Dynamic Optimization of Construction Time-Cost for Deep and Large Foundation Pit Based on BIM Technology and Genetic Algorithm

Abstract

With the increasingly fierce market competition, optimizing the construction time-cost of deep and large foundation pit construction projects has become one of the key factors for construction enterprises to remain invincible. By dynamically optimizing the time-cost, the optimal time corresponding to the lowest engineering cost can be found. Based on a comprehensive transportation hub project, considering the time value of capital and the reward and punishment of construction time, a time-cost dynamic optimization model is constructed. Relying on BIM technology, the feasibility of construction plan is analyzed from both qualitative and quantitative perspectives, and the project parameters and resource information is obtained accurately and quickly. Using the MATLAB program, time-cost optimization based on genetic algorithm is carried out, and the static and dynamic optimization results are compared. The results show that the dynamic optimization scheme reduces the total cost by 1.68% while reducing the total construction time by 8.47%. The dynamic optimization scheme extends the construction period by 2 days while reducing the total cost by 89,500 yuan compared to static optimization. The peak value of the fund demand curve before and after optimization has decreased from 128,000 yuan to 127,000 yuan. The time-cost dynamic optimization, considering the time value of capital is more in line with engineering reality, and the optimization results are more reliable and accurate. BIM technology can accurately and quickly obtain project parameters and resource information, solving problems such as complex processes in super deep excavation and huge engineering data statistics. The genetic algorithm can efficiently and accurately search for the optimal solution within the global domain. This study combines BIM technology with the genetic algorithm to solve the dynamic optimization problem of construction period cost for deep and large foundation pits. The research results of this study provide a theoretical reference for the optimization of schedule cost for similar projects.

1. Foreword

With the rapid development of underground space, complex super and deep foundation pit construction projects are gradually increasing, and market competition is becoming increasingly fierce. Therefore, through the optimization of construction project management, in order to shorten the construction time, reduce costs, balance resources, and improve the comprehensive benefits of project management, these become the keys to an invincible position of construction enterprises. By optimizing the construction time-cost, comparing different construction times and corresponding project costs, the optimal construction time can be found when the project cost is lowest [1]. The genetic algorithm (GA) has a high solving efficiency and good search characteristics, and has been widely used in solution optimization in various industries. Luo Yi et al. [2] combined the small population real-coded genetic algorithm with the BP neural network to optimize the design of the voltage sharing circuit of the high-voltage DC voltage divider. Gao Jian et al. [3] established a 0–1 linear programming model for optimal water distribution in branch and lateral canals in irrigation districts, and analyzes the advantages and disadvantages of using discrete binary particle swarm algorithm (BPSO) and genetic algorithm (GA) to optimize water distribution in irrigation districts. Zhang Xiaocun et al. [4] used a double-objective genetic algorithm based on discrete variables to optimize the cross-section design of concrete frame columns, using carbon emissions and cost as indicators. Some scholars have also combined artificial neural networks with genetic algorithms for scheme optimization and prediction. Khalaj G. et al. [5,6] predicted the martensite fraction of microalloyed steel and simulated the correlation between heat treatment, chemical composition, and bainite fraction of pipeline steel by means of artificial neural networks. Wang Ruihang et al. [7] established a neural network model for load prediction based on a 4 million tons per year Fischer–Tropsch synthesis process. The genetic algorithm was used to optimize the initial weights and thresholds of the neural network to improve the accuracy of model prediction. Applying the GA to cost optimization can effectively improve the optimization efficiency and accuracy [8,9,10]. Feng Jingchun et al. [11,12] studied the cost optimization problem under the condition of minimizing the cost of project group owners using real number encoding and a genetic algorithm that preserves elite offspring. Li Aimin et al. [13] considered the time value of capital, established a construction time-cost dynamic optimization model, and solved it through genetic algorithm. Li Hongxian et al. [14] established a mathematical model for dynamic time/cost optimization and proposed an improved incentive genetic algorithm. Luo Gang et al. [15] overcame the shortcomings of traditional network planning optimization using genetic algorithms, making cost optimization more accurate and able to be solved more efficiently.

