The construction industry is one of the five pillar industries that support China's economic development and national economy. Due to the background of the great development situation of the construction industry and the strict control of the state, the market competition is becoming increasingly fierce, and the competition in the future construction industry market would undoubtedly be the double of competition price and quality which is right now. On the premises of ensuring the quality of the project, cost control and management are two important factors that should be maintained from the early phase of planning the project until the operation and maintenance stage, and the utilisation rate of various resources should be improved to the greatest extent. Only in this way the goal of maximising economic benefits can be achieved, thus creating the competitive advantage of enterprises [1,2]. Therefore, the cost control of the project in each stage has become one of the focuses of the project participants [3,4,5].

While promoting the application of advanced technology, it is necessary to integrate the resources in the construction process to ensure that all links and processes in the construction process are reasonably scheduled, so as to obtain the optimal scheme of construction dispatch and truly construct a building with low cost, short construction period and environmental protection [6, 7]. At present, BIM technology has been widely used in design, construction, operation and maintenance at various stages. In the optimisation process, all kinds of project information contained in the BIM model (such as geometric and physical information of buildings, material information, cost information, time information, change information, etc.) will be used as the data basis of optimisation [8,9]. The application of BIM technology in construction management plays an important role in promoting the modernisation of construction management. Applying BIM technology to prefabricated building construction is of great significance for improving the level of building construction management [10]. However, when the scale and complexity of buildings gradually increase to a certain degree, it is difficult to grasp all the information only by manpower, and it is impossible to solve all the problems in engineering construction by a single technology or method.

BIM technology has great advantages in visualisation, data preservation and updating but lacks quantitative theoretical calculation. Optimisation algorithm is a theoretical calculation based on the optimisation model. Although it has the advantages of thorough quantitative analysis, the integrity of data information cannot be guaranteed, and the presentation of results is not intuitive enough [11,12,13]. By combining BIM technology and the optimisation algorithm, we can make full use of the advantages of the emerging information technology, solve the problem of data acquisition and processing and improve the informatization level of engineering construction.

The application of BIM technology in optimisation of structural design will improve the work efficiency and quality, which is mainly reflected in the following three aspects [14,15,16,17]:

Project information files are generally stored in the form of paper or electronic documents, and there is no connection between them, which has great limitations in information storage, extraction, modification, update and sharing, especially in large-scale engineering projects. Using BIM technology to store these scattered and independent project information in a shared database can not only guarantee the uniqueness, integrity and accuracy of information but also make the information data timely and traceable in the process of updating, which will greatly advance the efficiency.

Through BIM technology, the plane expression forms such as points, lines and planes in two-dimensional drawings are transformed into three-dimensional and spatial three-dimensional expression forms, so as to realise the visual design of buildings. Designers can intuitively express their own design intent so that all participants in the project can clearly and intuitively understand the design intent, effectively reduce the communication cost and make further acceleration of the project. Through the visual simulation of the BIM model, on one the hand, the feasibility and rationality of the design scheme can be verified, and it is convenient for designers to find and solve various design problems in time, such as the collision between disciplines, so as to improve the quality of the design scheme and reduce the risk of change in the construction stage; On the other hand, the BIM-4D model can be formed by adding the time node information to the three-dimensional model of the structure, and on this basis, the construction schedule and process can be visually simulated by using the construction simulation function so that the managers can arrange the construction resources more scientifically and reasonably, formulate the construction plan and effectively reduce the resource waste.

In the process of project design and construction, alteration of design often occurs. In the traditional work-flow, because the results cannot be automatically updated, all design results related to the alteration, such as drawings and calculation tables, must be manually searched and modified, which will obviously increase the risk in the process of design and construction. However, all kinds of data in the BIM model have certain relevance. When the alteration of the project is modified or adjusted, the related model and its information will be automatically updated.

The technology of construction simulation, on the one hand, can check out the collisions and conflicts in the design scheme, facilitate the engineers to optimise the design before the actual construction work and effectively reduce the occurrence of design alterations in the construction process. On the other hand, by adding information of the construction process and schedule to the BIM model, it can realise the simulation of process and progress in construction, which is beneficial for managers to make reasonable construction plans, accurately grasp the construction process, efficiently utilise construction resources and scientifically arrange construction sites. At present, there are many software programmes with functions of construction simulation, such as Navisworks software developed by Autodesk company which is often used to check the collision between components and the simulation of construction schedule [18]. Considering the common functions of software and the data link with modelling software, this paper chooses Navisworks software that is suitable for Revit to carry out collision detection and construction simulation for the BIM model.

Navisworks software is used to complete the collision inspection and construction simulation of the optimised 3D structure model. Among them, the workflow of collision inspection is shown in Figure 1:

Add files to be checked. The first step is to add NWC format files exported by Revit software to Navisworks software. The file with the NWC format is one of the three native file formats of Navisworks software, which can reduce the access time.

