Method for solving 3D parallel line layout considering adaptive material handling points and obstacles

Abstract

The application discloses a 3D parallel line layout solving method considering adaptive material loading and unloading points and obstacles, relates to the technical field of facility layout, and mainly comprises the following steps: establishing a target function, initializing parameters, generating an initial population, converting infeasible solutions in the initial population into feasible solutions, optimizing the initial population, removing duplicate solutions in the initial population and generating feasible solutions to fill the initial population, dividing the initial population into elite solutions and non-elite solutions, performing a tabu search operation on the elite solutions, performing a genetic operation on the non-elite solutions, combining the solutions after the two operations into a new population, outputting an optimal sequence and decision variables of the model according to the number of iterations, and solving the accurate coordinates of the material loading and unloading points on each facility and the final target value of the model by using the optimal sequence and the decision variables. The application considers adaptive material loading and unloading points and obstacle interference factors in three-dimensional space, and the obtained model is closer to the real situation, which is helpful for formulating more scientific facility planning and material handling strategies.

Description

Technical Field

[0001] This invention relates to the field of facility layout technology, specifically a 3D parallel layout solution method that takes into account adaptive material loading and unloading points and obstacles. Background Technology

[0002] The Parallel Row Ordering Problem (PROP) is a relatively new problem in facility layout. It aims to minimize material handling costs by arranging a series of facilities in parallel rows. It is commonly applied in the fermented food industry and similar industries that require zoned equipment layout. Parallel row layouts can improve material handling efficiency, enhance workshop response speed, and are highly suitable for flexible manufacturing workshops. Therefore, it plays a positive role in promoting the transformation and upgrading of the current manufacturing industry, and has received widespread attention in recent years.

[0003] Material Handling Points (MHPs) refer to specific locations within a factory or workshop where materials are moved between different processes or equipment. The rational design and layout of these locations significantly impact the efficiency of the entire production system. However, most current researchers fixate them at a single point at the center of the facility. Furthermore, obstacles often exist in workshop layouts, such as beams, cables, and pipes present from the initial construction phase. The impact of obstacles mainly manifests in forcing material handling paths to detour, restricting equipment placement, and reducing available space. For the sake of convenient problem assumptions, most researchers generally do not consider the existence of obstacles. Those who do consider obstacles often only discuss their interference in two-dimensional space, leading to significant discrepancies between research results and actual conditions, hindering the practical application of the research findings. Summary of the Invention

[0004] Therefore, the main objective of this invention is to provide a 3D parallel row layout solution method that considers adaptive material handling points and obstacles. The research object is expanded from a simple parallel row ordering problem with obstacles (PROP_O) to an adaptive material handling point parallel row ordering problem with obstacles (APPROP_O). Furthermore, the method considers obstacle interference and relaxes the constraints of the Material Handling Point Parallel Row Ordering Problem (MHP) during the calculation process, making the model more closely reflect actual production and living conditions. This helps enterprises formulate more scientific facility planning and material handling strategies.

[0005] The technical solution of this invention is a 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles, comprising the following steps:

[0006] Step S1: Collect facility layout information and establish an objective function involving the sum of the products of material handling costs, unit material handling volume between facilities, and handling distances;

[0007] Step S2: Initialize parameters, calculate the channel width and obstacle coordinates within the area, and identify devices that may cause height interference;

[0008] Step S3: Generate an initial population Pop, transform infeasible solutions in the initial population Pop into feasible solutions, and optimize the initial population Pop using a optimization strategy;

[0009] Step S4: Remove duplicate solutions from the initial population Pop and randomly generate the same number of feasible solutions to fill the initial population Pop;

[0010] Step S5: Calculate fitness and divide the initial population Pop into elite solutions Elite_r and non-elite solutions Nelite_r;

[0011] Step S6-1: Perform a tabu search operation on the elite solution Elite_r until the maximum number of times is reached, and obtain the solution after tabu search. The tabu search operation method is: with the goal of minimizing the target value, perform multiple neighborhood search operations on the elite solution Elite_r.

[0012] Step S6-2: Perform genetic operations on the non-elite solutions to obtain the genetically modified solutions. The genetic operations include selection, dominance crossover, and mutation operations.