The construction time-cost optimization based on genetic algorithms requires a large amount of engineering data, with the expansion of modern building scale and the increase in construction process complexity, the limitations of traditional optimization methods in obtaining engineering data are becoming increasingly prominent. Building Information Modeling (BIM), as an emerging information technology, is gradually being applied to engineering construction optimization [16,17,18]. Wang Yongquan et al. [19] constructed a schedule-cost optimization system for grid construction projects based on BIM and the genetic algorithm, fully leveraging the advantages of modern information technology and traditional theoretical methods. Wang Xumin et al. [20] studied the combination of NSGA—II algorithm and BIM5D to solve the construction time-cost optimization problem. BIM technology can accurately and quickly obtain project parameters and resource information, solving problems such as complex super and deep excavation processes and large engineering data statistics; the GA can efficiently search for the optimal solution within the global domain, improving optimization accuracy, combining BIM technology with GA for construction time-cost optimization, which can fully leverage the advantages of both.

In summary, the genetic algorithm has been widely applied in scheme optimization in various industries, and scholars have conducted extensive research and exploration. Some scholars have also combined BIM technology with genetic algorithms for time-cost optimization, but few have considered considering the time value of capital and the rewards and punishments of project duration. Because the deep and large foundation pit of the comprehensive transportation hub project has the characteristics of large engineering quantity, heavy labor, high cost, tight construction period, and complex structure, it is difficult to complete the time cost optimization using traditional optimization methods. At present, there is relatively little research on the combination of BIM technology and the GA for optimizing the construction cost of super large deep foundation pits in comprehensive transportation hub projects, taking into account the time value of funds and the rewards and punishments of the construction period. Therefore, this article conducted relevant research.

Based on the construction project of a deep and large foundation pit of a comprehensive transportation hub project, a dynamic optimization model for time-cost is established. It utilizes BIM technology to obtain, store, transmit, and update relevant data, and fully utilizes the advantages of genetic algorithm such as rigorous quantitative analysis and accurate calculation. By solving the model, the dynamic optimal solution is found. The research results of this article have solved the dynamic optimization problem of time cost for complex deep and large foundation pits, making the optimization results more in line with reality. The combination of BIM technology and genetic algorithm makes optimization faster and more accurate. The optimization method studied in this article can be generalized and applied, providing a theoretical reference for time-cost optimization of similar projects.

2. Construction Time-Cost Dynamic Optimization Model

2.1. Construction Time-Cost Function Relationship

The total engineering cost consists of direct and indirect costs; according to the current budget quota and inventory pricing standards, direct costs include labor costs, material costs, machinery costs, safety and civilized construction costs, unit price measure fees, and other measure fees, while indirect costs include regulatory fees and management fees.

According to the literature [4,8], the relationship between the time of work i and the direct cost is a quadratic function:

$$c_i=\frac{c_{iN}-c_{iM}}{t_{iN}^2-t_{iM}^2}{t}_i^2+\frac{c_{iM}{t}_{iN}^2-c_{iN}{t}_{iM}^2}{t_{iN}^2-t_{iM}^2}$$

(1)

In Equation (1): c_i and t_i represent the direct cost and time of work i, c_iN and c_iM represent the normal and ultimate costs of work i, and t_iN and t_iM represent the normal and ultimate time of work i.

The direct cost of the project (C₁) is the sum of the direct costs of each work i, then:

$$C_1={\displaystyle \sum }_{i=1}^n{c}_i$$

(2)

In Equation (2): n represents the number of jobs.

The relationship between indirect cost (C₂) and construction time is linear, then:

$$C_2=k\times T$$

(3)

In Equation (3): k represents the indirect cost coefficient, and T represents the optimized construction time.

Consider rewards for early completion of the project or penalties for project delay (C₃), then:

$$C_3=e\times (T-T_p)$$

(4)

In Equation (4): e represents the reward and punishment coefficient, and T represents the planned construction time.

