A construction scheduling method considering changes in labor efficiency

Abstract

A construction scheduling method considering changes in labor efficiency includes: establishing a labor efficiency function and a construction scheduling optimization objective function; generating an initial population containing a labor plan; duplicating the original population and performing crossover, mutation, and combination operations; establishing a labor allocation network and a labor allocation rule considering labor efficiency; allocating the planned labor plans corresponding to each individual according to the labor allocation network and the labor allocation rule to obtain a labor allocation plan corresponding to each individual in the population; calculating the objective function value according to the labor allocation plan, sorting and selecting the individuals in the population according to the objective function value, and generating a new population with the same number of individuals as the original population; if the objective function value converges, extracting the labor plan according to the population information of the last iteration to generate a construction scheduling plan. The present invention can realize labor allocation based on the highest overall labor efficiency and effectively avoid unreasonable labor arrangement in construction scheduling.

Description

Technical Field

[0001] The invention relates to the field of construction scheduling of engineering construction, and in particular to a construction scheduling method taking changes in labor efficiency into consideration. Background Art

[0002] Engineering construction includes three main stages: survey, design, and construction. The construction stage is the most expensive and important stage in engineering construction. Therefore, safe and efficient construction operations determine whether the engineering construction can be completed safely and with high quality. As the core key to ensure the smooth progress of construction operations, scientific and reasonable construction scheduling is crucial.

[0003] Construction scheduling mainly includes the coordination of construction progress, human resources, equipment and other resources. At present, when carrying out construction scheduling work at the construction site, managers usually use the critical chain method to carry out scheduling work based on the total construction period plan of the project and the expenditure during the construction process, and formulate corresponding progress plans, labor plans, etc.

[0004] However, simply using the critical chain method can usually only meet the optimization of the construction period or funding goals, and cannot coordinate and take into account the funding and construction period goals. As a result, the construction period and funding arrangements are not optimally coordinated, resulting in a waste of time and money.

[0005] Although a large number of scholars have also carried out collaborative optimization of construction scheduling objectives based on multi-objective optimization algorithms, these methods usually focus on the optimization of objectives such as funding, construction period, and quality, and do not consider the impact of changes in labor efficiency on construction scheduling during the scheduling process. However, according to practical experience and research, the amount of labor input in the construction scheduling process has a significant impact on labor efficiency, because when there is too much labor, it will cause congestion on the construction surface, which is particularly obvious when rushing to meet the deadline. In the existing construction scheduling methods, the input of labor is only calculated according to the labor quota, ignoring the changes in labor efficiency, resulting in too many or too few people being invested, resulting in a waste of resources.

[0006] In addition, in the existing construction scheduling methods, labor plans are formulated according to the progress plan. The labor progress plan is often calculated based on the labor quota after the progress plan is completed, resulting in an uneven distribution of labor during the construction cycle. On the one hand, the number of workers on the construction site varies from time to time, resulting in additional expenses for indirect costs such as accommodation and safety. On the other hand, the unbalanced labor plan also creates pressure on construction management. Summary of the invention

[0007] In view of this, the present invention provides a construction scheduling method that takes changes in labor efficiency into consideration. On the one hand, the method takes labor efficiency into consideration, and on the other hand, incorporates the uniformity of labor distribution as an objective function into the optimization process, in order to achieve the construction scheduling goals in four dimensions of construction period, funding, labor efficiency, and labor uniformity while taking changes in labor efficiency into consideration, break through the existing extensive construction scheduling, and improve the industry level of construction scheduling.

[0008] A construction scheduling method considering changes in labor efficiency includes the following steps:

[0009] Step 1: Establish labor efficiency function and construction scheduling optimization objective function;

[0010] Step 2: generating an initial population, wherein the initial population includes a labor force planning scheme;

[0011] Step 3: Copy the original population and perform crossover, mutation, and combination operations;

[0012] Step 4: Establish a labor distribution network;

[0013] Step 5: Establish a labor allocation rule that takes labor efficiency into consideration;

[0014] Step 6: Allocate the labor plan corresponding to each individual according to the labor allocation network established in step 4 and the labor allocation rule established in step 5, and obtain the labor allocation plan corresponding to each individual in the population;

[0015] Step 7: Calculate the objective function value according to the labor allocation plan, sort and select the individuals in the population according to the objective function value, and generate a new population with the same number of individuals as the original population;

[0016] Step 8: Determine whether the objective function value converges. If it converges, extract the labor plan according to the population information of the last iteration and generate a construction scheduling plan; if it does not converge, return to step 3.

