Improved subtraction-based average optimization algorithm considering building engineering design problem
By improving the average optimization algorithm, combined with TENE chaotic mapping and golden sarnery functions, the traditional optimization methods are solved in the design of low efficiency and easy to fall into local best in construction engineering design, and achieve more efficient and accurate optimization results.
Patent Information
- Application Number
- CN202411518944.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-29
- Publication Date
- 2025-01-28
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
When traditional optimization methods deal with large-scale, multi-objective and complex constraint problems in architectural engineering design, they are inefficient and easily fall into local optimal solutions, making it difficult to find global optimal solutions.
The average optimization algorithm of the improved subtraction is adopted to generate the initial population and search path through the TENE chaotic mapping, combined with the golden sarnex function to avoid local optimal optimal. Based on the CEC2005 benchmark test function, other algorithms are compared, and the effectiveness of the algorithm in actual construction engineering projects.
The efficiency and accuracy of construction engineering design optimization problems have been improved, the restrictions on local optimal solutions have been overcome, and global convergence and computing efficiency are achieved.
Smart Images
Figure CN119378074A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of engineering technology, and more particularly to an improved subtraction average optimization algorithm considering architectural engineering design problems. Background Art
[0002] Optimization is a critical and complex challenge in architectural engineering design. The engineering design process usually involves multiple conflicting objectives and constraints, such as cost, material usage, structural strength, energy efficiency, and aesthetics. These objectives and constraints must not only be considered individually, but also must be balanced and compromised with each other to achieve the optimal design. Traditional optimization methods, such as linear programming, nonlinear programming, and dynamic programming, although they can solve these problems to a certain extent, often show certain limitations when dealing with large-scale, multi-objective, and complex constrained optimization problems. These methods are less efficient when dealing with complex nonlinear relationships and high-dimensional design spaces, and are prone to fall into local optimal solutions, making it difficult to find the true global optimal solution.
[0003] Engineering design problems usually require designing under a set of strict specification constraints while making trade-offs between conflicting optimization objectives. For example, the cost of the project and the robustness of the product, the weight and size of the product, the choice of materials and environmental impact are all factors that need to be balanced. This trade-off process complicates the design problem and requires more advanced optimization techniques to solve it effectively. Therefore, engineering design problems can be modeled as constrained multi-objective optimization problems (CMOP). In this modeling, designers not only need to meet various hard constraints, but also need to find the best solution between multiple optimization objectives.
[0004] Since the objective functions of many engineering design problems are discontinuous, and the objective functions of some problems lack prior knowledge, it is difficult to model them through simulation. Often, the objective function can only be optimized as a black box, which greatly increases the difficulty of the optimization problem. Therefore, it is necessary to design accurate and efficient optimization algorithms to optimize the problem. In addition, these intelligent algorithms can better explore complex design spaces and overcome the limitations of local optimal solutions through group search and adaptive mechanisms. However, these intelligent algorithms also have some disadvantages, such as slow convergence speed, high computational cost, and decreased performance on high-dimensional problems.
[0005] Therefore, in order to overcome the above problems, an improved subtraction average optimization algorithm based on building engineering design problems is studied, aiming to improve the efficiency and accuracy of solving building engineering design optimization problems, which has important practical significance and application value. Summary of the invention
[0006] The purpose of the present invention is to provide a risk management method based on an improved subtraction mean optimization algorithm considering construction engineering design problems, specifically an improved subtraction mean optimization algorithm for engineering design problems, comprising the following steps: 1. Analyze and process actual construction engineering projects and establish a mathematical model; 2. Generate the initial value of the initial population and the search path in the dynamic update process through Tene chaos mapping; 3. Prevent the algorithm from falling into local optimality through the golden sine function; 4. Compare WOA, GWO, DBO, and SABO algorithms according to the CEC2005 benchmark test function; 5. Verify the effectiveness of the algorithm of the present invention according to the actual mathematical model of the construction engineering project. The present invention can more accurately and comprehensively reduce the risk of construction engineering by establishing a construction engineering design model based on time-cost-resources.
[0007] In order to achieve the above object, the present invention adopts the following technical solution: An improved subtraction average optimization algorithm considering architectural engineering design problems includes the following specific steps: Step 1: Analyze and process the actual construction project and establish a mathematical model; Step 2: Generate the initial value of the initial population and the search path during the dynamic update process through Tene chaotic mapping; Step 3: Use the golden sine function to prevent the algorithm from falling into the local optimum; Step 4: Compare WOA, GWO, DBO, and SABO algorithms based on the CEC2005 benchmark function; Step 5: Verify the effectiveness of the algorithm of the present invention based on the actual mathematical model of the construction project.
[0008] Preferably, in step 1, the actual construction project is analyzed and processed to establish a mathematical model. The specific process is as follows: Step 1.1: Objective function: In actual construction projects, in addition to the consumption of time, it is also necessary to comprehensively consider a variety of factors to ensure the smooth progress and ultimate success of the project. The fundamental task of multi-objective optimization problems is to balance the optimization of construction period, quality, and cost targets, find a relatively satisfactory solution, and achieve the optimal solution for one of the three major targets while the other targets are relatively satisfactory. In order to effectively solve the optimization problem of construction projects, the present invention proposes an improved optimization algorithm based on subtraction averaging. The goal of optimization is to improve the overall efficiency and sustainability of construction projects by minimizing key indicators such as cost, construction period, and resources.
