them, δ(t i ,t k ) represents the type similarity between coil c i and coil c k , and t k represents the type of coil c k .

[0072] Calculate the Manhattan distance between storage location j and storage location m according to the storage locations. The calculation formula is as follows:

[0073] d jm =|x j -x m |+|y j -y m |+|z j -z m |;

[0074] Among them, d jm represents the Manhattan distance between storage location j and storage location m, and x m , y m and z m represent the horizontal position, vertical position and vertical position of storage location m respectively.

[0075] Furthermore, the establishment of the identity model further includes the following steps:

[0076] Based on the Manhattan distance d jm between storage location j and storage location m, calculate the similarity between storage location j and storage location m. The calculation formula is: Among them, s jm represents the similarity between storage location j and storage location m, and d max is the Manhattan distance between the two farthest storage locations in the warehouse;

[0077] Based on the similarity s jm and the type similarity δ(t i ,t k ), construct the identity model, specifically as follows:

[0078]

[0079] Among them, f2 represents the aggregation degree of type-similar coils, N is the number of coils to be allocated, M is the number of available storage locations, and x ij represents whether coil c i is allocated to storage location j, and x km represents whether coil c k is allocated to storage location m.

[0080] Step S3: According to the actual storage locations, establish the hard constraints and dynamic constraints of the model, and establish the multi-objective storage location allocation optimization model.

[0081] Specifically, the constraint conditions include uniqueness constraint, capacity constraint, stacking layer limit, and safety distance constraint;

[0082] The uniqueness constraint is specifically as follows:

[0083]

[0084] The capacity constraint is specifically as follows:

[0085]

[0086] Among them, S j represents the maximum bin capacity;

[0087] The stacking layer limit is specifically as follows:

[0088]

[0089] Among them, h j represents the maximum stacking layer number;

[0090] The safety distance constraint is specifically as follows:

[0091] Satisfy d jm < d s ;

[0092] Among them, d s represents the maximum safety distance.

[0093] Step S4: Using the empty bin as the solution space, the model is weighted by the analytic hierarchy process, and the improved whale optimization algorithm is used to solve the optimized model to obtain the optimal allocation plan.

[0094] Specifically, use the analytic hierarchy process (as shown in Table 1):

[0095] Table 1 Judgment matrix

[0096]

[0097] Taking the scheduling time and the coil identity characteristics, after weighted processing and summing, the weight values α1 and α2 are obtained, and α1 + α2 = 1. The model obtained after processing and weighting the multi-objective model is: min F = 0.833f1 + 0.167f2;

[0098] As Figure 3 shown, the steps of the improved whale optimization algorithm are:

[0099] Initialize the parameters, set the population size N, the maximum number of iterations t max , and initialize the whale position;

[0100] Calculate the fitness of the whale population, find the optimal fitness and retain it;

[0101] Update the positions of the whale population through the mechanism of whales surrounding prey, spiral predation mechanism and interactive search mechanism, and update the positions by comparing the fitness of the old and new positions;

[0102] If the maximum number of iterations is not reached, jump to the position of updating the whale population to continue the iteration, otherwise output the optimal solution;

[0103] Furthermore, the initial positions of the whales adopt Logistic-Tent chaotic mapping, and its formula is:

[0104]

[0105] where, x n represents the iteration variable value at the nth iteration in the Logistic-Tent chaotic mapping, x n+1 represents the iteration variable value at the (n + 1)th iteration in the Logistic-Tent chaotic mapping, r represents the control parameter of the chaotic mapping, and r ∈ (0, 4); The traditional whale optimization algorithm uses a random initialization method, which is prone to generating local optimal solutions and reducing the optimization speed of the algorithm. Logistic-Tent chaotic mapping has better ergodicity and uniform distribution characteristics;

[0106] Furthermore, the formula for the mechanism of whales surrounding prey is:

[0107] X(t + 1) = X * (t) - (2a·r - a)·D;

[0108] D = |C·X * (t) - X(t)|;

[0109] where, X(t + 1) represents the position of the whale individual at the (t + 1)th iteration, D represents the distance vector between the current optimal solution and the search individual, X(t) represents the position of the whale individual at the tth iteration, t represents the number of iterations, X * (t) represents the optimal whale position at the tth iteration, C is a random coefficient for controlling the distance, r represents a random vector between [0, 1]. The traditional whale optimization algorithm uses a linear convergence factor, which is prone to causing an imbalance between exploration and exploitation, resulting in premature convergence and falling into local optima. Therefore, a non-linear convergence factor is introduced:

[0110]

[0111] Among them, a represents the non-linear convergence factor, μ represents the coefficient controlling the change of the convergence factor, which is selected according to actual needs (such as Figure 2 ), t represents the current iteration number, t max represents the maximum iteration number.

