Vertical prefabricated part storage yard storage location distribution method based on multi-objective optimization

Abstract

The invention provides a vertical prefabricated part storage yard storage location distribution method based on multi-objective optimization. The method comprises the following steps: firstly, constructing a storage yard storage location optimization data set according to a storage yard storage condition, entering prefabricated part information and a joist barrow working state; then, on the premise of resource constraint and space constraint, a storage yard storage location optimization model is constructed with the purposes of improving the operation parallelism degree of a multi-truss vehicle, reducing the entering carrying completion time and storing related prefabricated parts nearby; on the basis of the storage yard storage location optimization data set and the model, an improved non-dominated sorting genetic algorithm NSGA-II is adopted, and through fitness value evaluation, non-dominated sorting, congestion degree calculation and multiple times of preferential iteration, a plurality of high-quality solutions on the Pareto leading edge are output; and finally, selecting an individual with all optimal target values and minimum chromosome codes as an optimal stockpiling scheme, and carrying out visual display. Reasonable reference is provided for the fabricated building factory, storage yard management is standardized, space utilization is optimized, and storage yard operation efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optimized management of precast component yards for prefabricated buildings, and particularly to a storage location allocation method for vertical precast component yards based on multi-objective optimization. Background Art

[0002] With the popularization and application of prefabricated buildings, the proportion of precast components in building construction has gradually increased. As an important place for storing, transporting, and assembling precast components, the management and optimization of prefabricated building yards have become an important link in improving construction efficiency and reducing costs. The reasonable allocation of storage locations for precast components not only relates to the effective utilization of yard space but also directly affects cost control and construction progress. In this context, the optimization of storage location allocation for precast components is particularly crucial, which involves how to efficiently manage and allocate the storage locations of the yard to quickly and accurately complete the storage and retrieval operations of precast components.

[0003] However, at present, the storage location allocation of precast components in prefabricated buildings still relies on manual experience, resulting in problems such as waste of yard space, chaotic stacking, increased handling paths, and inconvenient scheduling of precast components. Therefore, how to achieve automatic allocation of storage locations for precast components through automated or intelligent technical means is an urgent problem to be solved.

[0004] The storage location allocation of precast components essentially belongs to a type of combinatorial optimization problem. Due to involving a large number of decision variables, multi-objective optimization, and complex constraints, the solution space is extremely large and is usually classified as an NP-hard problem. With the wide application of intelligent optimization algorithms, such complex optimization problems can find relatively ideal solutions in a short time. In the field of storage location allocation for goods in container ports and warehouses, there are relatively mature theories and methods, but in prefabricated building yards, relevant research is still scarce. Due to the diverse specifications of precast components and specific requirements for stacking methods, the complexity of storage location planning has been significantly improved, which poses higher adaptability and refinement requirements for optimization methods. Summary of the Invention

[0005] The purpose of the present invention is to provide a storage location allocation method for vertical precast component yards based on multi-objective optimization. For the stacking method of vertical precast components that need to be placed vertically in a single layer, based on the yard layout, a storage location allocation method for vertical precast component yards based on multi-objective optimization is provided, which is of great significance for optimizing the management of precast component yards in prefabricated buildings, providing guidance and decision-making support for relevant enterprises, and filling the gap in existing research.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: A storage location allocation method for vertical precast component yards based on multi-objective optimization, comprising the following steps: S1. Obtain the yard storage situation, information on incoming precast components, and the working status of the gantry cranes, and construct an optimization dataset for yard storage positions; S2. On the premise of resource constraints and space constraints, with the goals of improving the parallelism of multi-gantry crane operations, reducing the completion time of incoming handling, and storing associated components nearby, construct an optimization model for yard storage positions; S3. Based on the optimization dataset and model of yard storage positions, adopt the improved non-dominated sorting genetic algorithm NSGA-II. Through fitness value evaluation, non-dominated sorting, and crowding degree calculation, perform several rounds of optimal selection and iteration, and output multiple high-quality solutions on the Pareto front; S4. Select the individual with the best objective values and the smallest chromosome encoding among the high-quality solutions as the optimal storage plan, and visually display it in the form of a three-dimensional coordinate system.

[0007] Furthermore, the yard storage situation includes the yard layout, storage position distribution information, and the total storage quantity and allocated storage position information of each yard at the moment of incoming precast components; the information on incoming precast components includes the incoming order, component number, destination, and departure time of incoming vertical precast components; the working status of the gantry cranes refers to whether the gantry cranes are working and their average moving speed.

[0008] Furthermore, the resource constraints and space constraints are constructed based on the optimization dataset of yard storage positions, and the conditions of the resource constraints and space constraints are represented by the following formulas (1)-(5): (1); (2); (3); (4); (5); In formulas (1)-(5): represents the incoming order of a batch of precast components; represents the yard number; represents the column number in the yard; represents the row number in the yard; , , all represent the maximum values of the numbers; represents the initial container quantity of yard ; formula (1) means that one precast component in the yard can only occupy one storage position; formula (2) means that one storage position in the yard can store at most one precast component. If , it means the storage position is vacant. If , indicating that the storage location is occupied; Equation (3) indicates that the initial position of each yard gantry crane is in the first row; Equation (4) indicates that the number of precast components allocated in the yard should be less than the yard capacity; Equation (5) defines the value range of the decision variables.