[0013] Step S7: Combine the solutions obtained from the tabu search with the solutions obtained from the genetics process to form a new population;

[0014] Step S8: Determine whether the number of iterations has reached the maximum number of generations Max_gen. If not, return to step S4 to continue iterative calculation. If it has, output the first y optimal sequences of the PROP_O model based on the number of solutions y, and calculate the relevant decision variables.

[0015] Step S9: Substitute the optimal sequence and relevant decision variables of the PROP_O model into the MILP model, and use the exact solver to obtain the precise coordinates of the material loading and unloading points on each facility and the final target value of the APPROP_O model.

[0016] The technical effects of this invention are:

[0017] 1. Based on the parallel row sorting problem model, this invention considers adaptive material loading and unloading points and obstacle interference factors in three-dimensional space, making the resulting model closer to actual production and living conditions, which helps to formulate more scientific facility planning and material handling strategies.

[0018] 2. The algorithm in this invention is a two-stage Advantage Genetic Algorithm Tabu Search (AGATS), which combines the characteristics of combinatorial optimization and continuous optimization. It can effectively integrate the solution requirements of both discrete and continuous aspects, thereby improving the solution quality. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below.

[0020] Figure 1 This is a flowchart of the algorithm of the present invention;

[0021] Figure 2 This refers to the process of encoding, decoding, and converting infeasible solutions in this invention;

[0022] Figure 3 This is a schematic diagram of the 2-opt operation and the inversion operation in this invention;

[0023] Figure 4 This is a schematic diagram of the advantageous cross-operation in this invention;

[0024] Figure 5 This is a box plot showing the solution results of GATS and AGATS in this invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Example:

[0028] A method for solving 3D parallel row layouts considering adaptive material loading / unloading points and obstacles includes the following steps:

[0029] Step S1: Material handling cost is determined by the sum of the products of the unit interactive material handling volume and the handling distance between facilities. It is a key indicator for evaluating the quality of the layout. Therefore, we collect facility layout information and establish an objective function involving the sum of the products of material handling cost, unit interactive material handling volume between facilities, and handling distance:

[0030]

[0031] Equations (2) to (7) are used to calculate the material handling distance from facility i to facility j in the Y and Z directions:

[0032]

[0033] Equation (8) is used to calculate the x-coordinate of facility i in the first row; (9) is used to calculate the x-coordinate of facility i in the second row:

[0034]

[0035]

[0036] Equations (10) to (13) are used to determine the permissible range of material loading and unloading points on facility i:

[0037]

[0038] Equations (14) to (17) are used to calculate the horizontal and vertical coordinates of the material loading and unloading points on facility i:

[0039] Equations (18) to (23) are used to calculate the material handling distance from facility i to facility j in the X direction:

[0040]

[0041]

[0042] Equations (24) and (25) are used to prevent overlapping interference between facilities within the same line of work:

[0043]

[0044] Equations (26) and (27) are used to prevent overlapping interference between the facilities in the first row and obstacles on the ground; equations (28) and (29) are used to prevent overlapping interference between the facilities in the second row and suspended obstacles.

[0045]

[0046] Equations (30) to (38) are used to determine the decision variables; equations (39) and (40) give the domain of the decision variables:

[0047]

[0048]

[0049] Where n is the number of facilities; n r For the number of facilities in a single row, when r = 1, n r This represents the number of facilities in the first row. When r = 2, n r The second row represents the number of facilities; m represents the number of obstacles; N represents the set of facilities, N = {1, 2, ..., n}; K represents the set of obstacles, K = {1, 2, ..., m}; N r For a single-line facility set, when r=1, N r This represents the set of facilities in the first row. When r = 2, N r This represents the set of facilities in the second row; i, j, s are facility numbers, i, j, s ∈ N; k is the obstacle number, k ∈ K; l i Let l be the length of facility i in the X direction; j Let w be the length of facility j in the X direction; i w is the length of facility i in the Y direction; j Let h be the length of facility j in the Y direction; i Let lo be the length of facility i in the Z direction; k Let k be the length of obstacle k in the X direction; wo k Let h be the length of obstacle k in the Y direction; ho k Let zo be the length of obstacle k in the Z direction; k Let f be the coordinates of the geometric center of obstacle k in the Z direction; ij The material flow between facility i and facility j;