The total cost of the project (C) is:

$$C={\displaystyle \sum }_{i=1}^n{c}_i+k\times T+e\times (T-T_p)$$

(5)

2.2. Dynamic Optimization Model

In this study, the net present value (Pc) of the cost is taken as the economic evaluation index; the direct costs are paid in one lump sum based on the intermediate time points of each work; the indirect costs are calculated as interest at the end of each interest time; and the project rewards and punishments are calculated as interest at the end of each project time. The dynamic optimization model for construction time-cost is:

$$\min P_C={\displaystyle \sum }_{i=1}^n{c}_i{(1+r)}^{-(E{S}_i+t_i/2)}+C_2\times \frac{{(1+r)}^T-1}{r{(1+r)}^T}+C_3\times {(1+r)}^{-T}$$

(6)

$$\mathrm{s}.\mathrm{t}. \left\{\begin{array}{l}{t}_i,E{S}_i\ge 0\\ t_{iM}^{}\le t_i\le t_{iN}^{}\\ c_i{}_N\le c_i\le c_{iM}^{}\\ E{S}_i^{}=\max \{E{S}_h+t_i\},E{S}_1^{}=0\\ T=\max \{E{S}_k+t_k\}\end{array}\right.$$

(7)

In Equations (6) and (7): ES_i is the earliest start time for work i, ES₁ is the earliest start time for work without prior work, ES_h is the earliest start time of the immediate work of work i, ES_k and t_k are the earliest start time and work time of the work without immediate work, r is the discount rate, and other parameters are the same as above.

3. Construction Time-Cost Dynamic Optimization

3.1. Project Overview

The total construction area of a certain comprehensive transportation hub project is 170,000 square meters, which is a link project to achieve various comprehensive zero transfer transportation. The east–west length of the project foundation pit is about 648~706 m, the north–south width is about 85~162 m, the depth is about 8~18 m, and the area of the foundation pit is about 100,000 m². The open cut method is used for construction, with a total excavation volume of approximately 1,300,000 m³. In order to ensure the stability of the slope, retaining piles, anchor cables and slope excavation, the soil nailing wall and other forms of support have been adopted.

The planned construction time for the foundation pit project is 4 months with a daily earthwork excavation volume of approximately 12,500 m³, indicating high construction intensity. The construction area is located in front of the building of the high-speed railway station, with a large flow of vehicles and people, and a complex construction environment. The requirements for safe and civilized construction and environmental protection are high; there may be policy shutdown in the late construction time, resulting in a less effective working time and a tight schedule. The construction of foundation pit engineering directly affects the construction progress of the main structure in the later stage, and has a significant impact on the engineering cost. Therefore, it is particularly important for the project to optimize the construction time-cost and find the lowest cost optimized schedule.

The construction of foundation pits is divided into four construction processes: retaining cast-in-place piles (GZ), crown beam (GL), excavation (WT), and foundation pit support (ZH), with layered and segmented organization of flow construction. The retaining cast-in-place piles and crown beams are not layered, and the flow construction is organized by two and three sections, respectively. Excavation and foundation pit support are divided into five construction layers: the first layer of excavation is divided into four construction sections, and the second to fifth layers of excavation and the first to fifth layers of the foundation pit support are both divided into two construction sections, which are divided into a total of 27 tasks; the initial network plan is shown in Figure 1. The meaning of the letter abbreviations in Figure is annotated below

Table 1. Limit time and direct cost rate.

Work Code	Limit Time/Day	Direct Cost Rate/Yuan Per Day
GZ	28	9300
GL	12	2700
WT	70	3900
ZH	70	5200

Annotation: GZ represents retaining cast-in-place pile, GL represents crown beam, WT represents excavation, ZH represents foundation pit support.

and

Table 2. Dynamic optimization results.