[0009] Furthermore, the yard storage location optimization model is represented by the following Equations (6)-(13): (6); (7); (8); (9); (10); (11); (12); (13); Equations (6)-(8) are the objective functions for storage location allocation, where: indicates minimizing the stockpiles between yards to achieve the purpose of improving the parallel operation degree of multiple gantry cranes; indicates minimizing the handling completion time; indicates storing associated precast components nearby; indicates the longitudinal length of the storage location in the yard, and the moving cost of the gantry crane between columns is ignored; indicates the average speed of the gantry crane movement; In Equations (9)-(13): is a 0-1 decision variable. When the precast component is allocated to the storage location , its value is 1, otherwise 0; indicates the precast component and the correlation coefficient between them; , are weights, and their sum is 1. The selection of weights can be adjusted according to requirements; is a 0-1 decision variable. When the precast component and have the same destination, its value is 1, otherwise 0; , respectively indicate the destinations of the precast components and ; indicates the precast component and The departure time proximity. If the difference in departure times between two components is small, their relationship is closer; , respectively represent the precast components and departure times; , respectively represent the maximum and minimum values of the departure times of all precast components; represents the distance between the precast components and . If and are located in the same storage yard, the distance is the absolute difference in row numbers; otherwise, the distance is set to a relatively large value D; , respectively represent the row numbers where the precast components and are located; represents the distance between columns in the storage yard; , respectively represent the column numbers where the precast components and are located; , respectively represent the storage yard numbers where the precast components and are located.

[0010] Furthermore, the specific implementation of S3 is as follows: S31. Initialize relevant parameters, set the population size N, the individual crossover probability , the individual mutation probability and the maximum number of iterations T, and process the storage location optimization data set to extract the storage yard storage situation, the entry order of precast components, the destination, and the departure time; S32. Perform three-layer chromosome coding. Each chromosome coding is an individual, generating an initial community that meets the population size N. At the same time, check for individual duplicates. Convert the individuals to strings and hash them for comparison, and add the different individuals to the initial parental population ; In the three-layer chromosome coding, the coding order of the chromosome from left to right is the order of the precast components entering the yard. Each column represents the coordinates of the precast component in the storage yard. Each column of coordinates is composed of the storage yard number, the column number, and the row number. Generate 3 random integers within their respective value ranges as a storage location coordinate and add it to a column of the chromosome until the length of the chromosome reaches the number of precast components entering the yard, and ensure that the coordinates do not repeat, thus forming a complete chromosome. Each chromosome represents a stacking plan for the precast vertical components entering the yard; S33. By traversing the parental population , randomly select two parent individuals for crossover operation. According to the decimal number within the range of (0, 1) randomly generated and the crossover probability decide whether to perform two-point crossover, and generate a legal offspring population with the same size as the parent population after duplicate removal and patching ; In the said crossover operation, traverse half of the population, and randomly select two parent individuals from the parent population . The selected parent individuals will not be selected repeatedly. If the randomly generated decimal number is less than the individual crossover probability , then perform two-point crossover on the two parent individuals, that is, randomly select two crossover points, exchange the segments between the two parents at the crossover points, and check for duplicate columns and perform replacement patching to obtain two offspring individuals after crossover; if the randomly generated decimal number is greater than the individual crossover probability , then directly copy the parent individuals to the offspring until the number of offspring individuals meets the population size; thus generate an offspring population with the same size of N . After that, check whether there are duplicate individuals among them. If so, replace them with newly randomly generated legal individuals; S34. Perform mutation operation, traverse the offspring population , and randomly update the individual coordinate values and patch duplicate individuals according to the decimal number within the range of (0, 1) randomly generated and the crossover probability to update it to the mutated offspring population ; In the said mutation operation, for each individual in the offspring population after crossover , if the randomly generated decimal number is less than the individual mutation probability , then randomly regenerate a random dimension of one of its column coordinates, update the individual coordinate values, and at the same time check for duplicate columns and perform replacement patching; if the randomly generated decimal number is greater than the individual mutation probability , then do not mutate the individual; then for the mutated offspring population , check whether there are duplicate individuals among them; S35. Combine the parent population and the offspring population into a temporary population with a size of 2N , design a fitness function according to the optimization objective and calculate the fitness value to evaluate the pros and cons of each individual, that is, calculate the parallelism of the gantry crane operation, the handling completion time, and the adjacency of related components; S36. Perform fast non-dominated sorting, assign each individual in the temporary population to different domination levels. There is no mutual domination relationship among individuals in the same domination level, while in different domination levels, individuals with smaller domination level numbers dominate individuals with larger domination level numbers; S37. Calculate the crowding degree of each individual among the non-dominated solutions of each layer , that is, the sparsity degree of the solutions around the individual; S38. Perform the selection operation. Based on the fast non-dominated sorting and crowding degree calculation, select the top N optimal individuals from the temporary population to form a new parental population to enter the next generation; S39. Repeat steps S33 - S38 to continuously iterate and optimize the population until the maximum iteration number T is reached, and obtain the Pareto front that meets all optimization objectives.