[0050] Let be the minimum height that the material loading / unloading point can be arranged on facility i, where The maximum height at which the material loading and unloading point can be located on facility i, where Let be the minimum length that the material loading / unloading point can be arranged on facility i, where Let be the minimum length that the material loading / unloading point can be arranged on facility i, where r is the channel width;

[0051] xp i Let yp be the coordinates of the material loading / unloading point of facility i in the X direction; i Let zp be the coordinates of the material loading / unloading point of facility i in the Y direction; ixp represents the coordinates of the material loading / unloading point of facility i in the Z direction. j Let yp be the coordinates of the material loading / unloading point of facility j in the X direction; j Let zp be the coordinates of the material loading / unloading point of facility j in the Y direction; j Let be the coordinates of the material loading / unloading point of facility j in the Z direction; Let r be the coordinate of the geometric center point of facility i in the X direction, and when r = 1, This represents the x-coordinate of facility i in the first row. When r = 2, Represents the x-coordinate of facility i in the second row; Let be the coordinates of the geometric center point of facility j in the X direction. When r = 1, This represents the x-coordinate of facility j in the first row. When r = 2, This represents the x-coordinate of facility j in the second row; xo k Let x be the coordinates of the geometric center of obstacle k in the X direction; Let r be the distance in the X direction between the material loading and unloading points of facility i and facility j in a certain row. When r = 1, facilities i and facility j are both in the first row. When r = 2, facilities i and facility j are both in the second row. Let D be the distance in the X direction between the material loading and unloading points of facility i and facility j, where facility i and facility j are located in different rows; ij r Let r be the sum of the distances in the Y and Z directions between the material loading and unloading points of facilities i and j within a certain row. When r = 1, facilities i and j are both in the first row; when r = 2, facilities i and j are both in the second row. ij 12 Let α be the sum of the distances in the Y and Z directions between the material loading and unloading points of facility i and facility j, where facility i and facility j are located in different rows; ij Let α be a 0-1 variable. If facility i is in the same row as facility j, and facilities i and j are both on the same side of obstacle k, then α ij =1, otherwise α ij =0; β ik Let β be a 0-1 variable. If facility i and obstacle k are in the same row, and facility i is placed to the left of obstacle k, then β ik =1, otherwise β ik =0; β jk Let β be a 0-1 variable. If facility j and obstacle k are in the same row, and facility j is placed to the left of obstacle k, then β jk =1, otherwise β jk =0; q ijk Let q be a 0-1 variable. If facility i is to the left of facility j, and both i and j are to the left of the obstacle, then q ij1 =1, otherwise qij1 =0, if facility i is to the left of facility j, and both i and j are to the right of the obstacle, then q ij2 =1, otherwise q ij2 =0; q jik Let q be a 0-1 variable. If facility j is to the left of facility i, and both i and j are to the left of the obstacle, then q ji1 =1, otherwise q ji1 =0, if facility j is to the left of facility i, and both i and j are to the right of the obstacle, then q ji2 =1, otherwise q ji2 =0; q isk Let q be a 0-1 variable. If facility i is to the left of facility s, and both i and s are to the left of the obstacle, then q is1 =1, otherwise q is1 =0, if facility i is to the left of facility s, and both i and s are to the right of the obstacle, then q is2 =1, otherwise q is2 =0; γ ij Let γ be a 0-1 variable. If facility i is in the same row as facility j and facility i is to the left of facility j, then γ ij =1, otherwise γ ij =0;

[0052] Step S2: Initialize parameters, calculate the channel width and obstacle coordinates within the region, and identify devices that may cause height interference. The initialization parameters mainly include population size N, maximum number of generations Max_gen, crossover rate Pc, mutation rate Pm, selection rate S, elite rate Elite, maximum number of generations for tabu search Ts_gen, initial tabu table length Ts_len, and the number of solutions y.

[0053] Step S3: Generate an initial population Pop, transform infeasible solutions in the initial population Pop into feasible solutions, and optimize the initial population Pop using a optimization strategy.