[0017] Furthermore, in step 1, a labor efficiency function is established, which specifically includes:

[0018] Average working area per capita Affected by the size of the working surface s and the number of construction workers n, it can be represented by formula (1):

[0019]

[0020] Based on the reference per capita working area size s0 and reference labor efficiency v0, a large number of data on similar scenes and types of operations are statistically analyzed and fitted to establish the per capita working area size in actual construction. The relationship between ρ and labor efficiency v is represented by formula (2):

[0021]

[0022] Combining equation (2) with equation (1), we can establish the function v(n) of labor efficiency v with respect to the number of construction workers n on the work surface:

[0023]

[0024] Furthermore, the optimization of construction scheduling objectives includes the total construction cost C, the total construction period T, the overall labor efficiency V during the construction process, and the uniformity of labor allocation U during the construction process. The construction scheduling optimization objective function established in step 1 is expressed by equations (4), (5), (6), (7), (8), and (9):

[0025] C=FC+IC+HC Formula (4)

[0026] T=max{t f Formula (5)

[0027]

[0028] Where FC represents fixed expenses, including materials, equipment, etc.; IC represents indirect expenses; HC represents human resource expenses; t f Indicates the time point when the last unit to be constructed ends; V t represents the overall labor efficiency of the construction day on the tth day, and the overall labor efficiency V of the project is calculated based on it; k represents the number of units carrying out construction work on the tth day; w i It means that the construction units on the tth day have a significant impact on the calculation of V t The weight of t represents the number of workers involved in the construction every day; μ represents the average number of construction workers per day during the entire construction period.

[0029] Furthermore, step two specifically includes: using the NSGA-III algorithm to randomly generate several initial populations, the populations are composed of several individuals, the individuals are represented by their genes, the genes contain several gene fragments, wherein the individual genes corresponding to the several individuals included in the initial population all represent a labor plan, and the fragments in the several genes contained therein are the total number of labor forces specific to a certain day, and the labor plan includes a planned construction period and the daily labor input.

[0030] Furthermore, in step three, the original population is replicated and crossover and mutation operations are performed. The specific steps are as follows:

[0031] (1) Cross

[0032] For the existing population, binary crossover is used to simulate the crossover behavior of biological chromosomes. By randomly selecting an individual, whose gene expression is represented by vector n, two gene fragments (n l , n m ) to perform crossover operations to generate new gene expression Generate new individuals. The specific mathematical transformation of this process is as follows:

[0033]

[0034]

[0035]

[0036] Where u is a random number in the range of (0,1), η is the distribution parameter, which is 1 here;

[0037] (2) Variation

[0038] For the existing population, some individuals are randomly selected, and their gene expression is represented by vector n. r Random mutation to generate new fragment n′ r To generate new individuals, the mathematical expression of this process is carried out through the following formula:

[0039] n r ′=n r +δ·(bl) Formula (13)

[0040]

[0041] Where b and l represent the maximum and minimum values ​​of the corresponding values ​​of different dimensions in the individual gene respectively; δ is the mutation parameter, which is affected by the mutating gene, the individual range and the current random state; p is a random number in the interval [0,1]; η m is the distribution index, which is 1 here.

[0042] Furthermore, step four specifically includes:

[0043] The construction project is discretized into several units that need to carry out construction work. Each unit contains the corresponding engineering quantity information and the type of workers required. According to the labor planning scheme generated by the multi-objective optimization module, a dynamic allocation network is established. In the allocation network, each construction unit is a node to be constructed in the allocation network, which is divided into completed units, constructable units, and temporarily unconstructable units. The planned labor force on the tth day is the input node, and the equivalent overall labor efficiency V on the tth day is the input node. t It serves as the output node;

[0044] The individual genes generated by the multi-objective optimization module are discretized into the planned labor force for each day, and according to the arrangement of the genes, for any gene fragment on the tth day, it will be set as the planned labor force on the tth day as the input node, and the labor force is allocated to all constructible units on the tth day through the allocation rule submodule, and finally flows to the output node on the tth day according to the labor allocation result, and then combined with the labor efficiency function of the labor efficiency function module, the equivalent overall labor efficiency V on the tth day is calculated. t ;

[0045] At the same time, according to the labor force allocated to each constructible unit on the tth day, the completion status of the project volume of each constructible unit on the tth day is calculated, and the remaining project volume to be completed is updated, and then the status of each construction unit on the t+1th day is judged to determine the completed units, constructible units, and temporarily unconstructible units on the t+1th day.