[0011] Furthermore, designing the fitness function and calculating the fitness value includes: Calculate the parallelism of the gantry crane operation. The more balanced the stockpiles in multiple yards are, the higher the parallelism of the gantry crane operation. That is equivalent to calculating the difference in the number of precast components between the yard with the largest stockpile and the yard with the smallest stockpile; see formula (6); Calculate the completion time of the precast component's in-yard handling. Assume that there is only one gantry crane in each yard, which can only move along the column direction, and the spacing between each row is equal. Based on the current stockpile situation in the yard, perform storage location allocation according to the in-yard order. The initial position of the gantry crane in each yard is in the first row, and it moves continuously according to the allocated storage location. Calculate the sum of the moving distances of all gantry cranes, and then divide it by the average speed of the gantry crane, which is the completion time of the in-yard handling; see formula (7); Calculate the adjacency of associated components. That is, following the principle of storing associated precast components nearby, allocate precast components that are associated with each other to nearby storage locations to make the associated precast components more concentrated in storage to reduce the gantry crane's moving cost. This objective can be calculated by minimizing the sum of the product of the relationship coefficient between precast components and the storage distance; see formula (8).

[0012] Furthermore, the specific steps of the fast non-dominated sorting include the following: S361. Initial setting. Take the fitness values of all individuals in the temporary population as input, and use with an initial value of 0 to represent the number of individuals dominated by other individuals, and use initially empty to represent the set of other individuals dominated by the individual , and use to represent the individual index used to store the first non-dominated layer; S362. Determine the dominance relationship. For each pair of individuals and in the population, if the individual is not inferior to the individual in all objectives and is superior to in at least one objective, then dominate , and add to ; if dominates , then increase the count of ; S363. Traverse all individuals. If the domination count of an individual is , add it to the frontier set of layer 0 ; S364. Construct frontiers of higher layers. Starting from , for each individual in the current layer, traverse all individuals dominated by , subtract 1 from the domination count of . If , add to the frontier set of the next layer , , increment step by step and repeat this process until no new frontiers are generated; S365. Return all frontiers front. The individual indices in each frontier correspond to a non - dominated layer.

[0013] Furthermore, the crossover and mutation operations both adopt adaptive crossover and mutation operators, that is, the crossover and mutation probabilities are adaptively adjusted as the number of iterations increases. In the initial stage of iteration, the population diversity is high, and the crossover and mutation probabilities are relatively low; in the later stage of iteration, increase the crossover and mutation probabilities to encourage the generation of new individuals, expand the search range, and avoid falling into local optimal solutions; specifically, it is represented by the following formulas (14) - (15): (14); (15); In formulas (14) - (15): represents the initial minimum crossover probability; represents the initial minimum mutation probability; represents the final maximum crossover probability; represents the final maximum mutation probability; represents the current number of iterations; represents the maximum number of iterations.

[0014] Furthermore, the larger the value of the crowding degree, the sparser the solutions around the individual, the higher the contribution to the diversity in the population, and the more promising it is to be selected as the parent population for the next iteration; the calculation formula of the crowding degree is represented by the following formula (16): (16); In formula (16): represents the crowding degree of individual ; represents the value of individual on the th target; represents the number of targets; represents the maximum value of the th target; represents the minimum value of the th target.

[0015] Furthermore, the selection operation based on fast non - dominated sorting and crowding degree calculation selects the top N optimal individuals from the temporary population to form a new parental population to enter the next generation. The specific selection method is as follows: S381. Starting from , if the number of individuals in the front - front is less than the population size N, then add the individuals in until the remaining solution quantity is not enough to merge another complete non - dominated front - front; S382. Assume that is the last non - dominated front - front that cannot be accommodated. Sort the elements in in descending order according to the crowding degree, and select the elements with higher rankings in turn to add to until the population size is N.

[0016] From the above technical solutions, it can be seen that compared with the prior art, the present invention has the following advantages: (1) The present invention proposes a multi - objective optimization method. In view of the characteristics of vertical precast components, according to the influence of key factors such as the entry order, destination, and departure time of precast components during their storage location allocation process on the stacking location, and combined with the resource and space constraints of the storage yard, it comprehensively optimizes the three core objectives of actual storage yard management. The stacking plan generated by this method can not only significantly improve the operation efficiency of the storage yard, but also effectively reduce resource waste and management costs, providing a scientific and efficient optimization solution for storage yard management.

[0017] (2) Based on the improved non - dominated sorting genetic algorithm NSGA - II, the present invention adopts a three - layer chromosome encoding, directly mapping the entry order of vertical precast components and the storage yard coordinates into the chromosome, so that each column can clearly represent the position of precast components in the storage yard. This encoding method can adapt to complex constraint conditions, simplify the decoding and fitness evaluation processes, and at the same time enhance the search ability of the genetic algorithm. It supports the decoupled optimization of objectives through hierarchical design, and the three - layer structure mutation operation provides greater flexibility, improving the diversity of solutions and the global search efficiency, and helping to quickly find the optimal storage location allocation plan that meets the requirements.

