3D parallel layout solving method considering adaptive material loading and unloading points and obstacles

Abstract

A 3D parallel 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 an objective function, initializing parameters, generating an initial population, converting an infeasible solution in the initial population into a feasible solution, and optimizing the initial population. Removing repeated solutions in the initial population, randomly generating feasible solutions to fill the initial population, dividing the initial population into an elite solution and a non-elite solution, performing tabu search operation on the elite solution, performing genetic manipulation on the non-elite solution, combining the solutions after the two operations into a new population, and outputting an optimal sequence and a decision variable of a model according to the number of iterations. Utilizing the optimal sequence and the decision variable to solve and obtain the accurate coordinate of the material loading and unloading point on each facility and the final target value of the model; according to the method, adaptive material loading and unloading points and obstacle interference factors in a three-dimensional space are considered, the obtained model is closer to the real situation, and subsequent making of a more scientific facility plan and a material carrying strategy is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of facility layout, and specifically to a 3D parallel row layout solution method considering adaptive material handling points and obstacles. Background Art

[0002] The Parallel Row Ordering Problem (PROP) is a relatively novel problem in facility layout. Aiming at minimizing the material handling cost, it studies how to arrange a series of facilities in parallel rows, and is often applied to the fermentation food industry and similar industries that require equipment to be arranged in zones. The parallel row layout can improve the material handling efficiency, enhance the workshop response speed, and is very suitable for flexible manufacturing workshops, which has a positive promoting effect on the transformation and upgrading of the current manufacturing industry. Therefore, PROP has received extensive attention in recent years.

[0003] Material Handling Points (MHP) refer to specific positions where materials are handled between different processes or equipment in a factory or workshop. The reasonable design and layout of these positions have an important impact on the efficiency of the entire production system. However, currently, the vast majority of researchers fix them at a single point in the center of the facility. In addition, there are often obstacles in the workshop layout, such as beams, cables, and pipes existing at the beginning of the factory construction. The influence of obstacles is mainly reflected in the detour of the material handling path, the limitation of equipment placement, and the reduction of available layout space. For the convenience of problem assumption, most researchers generally do not consider the existence of obstacles. Some researchers who consider obstacles only discuss the interference situation of obstacles in the two-dimensional space, resulting in a large deviation between the research results and the actual situation, which is not conducive to the popularization and application of research results in reality. Summary of the Invention

[0004] In view of this, the main purpose of the present invention is to provide a 3D parallel row layout solution method considering adaptive material handling points and obstacles, which expands the research object from the simple Parallel Row Ordering Problem With Obstacles (PROP_O) to the Adaptive Material Handling Point Parallel Row Ordering Problem With Obstacles (APPROP_O), and considers obstacle interference and relaxes the constraints of MHP during the calculation process, making the model closer to the actual production and living situation, and helping enterprises formulate more scientific facility planning and material handling strategies.

[0005] The technical solution of the present invention is a 3D parallel layout solving method considering adaptive material handling points and obstacles, including the following steps:

[0006] Step S1: Collect facility layout information and establish an objective function involving the sum of material handling costs, the amount of unit interactive materials between facilities, and the product of handling distances.

[0007] Step S2: Initialize parameters, calculate the channel width within the area, obstacle coordinates, and determine the equipment that may cause height interference.

[0008] Step S3: Generate an initial population Pop, convert the infeasible solutions in the initial population Pop into feasible solutions, and optimize the initial population Pop using an optimal solution strategy.

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

[0010] Step S5: Calculate the fitness 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 solutions Elite_r until the upper limit of the number of times is reached to obtain the solutions after the tabu search. The tabu search operation method is as follows: with the aim of minimizing the objective value as much as possible, perform multiple neighborhood search operations on the elite solutions Elite_r.

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

[0013] Step S7: Combine the solutions after the tabu search and the solutions after the genetic operations into a new population.

[0014] Step S8: Determine whether the number of iterations has reached the maximum genetic algebra Max_gen. If not, return to Step S4 to continue the iterative calculation. If so, output the first y optimal sequences of the PROP_O model according to the number of substituted solutions y, and calculate the relevant decision variables.

[0015] Step S9: Substitute the optimal sequences and relevant decision variables of the PROP_O model into the MILP model and solve it using an exact solver to obtain the exact coordinates of the material handling points on each facility and the final objective value of the APPROP_O model.