[0046] Furthermore, the labor allocation rule in step 5 is an allocation rule based on the gradient descent algorithm, which calculates the per capita work area of ​​each unit according to the number of laborers obtained by each unit. Then, based on the functional relationship f between per capita construction area and labor efficiency obtained in step 1 and v(n) derived from f, the equivalent overall labor efficiency V on day t is calculated. t , and use the gradient descent algorithm to obtain the optimal number of labor forces obtained by each unit.

[0047] Furthermore, step six specifically includes:

[0048] First, at time t, there are k constructible units in total. Initially, a random allocation scheme is generated, and V is calculated using equations (17), (18), and (19). t For each constructible unit, the number of workers n received (i) Gradient of (i=1,2,…,k):

[0049]

[0050] Where v i represents the labor efficiency of construction unit i; v o,i represents the reference labor efficiency v0 of construction unit i; s (i) represents the size s of the working surface of construction unit i, It represents the reference per capita working area size s0;

[0051] Then, according to the gradient descent, the adjustment amount of the allocation scheme is calculated and the allocation vector n is introduced. t =(n (1) 、n (2) , ..., n (k)) is used to represent the labor quantity information received by each constructible unit on the tth day. By setting the learning rate α in the gradient descent algorithm, the adjustment amount of the allocation scheme is calculated:

[0052]

[0053] n t (n (1) ,n (2) ,…,n (3) )→n t (n (1) +Δn (1) ,n (2) +Δn (2) ,…,n (k) +Δn (k) ) Formula (21)

[0054] Vector n t After the update occurs, the corresponding V t Will also be updated to And calculate ΔV t :

[0055]

[0056] By using the above rules, we can calculate the equivalent overall labor efficiency V on the tth day: t The largest workforce allocation program.

[0057] Furthermore, the sorting and selection operations in step seven specifically include:

[0058] (1) Sorting

[0059] Step 3: Update the replicated population through crossover and mutation, and mix the updated population with the original population. Based on the target value distribution of each individual in the mixed population, divide each individual into non-dominated layer and dominant layer (F1, F2, ..., F n );

[0060] (2) Select

[0061] For the sorted individuals, a number of individuals of the same size as the original population is selected to form a new population. When selecting a number of individuals of the same size as the original population, a limited number of individuals are selected from the last dominant layer and incorporated into the new population. The steps of screening the individuals in the last dominant layer again specifically include:

[0062] By generating equally spaced reference points, where d represents the target dimension and y represents the highest non-dominated layer containing the selected individuals;

[0063] According to the minimum values ​​of each dimension of the objective function in the non-dominated layer F1, the set Z is constructed by formula (24); according to the dominant layer F y The maximum values ​​of each dimension of the objective function are used to form a set S through formula (25); considering the different dimensions of different objective values, they are normalized respectively and expressed by formula (26):

[0064]

[0065]

[0066]

[0067] Then, the distance between each individual and the reference plane is calculated based on the normalized results, and the selection operation is performed from near to far, and the number of individuals in the selected new population is made consistent with that of the original population.

[0068] The present invention establishes a construction scheduling optimization model based on NSGA-III, which collaboratively considers the construction period, construction funds, overall construction labor efficiency, and labor distribution balance thinking goals, realizes multi-objective optimization of construction scheduling, and improves the scientific nature of construction scheduling and the accuracy of optimization solution; establishes a labor dynamic allocation network, and realizes dynamic labor allocation based on days; proposes a gradient descent allocation rule, considers the law of labor efficiency changes in the labor allocation process, realizes labor allocation based on the highest overall labor efficiency, and effectively avoids irrational labor arrangement in construction scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flowchart of a construction scheduling method taking into account changes in labor efficiency according to an embodiment of the present invention;

[0070] Figure 2 is a schematic diagram of a dynamic allocation network;

[0071] Figure 3 It is a schematic diagram comparing the construction progress schemes before and after the application of the present invention;

[0072] Figure 4 It is a schematic diagram comparing labor force allocation schemes before and after the application of the present invention. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] See also Figure 1 , an embodiment of the present invention provides a construction scheduling method considering changes in labor efficiency, comprising the following steps:

[0075] Step 1: Establish labor efficiency function and construction scheduling optimization objective function;

[0076] The construction scheduling scheme of the present invention taking into account the change of labor efficiency first needs to determine the construction scene and determine the reference per capita working area size s0 and the reference labor efficiency v0 according to historical construction data, and determine the relationship between labor efficiency v and per capita construction area by function fitting and machine learning. The mapping relationship between them is the labor efficiency function f.