Work	Construction Cost/Day	Critical or Not	Work Name	Construction Cost/Day	Critical or Not
		Before/After Optimization			Before/After Optimization
GZ1	9	Yes/Yes	WT 4-2	16	Yes/Yes
GZ2	27	Yes/Yes	WT 5-1	2	Yes/Yes
GL1	4	No/No	WT 5-2	16	Yes/Yes
GL2	8	No/No	ZH 1-1	14	No/No
GL3	3	Yes/Yes	ZH 1-2	2	No/Yes
WT 1-1	2	No/No	ZH 2-1	14	No/Yes
WT 1-2	7	No/No	ZH 2-2	2	No/Yes
WT 1-3	5	No/No	ZH 3-1	14	No/Yes
WT 1-4	3	Yes/Yes	ZH 3-2	2	No/Yes
WT 2-1	2	Yes/Yes	ZH 4-1	14	No/Yes
WT 2-2	13	Yes/Yes	ZH 4-2	2	No/Yes
WT 3-1	2	Yes/Yes	ZH 5-1	14	No/Yes
WT 3-2	15	Yes/Yes	ZH 5-2	2	No/Yes
WT 4-1	2	Yes/Yes

Annotation: GZi represents the i-th construction section of retaining cast-in-place pile, GLi represents the i-th construction section of crown beam, WTi-j represents the j-th construction section of the i-th construction layer of excavation, ZHi-j represents the j-th construction section of the i-th construction layer of foundation pit support.

. The key route is GZ1-GZ2-GL3-WT1-4-WT2-1-WT2-2-WT3-1-WT3-2-WT4-1-WT4-2-WT5-1-WT5-2-ZH5-2 with a construction period of 118 days. The construction period for other non-line projects is between 93 and 115. So, the planned construction period is 118 days, which meets the contract requirements.

3.2. Genetic Algorithm

The genetic algorithm simulates the evolution process of genetic variation of biological chromosomes, reflecting the rule of survival of the fittest [21]. Through selection, crossover, variation and other genetic processes, individuals who adapt to the genetic environment are retained to continue inheritance, and those who cannot adapt are eliminated. After screening, the optimal individuals are gradually propagated to the next generation. Repeat the above genetic steps until the termination conditions are met, and find the optimal answer globally. The steps for solving a genetic algorithm based on MATLAB’s programming are as follows:

(1) Determine variables and parameters. The time of each work determines the total cost of the project and is a decision variable that affects the target value. Project parameters include logical relationships, normal time, ultimate time, normal cost, and ultimate cost. Genetic parameters include individual coding string length L, population size P, iteration frequency G, crossover probability P_c, and mutation probability P_m. This project takes the number of jobs as the string length, i.e., L = 27. P, G, P_c, and P_m are 400, 1200, 0.5, and 0.0003, respectively.

(2) Parameter coding. In order to facilitate genetic algorithm solving, the actual problem is transformed into a problem represented by parameters. There are 27 works involved in the construction of the foundation pits in this study, with a large capacity. To simplify the encoding and decoding steps, real number encoding is used. Each chromosome has 27 genes, representing 27 works. The attributes of the genes include work name, time, earliest start time of work, and previous work. The chromosome composition is shown in Figure 2.

(3) Initialize population. This study randomly generates an initial population that satisfies constraint conditions and basic assumptions as the initial solution of the problem. If the population size is too large, it will result in individual optimal solutions not dominating the evolutionary direction of all solution. If the population size is too small, it will cause the genetic algorithm to converge prematurely, leading to inaccurate solution results. This study randomly initializes the population with a population size of 400.

(4) Fitness evaluation. Fitness reflects the degree to which individuals approach the objective function. In this study, the objective function shown in Equation (6) is the fitness function to calculate the fitness value. The smaller the fitness value, the better the individual, the greater their chances of reproduction, and the greater the probability of being selected for the next genetic operation

(5) Genetic manipulation. Through selection, crossover, and mutation operations, the reproductive function of organisms is simulated, new individuals are generated, and better populations are formed. This study uses the Monte Carlo selection method and uniform crossover method to randomly select a node for variation of construction status. If the result is satisfactory, the optimal solution is output. Otherwise, steps (4)–(5) will be repeated until the result is satisfactory.