[0054] Considering that obstacles and facilities cannot overlap, infeasible solutions must be transformed into feasible solutions during the decoding process and all subsequent operations. To address the characteristics of the problem, this invention designs a segmented encoding and decoding method. A feasible solution can be represented as [R1, R2], both encoded using real numbers. Let the problem size be n, where the number of facilities in the first row is t, and the number of facilities in the second row is nt. However, since the interference of obstacles in the horizontal direction is considered in the first row, the actual problem size is n+1. R1 represents the first t+1 terms of the solution, where the index n+1 represents the obstacle. Considering that obstacles and facilities cannot overlap, infeasible solutions must be transformed into feasible solutions during the decoding process and all subsequent operations. Taking n=9 as an example, the encoding, decoding, and transformation of infeasible solutions for this sequence are as follows: Figure 2As shown. Given the sequence [3,1,4,10,2,9,5,6,7,8], where t=4, and number 10 represents an obstacle, assuming that the facility on the left side of the obstacle interferes at this time, the facility on the left side of the obstacle is moved to be close to the right side of the obstacle until the non-overlapping constraint condition is met.

[0055] Furthermore, the feasibility of a solution is determined as follows: calculate the coordinates of the obstacle and the facility to its left, and determine whether they overlap based on their lengths. If they overlap, the solution is infeasible. If it is infeasible, insert the facility that overlaps with the obstacle to the right of the obstacle, making sure it is flush with the obstacle without any gaps. Then, check for overlap again and repeat the above steps until they no longer overlap.

[0056] Due to the presence of obstacles, there may be gaps between the facility and the obstacle, causing the horizontal coordinate of the facility on the right side of the obstacle to increase, thus increasing the facility's transport distance. Therefore, this invention also designs an optimal solution strategy, which mainly includes the following steps:

[0057] Step 1) Set the population size N and the desired minimum gap min_gap. The minimum gap can be set to a reasonable value according to the user's needs.

[0058] Step 2) Randomly generate a solution set consisting of N solutions that satisfy the condition that the gap is less than the minimum gap min_gap.

[0059] Step 3) With the goal of minimizing the target value, use a roulette wheel to select N / 2 solutions from the solution set of Step 2);

[0060] Step 4) Randomly generate N / 2 solutions and combine them with the solutions selected by the roulette wheel operation in Step 3) to form a new initial population Pop of size N.

[0061] Based on this strategy, the generation of the initial population not only follows the problem-oriented principle, ensuring that individuals in the population have a certain degree of domain awareness and problem characteristics in the early stages, but also ensures the diversity of the population by introducing random sequences.

[0062] Step S4: Remove duplicate solutions from the initial population Pop and randomly generate the same number of feasible solutions to fill the initial population Pop;

[0063] Step S5: Calculate fitness and divide the initial population Pop into elite solutions Elite_r and non-elite solutions Nelite_r;

[0064] Step S6-1: Perform a tabu search operation on the elite solution Elite_r until the maximum number of times is reached, and obtain the solution after tabu search. The tabu search operation method is: with the goal of minimizing the target value, perform multiple neighborhood search operations on the elite solution Elite_r.

[0065] The main idea of ​​the elite strategy is to directly retain the best-performing individual in the current population (i.e., the individual with the highest fitness) to the next generation during each generation's selection process. This ensures the inheritance of superior genes and avoids the loss of excellent individuals during selection. Therefore, this invention performs a tabu search on the elite solutions of each generation. If a neighboring solution obtained after the tabu search is better than the current solution, it is replaced with the new elite solution. The specific neighbor search operation includes an equal number of 2-opt operations and a reversal operation, the sum of which is the problem size. As the problem size increases, the number of neighbor search operations also increases. Figure 3 As shown, 2-opt is Figure 3 In a random sequence, two numbers are randomly selected and their positions are swapped. The result is a mirror image of any two random numbers that can be mirrored.

[0066] Step S6-2: Perform genetic operations on the non-elite solutions to obtain the genetically derived solutions. The genetic operations include selection, dominance crossover, and mutation. The selection operation also uses roulette wheel selection with the goal of minimizing the target value. The selected solutions are used for subsequent operations, while the unselected solutions are used as variables for dividing elite solutions in the next iteration. For example, if there are 100 solutions in a generation, 60 of them are selected using roulette wheel selection for subsequent operations, and the remaining solutions are retained. After the current iteration, these 40 retained solutions are compared to select the elite solutions, and then the next iteration is performed.

[0067] The mutation operation is a 2-opt operation, which directly generates a new solution based on the original solution.