[0077] Specifically:

[0078] (1) Labor efficiency function

[0079] During the construction process, the labor efficiency of workers will be affected by factors such as the size of the construction site and the number of workers working at the same time. The degree of this influence will vary in different construction scenarios. There are significant differences in building construction, road construction, and water conservancy construction. In order to adapt to different construction scenarios, historical construction data of different types of scenarios will be analyzed, and statistical methods will be used to fit labor efficiency functions for different types of operations.

[0080] In this invention, the main focus is on the size of the per capita working area during construction. Impact on labor efficiency, including per capita working area Affected by the size of the working surface s and the number of construction workers n. It can be represented by formula (1):

[0081]

[0082] During construction, the workers' working space has a significant impact on labor efficiency. A narrow space will reduce labor efficiency, while a spacious working space will improve labor efficiency to a certain extent. In order to ensure the rationality of the work, for different construction scenarios and types of operations, it is necessary to investigate and statistically analyze the reference per capita working area size s0 and the reference labor efficiency v0 under the reference per capita working area size s0. This step needs to be dynamically adjusted for different operation scenarios and types of operations.

[0083] Furthermore, based on the reference per capita work area size s0 and reference labor efficiency v0, by statistically analyzing a large number of data of similar scenes and work types, the per capita work area size in actual construction can be established using the fitting method. The relationship between ρ and labor efficiency v is represented by formula (2).

[0084]

[0085] This functional relationship f can be established for different construction scenarios and types of operations through methods such as function fitting and machine learning. Furthermore, by combining equation (2) and equation (1), we can establish a function v(n) of labor efficiency v with respect to the number of construction workers n on the work surface.

[0086]

[0087] (2) Construction scheduling optimization objective function

[0088] Working area per capita Will determine the labor efficiency v, this law is represented by the function f in formula (2). On this basis, the optimization construction scheduling target must be determined in the construction scheduling process. The present invention focuses on four targets, namely the total construction cost C, the total construction period T, the overall labor efficiency V in the construction process, and the uniformity of labor allocation U in the construction process. Among them, the total construction cost C and the total construction period T are the direct targets of scheduling, and the overall labor efficiency V in the construction process and the uniformity of labor allocation U in the construction process are intermediate targets, and their values ​​directly affect the total construction cost and the total construction period. The functional expression of the above targets is expressed by formulas (4), (5), (6), (7), (8), and (9).

[0089] C=FC+IC+HC Formula (4)

[0090] T=max{t f Formula (5)

[0091]

[0092] Where FC represents fixed expenses, including materials, equipment, etc.; IC represents indirect expenses; HC represents human resource expenses; t f Indicates the time point when the last unit to be constructed ends; V t represents the overall labor efficiency of the construction day on the tth day, and the overall labor efficiency V of the project is calculated based on it; k represents the number of units carrying out construction work on the tth day; w i It means that the construction units on the tth day have a significant impact on the calculation of V t The weight of t represents the number of workers involved in the construction every day; μ represents the average number of construction workers per day during the entire construction period.

[0093] Step 2: Generate an initial population, wherein the initial population includes a labor force planning scheme;

[0094] In the present invention, the labor planning scheme during the construction process is the only variable that determines the value of the objective function, and the information contained includes the planned construction period and the daily labor input. Using the NSGA-III algorithm, several initial populations are randomly generated, and the population consists of several individuals. The individuals are represented by their genes, and the genes contain several gene fragments. The individual genes corresponding to the several individuals included in the initial population each represent a labor planning scheme, and the fragments in the several genes contained therein are the total number of labor forces specific to a certain day.

[0095] Step 3: Copy the original population and perform crossover, mutation, and combination operations;

[0096] Since the number of individuals in the population is limited, in order to enrich the labor plan as much as possible and avoid falling into the local optimum. Considering that it is impossible to enumerate the labor plan endlessly, the original population individuals are processed by crossover and mutation, and the individual genes (labor plan) are continuously adjusted. In this step, the original population is first copied, and then the copied population is crossover and mutation operations are performed, and the copied population after the operation is merged with the original population to obtain a combined population with twice the number of individuals in the original population.

