A tower crane group construction arrangement multi-objective optimization method integrating ergonomics, cost and safety

Abstract

This invention relates to a multi-objective optimization method for the construction layout of tower crane groups, integrating efficiency, cost, and safety. The method includes: S1, collection of basic engineering data and alternative tower crane data; S2, construction of tower crane efficiency and safety spaces; S3, construction of a multi-objective optimization mathematical model for tower crane group layout; S4, solving the multi-objective optimization mathematical model; and S5, Pareto solution set decision based on cluster analysis. This invention achieves comprehensive optimization of tower crane group layout schemes in terms of efficiency, economy, and safety by constructing and solving a multi-objective optimization model that integrates maximizing efficiency equivalent, minimizing cost equivalent, and minimizing safety equivalent. Based on multiple feasible layout schemes corresponding to the optimization results, it can generate representative layout schemes of three typical strategies: "high efficiency," "balanced," and "high safety," enhancing the engineering practicality and decision support capabilities of the results, and improving the flexibility and efficiency of scheme selection.

Description

Technical Field

[0001] This invention belongs to the field of building construction technology, specifically relating to a multi-objective optimization method for the construction layout of tower crane groups that integrates efficiency, cost, and safety. Background Technology

[0002] Tower cranes are core equipment for the vertical and horizontal transportation of materials at construction sites of large public buildings, high-rise buildings, and complex industrial facilities. Their deployment and operational efficiency directly affect project progress and costs. For large-scale construction projects, a single tower crane often cannot meet the requirements of full coverage and high efficiency on the construction site. Therefore, it is necessary to use a group of tower cranes to carry out coordinated lifting tasks.

[0003] However, the layout of tower crane groups generally faces problems such as limited site space, mutual interference between work areas, and high potential collision risks, which directly affect the efficiency of construction organization, the cost of equipment investment, and the safety of on-site operation. As a complex decision-making problem involving multiple factors and objectives, the layout of tower crane groups requires a comprehensive trade-off between conflicting goals such as efficiency, cost, and safety. An unreasonable layout plan can easily lead to reduced work efficiency, delayed construction progress, and prominent safety hazards. How to rationally allocate tower crane resources and optimize the layout of tower crane groups often becomes a key and difficult point in engineering construction organization design. Conventional tower crane layouts are mainly planned and designed based on manual experience according to the construction schedule and site conditions. When it comes to the layout of tower crane groups, not only is the design cycle long, but it is also difficult to coordinate the inherent contradictions between the construction period, cost, and safety, which may lead to coverage blind spots, resource waste, or safety hazards.

[0004] Therefore, to address the aforementioned issues, a multi-objective optimization method for the construction layout of tower crane groups, integrating efficiency, cost, and safety, is proposed to improve the scientific and refined level of management for large-scale engineering projects. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings and deficiencies of existing technologies by providing a multi-objective optimization method for the construction layout of tower crane groups that integrates efficiency, cost, and safety, aiming to achieve comprehensive optimization of tower crane group layout schemes in terms of operational efficiency, economy, and safety.

[0006] The technical problem solved by this invention is achieved through the following technical solution: A multi-objective optimization method for the construction layout of tower crane groups that integrates efficiency, cost, and safety, comprising the following steps: S1. Collection of basic engineering data and tower crane alternative data Obtain the building area based on the on-site construction layout. and layout area Collect a list of alternative tower crane models and their corresponding optional boom lengths. Lifting performance curve; S2, Construction of Tower Crane Efficiency Space and Safety Space Based on the working characteristics of tower cranes and in conjunction with tower crane lifting performance curves and relevant specifications, the efficiency space, safety space, and cross space of tower cranes are defined; the efficiency space and safety space are matched for individual tower cranes, and the cross space is matched for tower crane groups. S3. Construction of a multi-objective optimization mathematical model for tower crane group layout Establish decision variables including tower crane plane coordinates and boom length index; establish an objective function system including three objectives: maximizing work efficiency equivalent, minimizing cost equivalent, and minimizing safety equivalent; establish three constraints including equipment layout range constraints, equipment safety space constraints, and minimum coverage constraints; the decision variables, objective function system, and constraints constitute a multi-objective optimization mathematical model for tower crane group layout. S4. Solving the Multi-Objective Optimization Mathematical Model The multi-objective optimization mathematical model for the tower crane group layout was solved using the NSGA-II algorithm, by sequentially initializing the population. Generate offspring population Generate candidate population Generate a new generation of population 1. Obtain the Pareto front solution set by analyzing the loop and outputting the Pareto solution set; S5. Pareto solution set decision based on cluster analysis Cluster analysis is performed on the Pareto front solution set to obtain the engineering decision-making strategy.