[0016] The technical effect of the present invention is:

[0017] 1. Based on the parallel sorting problem model, the present invention takes into account the adaptive material loading and unloading points and obstacle interference factors in three-dimensional space, making the obtained model closer to the actual production and living conditions, and contributing to the subsequent formulation of more scientific facility planning and material handling strategies.

[0018] 2. The algorithm in the present invention is the two-stage Advantage Genetic Algorithm Tabu Search (AGATS), which has the characteristics of both combinatorial optimization and continuous optimization, can effectively integrate the solution requirements of discreteness and continuity, and improves the solution quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments.

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

[0021] Figure 2 is the process of encoding, decoding and transforming infeasible solutions in the present invention;

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

[0023] Figure 4 is the schematic diagram of the advantage crossover operation in the present invention;

[0024] Figure 5 is the box plot of the solution results obtained by GATS and AGATS respectively in the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0025] The following will further elaborate on the present invention in combination with the embodiments and the drawings.

[0026] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention, rather than all of 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 fall within the scope of protection of the present invention.

[0027] Embodiment:

[0028] A 3D parallel layout solution method considering adaptive material loading and unloading points and obstacles includes the following steps:

[0029] Step S1: The material handling cost is determined by the sum of the products of the unit interactive material handling volume between facilities and the handling distance, which is a key indicator for evaluating the layout quality. Therefore, collect the facility layout information and establish an objective function involving the sum of the material handling cost, the product of the unit interactive material handling volume between facilities, and the 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 abscissa of facility i in the first row; (9) is used to calculate the abscissa of facility i in the second row:

[0034]

[0035]

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

[0037]

[0038] Equations (14) to (17) are used to calculate the abscissa and ordinate 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 in the same row:

[0043]

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

[0045]

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

[0047]

[0048]

[0049] Among them, n is the number of facilities; n r is the number of facilities in a single row. When r = 1, n r represents the number of facilities in the first row. When r = 2, n r represents the number of facilities in the second row; m is the number of obstacles; N is the set of facilities, N = {1, 2, …, n}; K is the set of obstacles, K = {1, 2, …, m}; N r is the set of single-row facilities. When r = 1, N r represents the set of facilities in the first row. When r = 2, N r 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 is the length of facility i in the X direction; l j is the length of facility j in the X direction; w i is the length of facility i in the Y direction; w j is the length of facility j in the Y direction; h i is the length of facility i in the Z direction; lo k is the length of obstacle k in the X direction; wo k is the length of obstacle k in the Y direction; ho k is the length of obstacle k in the Z direction; zo k is the coordinate of the geometric center point of obstacle k in the Z direction; f ij is the material flow volume between facility i and facility j;

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

[0051] xp i is the coordinate of the material loading and unloading point of facility i in the X direction; yp i is the coordinate of the material loading and unloading point of facility i in the Y direction; zp iThe coordinate of the material loading and unloading point of facility i in the Z direction; xp j The coordinate of the material loading and unloading point of facility j in the X direction; yp j The coordinate of the material loading and unloading point of facility j in the Y direction; zp j The coordinate of the material loading and unloading point of facility j in the Z direction; The coordinate of the geometric center point of facility i in the X direction, when r = 1, Represents the abscissa of facility i in the first row, when r = 2, Represents the abscissa of facility i in the second row; The coordinate of the geometric center point of facility j in the X direction, when r = 1, Represents the abscissa of facility j in the first row, when r = 2, Represents the abscissa of facility j in the second row; xo k The coordinate of the geometric center point of obstacle k in the X direction; The distance between the material loading and unloading points of facility i and facility j in the X direction within a certain row. When r = 1, both facility i and facility j are in the first row. When r = 2, both facility i and facility j are in the second row; The distance between the material loading and unloading points of facility i and facility j in the X direction, at this time facility i and facility j are arranged in different rows; D ij r The sum of the distances between the material loading and unloading points of facility i and facility j in the Y direction and Z direction within a certain row. When r = 1, both facility i and facility j are in the first row. When r = 2, both facility i and facility j are in the second row; D ij 12 The sum of the distances between the material loading and unloading points of facility i and facility j in the Y direction and Z direction, at this time facility i and facility j are arranged in different rows; α ij Is a 0 - 1 variable. If facility i and facility j are in the same row and both facility i and j are on the same side of obstacle k, then α ij = 1, otherwise α ij = 0; β ik Is a 0 - 1 variable. If facility i and obstacle k are in the same row and facility i is arranged on the left side of obstacle k, then β ik = 1, otherwise β ik = 0; β jk Is a 0 - 1 variable. If facility j and obstacle k are in the same row and facility j is arranged on the left side of obstacle k, then β jk = 1, otherwise β jk = 0; q ijk Is a 0 - 1 variable. If facility i is on the left side of facility j and both i and j are on the left side 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 is 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 is 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 is a 0-1 variable. If facility i and facility j are in the same row 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 within the area, obstacle coordinates, and identify devices that may have height interference. Among them, the initialized parameters mainly include population size N, maximum genetic algebra Max_gen, crossover rate Pc, mutation rate Pm, selection rate S, elite rate Elite, maximum tabu search algebra Ts_gen, initial tabu list length Ts_len, and the number of substitution solutions y.