[0097] Specifically:

[0098] (1) Cross

[0099] For the existing population, binary crossover is used to simulate the crossover behavior of biological chromosomes. By randomly selecting an individual (whose gene expression is represented by vector n), l , n m ) to perform crossover operations to generate new gene expression Generate new individuals. The specific mathematical transformation of this process is as follows:

[0100]

[0101]

[0102] Where u is a random number in the range of (0,1), and η is a distribution parameter, which is 1 here.

[0103] (2) Variation

[0104] For the existing population, some individuals are randomly selected (their gene expression is represented by vector n), and some of their fragments (n r ) random mutations to generate new fragments (n′ r ) to generate new individuals, the mathematical expression of this process is carried out through the following formula:

[0105] n r ′=n r+δ·(bl) Formula (13)

[0106]

[0107] Where b and l represent the maximum and minimum values ​​of the corresponding values ​​of different dimensions in the individual gene respectively; δ is the mutation parameter, which is affected by the mutating gene, the individual range and the current random state; p is a random number in the interval [0,1]; η m is the distribution index, which is 1 here.

[0108] Step 4: Establish a labor distribution network;

[0109] Since the labor plan represented by the gene of individuals in the population is the planned labor input for each day during the construction period, but there are several construction units that need to work every day, in order to clearly define the labor for different units, it is necessary to establish a labor allocation network that progresses with the construction schedule to allocate the planned labor input for each day. In this step, based on the labor plan corresponding to the individuals in the population, the planned labor input is discretized by day to establish a labor allocation network.

[0110] Specifically:

[0111] The construction project is discretized into several units that need to carry out construction work. Each unit contains the corresponding engineering quantity information and the type of workers required. In addition, a dynamic allocation network is established based on the labor planning scheme generated by the multi-objective optimization module. In the allocation network, each construction unit is a node to be constructed in the allocation network, which is divided into completed units 4, constructable units 2, and temporarily unconstructable units 3. The planned labor force on the tth day is input node 1, and the equivalent overall labor efficiency V on the tth day is t Then as output node 5, the process is Figure 2 Hint.

[0112] In this process, the individual genes generated by the multi-objective optimization module are discretized into the planned labor force for each day, and according to the arrangement of the genes, for any gene fragment on the tth day, it will be set as the planned labor force on the tth day as input node 1, and the labor force is allocated to all constructible units 2 on the tth day through the allocation rule submodule, and according to the labor allocation result, it finally flows to the output node 5 on the tth day, and then combined with the labor efficiency function of the labor efficiency function module, the equivalent overall labor efficiency V on the tth day is calculated. t .

[0113] At the same time, according to the labor force allocated to each constructible unit 2 on the t day, the completion status of the project of each constructible unit 2 on the t day is calculated, and the remaining project volume to be completed is updated, and then the status of each construction unit on the t+1 day is judged to determine the completed unit 4, constructible unit 2 and temporarily unconstructible unit 3 on the t+1 day.

[0114] Step 5: Establish a labor allocation rule that takes labor efficiency into consideration;

[0115] In the previous step, a labor allocation network was established. In order to clarify the allocation rule of labor in the allocation process, the present invention proposes an allocation rule based on gradient descent.

[0116] Specifically:

[0117] In the allocation network submodule, the equivalent overall labor efficiency V on day t can be calculated based on the output node 5 on day t. t , the calculation method needs to be based on a clear allocation rule to maximize the equivalent overall labor efficiency V on the tth day t Therefore, the present invention proposes an allocation rule based on a gradient descent algorithm, which calculates the per capita working area of ​​each unit according to the number of laborers obtained by each unit. Then, based on the functional relationship f between per capita construction area and labor efficiency obtained in step 1 and v(n) derived from f, the equivalent overall labor efficiency V on day t is calculated. t , and use the gradient descent algorithm to obtain the optimal number of labor forces obtained by each unit.

[0118] Step 6: Based on the labor allocation network established in the fourth step and the labor allocation rule established in the fifth step, in the established labor allocation network, the labor plan corresponding to each individual is allocated according to the planned labor at each moment, and the labor allocation plan corresponding to each individual in the population is obtained; the specific steps are as follows:

[0119] First, at time t, there are k constructible units 2. Initially, a random allocation scheme is generated, and V is calculated using equations (17), (18), and (19). t For each constructible unit 2, the number of workers n received (i) The gradient of (i=1,2,…,k).