[0007] Furthermore, the tower crane efficiency space of S2 is divided into an efficiency space and a high-efficiency space. The efficiency space is defined as a circle centered on the center of the tower crane body and extending for a distance of [missing information - likely a length of arm length]. The high-efficiency space is a circular coverage area with a radius of [radius value missing]. The high-efficiency space is determined based on the tower crane's lifting performance curve, defined as the maximum load capacity in the tower crane's 2x lifting mode, with the tower crane's tower body center as the center. Corresponding load radius A circular region with radius [missing information]; the overlapping portion of the efficiency spaces of multiple tower cranes is defined as the intersection space, and [missing information] is determined based on the number of tower cranes covering this intersection space. Define it as different orders of " "Stage intersection space"; the tower crane safety space is the radius around the center of the tower crane tower body. The corresponding circular coverage area.

[0008] Moreover, the S3 is aimed at The decision variables for each tower crane use a hybrid approach of "continuous + discrete," meaning the crane's planar coordinates are continuous variables, while the boom length index is a discrete variable. These decision variables include the planar coordinates of each tower crane. and its arm length gear index Arm length gear index List of arm lengths middle Corresponding serial number ; The objective function system consists of three objective functions: efficiency equivalent, cost equivalent, and safety equivalent, aiming to maximize efficiency equivalent, minimize cost equivalent, and minimize safety equivalent. Efficiency Used to comprehensively evaluate the overall operational efficiency of a tower crane group, based on the efficiency equivalent of each tower crane. The operational capacity of a single tower crane is reflected by the combined effects of the tower crane's efficient space ratio, high-efficiency space ratio, and non-intersecting space ratio, as measured by coverage rate. and penalty items This reflects the coverage of the tower crane group over the building area; the coverage rate The ratio of the total area covered by the cluster of towers to the area of ​​the building area; coverage rate below the cluster's critical penalty coverage rate. Then a punishment will be imposed; The objective function for maximizing the efficiency equivalent is defined as: (1) (2) (3) (4) (5) in: For the number of tower cranes, This is the average efficiency equivalent of the tower crane. For tower cranes The work efficiency equivalent, For the coverage of the tower group, As a penalty item, For the critical penalty coverage of the tower group, The penalty coefficient is... The total area covered by the efficiency space of the tower group. The area of ​​the building area. For tower cranes Efficiency space area For tower cranes High-efficiency space area, For tower cranes The area of ​​the non-overlapping area with other tower cranes; Cost equivalent The overall impact of tower crane group efficiency on project cost is comprehensively reflected by the efficiency equivalent of each tower crane. A higher efficiency equivalent reflects the economic advantages it brings in long-term operation, and a lower cost equivalent. The objective function for minimizing the cost equivalent is defined as follows: (6) Safety equivalent As an equivalent quantity of unsafety, it comprehensively reflects the degree of safety risk of cross-operations in multiple towers, and is affected by the combined influence of the cross space area at each level as the cross level increases. As the number of elements increases, increasing order weights are assigned to cross spaces of different orders. The overall safety equivalent is constituted by weighted summation; The objective function for minimizing the safety equivalent is defined as: (7) in: For tower cranes Area of ​​the intersecting space, For tower cranes Cross weights, as Increased with the increase, The maximum number of cross-orders equals the total number of tower cranes. ; The equipment layout constraint is that the tower crane's tower body must be located within the layout area, meaning that the tower crane's coordinates must all be within the layout area: (8) in: , For tower cranes Coordinates in a plane coordinate system To arrange the area; The equipment safety space constraint is that the end of the boom of any tower crane cannot encroach on the safety space of other tower cranes, i.e., the minimum center-to-center distance constraint between any two tower cranes: (9) in: For tower cranes and tower crane geometric distance, For tower cranes arm length, For tower cranes arm length, For tower crane safety distance; The coverage constraint requires that, under any arrangement scheme, the total tower coverage rate must be greater than or equal to the minimum coverage rate. .