[0018] (3) The present invention is based on the improved non-dominated sorting genetic algorithm NSGA-II, and introduces an adaptive linear adjustment mechanism for the crossover and mutation probabilities. This mechanism dynamically adjusts the probability values according to the number of iterations to better balance the population diversity and optimization efficiency. In the initial stage of the algorithm, due to the high diversity of the population, the crossover and mutation probabilities are set low to avoid excessive perturbation and retain the genetic information of excellent individuals. As the number of iterations increases, the crossover and mutation probabilities gradually increase, enabling the algorithm to generate more new individuals in the later stage, expand the search range, and thus reduce the risk of falling into local optimal solutions. This dynamic adjustment strategy effectively improves the global search ability and convergence performance of the algorithm, making the optimization process more stable and efficient, and providing strong support for solving complex storage location allocation problems. Description of the Drawings

[0019] Figure 1 is the flowchart of the method steps of the present invention; Figure 2 is the layout schematic diagram of the precast component yard in the present invention; Figure 3 is the schematic flowchart of solving the yard storage location optimization model by using the improved NSGA-II algorithm in the present invention; Figure 4 is the schematic diagram of the three-layer chromosome coding in the genetic algorithm of the present invention; Figure 5 is the schematic diagram of the crossover operation in the genetic algorithm of the present invention; Figure 6 is the schematic diagram of the mutation operation in the genetic algorithm of the present invention; Figure 7 is the three-dimensional schematic diagram of the non-dominated layer in the genetic algorithm of the present invention; Figure 8 is the visualization display diagram of the yard storage location allocation scheme in the example of the present invention. Detailed Embodiment

[0020] The following is a detailed description of a preferred embodiment of the present invention with reference to the drawings.

[0021] As Figure 1 shown, the vertical precast component yard storage location allocation method based on multi-objective optimization includes the following steps: S1. Obtain the yard stacking situation, the information of the incoming precast components, and the working status of the gantry crane, and construct a yard storage location optimization data set; The yard storage situation described in this preferred embodiment includes the yard layout, storage location distribution information, and the total storage quantity and allocated storage location information of each yard at the moment when precast components enter the yard; the information of the incoming precast components includes the incoming order, component number, destination, and departure time of the incoming vertical precast components; the working state of the gantry crane refers to whether the gantry crane is working and its average moving speed.

[0022] Specifically, as Figure 2 shown in the precast component yard layout, the following yard storage situation can be obtained: Yard storage situation: The process of precast components entering the yard is that the produced precast components are transported to the parking area of the transport trolley at the head of the yard by the transport trolley and then lifted to the corresponding position for storage by the gantry crane; in the Figure 2 yard scene shown, there are a total of 3 yards, each yard is equipped with a gantry crane, and 2 columns and 20 rows of storage locations are set. Each storage location is uniquely identified by a coordinate (yard number, column number, row number), and the sizes of the storage locations are all the same; Information of incoming precast components: Assume at a certain moment, 10 vertical precast components need to enter the yard for storage, and different destinations are represented by numbers. The information of the incoming precast components is shown in Table 1; Table 1 Information of incoming vertical precast components

[0023] Working state of the gantry crane: At a certain moment, the gantry cranes are all idle, and their average moving speed is set to .

[0024] S2. On the premise of resource constraints and space constraints, aiming at improving the parallelism of multi-gantry crane operation, reducing the completion time of incoming handling, and storing associated components nearby, a yard storage location optimization model is constructed; Specifically, the resource constraints and space constraints are constructed based on the yard storage location optimization data set, and the conditions of the resource constraints and space constraints are represented by the following formulas (1)-(5): (1); (2); (3); (4); (5); In formulas (1)-(5): represents the incoming order of a batch of precast components; represents the yard number; represents the column number in the yard; Indicates the row number in the storage yard; , , All represent the maximum value of the number; Indicates the storage yard The initial number of containers; Formula (1) indicates that a precast component in the storage yard can only occupy one storage location; Formula (2) indicates that at most one precast component can be stacked in one storage location in the storage yard. If , it indicates that the storage location is vacant. If , it indicates that the storage location is occupied; Formula (3) indicates that the initial position of each storage yard crane is in the first row; Formula (4) indicates that the number of precast components allocated to the storage yard should be less than the storage yard capacity; Formula (5) defines the value range of the decision variable.

[0025] Furthermore, the storage yard storage location optimization model is represented by the following Formulas (6)-(13): (6); (7); (8); (9); (10); (11); (12); (13); Formulas (6)-(8) are the objective functions for storage location allocation, where: Indicates minimizing the stacking quantity between storage yards to achieve the purpose of improving the parallel operation degree of multiple cranes; Indicates minimizing the handling completion time; Indicates storing related precast components nearby; Indicates the longitudinal length of the storage location in the storage yard, and the movement cost of the crane between columns is ignored; Indicates the average speed of the crane movement; In Formulas (9)-(13): Is a 0-1 decision variable. When the precast component is allocated to the storage location , the value is 1, otherwise it is 0; Indicates the precast component and The correlation coefficient between them; , Are weights, and the sum is 1. The selection of weights can be adjusted according to requirements; is a 0-1 decision variable, and the precast component and take the value of 1 when they have the same destination, otherwise 0; and respectively represent the destinations of the precast components and ; represents the closeness of the departure times of the precast components and . If the difference in departure times between two components is small, their relationship is closer; and respectively represent the departure times of the precast components and ; and respectively represent the maximum and minimum values of the departure times of all precast components; represents the distance between the precast components and . If and are in the same storage yard, the distance is the absolute difference in row numbers, otherwise the distance is set to a relatively large value D; and respectively represent the row numbers where the precast components and are located; represents the distance between columns in the storage yard; and respectively represent the column numbers where the precast components and are located; and respectively represent the storage yard numbers where the precast components and are located.