[0053] Step S3: Generate the initial population Pop, convert the infeasible solutions in the initial population Pop into feasible solutions, and optimize the initial population Pop using the optimal solution strategy.

[0054] Considering that there should be no overlap between the obstacle and the facilities, during the decoding process and all subsequent operations, infeasible solutions need to be converted into feasible solutions. For the characteristics of the problem, the present invention designs a segmented encoding and decoding method. The feasible solution can be expressed as [R1, R2], and both use real number encoding. Let the problem scale be n, where the number of facilities in the first row is t and the number of facilities in the second row is n - t. However, due to considering the obstacle interference in the horizontal coordinate direction in the first row, the actual problem scale is n + 1. R1 is the first t + 1 items of the solution, where the serial number n + 1 represents the obstacle. Considering that there should be no overlap between the obstacle and the facilities, during the decoding process and all subsequent operations, infeasible solutions need to be converted into feasible solutions. Taking n = 9 as an example, the encoding, decoding, and conversion of infeasible solutions of this sequence are as follows Figure 2As shown. The given sequence is [3, 1, 4, 10, 2, 9, 5, 6, 7, 8], where t = 4, and the serial number 10 represents an obstacle. Assuming that there is interference in the facilities on the left side of the obstacle at this time, the facilities on the left side of the obstacle are moved to be closely adjacent to the right side of the obstacle until the non-overlapping constraint condition is satisfied.

[0055] In addition, the method for judging the solution feasibility is as follows: Calculate the coordinates of the obstacle and the facilities on its left side, and determine whether there is overlap in combination with its length. If there is overlap, this solution is an infeasible solution. If it is an infeasible solution, the facilities that overlap with the obstacle are inserted to the right side of the obstacle and are closely adjacent to the obstacle without gaps. Then continue to judge whether there is overlap, and repeat the above operations until there is no overlap.

[0056] Due to the existence of the obstacle, there may be gaps between the facilities and the obstacle, resulting in an increase in the abscissa of the facilities on the right side of the obstacle and thus increasing the handling distance of the facilities. Therefore, the present invention also designs an optimal solution strategy, which mainly includes the following steps:

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

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

[0059] Step 3) With the aim of making the target value as small as possible, select N / 2 solutions from the solution set in Step 2) by using the roulette wheel operation;

[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 with a size of N.

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

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

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

[0064] Step S6-1: Perform the tabu search operation on the elite solutions Elite_r until the upper limit of the number of times, and obtain the solutions after the tabu search. Among them, the tabu search operation method is as follows: With the aim of making the target value as small as possible, perform multiple neighborhood search operations on the elite solutions Elite_r;

[0065] The main idea of the elite strategy is that in the selection process of each generation, the best individual in the current population, that is, the individual with the highest fitness, is directly retained in the next generation. This approach can ensure the inheritance of excellent genes and avoid the loss of outstanding individuals that may occur during the selection process. Therefore, the present invention performs tabu search on the elite solution of each generation. If the neighborhood solution after tabu search is better than the current solution, it is replaced with a new elite solution. The specific neighborhood search operations include an equal number of 2-opt operations and inversion operations, and the sum of the two numbers is the size of the problem scale. As the problem scale increases, the neighborhood search operations also increase. As Figure 3 shown, it can be seen that 2-opt is Figure 3 to randomly select two numbers from the random sequence in and swap their positions, and for inversion, all the numbers that can be mirrored between two randomly selected numbers are mirror-processed.