[0068] Crossover allows the exchange of genetic information between parent individuals, resulting in new offspring. This not only maintains population diversity but also enhances the fitness of offspring, improving overall algorithm performance. However, in traditional genetic algorithms, some valuable genetic information may be discarded during crossover, potentially leading to a decrease in the fitness of offspring. To address this shortcoming, this invention proposes a superior crossover operation, the specific process of which is as follows: Figure 4 As shown, two adjacent solutions are considered as two parents. In these parents, the individual with the smaller objective value is called the dominant individual, and the individual with the larger objective value is called the non-dominant individual. During crossover, under the condition of feasibility, the two rows are segmented and operated on. For the first segment, two crossover points are randomly selected from positions 1 to t+1 of the dominant individual, and this segment is passed on to the offspring. Then, non-dominant individuals are scanned from left to right. If an element is not in the offspring, it is passed on to the same position in the offspring. Finally, the remaining elements are randomly assigned. The same operation is performed on the second segment, combining the first and second segments into the offspring solution.

[0069] Step S7: Combine the solutions obtained from the tabu search with the solutions obtained from the genetics process to form a new population;

[0070] Step S8: Determine whether the number of iterations has reached the maximum number of generations Max_gen. If not, return to step S4 to continue iterative calculation. If it has, output the first y optimal sequences of the PROP_O model based on the number of solutions y, and calculate the relevant decision variables.

[0071] Step S9: Substitute the optimal sequence and relevant decision variables of the PROP_O model into the Mixed-integer linear programming (MILP) model, and use the exact solver Gurobi to solve it, to obtain the exact coordinate values ​​of each facility and the final objective value of the APPROP_O model.

[0072] The feasible solutions to PROP_O obtained by the algorithm can be used to determine the decision variable α. ij β ik q ijk γ ij The value of is used to substitute the feasible solution and decision variables into the MILP model shown in equation (1) above, and further optimize it using the exact solver Gurobi. The model of PROP_O can be understood as the model of APPROP_O with the aforementioned equations (10) to (17) removed. At the same time, the calculation method of material handling distance is changed from using the coordinate difference of material loading and unloading points on the facility to using the coordinate difference of the facility. Finally, the exact coordinates of MHP on each facility and the final target value of APPROP_O are obtained.

[0073] The following is a demonstration of the actual operation of this embodiment:

[0074] Program testing environment:

[0075] The simulation environment consisted of an Intel(R) Core(TM) i5-9300H processor with a clock speed of 2.4GHz, a Windows 11 operating system, and 16.00GB of memory. Matlab R2023a was used to call the exact solver Gurobi to solve the model, and the results were used as the basis for the algorithm.

[0076] To further verify the performance of the AGATS algorithm disclosed in this invention, 13 cases with sizes ranging from 9 to 49 were selected. The conventional Genetic Algorithm Tabu Search (GATS) and the AGATS algorithm of this invention were used to solve the problems. Each case was run ten times, and the results were stored. The obtained data were then percentage-processed using a formula, with the processed value being the solution bias Gap. The formula for Gap is Gap = (gG) / G × 100%, where g is the current target value, and G is the minimum target value among the 20 data points in the same group. A box plot was then created using the processed data. Figure 5 As shown, the solid red line, the dashed black line, the top and bottom edges of the rectangular box, and the top and bottom solid black lines represent the median, mean, upper and lower quartiles, and extreme values ​​of the data, respectively.

[0077] Depend on Figure 5 It can be seen that both GATS and AGATS exhibit good performance when solving problems of size 9 to 15. However, as the problem size increases, the box plot of AGATS is more compact than that of GATS, reflecting that the solution results of AGATS are more concentrated, with less fluctuation and stronger stability. Furthermore, in solving medium to large-scale problems, the average objective value of AGATS is significantly lower than that of GATS, further indicating that AGATS has higher reliability in solution quality and its results have less dispersion.

[0078] In summary, this invention addresses the shortcomings of 3D parallel row layout research in the presence of obstacles and material loading / unloading points in workshops. It proposes a 3D parallel row sorting problem that considers adaptive material loading / unloading points and obstacles. To address the dual characteristics of this problem, an AGATS algorithm combining intelligent algorithms and linear programming is constructed. The superior performance of the proposed algorithm is verified by solving standard examples.