[0026] S3. Based on the storage location optimization data set and model of the storage yard, the improved non-dominated sorting genetic algorithm NSGA-II is used. Through fitness value evaluation, non-dominated sorting, and crowding degree calculation, several optimal iterations are performed to output multiple high-quality solutions on the Pareto front; as Figure 3 shown, it is specifically implemented through the following steps: S31. Initialize relevant parameters, set the population size N, the individual crossover probability , the individual mutation probability , and the maximum number of iterations T, and process the storage location optimization data set to extract the storage situation of the storage yard, the arrival order of precast components, destinations, and departure times; S32. Perform three - layer chromosome encoding. Each chromosome encoding is an individual, generating an initial population that meets the population size N. At the same time, check for duplicate individuals. Convert the individuals into strings and hash them for comparison, and add the non - identical individuals to the initial parental population ; As Figure 4 shown, in the three - layer chromosome encoding, the encoding order of the chromosome from left to right is the order of the pre - fabricated components entering the site. Each column represents the coordinates of the pre - fabricated component in the storage yard. Each column of coordinates is composed of a storage yard number, a column number, and a row number. Generate 3 random integers within their respective value ranges as a storage location coordinate and add it to a column of the chromosome until the length of the chromosome reaches the number of pre - fabricated components entering the site, and ensure that the coordinates are not repeated. Thus, a complete chromosome is formed, and each chromosome represents a stacking plan for the vertical pre - fabricated components entering the site; S33. By traversing the parental population , randomly select two parental individuals for crossover operation. According to the randomly generated decimal within the range of (0, 1) and the crossover probability , determine whether to perform two - point crossover, and generate a legal offspring population with the same scale as the parental population after de - duplication and patching ; In the crossover operation, traverse half of the population. Randomly select two parental individuals from the parental population . The selected parental individuals will not be selected repeatedly. If the randomly generated decimal is less than the individual crossover probability , then perform two - point crossover on the two parental individuals, that is, randomly select two crossover points, exchange the segments between the two parental individuals at the crossover points, and check for duplicate columns and perform replacement patching to obtain two offspring individuals after crossover; if the randomly generated decimal is greater than the individual crossover probability , then directly copy the parental individuals to the offspring until the number of offspring individuals meets the population size; thus generating an offspring population with the same population size of N . After that, check whether there are duplicate individuals among them. If so, replace them with newly randomly generated legal individuals; As Figure 5 shown, the specific method of the two - point crossover operation is: randomly select two crossover points, exchange the segments between the two parental individuals at the crossover points, and check whether there are duplicate columns. For the detected duplicate columns; as Figure 5 there is a duplicate column (2, 0, 9) in it, replace the later duplicate column with a newly randomly generated coordinate (0, 0, 6) for patching, so as to obtain two legal offspring individuals after crossover; S34. Perform mutation operation. Traverse the offspring population , according to the randomly generated decimal within the range of (0, 1) and the crossover probability Randomly update the individual coordinate values and repair duplicate individuals, thereby updating to the mutated offspring population ; In the mutation operation, for the offspring population after crossover For each individual in it, if the randomly generated decimal is less than the individual mutation probability , then randomly regenerate a random dimension of one of its column coordinates, update the individual coordinate value, and at the same time check for duplicate columns and perform replacement repairs; if the randomly generated decimal is greater than the individual mutation probability , then do not mutate this individual; then for the mutated offspring population , check whether there are duplicate individuals in it.

[0027] As Figure 6 shown, the mutation operation randomly regenerates a random dimension of one of its column coordinates, updates the individual coordinate value, as Figure 6 in which the second and third dimension coordinate values of the 5th column (2, 1, 8) are mutated to obtain the coordinates (2, 0, 4). After mutation, duplicate columns are also checked and replaced and repaired if any to ensure the legality of the individual.

[0028] In the specific operation, the crossover and mutation operations both adopt adaptive crossover and mutation operators, that is, the crossover and mutation probabilities are adaptively adjusted as the number of iterations increases. In the initial stage of iteration, the population diversity is high and the crossover and mutation probabilities are low; in the later stage of iteration, the crossover and mutation probabilities are increased to encourage the generation of new individuals, expand the search range, and avoid falling into local optimal solutions; specifically, it is represented by the following formulas (14)-(15): (14); (15); In formulas (14)-(15): represents the initial minimum crossover probability; represents the initial minimum mutation probability; represents the final maximum crossover probability; represents the final maximum mutation probability; represents the current number of iterations; represents the maximum number of iterations.

[0029] S35. Combine the parent population and the offspring population into a temporary population of size 2N , design a fitness function according to the optimization objective and calculate the fitness value to evaluate the quality of each individual, that is, calculate the parallelism of the crane operation, the handling completion time, and the adjacency of related components.