[0009] Moreover, S4 specifically refers to: (1) Initialize the population Each individual in the population is represented as This corresponds to a tower crane group layout scheme, and an initial solution set containing several individuals is generated by initializing the population; (2) Generate offspring population For the current population Perform crossover and mutation operations respectively to generate offspring populations. Crossover operations include simulated binary crossover of the tower crane's planar coordinate gene and probabilistic mixed crossover of the boom length index gene; mutation operations include polynomial mutation of the tower crane's planar coordinate gene and probabilistic mixed mutation of the boom length index gene. (3) Generate candidate populations parental population Offspring population Merge into candidate populations ; (4) Generate a new generation of population For candidate populations The non-dominated sorting, crowding sorting, and elite retention strategies were executed respectively to generate a new generation of population. ; (5) Cyclic discrimination and Pareto front solution set output Repeat steps (2)-(4) until the maximum number of iterations is reached. It also outputs the Pareto front solution set.

[0010] Moreover, S5 specifically refers to: (1) Standardize the objective function values ​​of individuals in the Pareto front solution set and form feature vectors: Perform Z-score standardization on the objective function values ​​of each individual in the Pareto front solution set to eliminate the influence of differences in the dimensions and numerical scales of different objective functions on the clustering results; The standardized objective function values ​​are used to construct the feature vector of this individual. , , , These are the standardized values ​​of the individual on the three objective functions of efficiency equivalent, cost equivalent, and safety equivalent, respectively. (2) Clustering algorithm is used to perform cluster analysis on the feature vectors of all individuals and divide them into three clusters corresponding to the three typical engineering trade-off strategies of "high efficiency", "balance" and "high safety": based on the feature vectors of all individuals For the sample set, the K-means clustering algorithm was used to cluster the Pareto front solution set into 3 clusters; the 3 clusters represent the three typical engineering trade-off strategies corresponding to different objective trade-off tendencies: "high efficiency", "equilibrium" and "high safety". (3) Select the individual closest to the centroid of the cluster as the representative scheme of the cluster: In order to ensure that each strategy outputs a representative and easy-to-implement recommended scheme, select the individual closest to the centroid of the cluster as the representative scheme of the cluster. (4) Managers select decision-making options based on project preferences. The representative solutions of the three clusters are output as a candidate recommendation set to the manager, and the manager can select according to the project preference. When the project schedule prioritizes hoisting efficiency, the representative solution of the "high efficiency" cluster is selected; when the project pursues comprehensive performance, the representative solution of the "balanced" cluster is selected; when the project has high requirements for safety control, the representative solution of the "high safety" cluster is selected.

[0011] The advantages and beneficial effects of this invention are as follows: 1. This invention aims to overcome the shortcomings of relying on experience for the layout of tower crane groups at large-scale construction sites, the long design cycle of the scheme, and the difficulty in coordinating and balancing conflicting objectives such as efficiency, cost, and safety. By constructing and solving a three-objective optimization model that integrates the maximum efficiency equivalent, the minimum cost equivalent, and the minimum safety equivalent, the invention achieves comprehensive optimization of the tower crane group layout scheme in terms of efficiency, economy, and safety. 2. This invention overcomes the shortcomings of traditional methods that rely on experience and are difficult to quantify and coordinate multiple objectives. By constructing a multi-objective optimization mathematical model that integrates work efficiency equivalent, cost equivalent, and safety equivalent, it achieves quantitative analysis and collaborative optimization of construction efficiency, economy, and safety risks, providing a scientific basis for layout scheme formulation. 3. Based on multiple feasible layout schemes corresponding to the optimization results, this invention can generate representative layout schemes of three typical strategies: "high efficiency", "balanced" and "high safety", thereby enhancing the engineering practicality and decision support capabilities of the results and improving the flexibility and efficiency of scheme selection. Attached Figure Description