[0120]

[0121] Where v i represents the labor efficiency of construction unit i; v o,i represents the reference labor efficiency v0 of construction unit i; s (i) represents the size s of the working surface of construction unit i, Represents the reference average working area size s0.

[0122] Then, according to the gradient descent, the adjustment amount of the allocation scheme is calculated. Here, the allocation vector n is introduced t =(n (1) 、n (2) , ..., n (k) ) is used to represent the labor quantity information received by each constructible unit 2 on day t. By setting the learning rate α in the gradient descent algorithm, the adjustment amount of the allocation scheme can be calculated:

[0123]

[0124] n t (n (1) ,n (2) ,…,n (3) )→n t (n (1) +Δn (1) ,n (2) +Δn (2) ,…,n (k) +Δn (k) ) Formula (21)

[0125] Vector n t After the update occurs, the corresponding V t Will also be updated to And calculate ΔV t :

[0126]

[0127]

[0128] By using the above rules, the equivalent overall labor efficiency V on day t can be calculated: t The largest workforce allocation program.

[0129] Step 7: Calculate the objective function value according to the labor allocation plan, sort and select the individuals in the population according to the objective function value, and generate a new population with the same number of individuals as the original population;

[0130] Specifically, according to the labor allocation plan obtained from the labor plan corresponding to each individual in the population, the objective functions established in step 1 are used to calculate the values ​​of each objective function. Then, according to the objective function values ​​corresponding to each labor plan, the individuals in the population corresponding to the labor plan are sorted and selected to generate a new generation of population.

[0131] Specifically:

[0132] (1) Sorting

[0133] Step 3: Update the replicated population through crossover and mutation, and mix the updated population with the original population. Based on the target value distribution of each individual in the mixed population, divide each individual into non-dominated layer and dominant layer (F1, F2, ..., F n ).

[0134] (2) Select

[0135] For the sorted individuals, the number of individuals that is consistent with the original population size is selected to form a new population, and this process is considered to be the end of one iteration. However, due to the consistency of the objective function values ​​corresponding to different individuals, different individuals will be in the same dominance layer, so when selecting the number of individuals with the same size as the original population, it is necessary to select a limited number of individuals in the last dominance layer and include them in the new population, which requires another screening of the individuals in the last dominance layer.

[0136] Therefore, the reference point method is introduced, and Das and Dennis's Method is adopted to define the reference point. By generating equally spaced reference points, where d represents the target dimension, which corresponds to 4 objective functions in the present invention, and y represents the highest non-dominated layer containing the selected individuals.

[0137] First, according to the minimum values ​​of each dimension of the objective function in the non-dominated layer F1, a set Z is formed, and then, according to equation (24); y The maximum values ​​of each dimension of the objective function are taken to form a set S, which is expressed by formula (25). Considering that the dimensions of different objective values ​​are different, they are normalized respectively and expressed by formula (26).

[0138]

[0139]

[0140]

[0141] Then, the distance between each individual and the reference plane is calculated based on the normalized results, and the selection operation is performed from near to far, and the number of individuals in the selected new population is made consistent with that of the original population.

[0142] Step 8: Determine whether the objective function value converges. If it converges, extract the labor plan according to the population information of the last iteration and generate a construction scheduling plan; if it does not converge, return to step 3.

[0143] According to the objective function value corresponding to the labor planning scheme, determine whether the objective function distribution converges. If not, iterate the process from the third step to the sixth step until the distribution of each objective function value converges, and record the population information of the last iteration; the first step generates the initial population, but after the second to sixth steps, the population is updated, and then the second to sixth steps are repeated for the updated population. After each cycle, it is determined whether the objective function converges as the criterion for the end of the cycle.

[0144] According to the labor planning plan, the construction start and end time of each construction unit can be determined, and then the construction progress can be automatically generated. In the process of generating the labor allocation plan from the labor planning plan, the financial expenditure can be calculated, and the labor planning plan and construction progress plan can be summarized to obtain the construction scheduling plan.

[0145] Application results analysis:

[0146] Through a case analysis of a certain construction project, by using the construction scheduling method of the present invention before and after the comparative analysis, the construction period can be shortened by 14.6% (such as Figure 3 As shown), the cost can be reduced by 2%, the labor efficiency can be increased by up to 30%, and the uniformity of human resource allocation can be improved by 90% (as shown Figure 4 As shown in the figure), it effectively reduces construction costs and improves the rationality of human resource allocation.