Select the object to be inspected and set the collision type. Find and click the ‘Clash Detective’ option from the function bar at the top of the page and select the objects and collision types involved in the pop-up option box;

Run collision inspection and output inspection report. After setting in the editing window, click the ‘Check’ button at the bottom right of the interface to start the process of collision inspection. Afterward, the collision results can be seen on the interface and automatically output the inspection report, in which the collision points are sorted, and the specific location of the collision points can be located according to the serial number. In addition, each collision point can also be located according to its position description. The collision inspection uses the ‘Clash Detective’ function of Navisworks software, while the construction simulation uses the ‘Time Liner’ function.

In this paper, an optimised architecture system combining BIM technology and immune genetic algorithm is constructed, as shown in Figure 2, in which the cooperation between BIM and immune genetic algorithm is mainly accomplished through the docking of MATLAB and Navisworks. Firstly, according to the design drawing, BIM is used to accurately model the building structure, and then, the model is imported into Navisworks to complete the calculation and analysis of the building structure. Then, the engineering data required for structural design and cost are generated into Excel file A, and the immune genetic algorithm program is run in MATLAB to optimise the file A and output the result, which is Excel file B. Finally, file B is imported into Navisworks, and the structure is analysed and calculated again, where a new design scheme is generated and exported. The derived scheme of structural design can continue to guide the construction and other work by using the BIM model.

In the whole process of construction, the dispatching work in the assembly stage is the most important, which includes the hoisting of prefabricated components, the construction of cast-in-place structures and the connection between prefabricated components and cast-in-place parts. As the key work in the whole construction process, the limit in assembly time determines the deadline of the manufacturing stage and the transportation stage. Therefore, it is the primary task to obtain the optimal scheduling scheme with the shortest construction period in the assembly stage.

The scheduling scheme of construction affects the length of the assembly period; so, it is necessary to determine a construction scheduling scheme that meets the resource constraints of personnel and equipment and has the shortest assembly time at the assembly stage. This kind of problem is regarded as resource-constrained project scheduling problem, and its purpose is to find out the scheduling scheme with the shortest construction period (or the lowest cost). A complete engineering project is composed of many works with the predecessor and successor, and the determination of the scheduling scheme must meet the predecessor and successor constraints among all the project, as well as the upper limit of engineering project resources [19, 20].

In the assembly stage of prefabricated building construction, hoisting of prefabricated components is the main work, which should be assumed that all resources are available before the construction of the standard floor [21]; the hoisting components are transported to the construction site after being manufactured and qualified by the prefabrication factory, which is different from the construction of cast-in-place structures. The assembly stage is less affected by the environment and climate, and the construction of the standard layer is repetitive; so, it can be assumed that the construction efficiency of each layer is the same, and the assembly period can be expressed by the product of the assembly time of each layer and the number of assembly layers.

Therefore, the establishment of the BIM model in this paper is based on the following hypothesis:

All activities and required resources are ready before the start of the project;

The construction environment is normal, and the working efficiency of tower cranes and construction workers in each standard layer is the same.

Assuming that a project is made up of n+2 tasks, that is, V = { 1, … , n+2}, in which activities 1 and n+2 represent the tasks at the beginning and the end, respectively, which only represent the logical relationship of the tasks. There are a limited number of renewable resources in these activities, of which the maximum capacity of the kth resource is R_{k} (k = 1, 2, … , R). In addition, at any time, the sum of the usage of the kth renewable resource by various activities cannot exceed its upper capacity limit R_{k}.

The time required in activities _{i}_{k}_{n}_{+2} = Σ_{i}

First, the objective function of the minimum chemical period is established:

Then, Eq. (2) is used to express the processor activity constraint relation of activities

Eq. (3) represents the resource constraint of activities, that is, the total demand for renewable resources k by all activities at any time shall not exceed its upper limit R_{k}:

Eq. (4) indicates that the time is a discrete value;

According to Eq. (5), the start time of all construction activities is not negative:

Among them, _{ik}

The structural model of this project is established by Revit software, and the manufacturing process is shown in Figure 3.

The specific steps are as follows:

Click ‘add new project’ to create a template file of project. Usually, the system will create the template file that Revit comes with by default. If there is no special requirement, the default template file can be used.

Enter the interface to edit the elevation and grid of the project according to the design scheme. First draw the elevation, then draw the grid and finally set and mark their 2D and 3D attributes and dimensions.

Map the site. Because the location of this project is flat and there is no complicated information parameter of landform, the layout of the site can be completed quickly. In case of the complex site, complex terrain can be drawn by importing site CAD files. Then according to the specific elevation of the project, draw the building floor. Finally, make relevant settings for the site;

Draw columns and columns. Click ‘Column’ in the column of ‘Common’ tab to map. Since there is no concrete column in the default template, it is necessary to select the concrete rectangular column in ‘Load cluster’ and then set the size and placement position of the column. Just like the operation of mapping columns, click the ‘Beam’ button in the column of ‘Common use’ tab. After mapping a beam, the ‘Array’ function can be used to get a row of beams.

Draw other components, such as walls, boards and stairs according to the building layout plan.