[0012] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the tower crane space model of the present invention; Figure 3 This is a graph showing the lifting performance of the tower crane according to the present invention; Figure 4 This is a site plan; Figure 5 The plan includes floor plans of the original layout and the high-efficiency layout. Detailed Implementation

[0013] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0014] like Figure 1 As shown, a multi-objective optimization method for the construction layout of tower crane groups integrating efficiency, cost, and safety is innovative in that the method consists of the following steps: S1. Collection of basic engineering data and tower crane alternative data Obtain the building area based on the on-site construction layout. and layout area Collect a list of alternative tower crane models and their corresponding optional boom lengths. Lifting performance curve; S2, Construction of Tower Crane Efficiency Space and Safety Space Based on the working characteristics of tower cranes and in conjunction with tower crane lifting performance curves and relevant specifications, the efficiency space, safety space, and cross space of tower cranes are defined; the efficiency space and safety space are matched for individual tower cranes, and the cross space is matched for tower crane groups. The tower crane efficiency space is divided into an efficiency space and a high-efficiency space. The efficiency space is defined as a circle centered on the center of the tower crane body and extending along the boom length. A circular coverage area with a radius of [radius value]; the high-efficiency space is based on the tower. Figure 3 The lifting performance curve is determined as the maximum load in the tower crane's 2x mode, with the tower crane's tower body center as the center. Corresponding load radius A circular region with radius [missing information]; the overlapping portion of the efficiency spaces of multiple tower cranes is defined as the intersection space, and [missing information] is determined based on the number of tower cranes covering this intersection space. Define it as different orders of " "Stage intersection space"; the tower crane safety space is the radius around the center of the tower crane tower body. The corresponding circular coverage area.

[0015] S3. Construction of a multi-objective optimization mathematical model for tower crane group layout Establish decision variables including tower crane plane coordinates and boom length index; establish an objective function system including three objectives: maximizing work efficiency equivalent, minimizing cost equivalent, and minimizing safety equivalent; establish three constraints including equipment layout range constraints, equipment safety space constraints, and minimum coverage constraints; the decision variables, objective function system, and constraints constitute a multi-objective optimization mathematical model for tower crane group layout. against The decision variables for each tower crane use a hybrid approach of "continuous + discrete," meaning the crane's planar coordinates are continuous variables, while the boom length index is a discrete variable. These decision variables include the planar coordinates of each tower crane. and its arm length gear index Arm length gear index List of arm lengths middle Corresponding serial number ; The objective function system consists of three objective functions: efficiency equivalent, cost equivalent, and safety equivalent, aiming to maximize efficiency equivalent, minimize cost equivalent, and minimize safety equivalent. Efficiency Used to comprehensively evaluate the overall operational efficiency of a tower crane group, based on the efficiency equivalent of each tower crane. The operational capacity of a single tower crane is reflected by the combined effects of the tower crane's efficient space ratio, high-efficiency space ratio, and non-intersecting space ratio, as measured by coverage rate. and penalty items This reflects the coverage of the tower crane group over the building area; the coverage rate The ratio of the total area covered by the cluster of towers to the area of ​​the building area; coverage rate below the cluster's critical penalty coverage rate. Then a punishment will be imposed; The objective function for maximizing the efficiency equivalent is defined as: (1) (2) (3) (4) (5) in: For the number of tower cranes, This is the average efficiency equivalent of the tower crane. For tower cranes The work efficiency equivalent, For the coverage of the tower group, As a penalty item, For the critical penalty coverage of the tower group, The penalty coefficient is... The total area covered by the efficiency space of the tower group. The area of ​​the building area. For tower cranes Efficiency space area For tower cranes High-efficiency space area, For tower cranes The area of ​​the non-overlapping area with other tower cranes; Cost equivalent The overall impact of tower crane group efficiency on project cost is comprehensively reflected by the efficiency equivalent of each tower crane. A higher efficiency equivalent reflects the economic advantages it brings in long-term operation, and a lower cost equivalent. The objective function for minimizing the cost equivalent is defined as follows: (6) Safety equivalent As an equivalent quantity of unsafety, it comprehensively reflects the degree of safety risk of cross-operations in multiple towers, and is affected by the combined influence of the cross space area at each level as the cross level increases. As the number of elements increases, increasing order weights are assigned to cross spaces of different orders. The overall safety equivalent is constituted by weighted summation; The objective function for minimizing the safety equivalent is defined as: (7) in: For tower cranes Area of ​​the intersecting space, For tower cranes Cross weights, as Increased with the increase, The maximum number of cross-orders equals the total number of tower cranes. ; The equipment layout constraint is that the tower crane's tower body must be located within the layout area, meaning that the tower crane's coordinates must all be within the layout area: (8) in: , For tower cranes Coordinates in a plane coordinate system To arrange the area; The equipment safety space constraint is that the end of the boom of any tower crane cannot encroach on the safety space of other tower cranes, i.e., the minimum center-to-center distance constraint between any two tower cranes: (9) in: For tower cranes and tower crane geometric distance, For tower cranes arm length, For tower cranes arm length, For tower crane safety distance; The coverage constraint requires that, under any arrangement scheme, the total tower coverage rate must be greater than or equal to the minimum coverage rate. .