3.3. Construction Time-Cost Optimization Process

Combined with the project data, the time-cost optimization process based on BIM technology and genetic algorithm is established, as shown in Figure 3. This process mainly includes the BIM module and GA module. The ultimate goal of the BIM module is to obtain project parameter information for feasible solutions. The main function of the GA module is to dynamically optimize the time-cost through MATLAB programming. The specific steps are as follows:

(1) This study establishes a BIM model and exports engineering quantity files based on BIM calculations. Based on the budget quota, the time of each work is calculated and the network diagram is drawn, as shown in Figure 1.

(2) This study imports engineering quantity files into BIM pricing software. Combining budget quotas and pricing standards, pricing files are generated. The direct cost of the project is 5.7331 million yuan, and the indirect cost is 770,200 yuan.

(3) Based on the BIM model, a 3D site layout is conducted and a 3D site layout model file is generated.

(4) The network diagram file, 3D site layout model file, and pricing file are imported into the BIM5D construction management platform to complete the association of model, schedule, and cost information. The feasibility of the plan is judged through BIM5D construction simulation. If the plan can be successfully implemented, it indicates from a qualitative perspective that the plan is feasible. For qualitatively feasible solutions, quantitative parameters such as labor, funds, and materials are output through the BIM5D platform. If the output parameters meet the actual needs of the project, it indicates that the scheme is feasible from a quantitative perspective. For schemes that meet the requirements for qualitative and quantitative evaluation, the required project parameter information for optimization is output through the BIM5D platform.

(5) Through MATLAB programming, the dynamic optimization of time-cost is carried out based on the genetic algorithm. According to the solution steps introduced in Section 3.2 of this article, after iterative convergence, the optimized solution is obtained.

(6) According to the optimized plan, the pricing file and network diagram are adjusted and step (4) is repeated. If the optimization plan is feasible in both qualitative and directional aspects, the optimal plan is obtained. Otherwise, steps (1)–(6) will be repeated until the solution is feasible.

4. Analysis of Optimization Results

Based on the management philosophy of “full space, sufficient time”, the project is organized via flow construction. In the initial schedule, GZ, GL and WT are key works. The project contract time is 122 days, and the initial planned time is 118 days. The initial network plan meets contract requirements. According to the contract, the penalty for project delay is 100,000 yuan per day. After calculation, the direct cost of the project under normal construction time is 5.7331 million yuan. The limit time and direct cost rate of each work are shown in Table 1. The indirect rate is 6527 yuan per day.

4.1. Dynamic Optimization of Construction Time-Cost and Result Analysis

The annual interest rate of the project loan is 6%. By incorporating project parameter information into Equations (6) and (7) and using MATLAB programming, the dynamic optimization of time-cost is carried out based on the genetic algorithm. After 1200 iterations, the optimal solution is obtained by satisfying the termination conditions. Figure 4 shows the minimum and mean values of the population for each iteration, and the convergence of the calculation results is good. Table 2 shows the optimization results, with multiple critical paths. The optimal present value of the total cost of the deep excavation project is 6.3938 million yuan, and the present value of direct costs is 5.6295 million yuan. The optimal construction time is 108 days.

(1) Comparing Figure 1, Table 1 and Table 2, the time of each work is between the normal and limit values, and critical work is not compressed into non-critical work. The method of searching for the optimal solution using genetic algorithm is in line with engineering practice and basic assumptions, and the results obtained are true and reliable.

(2) The total cost of optimization is increased from 6.5033 million yuan to 6.3938 million yuan, and the construction time is changed from 118 days to 108 days. The construction time is shortened by 10 days, and the total cost is reduced by 109,500 yuan. The optimization effect is good. Some individuals in each generation of population are close to or equal to the optimal solution, which is a feasible solution for project implementation and can be selected based on engineering practice.