[0030] The design of the fitness function and the calculation of the fitness value include: Calculate the parallelism of the operation of the gantry crane. The more balanced the stockpiles in multiple yards are, the higher the parallelism of the gantry crane operation, which is equivalent to calculating the difference in the number of precast components between the yard with the largest stockpile and the yard with the smallest stockpile; see formula (6). Calculate the completion time of the in-yard handling of precast components. Assume that there is only one gantry crane in each yard, which can only move along the column direction, and the spacing between each row is equal. Based on the current stockpile situation in the yard, storage locations are allocated according to the in-yard order. The initial position of the gantry crane in each yard is in the first row, and it moves continuously according to the allocated storage locations. Calculate the sum of the moving distances of all gantry cranes and then divide it by the average speed of the gantry crane, which is the completion time of the in-yard handling; see formula (7). Calculate the adjacency of associated components. That is, following the principle of storing associated precast components nearby, allocate precast components that are associated with each other to nearby storage locations, so that the associated precast components are stored more concentratedly to reduce the moving cost of the gantry crane. This goal can be calculated by minimizing the sum of the products of the relationship coefficients and the storage distances between precast components; see formula (8).

[0031] S36. Perform fast non-dominated sorting and assign each individual in the temporary population to different domination levels. There is no mutual domination relationship between individuals in the same domination level, while in different domination levels, individuals with smaller domination level numbers dominate individuals with larger domination level numbers.

[0032] Specifically, the fast non-dominated sorting specifically includes the following steps: S361. Initial setup. Take the fitness values of all individuals in the temporary population as input. Use with an initial value of 0 to represent the number of individuals dominated by other individuals. Use initially empty to represent the set of other individuals dominated by individual . Use to represent the index of individuals used to store the first non-dominated level. S362. Determine the domination relationship. For each pair of individuals and in the population, if individual is not inferior to individual in all objectives and is superior to in at least one objective, then dominates , and add to ; if dominates , then increase the count of . S363. Traverse all individuals. If individual The dominated count , add it to the front set of layer 0 ; S364. Construct higher-level fronts. Starting from , for each individual in the current layer , traverse all the individuals dominated by , subtract 1 from the dominated count . If , add to the front set of the next layer , increment step by step and repeat this process until no new fronts are generated; S365. Return all fronts . The individual indices in each front correspond to a non-dominated layer.

[0033] S37. Calculate the crowding degree of each individual among the non-dominated solutions in each layer , that is, the sparsity degree of the solutions around the individual; Specifically, the larger the value of the crowding degree, the sparser the solutions around the individual, the higher the contribution to the diversity in the population, and the more promising to be selected as the parent population for the next iteration; the calculation formula of the crowding degree is expressed by the following formula (16): (16); In formula (16): represents the crowding degree of individual ; represents the value of individual on the th objective; represents the number of objectives; represents the maximum value of the th objective; represents the minimum value of the th objective.

[0034] S38. Perform the selection operation. Based on the fast non-dominated sorting and crowding degree calculation, select the top N optimal individuals from the temporary population to form a new parent population to enter the next generation.

[0035] Specifically, the selection operation based on the fast non-dominated sorting and crowding degree calculation selects the top N optimal individuals from the temporary population to form a new parent population to enter the next generation. The specific selection method is as follows: S381. Starting from , if the front If the number of individuals in [the set] is less than the population size N, then add the individuals in [the set] until the remaining number of solutions is not enough to merge another complete non-dominated front; S382. Assume that is the last non-dominated front that cannot be accommodated. Sort the elements in in descending order of crowding degree, and select the elements with higher ranks in the sorting and add them to [the set] one by one until the population size is N.

[0036] S39. Repeat steps S33 - S38 to continuously iterate and optimize the population until the maximum number of iterations T is reached, and obtain the Pareto front that meets all optimization objectives.

[0037] The schematic diagram of the non-dominated layer obtained in this step is as shown in Figure 7 which shows the trade-off relationship between different objectives and the distribution of each solution in the objective space.

[0038] S4. Select the individual with the best values for all objectives and the smallest chromosome encoding among the high-quality solutions as the optimal stacking plan, and visualize it in the form of a three-dimensional coordinate system.

[0039] The optimal stacking plan is shown in Table 2 below, and the visualization in the form of a three-dimensional coordinate system is as shown in Figure 8 ; Table 2 Optimal Stacking Plan

[0040] The above-described embodiments are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization, characterized in that: The following steps are involved: S1. Obtain the stockpile situation in the yard, the information of the prefabricated components entering the yard, and the working status of the gantry crane, and construct a data set for optimizing the storage space in the yard; S2. Based on resource constraints and space constraints, the yard storage optimization model is constructed with the goal of improving the parallel operation of multi-truss vehicles, reducing the completion time of entry and transportation, and storing related components nearby; S3. Based on the storage yard storage optimization data set and model, the improved non-dominated sorting genetic algorithm NSGA-II is used to output multiple high-quality solutions on the Pareto frontier through fitness value evaluation, non-dominated sorting and congestion calculation, and several optimal iterations; S4. Select the individual with the best target values ​​and the smallest chromosome code from the high-quality solutions as the optimal storage solution, and visualize it in the form of a three-dimensional coordinate system.

2. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 1 is characterized in that: The stockpile situation of the yard includes the yard layout, storage location distribution information, and the total stockpile quantity and allocated storage location information of each yard at the time of entry of prefabricated components; the information of the prefabricated components entering the yard includes the entry order, component number, destination and departure time of the entering vertical prefabricated components; the working status of the gantry crane refers to whether the gantry crane is working and its average moving speed.

3. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 1 is characterized in that: The resource constraint and space constraint are constructed based on the storage yard storage optimization data set. The resource constraint and space constraint conditions are expressed by the following formulas (1)-(5): （1）； （2）； （3）； （4）； （5）； In formulas (1)-(5): Indicates the order in which a batch of prefabricated components enter the site; Indicates the number of the storage yard; Indicates the column number in the yard; Indicates the row number in the yard; , , Both represent the maximum value of the number; Indicates the yard The initial box quantity; Formula (1) indicates that a prefabricated component can only occupy one storage space in the yard; Formula (2) indicates that a storage space in the yard can only store one prefabricated component at most. , indicating that the storage space is vacant, if , indicating that the storage space is occupied; Formula (3) indicates that the initial position of each yard gantry car is in the first row; Formula (4) indicates that the allocation in the yard The number of prefabricated components must be less than the yard capacity; Formula (5) defines the value range of the decision variable.

4. According to claim 1, a method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization is characterized in that: The storage yard storage optimization model is expressed by the following formulas (6)-(13): （6）； （7）； （8）； （9）； （10）； （11）； （12）； （13）； Formulas (6)-(8) are the objective functions of storage allocation, where: It means minimizing the stockpile volume between each yard, so as to achieve the purpose of improving the parallel operation of multiple gantry vehicles; It means minimizing the time of completion of the transportation; Indicates that the associated prefabricated components are stored nearby; represents the longitudinal length of the storage space in the yard, and the cost of moving the gantry truck between the rows is negligible; It indicates the average speed of the gantry crane; In formulas (9)-(13): is a 0-1 decision variable, prefabricated components Assigned to storage The value is 1 when it is, otherwise it is 0; Represents prefabricated components and The correlation coefficient between , is the weight, the sum is 1, and the weight selection can be adjusted according to needs; is a 0-1 decision variable, prefabricated components and The value is 1 if the destinations are the same, otherwise it is 0; , Respectively represent prefabricated components and destination; Represents prefabricated components and If the departure time difference between two components is small, their relationship is closer; , Respectively represent prefabricated components and Departure time; , Respectively represent the maximum and minimum departure time of all prefabricated components; Represents prefabricated components and If the distance between and If they are in the same dump, the distance is the absolute difference in the row numbers, otherwise the distance is set to a larger value. ; , Respectively represent prefabricated components and The row number you are in; Indicates the distance between columns in the yard; , Respectively represent prefabricated components and The column number; , Respectively represent prefabricated components and The yard number where the storage is located.

5. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 1 is characterized in that: The S3 is specifically implemented by the following steps: S31. Initialize relevant parameters, set population size N, individual crossover probability , individual mutation probability and the maximum number of iterations T, and process the storage optimization data set to extract the yard stockpiling situation, the entry sequence of prefabricated components, the destination and the departure time; S32. Perform three-layer chromosome encoding, where each chromosome encoding is an individual, to generate an initial population that satisfies the population size N. At the same time, check for individual duplication, convert the individual into a string and hash it for comparison, and add different individuals to the initial parent population. ; In the three-layer chromosome coding, the coding order of the chromosome from left to right is the order of the prefabricated components entering the site, and each column represents the coordinates of the prefabricated components in the yard. Each column of coordinates is composed of the yard number, column number, and row number. Three random integers are generated within their respective value ranges as a storage coordinate and added to a column of the chromosome until the length of the chromosome reaches the number of prefabricated components entering the site, and it is ensured that the coordinates are not repeated, thereby forming a complete chromosome. Each chromosome represents a stacking plan for the vertical prefabricated components entering the site; S33, by traversing the parent population , randomly select two parent individuals for crossover operation, according to the randomly generated decimals and crossover probabilities in the range of (0,1) Decide whether to perform a two-point crossover and generate a legal offspring population of the same size as the parent after deduplication and patching ; In the crossover operation, half of the population is traversed, and the parent population Two parent individuals are randomly selected from the parent generation, and the selected parent individuals will not be selected repeatedly. If the randomly generated decimal is less than the individual crossover probability , then the two parent individuals are subjected to a two-point crossover, that is, two crossover points are randomly selected, the fragments between the two parent generations are exchanged, and the duplicate columns are checked and replaced to obtain two offspring individuals after the crossover; if the randomly generated decimal is greater than the individual crossover probability , the parent individuals are directly copied to the offspring until the number of offspring individuals meets the population size; in this way, a offspring population with the same population size of N is generated. Finally, check whether there are duplicate individuals. If there are, replace them with new legal individuals generated randomly. S34, perform mutation operation and traverse the offspring population , based on a randomly generated decimal in the range (0,1) and the crossover probability Randomly update individual coordinate values ​​and patch duplicate individuals to update the mutated offspring population ; In the mutation operation, for the offspring population after crossover For each individual in, if the randomly generated decimal is smaller than the individual mutation probability , then randomly regenerate the random dimension of a column of coordinates, update the individual coordinate values, check for duplicate columns and replace them; if the randomly generated decimal is greater than the individual mutation probability , then the individual will not be mutated; then the mutated offspring population , check whether there are repeated individuals; S35, the parent population and progeny population Merge into a temporary population of size 2N , design the fitness function according to the optimization goal and calculate the fitness value to evaluate the quality of each individual, that is, calculate the parallelism of the gantry operation, the handling completion time and the proximity of the associated components; S36, perform fast non-dominated sorting, and convert the temporary population Each individual in the dominance layer is assigned to a different dominance layer. There is no mutual dominance relationship between individuals in the same dominance layer. In different dominance layers, individuals with smaller dominance layer numbers dominate individuals with larger dominance layer numbers. S37. Calculate the crowding degree of each individual in the non-dominated solution of each layer , that is, the sparsity of the solution around the individual; S38, perform selection operation, based on fast non-dominated sorting and crowding calculation, from the temporary population Select the first N best individuals to form a new parent population Enter the next generation; S39. Repeat steps S33-S38 to continuously iterate and optimize the population until the maximum number of iterations T is reached, and a Pareto front that satisfies all optimization objectives is obtained.

6. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 5, characterized in that: Designing a fitness function and calculating the fitness value include: Calculate the parallelism of the gantry crane operation. The more balanced the stockpiles of multiple yards are, the higher the parallelism of the gantry crane operation is. This is equivalent to calculating the difference in the number of prefabricated components between the yard with the largest stockpiles and the yard with the smallest stockpiles; see formula (6); Calculate the completion time of the entry and transportation of prefabricated components. Assume that there is only one gantry truck in each yard, which can only move in the direction of the row, and the spacing between each row is equal. Based on the current stockpile situation in the yard, the storage space is allocated according to the entry order. The initial position of the gantry truck in each yard is in the first row. It moves continuously according to the allocated storage space. The sum of the moving distances of all gantry trucks is calculated and then divided by the average speed of the gantry truck to obtain the completion time of the entry and transportation; see formula (7); The proximity of associated components is calculated, that is, in order to follow the principle of storing associated components nearby, the associated prefabricated components are allocated to storage locations that are closer, so that the associated prefabricated components can be stored more centrally to reduce the cost of moving the gantry truck. This goal can be calculated by minimizing the sum of the product of the relationship coefficient between the prefabricated components and the storage distance; see formula (8).

7. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 5, characterized in that: The fast non-dominated sorting specifically comprises the following steps: S361, initialization settings, using the fitness values ​​of all individuals in the temporary population as input, through The initial value is 0, indicating that the individual The number of individuals dominated by other individuals, through Initially empty to represent individual The set of other individuals dominated by represents the individual index used to store the first non-dominated layer; S362, determine the dominance relationship, for each pair of individuals in the population and , if the individual No less inferior than individuals on all goals , and is better than ,but Dominate , and Add to In; if Dominate , then increase Count of; S363, traverse all individuals, if the individual The dominated count , add it to the frontier set of level 0 ; S364, build a higher level frontier, from First, for each individual in the current layer , traverse All individuals controlled ,Will Dominated Count Subtract 1, if ,Will Join the Next Frontier Collection , Gradually increase by 1 and repeat this process until no new frontier is generated; S365, Return to All Frontiers , each individual index in the frontier corresponds to a non-dominated layer.

8. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 5, characterized in that: The crossover and mutation operations all use adaptive crossover and mutation operators, that is, the crossover and mutation probabilities are adaptively adjusted as the number of iterations increases. In the early iteration, the population diversity is high and the crossover and mutation probabilities are low. In the later iteration, the crossover and mutation probabilities are increased to encourage the generation of new individuals, expand the search range, and avoid falling into the local optimal solution. It is specifically expressed by the following formulas (14)-(15): （14）； （15）； In formula (14)-(15): represents the initial minimum crossover probability; represents the initial minimum mutation probability; represents the final maximum crossover probability; represents the final maximum mutation probability; Indicates the current iteration number; Indicates the maximum number of iterations.

9. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 5, characterized in that: The larger the value of the crowding degree is, the sparser the solutions around the individual are, the higher the diversity contribution in the population is, and the more likely it is to be selected as the parent population for the next iteration. The calculation formula of the crowding degree is expressed by the following formula (16): （16）； In formula (16): Represents an individual The degree of congestion; Represents an individual In the The value on the target; Indicates the number of targets; Indicates The maximum value of the targets; Indicates The minimum value of the target.

10. The method for allocating storage space in a vertical prefabricated component yard based on multi-objective optimization according to claim 5, characterized in that: The selection operation based on fast non-dominated sorting and crowding calculation is performed from the temporary population Select the first N best individuals to form a new parent population Entering the next generation, the specific selection method is as follows: S381, from Start, if the front If the number of individuals in is less than the population size N, Individuals are added until the number of remaining solutions is insufficient to merge a complete non-dominated frontier; S382, Assume that The last non-dominated frontier that cannot be accommodated is given according to the congestion degree Arrange the elements in descending order, select the top-ranked elements and add them to in one by one until the population size reaches N.

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