[0016] S4. Solving the Multi-Objective Optimization Mathematical Model The multi-objective optimization mathematical model for the tower crane group layout was solved using the NSGA-II algorithm, by sequentially initializing the population. Generate offspring population Generate candidate population Generate a new generation of population 1. Obtain the Pareto front solution set by analyzing the loop and outputting the Pareto solution set; The specific steps are as follows: (1) Initialize the population Each individual in the population is represented as This corresponds to a tower crane group layout scheme. An initial solution set containing several individuals is generated through an initial population method. A hybrid initialization population method combining random subsampling based on a global candidate point pool and farthest point sampling is adopted: First, a global candidate point pool is constructed, and Latin hypercube sampling (LHS) is used to generate the pool through hierarchical sampling within the minimum bounding rectangle of the layout area. There are 10 candidate points, of which... The number of candidate points is a factor. The population size is determined by the selection process within the designated area, followed by necessary point replenishment. This results in a relatively evenly distributed global candidate point pool across the designated area. Then, an initial population is generated by proportionally mixing random subsampling and farthest-point sampling strategies. Random subsampling is performed by randomly selecting points directly from the candidate pool. The sampling process involves selecting a point as the first tower crane position, then iteratively selecting candidate points that maximize the minimum Euclidean distance between the candidate and the set of selected positions, until the set is full. To avoid excessive clustering of tower crane locations within a single unit.

[0017] (2) Generate offspring population For the current population Perform crossover and mutation operations respectively to generate offspring populations. Crossover operations include simulated binary crossover for planar coordinate genes and probabilistic mixed crossover for arm length index genes. Mutation operations include polynomial mutation for planar coordinate genes and probabilistic mixed mutation for arm length index genes.

[0018] Specifically, let the parent generation be an individual. and The Middle The coordinates of the tower crane are respectively and Simulated binary crossover is performed independently for each dimension of coordinates, in order to For example: (10) in: For cross-calculation parameters; Specifically, the probabilistic hybrid crossover swaps the arm length indices of the two parents with a certain probability, and inherits the configuration of one parent in a one-way manner with a certain probability.

[0019] Specifically, polynomial mutation refers to the variation of a coordinate system with respect to each dimension. For example, in Perform within the interval: (11) in: Parameters for calculating variation.

[0020] Specifically, the probabilistic hybrid mutation operation uses probability... The arm length range index is fine-tuned in small steps, meaning the arm length range index value is the current index value plus or minus 1; this is done with probability. Make large jumps in the arm length level index, that is, randomly re-draw within the arm length configuration range.

[0021] (3) Generate candidate populations Parental population Offspring population Merge into candidate populations .

[0022] (4) Generate a new generation of population For candidate populations The non-dominated sorting, crowding sorting, and elite retention strategies were executed respectively to generate a new generation of population. .

[0023] Specifically, non-dominated ranking refers to ranking candidate populations. According to the Pareto dominance principle, it is divided into A cutting-edge level, namely , ,…, Crowding ranking refers to ranking based on the distribution density in the target space within the same frontier level; the elite retention strategy refers to filling the new generation of the population sequentially according to the non-dominant level. When a certain level cannot be fully filled, selection is made according to the crowding distance from largest to smallest until the new generation of the population is reached. The number of individuals reached .