[0066] Step S6-2: Perform genetic operations on the non-elite solutions to obtain the solutions after genetics. Among them, the genetic operations include selection, dominant crossover, and mutation operations. The selection operation also uses roulette wheel selection with the goal of minimizing the objective value as much as possible. Among them, the selected solutions are used for subsequent operations, and the unselected solutions are used as variables for dividing the elite solutions in the next iteration. For example, if there are 100 solutions in a certain generation, 60 of them are selected by roulette wheel for subsequent operations, and the remaining solutions are retained. After this iteration ends, they are compared with the 40 retained solutions to select the elite solutions, and then the next iteration is carried out.

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

[0068] The crossover operation allows the exchange of genetic information between parental individuals, thereby generating new offspring individuals. It can not only maintain the diversity of the population but also enhance the adaptability of the offspring individuals and improve the overall performance of the algorithm. In the crossover operation of traditional genetic algorithms, some valuable gene information may be discarded, and such information loss may lead to a decrease in the fitness of the offspring individuals. To make up for this deficiency, the present invention proposes a dominant crossover operation. The specific process is as Figure 4 shown. Take two adjacent solutions as two parents. Among the two parents, the individual with a smaller objective value is called the dominant individual, and the one with a larger objective value is called the non-dominant individual. During crossover, under the condition of feasibility, operate on two segments of rows. For the first segment, randomly select two crossover points from the 1 to t + 1 positions of the dominant individual, and inherit this segment of genes to the offspring. Then scan the non-dominant individual from left to right. If the element is not in the offspring, inherit this element to the same position in the offspring, and finally randomly allocate the remaining elements. Perform the same operation on the second segment, and combine the first segment and the second segment into the offspring solution.

[0069] Step S7: Combine the solutions after tabu search and the solutions after genetics into a new population;

[0070] Step S8: Determine whether the number of iterations reaches the maximum genetic algebra Max_gen. If not, return to Step S4 to continue iterative calculation. If so, output the first y optimal sequences of the PROP_O model according to the number of substitution 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 on each facility and the final objective value of the APPROP_O model.

[0072] A number of feasible solutions of PROP_O obtained by the algorithm can be used to determine the decision variables α ij , β ik , q ijk , γ ij values. Substitute the feasible solutions and decision variables into the MILP model shown in Equation (1) in the previous text, and use the exact solver Gurobi to further optimize. The PROP_O model can be understood as the APPROP_O model removing the aforementioned formulas (10) to (17), and at the same time, the calculation method of the material handling distance is changed from using the coordinate difference of the material loading and unloading points on the facility to using the coordinate difference of the facility to calculate. Finally, the exact coordinates of the MHP on each facility and the final objective value of the APPROP_O are obtained.

[0073] The following is the effect display in the actual operation of this embodiment:

[0074] Program test environment:

[0075] The simulation calculation environment is an Intel(R) Core(TM) i5-9300H processor with a main frequency of 2.4 GHz, Windows 11 operating system, 16.00 GB of memory. Use Matlab R2023a to call the exact solver Gurobi to solve the model, and use its results as the basis of the algorithm.

[0076] To further verify the solution performance of AGATS disclosed in the present invention, 13 examples with scales ranging from 9 to 49 are selected. The conventional Genetic Algorithm Tabu Search (GATS) and AGATS in the present invention are used to solve them respectively. Each example is run ten times, and the calculation results are stored. The obtained data is processed into percentages using a formula. The processed value is the solution deviation Gap, and its solution formula is Gap = (g - G) / G × 100%, where g is the current target value and G is the minimum target value among 20 data in the same group. The processed data is plotted as a box plot as Figure 5 shown, where the red solid line, black dashed line, upper and lower edge lines of the rectangular box, and upper and lower black solid lines represent the median, mean, upper and lower quartiles, and the maximum and minimum values of the data respectively.