According to the optimization results, the network diagram file, 3D site layout model file, and pricing file are adjusted and imported into the BIM5D construction management platform to simulate the construction process. The optimized plan runs smoothly, with no conflicts in various work arrangements, and the construction progress is reasonable and feasible.

(1) In the optimal solution network diagram, the key line route is changed from one to multiple, and the original key line remains unchanged, which conforms to the basic assumption. The optimization plan reached its peak on the 19th to 21st day of construction, with a total daily capital demand of 127,000 yuan. Based on the analysis of the project site situation, various resources and funding supply of the project can meet the needs of the optimized solution.

(2) After dynamic optimization, the unbalanced coefficient of fund demand changes from 2.08 to 2.16. The peak value of the fund demand curve before and after optimization does not change much, but the number of key routes increases, making project management more difficult. During the implementation of the project, the BIM5D construction management platform is used to monitor the progress of the project in real-time and verify the allocation of project resources and construction costs. Any deviations are identified and adjusted in a timely manner to ensure progress.

4.2. Static Optimization of Time-Cost

Without considering the time value of capital, the objective function is:

$$\min C={\displaystyle \sum }_{i=1}^n{c}_i+C_2+C_3$$

(8)

The parameters in Equation (8) are the same as before, while the constraints and other parameters remain unchanged. The total cost of static optimization is 6.4833 million yuan, and the optimized construction time is 106 days. The original key route remains unchanged. Comparing the results of static and dynamic optimization, the dynamic optimization can extend the construction time by 2 days while reducing the total cost by 89,500 yuan compared to static optimization. Dynamic optimization takes into account the time value of capital, which is more in line with the actual engineering situation. The optimization plan is more advantageous for the overall benefits of the project. The comprehensive transportation hub deep foundation pit project in this study was implemented according to the optimization results and successfully completed in December 2022. The project implementation process and results indicate that the optimization method and results presented in this article are accurate and reliable, effectively ensuring the smooth implementation of the project.

5. Conclusions

(1) Considering the time value of capital and the rewards and punishments for the construction time, a quadratic curve is used to represent the relationship between the direct cost and the construction time of each work, and the relationship between the construction time and cost function is determined. Taking the net present value of costs as the economic evaluation indicator, the direct costs are paid once at the intermediate time points of each work, the indirect costs are calculated once at the end of each interest period, and the project rewards and punishments are calculated once at the end of the project period. A dynamic optimization model of time-cost for deep foundation pits is established.

(2) BIM technology can quickly and accurately obtain project information, and genetic algorithms can search globally. By combining BIM technology with the genetic algorithm, the time-cost optimization process is established. By adopting a flow construction method, the construction of deep and large foundation pits in the project is decomposed into 27 works, and the project parameters are reasonably determined. The genetic parameters L, P, G, P_c, and P_m are 27, 400, 1200, 0.5, and 0.0003, respectively.

(3) The dynamic optimization scheme reduces the total cost by 1.68% while reducing the total construction time by 8.47%. The static optimization scheme reduces the total cost by 0.31% while reducing the total construction time by 10.17%. The dynamic optimization scheme extends the construction period by 2 days while reducing the total cost by 89,500 yuan compared to static optimization. Dynamic optimization considers the time value of funds, which is more in line with engineering reality and has greater guidance value for the project.

(4) Visual construction simulation is conducted on the dynamic optimization scheme using the BIM5D platform, and combined with the funding demand curve, the feasibility of the scheme is verified from both qualitative and quantitative perspectives. The peak value of the fund demand curve before and after optimization has not changed much, reaching 128,000 yuan and 127,000 yuan, respectively. The various resources and funding supply of the project can meet the needs of optimizing the operation of the plan. The uneven coefficient of fund demand has changed from 2.08 to 2.16, and the number of key routes has changed from one to multiple, making construction management more difficult. During the implementation of the project, real-time monitoring of the project progress is carried out using the BIM5D platform, and any deviations are promptly adjusted.