[0024] (5) Cyclic discrimination and Pareto solution output Repeat steps (2)-(4) until the maximum number of iterations is reached. It also outputs the Pareto front solution set.

[0025] S5. Pareto solution set decision based on cluster analysis (1) Standardize the objective function values ​​of individuals in the Pareto front solution set and form feature vectors: Perform Z-score standardization on the objective function values ​​of each individual in the Pareto front solution set to eliminate the influence of differences in the dimensions and numerical scales of different objective functions on the clustering results; The standardized objective function values ​​are used to construct the feature vector of this individual. , , , These are the standardized values ​​of the individual on the three objective functions of efficiency equivalent, cost equivalent, and safety equivalent, respectively. (2) Clustering algorithm is used to perform cluster analysis on the feature vectors of all individuals and divide them into three clusters corresponding to the three typical engineering trade-off strategies of "high efficiency", "balance" and "high safety": based on the feature vectors of all individuals For the sample set, the K-means clustering algorithm was used to cluster the Pareto front solution set into 3 clusters; the 3 clusters represent the three typical engineering trade-off strategies corresponding to different objective trade-off tendencies: "high efficiency", "equilibrium" and "high safety". (3) Select the individual closest to the centroid of the cluster as the representative scheme of the cluster: In order to ensure that each strategy outputs a representative and easy-to-implement recommended scheme, select the individual closest to the centroid of the cluster as the representative scheme of the cluster. (4) Managers select decision-making options based on project preferences. The representative solutions of the three clusters are output as a candidate recommendation set to the manager, and the manager can select according to the project preference. When the project schedule prioritizes hoisting efficiency, the representative solution of the "high efficiency" cluster is selected; when the project pursues comprehensive performance, the representative solution of the "balanced" cluster is selected; when the project has high requirements for safety control, the representative solution of the "high safety" cluster is selected.

[0026] Practical application and effect verification of the method of the present invention. Taking the selection and layout of a cluster of towers in a specific engineering project as an example, the site plan of the project is as follows: Figure 4 As shown, the planned number of tower cranes is... The number is 7. The alternative tower crane model is a common flat-top tower crane. Based on site conditions, the following list of tower crane boom lengths is provided. The corresponding boom length indices are 1, 2, and 3. Based on the lifting performance curve of this tower crane model, the efficient space radius corresponding to the 80-meter boom length tower crane is determined to be 29 meters, the efficient space radius corresponding to the 74-meter boom length tower crane is 29 meters, and the efficient space radius corresponding to the 70-meter boom length tower crane is 36 meters. Based on specifications and site conditions, the tower crane safety distance... Minimum coverage is 2 meters. The percentage is 90%. The relevant parameters for the multi-objective optimization mathematical model of tower crane group layout are set as follows: penalty coefficient. The critical penalty coverage for the group tower is 100. The cross-weights are 95% for tower cranes of levels 2 to 5 and above, respectively: 0.5, 0.6, 0.7, and 0.8.

[0027] After adopting the method described in this invention, representative layout schemes for three typical strategies—"high efficiency," "balanced," and "high safety"—are obtained, with specific indicators shown in Table 1. Taking the high efficiency scheme as an example, the original layout scheme and its plan view are shown below. Figure 5 As shown, the high-efficiency solution has a high efficiency equivalent. Cost equivalent Safety equivalent In terms of target indicators, it outperforms the original plan. Furthermore, in terms of tower coverage... While achieving further improvements, no third-order intersection spaces appeared, and the area of ​​the second-order intersection space was reduced by 70.28% compared to the original scheme, effectively alleviating spatial conflicts. Therefore, it is evident that the method described in this invention can effectively achieve multi-objective optimization of the construction layout of tower crane groups.

[0028] Table 1. Comparison of representative layout indicators between the original plan and the three typical strategies.