[0077] As Figure 5 can be seen, when solving problems with scales from 9 to 15, both GATS and AGATS show good performance. However, as the problem scale expands, the box plot of AGATS is more compact than that of GATS, which reflects that the solution results of AGATS are more concentrated, with smaller fluctuations and stronger stability. At the same time, in the solution of medium and large-scale problems, the average target value of AGATS is significantly lower than that of GATS, further indicating that AGATS has higher reliability in terms of solution quality and its results have smaller dispersion.

[0078] In summary, in view of the deficiencies in the 3D parallel layout research regarding the existence of obstacles and material handling points in the workshop, the present invention proposes a 3D parallel sequencing problem considering adaptive material handling points and obstacles. Aiming at the dual characteristics of this problem, an AGATS algorithm combining an intelligent algorithm and linear programming is constructed. Through the solution of standard examples, the superior performance of the proposed algorithm is verified.

[0079] The above is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles, characterized by: The following steps are involved: Step S1: Collect facility layout information and establish an objective function involving the sum of the product of material handling cost, unit interaction material handling volume between facilities, and handling distance: Among them, the constraints satisfied by the objective function are: Material handling distance constraints: Facility coordinate constraints: Material loading and unloading point layout range constraints: Horizontal and vertical coordinate constraints of material loading and unloading points: Material handling distance constraint from facility i to facility j: Anti-overlapping interference constraints for peer facilities: Anti-overlapping interference constraints between facilities and ground obstacles: Anti-overlap interference constraints between facilities and suspended obstacles: Decision variables and decision variable domain constraints: Where n is the number of facilities; r is the number of facilities in a single row, when r = 1, n r Indicates the number of facilities in the first row. When r = 2, n r represents the number of facilities in the second row; m is the number of obstacles; N is the set of facilities, N = {1,2,...,n}; K is the set of obstacles, K = {1,2,...,m}; N r is a single-row facility set, when r = 1, N r Represents the facility set of the first row. When r = 2, N r represents the facility set of the second row; i, j, s are the facility numbers, i, j, s∈N; k is the obstacle number, k∈K; l i is the length of facility i in the X direction; l j is the length of facility j in the X direction; w i is the length of facility i in the Y direction; w j is the length of facility j in the Y direction; h i is the length of facility i in the Z direction; lo k is the length of obstacle k in the X direction; wo k is the length of obstacle k in the Y direction; ho k is the length of obstacle k in the Z direction; k is the coordinate of the geometric center point of obstacle k in the Z direction; f ij is the logistics volume between facility i and facility j; is the minimum height at which the material loading and unloading point can be arranged on facility i, where is the maximum height at which the material loading and unloading point can be arranged on facility i, where is the minimum length of the material loading and unloading point that can be arranged on facility i, where is the minimum length of the material loading and unloading point that can be arranged on facility i, where r is the channel width; xp i is the coordinate of the material loading and unloading point of facility i in the X direction; yp i is the coordinate of the material loading and unloading point of facility i in the Y direction; zp i xp is the coordinate of the material loading and unloading point of facility i in the Z direction; j yp is the coordinate of the material loading and unloading point of facility j in the X direction; j is the coordinate of the material loading and unloading point of facility j in the Y direction; zp j is the coordinate of the material loading and unloading point of facility j in the Z direction; is the coordinate of the geometric center point of facility i in the X direction, when r = 1, Indicates the horizontal coordinate of facility i in the first row. When r=2, represents the horizontal coordinate of facility i in the second row; is the coordinate of the geometric center point of facility j in the X direction, when r = 1, Indicates the horizontal coordinate of facility j in the first row. When r=2, Indicates the horizontal coordinate of facility j in the second row; xo k is the coordinate of the geometric center point of obstacle k in the X direction; is the distance in the X direction between the material loading and unloading points of facility i and facility j in a row. When r=1, facility i and facility j are both in the first row. When r=2, facility i and facility j are both in the second row. is the distance between the material loading and unloading points of facility i and facility j in the X direction, when facility i and facility j are arranged in different rows; It is the sum of the distances between the material loading and unloading points of facility i and facility j in a row in the Y direction and the Z direction. When r=1, facility i and facility j are both in the first row, and when r=2, facility i and facility j are both in the second row. is the sum of the distances between the material loading and unloading points of facility i and facility j in the Y direction and the Z direction, when facility i and facility j are arranged in different rows; ij is a 0-1 variable. If facility i is in the same row as facility j, and facilities i and j are on the same side of obstacle k, then α ij =1, otherwise α ij =0;β ik is a 0-1 variable. If facility i and obstacle k are in the same row, and facility i is arranged on the left side of obstacle k, then β ik =1, otherwise β ik =0;β jk is a 0-1 variable. If facility j and obstacle k are in the same row and facility j is arranged on the left side of obstacle k, then β jk =1, otherwise β jk =0;q ijk is a 0-1 variable. If facility i is on the left side of facility j, and both i and j are on the left side of the obstacle, then q ij1 =1, otherwise q ij1 = 0, if facility i is on the left side of facility j, and both i and j are on the right side of the obstacle, then q ij2 =1, otherwise q ij2 =0;q jik is a 0-1 variable. If facility j is on the left side of facility i, and both i and j are on the left side of the obstacle, then q ji1 =1, otherwise q ji1 = 0, if facility j is on the left side of facility i, and both i and j are on the right side of the obstacle, then q ji2 =1, otherwise q ji2 =0;q isk is a 0-1 variable. If facility i is on the left side of facility s, and both i and s are on the left side of the obstacle, then q is1 =1, otherwise q is1 = 0, if facility i is on the left side of facility s, and both i and s are on the right side of the obstacle, then q is2 =1, otherwise q is2 =0;γ ij is 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 channel width and obstacle coordinates in the area, and determine the equipment that may cause high interference; Step S3: Generate an initial population Pop, transform the infeasible solutions in the initial population Pop into feasible solutions, and use the optimal solution strategy to optimize the initial population Pop; Step S4: remove duplicate solutions in the initial population Pop, and randomly generate the same number of feasible solutions to fill the initial population Pop; Step S5: Calculate the fitness Fitness, and divide the initial population Pop into elite solutions Elite_r and non-elite solutions Nelite_r; Step S6-1: Perform a taboo search operation on the elite solution Elite_r until the upper limit of the number of times is reached to obtain a solution after the taboo search, wherein the taboo search operation method is: perform multiple neighborhood search operations on the elite solution Elite_r with the purpose of minimizing the target value as much as possible; Step S6-2: Perform genetic operations on the non-elite solution to obtain a genetic solution, wherein the genetic operation includes selection, dominant crossover and mutation operations; Step S7: Combining the solution after taboo search and the solution after genetics into a new population; Step S8: Determine whether the number of iterations reaches the maximum genetic generation Max_gen. If not, return to step S4 to continue iterative calculation. If reached, output the first y optimal sequences of the PROP_O model according to the number of solutions y, and calculate the relevant decision variables. Step S9: Substitute the optimal sequence and related decision variables of the PROP_O model into the MILP model and solve it using the exact solver to obtain the precise coordinates of the material loading and unloading points at each facility and the final target value of the APPROP_O model.