[0112] Furthermore, the formula of the spiral predation mechanism is:

[0113] X(t + 1) = ∣X * (t) - X(t)∣·e bl ·cos(2πl) + X * (t);

[0114] Among them, X(t + 1) represents the position of the whale individual at the (t + 1)-th iteration, X(t) represents the position of the whale individual at the t-th iteration, X * (t) represents the optimal whale position at the t-th iteration, b represents the constant controlling the spiral shape, and l represents a random number between [-1, 1].

[0115] Furthermore, the formula of the global search mechanism is:

[0116] X(t + 1) = X rand (t) - A·|C·X rand (t) - X(t)|;

[0117] Among them, X rand (t) is the position randomly selected from other individuals, and C is the random coefficient controlling the distance; when the traditional whale optimization algorithm performs the global search behavior, although it helps to explore new areas, its blindness and inefficiency will limit the performance of the algorithm. Therefore, an interactive search mechanism is introduced to enhance the interaction between populations:

[0118]

[0119] Among them, X(t) represents the position of the whale individual at the t-th iteration, X(t + 1) represents the position of the whale individual at the (t + 1)-th iteration, φ and φ are the weight coefficients controlling the interaction intensity, and φ ∈ (0, 2), φ ∈ (0, 1), X k is a random individual, and X randp is an external random individual; the interactive search mechanism is used to enhance the information exchange between populations and improve the ability of the algorithm to find the optimal solution.

[0120] Furthermore, the fitness formula is:

[0121] f n (t) = B·[X * (t) - X(t)];

[0122]

[0123] Among them, f n (t) represents the degree of difference between the current whale individual position X(t) and the optimal whale position X * (t) at the t-th iteration, X * (t) represents the optimal whale position at the t-th iteration, X(t) represents the position of the whale at the t-th iteration, B represents the fitness coefficient, and t max represents the maximum number of iterations.

[0124] Furthermore, the formula for position update is:

[0125] X(t + 1) = |X(t) + f n (t)|;

[0126] Among them, X(t) represents the position of the whale at the t-th iteration, and f n (t) represents the degree of difference between the current whale individual position X(t) and the optimal whale position X * (t) at the t-th iteration, and X(t + 1) represents the position of the whale at the (t + 1)-th iteration.

[0127] It should be noted that in this article, 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 "comprises", "comprising" or any other variation thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device.

[0128] Finally, it should be noted that: The above are only 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 replacements for some of the technical features. Any modification, equivalent replacement, 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 steel coil storage location allocation method based on an improved whale optimization algorithm, characterized in that, The method includes the following steps: Step S1: Collect coil properties, storage location parameters, crane operation data, and historical order data, and establish an optimization model for reducing coil scheduling time; Step S2: Extract the categories of coils in the warehouse and establish an identity model; Step S3: According to the actual storage locations, establish hard constraints and dynamic constraints of the model, and establish a multi-objective storage location allocation optimization model; Step S4: Use the empty storage locations as the solution space, perform weighted processing on the model according to the analytic hierarchy process, and solve the optimization model through an improved whale optimization algorithm to obtain the optimal allocation plan.

2. The steel coil storage location allocation method based on the improved whale optimization algorithm according to claim 1, wherein The optimization model for reducing coil scheduling time is specifically as follows: Among them, f1 represents the optimization model for reducing the coil scheduling time, and x ij represents whether coil c i is assigned to storage location j, i represents the coil number, j represents the storage location number, and w i represents the turnover rate weight of coil c i , and t in,j is the time from the inbound port to storage location j, t j,out is the time from storage location j to the outbound port, N is the number of coils to be assigned, M is the number of available storage locations, and ρ i represents the turnover rate of coil c i , and ρ k represents the turnover rate of coil c k .

3. The steel coil storage location allocation method based on an improved whale optimization algorithm according to claim 2, wherein, The establishment of the identity model includes the following steps: Define the set of coil types and map them to numerical values, specifically as follows: Among them, t i represents the type of coil c i ; represent the three-dimensional coordinates of storage location j as (x j , y j , z j ), and the vector representation after allocating coil i to storage location j is (x j , y j , z j , t i ), where x j represents the horizontal position of storage location j, y j represents the longitudinal position of storage location j, and z j represents the vertical position of storage location j; Calculate the type similarity between coil c i and coil c k , and the calculation formula is: where δ(t i , t k ) represents the type similarity between coil c i and coil c k , t k represents the type of coil c k ; Calculate the Manhattan distance between storage location j and storage location m according to the storage locations, and the calculation formula is as follows: d jm = |x j - x m | + |y j - y m | + |z j - z m |; where d jm represents the Manhattan distance between storage location j and storage location m, and x m , y m and z m represent the horizontal position, vertical position, and vertical position of storage location m, respectively.