[0079] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for solving 3D parallel layout considering adaptive material loading / unloading points and obstacles, characterized in that, Includes the following steps: Step S1: Collect facility layout information and establish an objective function involving the sum of the products of material handling costs, unit material handling volume between facilities, and handling distances. The constraints satisfied by the objective function are as follows: Material handling distance constraints: Facility coordinate constraints: Constraints on the layout of material loading and unloading points: Material loading and unloading point horizontal and vertical coordinate constraints: Material handling distance constraints from facility i to facility j: Anti-overlapping interference constraints for facilities in the same area: Facility and ground obstacle anti-overlap interference constraints: Anti-overlap interference constraints between facilities and suspended obstacles: Decision variables and domain constraints of decision variables: Where n is the number of facilities; n r For the number of facilities in a single row, when r = 1, n r This represents the number of facilities in the first row. When r = 2, n r The second row represents the number of facilities; m represents the number of obstacles; N represents the set of facilities, N = {1, 2, ..., n}; K represents the set of obstacles, K = {1, 2, ..., m}; N r For a single-line facility set, when r=1, N r This represents the set of facilities in the first row. When r = 2, N r This represents the set of facilities in the second row; i, j, s are facility numbers, i, j, s ∈ N; k is the obstacle number, k ∈ K; l i Let l be the length of facility i in the X direction; j Let w be the length of facility j in the X direction; i w is the length of facility i in the Y direction; j Let h be the length of facility j in the Y direction; i Let lo be the length of facility i in the Z direction; k Let k be the length of obstacle k in the X direction; wo k Let h be the length of obstacle k in the Y direction; ho k Let zo be the length of obstacle k in the Z direction; k Let f be the coordinates of the geometric center of obstacle k in the Z direction; ij The material flow between facility i and facility j; Let be the minimum height that the material loading / unloading point can be arranged on facility i, where The maximum height at which the material loading and unloading point can be located on facility i, where Let be the minimum length that the material loading / unloading point can be arranged on facility i, where Let be the minimum length that the material loading / unloading point can be arranged on facility i, where r is the channel width; xp i Let yp be the coordinates of the material loading / unloading point of facility i in the X direction; i Let zp be the coordinates of the material loading / unloading point of facility i in the Y direction; i xp represents the coordinates of the material loading / unloading point of facility i in the Z direction. j Let yp be the coordinates of the material loading / unloading point of facility j in the X direction; j Let zp be the coordinates of the material loading / unloading point of facility j in the Y direction; j Let be the coordinates of the material loading / unloading point of facility j in the Z direction; Let r be the coordinate of the geometric center point of facility i in the X direction, and when r = 1, This represents the x-coordinate of facility i in the first row. When r = 2, Represents the x-coordinate of facility i in the second row; Let be the coordinates of the geometric center point of facility j in the X direction. When r = 1, This represents the x-coordinate of facility j in the first row. When r = 2, This represents the x-coordinate of facility j in the second row; xo k Let x be the coordinates of the geometric center of obstacle k in the X direction; Let r be the distance in the X direction between the material loading and unloading points of facility i and facility j in a certain row. When r = 1, facilities i and facility j are both in the first row. When r = 2, facilities i and facility j are both in the second row. Let D be the distance in the X direction between the material loading and unloading points of facility i and facility j, where facility i and facility j are located in different rows; ij r Let r be the sum of the distances in the Y and Z directions between the material loading and unloading points of facilities i and j within a certain row. When r = 1, facilities i and j are both in the first row; when r = 2, facilities i and j are both in the second row. ij 12 Let α be the sum of the distances in the Y and Z directions between the material loading and unloading points of facility i and facility j, where facility i and facility j are located in different rows; ij Let α be a 0-1 variable. If facility i is in the same row as facility j, and facilities i and j are both on the same side of obstacle k, then α ij =1, otherwise α ij =0; β ik Let β be a 0-1 variable. If facility i and obstacle k are in the same row, and facility i is placed to the left of obstacle k, then β ik =1, otherwise β ik =0; β jk Let β be a 0-1 variable. If facility j and obstacle k are in the same row, and facility j is placed to the left of obstacle k, then β jk =1, otherwise β jk =0; q ijk Let q be a 0-1 variable. If facility i is to the left of facility j, and both i and j are to the left of the obstacle, then q ij1 =1, otherwise q ij1 =0, if facility i is to the left of facility j, and both i and j are to the right of the obstacle, then q ij2 =1, otherwise q ij2 =0; q jik Let q be a 0-1 variable. If facility j is to the left of facility i, and both i and j are to the left of the obstacle, then q ji1 =1, otherwise q ji1 =0, if facility j is to the left of facility i, and both i and j are to the right of the obstacle, then q ji2 =1, otherwise q ji2 =0; q isk Let q be a 0-1 variable. If facility i is to the left of facility s, and both i and s are to the left of the obstacle, then q is1 =1, otherwise q is1 =0, if facility i is to the left of facility s, and both i and s are to the right of the obstacle, then q is2 =1, otherwise q is2 =0; γ ij Let γ be a 0-1 variable. If facility i is in the same row as facility j, and facility i is to the left of facility j, then γ ij =1, otherwise γ ij =0; Step S2: Initialize parameters, calculate the channel width and obstacle coordinates within the area, and identify devices that may cause height interference; Step S3: Generate an initial population Pop, transform infeasible solutions in the initial population Pop into feasible solutions, and optimize the initial population Pop using a optimization strategy; Step S4: Remove duplicate solutions from the initial population Pop and randomly generate the same number of feasible solutions to fill the initial population Pop; Step S5: Calculate fitness and divide the initial population Pop into elite solutions Elite_r and non-elite solutions Nelite_r; Step S6-1: Perform a tabu search operation on the elite solution Elite_r until the maximum number of times is reached, and obtain the solution after tabu search. The tabu search operation method is: with the goal of minimizing the target value, perform multiple neighborhood search operations on the elite solution Elite_r. Step S6-2: Perform genetic operations on the non-elite solutions to obtain the genetically modified solutions. The genetic operations include selection, dominance crossover, and mutation. Step S7: Combine the solutions obtained from the tabu search with the solutions obtained from the genetics process to form a new population; Step S8: Determine whether the number of iterations has reached the maximum number of generations Max_gen. If not, return to step S4 to continue iterative calculation. If it has, output the first y optimal sequences of the PROP_O model based on the number of solutions y, and calculate the relevant decision variables. Step S9: Substitute the optimal sequence and relevant decision variables of the PROP_O model into the MILP model, and use the exact solver to obtain the precise coordinates of the material loading and unloading points on each facility and the final target value of the APPROP_O model.

2. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The parameters include population size N, maximum number of generations Max_gen, crossover rate Pc, mutation rate Pm, selection rate S, elite rate Elite, maximum number of generations for tabu search Ts_gen, initial tabu list length Ts_len, and number of solutions y.

3. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The optimal solution strategy includes the following steps: Step 1) Set the population size N and the desired minimum gap min_gap; Step 2) Randomly generate a solution set consisting of N solutions that satisfy the condition that the gap is less than the minimum gap min_gap; Step 3) With the goal of minimizing the target value, use a roulette wheel to select N / 2 solutions from the solution set of Step 2); Step 4) Randomly generate N / 2 solutions and combine them with the solutions selected by the roulette wheel operation in Step 3) to form a new initial population Pop of size N.

4. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The neighborhood search operation includes an equal number of 2-opt operations and a reversal operation, the sum of which equals the problem size.

5. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The selection operation described in step S6-2 is as follows: with the goal of minimizing the target value, a roulette wheel selection is performed, the selected solution is used for subsequent operations, and the unselected solution is returned to be added to the elite solution partitioning of the next iteration.

6. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The dominant crossover operation described in step S6-2 is as follows: Select two adjacent solution individuals, with the one with the smaller objective value as the dominant individual and the one with the larger objective value as the non-dominant individual. Under the condition of satisfying the feasibility of the solution, randomly select a segment from the dominant individual and a replacement segment from the non-dominant individual for crossover combination to form a child solution individual.

7. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The mutation operation described in step S6-2 is a 2-opt operation.

8. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The decision variable is α. ij β ik q ijk γ ij .

9. The 3D parallel layout solution method considering adaptive material loading / unloading points and obstacles according to claim 1, characterized in that: The exact solver is the Gurobi solver.

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