According to the characteristics of the model, the natural number coding method is adopted to uniformly number all processes in the construction and assembly of the standard floor with natural numbers. If there are m processes, each process is numbered as 1, 2, 3, … , m according to technological constraints. The length of chromosome is m, and the number of procedure 1~m represents the gene value, where the information expressed by each gene is the sequence of processes corresponding to the current gene.

Take the order of 2-1-7-4-3-6-5 as an example; in the case of resource constraint, it is assumed that process 1 and process 7 need the same resource R1. If they can meet the constraint conditions of R1 resources at the same time, then process 1 and process 7 can be constructed in the meantime. If the constraint conditions of R1 resources are not met, the activity of process 1 should be implemented first, and after the activity of process 1 is finished, the activity of process 7 can be carried out.

To make the fitness value of each chromosome indicate the quality of the solution, transform the minimisation target into the maximisation target by Eq. (6):

Acquisition of fitness value: If the 1/

Roulette wheel strategy: assuming that there is _{i}_{i}_{i}

Partial-mapped crossover method is adopted. The process of crossing is shown in Figure 4. First, select the parent chromosome from the population; second, generate a chromosome length satisfying 0 ≤ _{1} ≤ _{2} and cut the chromosome into two segments; then, the positions of the captured two segments are exchanged, and finally, the conflict of coding repetition is solved.

MATLAB 2017a is used to program, and the genetic algorithm is used to solve the model, and the population size NP = 80 is set. maxgen = 200; Pc = 0.8; Pm = 0.2; generation gap probability Pe = 0.9; after 130 iterations, the shortest construction period is 8 days. Within the 8d construction period of a standard floor, arrange tasks of daily construction according to resource constraints, where the work in the first day is arranged for measuring unreeling, binding of cast-in-place steel bars, hoisting of external wall, formwork support of composite beams and plates of Unit 1 and measuring unreeling of Unit 2. The work schedule of every day is clear that the construction of a standard layer is carried out every 8 days, until the construction of all assembly floors of the project is completed.

Set the population size NP = 50; maxgen = 200; Pc = 0.8; Pm = 0.2. After 200 iterations, the optimal solution of the calculated construction period and cost is obtained, and its distribution decreases nonlinearly. In addition, there is an inverse relationship between the target of construction period and the cost target, where the shorter the construction period, the higher the cost. If managers want to shorten the manufacturing time of prefabricated components, they need to introduce high resource cost. Otherwise, they need to extend the time of producing. The corresponding values of objective function are shown in Table 1:

Function value of optimal solution

1 | 5.5 | 845657 |

2 | 5.7 | 810038 |

3 | 5.9 | 792742 |

4 | 6.1 | 762410 |

5 | 6.3 | 739823 |

6 | 6.5 | 712871 |

7 | 6.7 | 701287 |

8 | 6.9 | 671209 |

Solution 1 has the optimal duration that d1=5.5d, but the highest resource cost is c1=845,657. The optimal resource cost is solution 8 with c14=61,766 yuan, but its duration of construction is d14=6.9d, which is the longest. Different solutions in the optimal solution set correspond to different construction periods and resource costs, and decision makers need to choose the optimal solution according to the preference of construction period and resource costs.

To verify the rationality of the model optimisation, the Naviswork is used to check the collision of the optimised structural model and simulate the construction process. Accurately locate the location of collision through collision inspection and timely solve the design blind spots that are not easy to find, thus effectively improving the design quality and the work efficiency of designers. Using simulation of construction can solve the problems and contradictions that may occur in the actual construction as early as possible, so as to reduce risks, save costs and shorten the construction period. The simulation process of construction in this project is shown in Figure 5.

In the process of simulation, with the help of virtual technology, the simulation of technological process and the refined presentation of some special engineering components are realised, and compared with real objects, managers can optimise the construction plan to the maximum extent, which is of guiding significance to the node control of the constructor and the project management of the owner. In addition, as a bridge connecting the design and construction stages, the construction simulation function will play a great role in the disclosure work in the design and construction stages. The constructors can intuitively feel the process of design and construction in each component through the simulation test, effectively improve the dullness brought by traditional drawings and guide the work of construction accurately.

To ensure the optimal arrangement of resources in the scheduling plan and speed up the construction progress, this paper establishes a resource-constrained scheduling model with the objective function of the minimum duration and adopts genetic algorithm to solve the model, so as to obtain the scheduling plan that meets the shortest construction period of resource-constrained assembly and implement daily construction tasks as planned to ensure the construction progress. The results show that during the construction, the distribution of period cost decreases nonlinearly, and there is an inverse relationship between construction period target and cost target, where the shorter the construction period, the higher the cost. If managers want to shorten the manufacturing time of prefabricated components, they need to invest in high resource cost. Finally, by simulating the construction stage with BIM technology, managers can optimise the construction plan to the maximum extent which has guiding significance for the construction node control of the constructor and the project management.

#### Function value of optimal solution

1 | 5.5 | 845657 |

2 | 5.7 | 810038 |

3 | 5.9 | 792742 |

4 | 6.1 | 762410 |

5 | 6.3 | 739823 |

6 | 6.5 | 712871 |

7 | 6.7 | 701287 |

8 | 6.9 | 671209 |

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Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network