[0147] The present invention has the following characteristics:

[0148] (1) Considering changes in labor efficiency during construction scheduling

[0149] The present invention takes into account the change in labor efficiency due to the change in per capita construction area during the construction process, realizes that the dynamic change law of workers' labor efficiency is taken into account during the construction scheduling process, avoids the change in progress due to the change in labor efficiency, and ensures that the construction speed is achieved according to the established plan.

[0150] (2) Labor-driven construction scheduling optimization method

[0151] The present invention considers the balance of labor input as the goal of construction scheduling. During the construction process, labor input is used as a variable to drive the solution of the coordinated optimal scheduling plan, so that the obtained labor plan satisfies the uniform distribution within the construction period, effectively saving the indirect costs caused by uneven labor input.

[0152] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A construction scheduling method considering changes in labor efficiency, characterized in that: The steps include: Step 1: Establish labor efficiency function and construction scheduling optimization objective function; Step 2: generating an initial population, wherein the initial population includes a labor force planning scheme; Step 3: Copy the original population and perform crossover, mutation, and combination operations; Step 4: Establish a labor distribution network; Step 5: Establish a labor allocation rule that takes labor efficiency into consideration; Step 6: Allocate the labor plan corresponding to each individual according to the labor allocation network established in step 4 and the labor allocation rule established in step 5, and obtain the labor allocation plan corresponding to each individual in the population; Step 7: Calculate the objective function value according to the labor allocation plan, sort and select the individuals in the population according to the objective function value, and generate a new population with the same number of individuals as the original population; Step 8: Determine whether the objective function value converges. If it converges, extract the labor plan according to the population information of the last iteration and generate a construction scheduling plan; If it is judged not to converge, return to step 3; In step 1, a labor efficiency function is established, which includes: Average working area per capita Affected by the size of the working surface s and the number of construction workers n, it can be represented by formula (1): ； According to the reference per capita working area size and reference labor efficiency By statistically analyzing a large amount of data on similar scenes and types of operations, and using fitting methods, we can establish the average per capita operating area size in actual construction. The relationship between ρ and labor efficiency v is represented by formula (2): ； Combining equation (2) with equation (1), we can establish the function v(n) of labor efficiency v with respect to the number of construction workers n on the work surface: ； Step 6 specifically includes: First, at time t, there are k constructible units in total. Initially, a random allocation scheme is generated and calculated using equations (17), (18), and (19). The number of workers received for each constructible unit gradient: ； In the formula represents the labor efficiency of construction unit i; represents the reference labor efficiency of construction unit i ; represents the size s of the working surface of construction unit i, Indicates the reference per capita working area size ; Then, according to the gradient descent, the adjustment amount of the allocation scheme is calculated and the allocation vector n is introduced. t =(n (1) 、n (2) , ..., n (k) ) is used to represent the labor quantity information received by each constructible unit on the tth day. By setting the learning rate α in the gradient descent algorithm, the adjustment amount of the allocation scheme is calculated: ； Vector n t After the update occurs, the corresponding Will also be updated to , and calculate : ； By using the above rules, we can calculate the equivalent overall labor efficiency on day t: The largest workforce allocation program.

2. The construction scheduling method considering changes in labor efficiency as claimed in claim 1, characterized in that: The optimization objectives of construction scheduling include total construction cost C, total construction period T, overall labor efficiency V during construction, and uniformity of labor allocation U during construction. The construction scheduling optimization objective function established in step 1 is expressed by equations (4), (5), (6), (7), (8), and (9): ； In the formula, FC represents fixed expenses, including materials and equipment; IC represents indirect expenses; HC represents human resource expenses; Indicates the time point when the last unit to complete construction ends; represents the overall labor efficiency of the construction day on the tth day, and the overall labor efficiency V of the project is calculated based on it; k represents the number of units carrying out construction work on the tth day; It means that the construction units on day t have a significant impact on the calculation The weight of Indicates the number of workers involved in construction every day; It indicates the average number of construction workers per day during the entire construction period.