2. The 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles according to claim 1 is characterized by: The parameters include population size N, maximum genetic generation Max_gen, crossover rate Pc, mutation rate Pm, selection rate S, elite rate Elite, maximum taboo search generation Ts_gen, initial taboo table length Ts_len, and the number of solutions y.

3. The 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles according to claim 1 is characterized by: 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 satisfying that the gap is less than the minimum gap min_gap; Step 3) With the goal of minimizing the target value, a roulette wheel operation is used to select N / 2 solutions from the solution set of step 2); Step 4) randomly generates N / 2 solutions, which are combined with the solution selected by the roulette operation in step 3) to form a new initial population Pop of size N.

4. The 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles according to claim 1 is characterized by: The neighborhood search operation includes an equal number of 2-opt operations and inversion operations, and the sum of the two operations is the problem scale.

5. The 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles according to claim 1 is characterized by: The selection operation described in step S6-2 is: with the purpose of making the target value as small as possible, roulette wheel selection is performed, the selected solution is used for subsequent operations, and the unselected solution is returned to be added to the division of the elite solution of the next iteration.

6. The 3D parallel row layout solution method considering adaptive material loading and unloading points and obstacles according to claim 1 is characterized by: The dominant crossover operation described in step S6-2 is: select two adjacent solution individuals, take the one with the smaller target value as the dominant individual, and the one with the larger target value as the non-dominant individual. Under the condition of satisfying the feasibility of the solution, randomly select fragments in the dominant individual and the replacement fragments in the non-dominant individual to cross-combine as the offspring solution individual.

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

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

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