4. A coil storage location allocation method based on an improved whale optimization algorithm according to claim 3, characterized in that, The establishment of the identity model further includes the following steps: Based on the Manhattan distance d between storage location j and storage location m jm , calculate the similarity between storage location j and storage location m. The calculation formula is as follows: where s jm represents the similarity between storage location j and storage location m, and d max is the Manhattan distance between the two storage locations that are farthest apart in the warehouse; Based on the similarity s jm and the type similarity δ(t i , t k ), an identity model is constructed as follows: Among them, f2 represents the aggregation degree of steel coils with similar types, N is the number of steel coils to be allocated, M is the number of available storage positions, and x ij represents whether the steel coil c i is allocated to the storage position j, and x km represents whether the steel coil c k is allocated to the storage position m.

5. The steel coil storage location allocation method based on the improved whale optimization algorithm according to claim 4, characterized in that, The constraints include uniqueness constraint, capacity constraint, stacking layer limit, and safety distance constraint; The uniqueness constraint is specifically as follows: The capacity constraint is specifically as follows: Among them, S j represents the maximum bin capacity; The stacking layer limit is specifically as follows: where h j represents the maximum number of stacked layers; The safety distance constraint is specifically as follows: Satisfy d jm <d s ; Among them, d s represents the maximum safety distance.

6. The steel coil storage location allocation method based on an improved whale optimization algorithm according to claim 5, characterized in that The specific implementation process of Step S4 includes: The weighted single-objective model is: min F = α1f1 + α2f2; Among them, F represents the weighted single-objective function, and α1 and α2 represent the weights of the objective functions; The steps of the improved whale optimization algorithm are: Initialize parameters, set the population size N and the maximum number of iterations t max , and initialize the whale positions; Calculate the fitness of the whale population, find the optimal fitness and retain it, and the calculation formula of the fitness is as follows: f n f(t) = B·[X * (t) - X(t)]; Among them, f n (t) represents the degree of difference between the current whale individual position X(t) and the optimal whale position X * (t) at the t-th iteration, X * (t) represents the optimal whale position at the t-th iteration, X(t) represents the position of the whale at the t-th iteration, B represents the fitness coefficient, and t max represents the maximum number of iterations; Update the positions of the whale population through the mechanism of whales surrounding prey, spiral predation mechanism, and interactive search mechanism, and update the positions by comparing the fitness of the old and new positions. The calculation formula for updating the positions is as follows: X(t + 1) = |X(t) + f n (t)|; Among them, X(t) represents the position of the whale at the t-th iteration, and f n (t) represents the degree of difference between the current whale individual position X(t) and the optimal whale position X * (t) at the t-th iteration, and X(t + 1) represents the position of the whale at the (t + 1)-th iteration; If the maximum number of iterations is not reached, jump to the step of updating the positions of the whale population to continue the iteration, otherwise output the optimal solution.

7. A coil storage location allocation method based on an improved whale optimization algorithm according to claim 6, characterized in that The specific implementation process of Step S4 further includes: The improved whale optimization algorithm includes the following improvement steps: Use Logistic-Tent chaotic mapping to initialize the positions of the whale population, and the calculation formula is as follows: where x n represents the value of the iteration variable at the n-th iteration in the Logistic-Tent chaotic map, and x n+1 represents the value of the iteration variable at the (n + 1)-th iteration in the Logistic-Tent chaotic map. r represents the control parameter of the chaotic map, and r ∈ (0, 4); Introduce a non-linear convergence factor to dynamically adjust the exploration and exploitation capabilities of the algorithm, and the calculation formula of the non-linear convergence factor is as follows: Among them, a represents the non-linear convergence factor, μ represents the coefficient controlling the change of the convergence factor, t represents the current iteration number, and t max represents the maximum iteration number.

8. The steel coil storage location allocation method based on the improved whale optimization algorithm according to claim 5, characterized in that The improved whale optimization algorithm further includes: Introduce an interactive search strategy in the global search mechanism, and the calculation formula of the interactive search strategy is as follows: X(t + 1) = X(t) + φ(X(t) - X k ) + φ(X randp - X(t)); Where, X(t) represents the position of the whale individual at the t-th iteration, X(t + 1) represents the position of the whale individual at the (t + 1)-th iteration, φ and φ are weight coefficients that control the interaction intensity, and φ ∈ (0, 2), φ ∈ (0, 1), X k is a random individual, X randp is an external random individual.

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