[0029] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for multi-objective optimization of a tower crane group construction layout that fuses ergonomics-cost-safety, characterized in that: The steps of the method are as follows: S1. Collection of basic engineering data and tower crane alternative data Acquiring a building area according to a field construction layout With the layout area Collecting a list of tower crane alternative models and corresponding selectable arm lengths Lifting performance curves; S2, Construction of Tower Crane Efficiency Space and Safety Space Based on the working characteristics of tower cranes and in conjunction with tower crane lifting performance curves and relevant specifications, the efficiency space, safety space, and cross space of tower cranes are defined; the efficiency space and safety space are matched for individual tower cranes, and the cross space is matched for tower crane groups. S3. Construction of a multi-objective optimization mathematical model for tower crane group layout Establish decision variables including tower crane plane coordinates and boom length index; establish an objective function system including three objectives: maximizing work efficiency equivalent, minimizing cost equivalent, and minimizing safety equivalent; establish three constraints including equipment layout range constraints, equipment safety space constraints, and minimum coverage constraints; the decision variables, objective function system, and constraints constitute a multi-objective optimization mathematical model for tower crane group layout. S4. Solving the Multi-Objective Optimization Mathematical Model The multi-objective optimization mathematical model for the tower crane group layout was solved using the NSGA-II algorithm, by sequentially initializing the population. Generate offspring population Generate candidate population Generate a new generation of population 1. Obtain the Pareto front solution set by analyzing the loop and outputting the Pareto solution set; S5. Pareto solution set decision based on cluster analysis Cluster analysis is performed on the Pareto front solution set to obtain the engineering decision-making strategy.

2. The multi-objective optimization method for tower crane group construction layout integrating efficiency, cost, and safety as described in claim 1, is characterized in that: The tower crane efficiency space of S2 is divided into an efficiency space and a high-efficiency space. The efficiency space is defined by a circle centered on the center of the tower crane body and extending along the boom length. The high-efficiency space is a circular coverage area with a radius of [radius value missing]. The high-efficiency space is determined based on the tower crane's lifting performance curve, defined as the maximum load capacity centered on the tower crane's tower body in 2x mode. Corresponding load radius A circular region with radius [missing information]; the overlapping portion of the efficiency space of multiple tower cranes is defined as the intersection space, and [missing information] is determined based on the number of tower cranes covering this intersection space. Define it as different orders of " "Stage intersection space"; the tower crane safety space is the radius around the center of the tower crane tower body. The corresponding circular coverage area.

3. The multi-objective optimization method for tower crane group construction layout integrating efficiency, cost, and safety as described in claim 2, is characterized in that: The S3 is aimed at The decision variables for each tower crane use a hybrid approach of "continuous + discrete," meaning the crane's planar coordinates are continuous variables, while the boom length index is a discrete variable. These decision variables include the planar coordinates of each tower crane. and its arm length gear index Arm length gear index List of arm lengths middle Corresponding serial number ; The objective function system consists of three objective functions: efficiency equivalent, cost equivalent, and safety equivalent, aiming to maximize efficiency equivalent, minimize cost equivalent, and minimize safety equivalent. Efficiency Used to comprehensively evaluate the overall operational efficiency of a tower crane group, based on the efficiency equivalent of each tower crane. The operational capacity of a single tower crane is reflected by the combined effects of the tower crane's efficient space ratio, high-efficiency space ratio, and non-intersecting space ratio, as measured by coverage rate. and penalty items This reflects the coverage of the tower crane group over the building area; the coverage rate It is the ratio of the total area covered by the efficient space of the tower group to the area of ​​the building area; Coverage rate below the critical penalty coverage rate of the tower cluster Then a punishment will be imposed; The objective function for maximizing the efficiency equivalent is defined as: ； (1) ； (2) ； (3) ； (4) ； (5) in: For the number of tower cranes, This is the average efficiency equivalent of the tower crane. For tower cranes The work efficiency equivalent, For the coverage of the tower group, As a penalty item, For the critical penalty coverage of the tower group, The penalty coefficient is... The total area covered by the efficiency space of the tower group. The area of ​​the building area. For tower cranes Efficiency space area For tower cranes High-efficiency space area, For tower cranes The area of ​​the non-overlapping area with other tower cranes; Cost equivalent The overall impact of tower crane group efficiency on project cost is comprehensively reflected by the efficiency equivalent of each tower crane. A higher efficiency equivalent reflects the economic advantages it brings in long-term operation, and a lower cost equivalent. The objective function for minimizing the cost equivalent is defined as follows: ； (6) Safety equivalent As an equivalent quantity of unsafety, it comprehensively reflects the degree of safety risk of cross-operations in multiple towers, and is affected by the combined influence of the cross space area at each level as the cross level increases. As the number of elements increases, increasing order weights are assigned to cross spaces of different orders. The overall safety equivalent is constituted by weighted summation; The objective function for minimizing the safety equivalent is defined as: ； (7) in: For tower cranes Area of ​​the intersecting space, For tower cranes Cross weights, as Increase with the increase, The maximum number of cross-orders equals the total number of tower cranes. ; The equipment layout constraint is that the tower crane's tower body must be located within the layout area, meaning that the tower crane's coordinates must all be within the layout area: ； (8) in: , For tower cranes Coordinates in a plane coordinate system To arrange the area; The equipment safety space constraint is that the end of the boom of any tower crane cannot encroach on the safety space of other tower cranes, i.e., the minimum center-to-center distance constraint between any two tower cranes: ； (9) in: For tower cranes and tower crane geometric distance, For tower cranes arm length, For tower cranes arm length, For tower crane safety distance; The coverage constraint requires that, under any arrangement scheme, the total tower coverage rate must be greater than or equal to the minimum coverage rate. .