3. The construction scheduling method considering changes in labor efficiency as claimed in claim 1, characterized in that: Step 2 specifically includes: using the NSGA-III algorithm to randomly generate several initial populations, the population is composed of several individuals, the individuals are represented by their genes, the genes contain several gene fragments, wherein the individual genes corresponding to the several individuals contained in the initial population all represent a labor plan, and the fragments in the several genes contained therein are the total number of labor forces specific to a certain day, and the labor plan includes the planned construction period and the daily labor input.

4. The construction scheduling method considering changes in labor efficiency as claimed in claim 1, characterized in that: Step 3: Copy the original population and perform crossover and mutation operations. The specific steps are as follows: (1) Cross For the existing population, binary crossover is used to simulate the crossover behavior of biological chromosomes. By randomly selecting an individual, two gene fragments of Perform crossover operations to generate new gene expressions , generate new individuals, the specific mathematical transformation of this process is as follows: ； Where u is a random number in the range of (0,1), η is the distribution parameter, which is 1 here; (2) Variation For the existing population, some individuals are randomly selected and their fragments are Random mutations to generate new fragments To generate new individuals, the mathematical expression of this process is carried out through the following formula: ； Where b and l represent the maximum and minimum values ​​of the corresponding values ​​of different dimensions in individual genes respectively; δ is the mutation parameter, p is a random number in the interval [0,1]; is the distribution index, which is 1 here.

5. The construction scheduling method considering changes in labor efficiency as claimed in claim 1, characterized in that: Step 4 specifically includes: The construction project is discretized into several units that need to carry out construction work. Each unit contains the corresponding engineering quantity information and the type of workers required. According to the labor planning scheme generated by the multi-objective optimization module, a dynamic allocation network is established. In the allocation network, each construction unit is a node to be constructed in the allocation network, which is divided into completed units, constructable units, and temporarily unconstructable units. The planned labor force on the tth day is the input node, and the equivalent overall labor efficiency on the tth day is the input node. It serves as the output node; The individual genes generated by the multi-objective optimization module are discretized into the planned labor force for each day, and according to the arrangement of the genes, for any gene fragment on the tth day, it will be set as the planned labor force on the tth day as the input node, and the labor force will be allocated to all constructible units on the tth day through the allocation rule submodule, and according to the labor allocation result, it will eventually flow to the output node on the tth day, and then combined with the labor efficiency function of the labor efficiency function module to calculate the equivalent overall labor efficiency on the tth day. ; At the same time, according to the labor force allocated to each constructible unit on the tth day, the completion status of the project volume of each constructible unit on the tth day is calculated, and the remaining project volume to be completed is updated, and then the status of each construction unit on the t+1th day is judged to determine the completed units, constructible units, and temporarily unconstructible units on the t+1th day.

6. The construction scheduling method considering changes in labor efficiency as claimed in claim 5, characterized in that: The labor allocation rule in step 5 is an allocation rule based on the gradient descent algorithm. This rule calculates the per capita work area of ​​each unit according to the number of laborers obtained by each unit. Then, according to the functional relationship between per capita construction area and labor efficiency f obtained in step 1 and v(n) derived from f, the equivalent overall labor efficiency on day t is calculated. , and use the gradient descent algorithm to obtain the optimal number of labor forces obtained by each unit.

7. The construction scheduling method considering changes in labor efficiency as claimed in claim 1, characterized in that: The sorting and selection operations in step 7 specifically include: (1) Sorting Step 3: Update the replicated population through crossover and mutation, and mix the updated population with the original population. Based on the target value distribution of each individual in the mixed population, divide each individual into the non-dominated layer F1 and the dominant layer (F2, F3,…, F y ); (2) Selection For the sorted individuals, a number of individuals of the same size as the original population is selected to form a new population. When selecting a number of individuals of the same size as the original population, a limited number of individuals are selected from the last dominant layer and incorporated into the new population. The steps of screening the individuals in the last dominant layer again specifically include: By generating equally spaced reference points, where d represents the target dimension and y represents the highest non-dominated layer containing the selected individuals; According to the minimum values ​​of each dimension of the objective function in the non-dominated layer F1, the set Z is constructed by formula (24); according to the dominant layer F y The maximum values ​​of each dimension of the objective function are formed into a set through formula (25); S takes into account the different dimensions of different objective values ​​and performs normalization processing respectively, which is expressed by formula (26): ； Then, the distance between each individual and the reference plane is calculated based on the normalized results, and the selection operation is performed from near to far, and the number of individuals in the selected new population is made consistent with that of the original population.

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