4. The multi-objective optimization method for tower crane group construction layout integrating efficiency, cost, and safety as described in claim 1, characterized in that: Specifically, S4 is: (1) Initialize the population Each individual in the population is represented as This corresponds to a tower crane group layout scheme, and an initial solution set containing several individuals is generated by initializing the population; (2) Generate offspring population For the current population Perform crossover and mutation operations respectively to generate offspring populations. Crossover operations include simulated binary crossover of the tower crane's planar coordinate gene and probabilistic mixed crossover of the boom length index gene; mutation operations include polynomial mutation of the tower crane's planar coordinate gene and probabilistic mixed mutation of the boom length index gene. (3) Generate candidate populations parental population Offspring population Merge into candidate populations ; (4) Generate a new generation of population For candidate populations The non-dominated sorting, crowding sorting, and elite retention strategies were executed respectively to generate a new generation of population. ; (5) Cyclic discrimination and Pareto front solution set output Repeat steps (2)-(4) until the maximum number of iterations is reached. It also outputs the Pareto front solution set.

5. The multi-objective optimization method for tower crane group construction layout integrating efficiency, cost, and safety as described in claim 1, characterized in that: Specifically, S5 is: (1) Standardize the objective function values ​​of individuals in the Pareto front solution set and form feature vectors: Perform Z-score standardization on the objective function values ​​of each individual in the Pareto front solution set to eliminate the influence of differences in the dimensions and numerical scales of different objective functions on the clustering results; The standardized objective function values ​​are used to construct the feature vector of this individual. , , , These are the standardized values ​​of the individual on the three objective functions of efficiency equivalent, cost equivalent, and safety equivalent, respectively. (2) Clustering algorithm is used to perform cluster analysis on the feature vectors of all individuals and divide them into three clusters corresponding to the three typical engineering trade-off strategies of "high efficiency", "balance" and "high safety": based on the feature vectors of all individuals For the sample set, the K-means clustering algorithm was used to cluster the Pareto front solution set into 3 clusters; the 3 clusters respectively represent the three typical engineering trade-off strategies corresponding to different objective trade-off tendencies: "high efficiency", "balance" and "high safety". (3) Select the individual closest to the centroid of the cluster as the representative scheme of the cluster: In order to ensure that each strategy outputs a representative and easy-to-implement recommended scheme, select the individual closest to the centroid of the cluster as the representative scheme of the cluster. (4) Managers select decision-making options based on project preferences. The representative solutions of the three clusters are output as a candidate recommendation set to the manager, and the manager can select according to the project preference. When the project schedule prioritizes hoisting efficiency, the representative solution of the "high efficiency" cluster is selected; when the project pursues comprehensive performance, the representative solution of the "balanced" cluster is selected; when the project has high requirements for safety control, the representative solution of the "high safety" cluster is selected.

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