[0009] The duration objective function aims to minimize the total duration of the project. Suppose the total duration of the project is , then the construction period objective function can be expressed as: (1) The cost objective function mainly considers direct costs and indirect costs Assume the total project cost is , then the cost objective function can be expressed as: {f}_{2}=minC=min(DC+IC)=\sum\left [ {{C}^{{1}^{min}}_{ij}+\frac {{C}^{{1}^{max}}_{ij}-{C}^{{1}^{min}}_{ij}} {\left ( {{t}^{min}_{ij}-{t}^{max}_{ij}} \right )^{2}}\cdot \left ( {{t}_{ij}-{t}^{max}_{ij}} \right )^{2}} \right ]+{T}_{o}{C}_{o} (2) The resource objective function considers the total amount of resources of each sub-project during the project construction process. Let the total project resources be , then the resource objective function can be expressed as: (3) in, It is the collection of all lines in the double-code network plan diagram of the engineering project; It is the collection of all processes on a critical path in the network planning diagram; They are total number of processes, total minimized project time, total resource types, and number of resources per day; For process the actual duration of Process the minimum and maximum direct costs; Process the minimum and maximum duration of The date agreed upon in the contract; is the indirect cost rate during the contract period; The total project time is The amount of resources that the day's plan uses.
[0010] Step 1.2: Constraints: In order to ensure the feasibility of the optimization results, the present invention introduces the following constraints on the basis of the objective function: 1) Time constraint: In order to ensure that the project is completed within the specified time, the time constraint stipulates that the completion time of each process cannot exceed the maximum allowable duration of the project, and cannot be less than the minimum allowable duration of the project. The completion time of the process is The maximum and minimum allowable durations of the project are , then the time constraint can be expressed as: (4) 2) Cost constraint: In construction project optimization, cost control is one of the key constraints. Cost constraint aims to ensure that the total cost of the project does not exceed the budget. Set the total budget of the project , No. The cost of the process is In order to ensure that the total cost of the entire project is within the budget, the cost constraint can be expressed as: (5) 3) Resource constraints: In order to ensure the reasonable allocation and use of project resources, the resource constraints stipulate that the total usage of each resource cannot exceed its maximum available amount. The maximum available amount of this resource is , No. The subproject uses The resources are , then the resource constraint can be expressed as: (6) By introducing the above constraints, we can ensure that various resources are reasonably allocated during the optimization process, the project can be completed within the specified time, and the technical requirements can be met, thereby ensuring the feasibility and effectiveness of the optimization results.
[0011] In summary, the multi-objective function model of the project can be obtained through formula (1-6) as follows: {f}_{2}=minC=min(DC+IC)=\sum\left [ {{C}^{{1}^{min}}_{ij}+\frac {{C}^{{1}^{max}}_{ij}-{C}^{{1}^{min}}_{ij}} {\left ( {{t}^{min}_{ij}-{t}^{max}_{ij}} \right )^{2}}\cdot \left ( {{t}_{ij}-{t}^{max}_{ij}} \right )^{2}} \right ]+{T}_{o}{C}_{o} (7) Preferably, in step 2, the initial value of the initial population and the search path in the dynamic update process are generated by Tene chaotic mapping. The specific process is as follows: Tene chaos mapping is a commonly used chaotic sequence generation method, which has good ergodicity and initial value sensitivity. The introduction of Tene chaos mapping can increase the randomness and diversity of the algorithm, thereby improving the optimization effect. The formula of Tene chaos mapping is as follows: (8) in, is the chaotic mapping parameter, usually taking a value between (0, 4).
[0012] In the optimization algorithm, Tene chaotic mapping is used to generate the initial value of the initial population and the search path during the dynamic update process. The nonlinear and chaotic characteristics of this mapping help the algorithm maintain sufficient diversity in the search space and avoid falling into the local optimal solution.
[0013] Preferably, in step 3, the golden sine function is used to prevent the algorithm from falling into a local optimum. The specific process is as follows: The golden sine function is derived from the mathematical properties of the golden section and its expression is: (9) In order to enhance the global search capability of the algorithm, the present invention introduces the golden sine function. The golden sine function can provide an effective search method by combining the golden ratio and the periodicity of the sine function to avoid the algorithm falling into the local optimum. Its formula is as follows: (10) in, is the golden ratio; is the current iteration number.
[0014] Preferably, in step 4, the WOA, GWO, DBO and SABO algorithms are compared according to the CEC2005 benchmark test function.
[0015] Preferably, in step 5, the effectiveness of the algorithm of the present invention is verified based on an actual mathematical model of a construction project.
[0016] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses an improved subtraction mean optimization algorithm that takes into account the design problems of architectural engineering, which can solve the global convergence, computational efficiency and development imbalance of engineering design problems in a practical way. It solves the problems that traditional algorithms are prone to fall into local optimal solutions, slow convergence speed and imbalance between exploration and development in multimodal function optimization. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] Figure 1 A schematic diagram of the process of the method proposed in the present invention; Figure 2 A comparison diagram of the parameter space and convergence curve of the benchmark function F (3, 4, 5, 6, 8, 9) obtained by the method proposed in the present invention and the other five methods; Figure 3 This is a double-code network plan diagram for a construction project in S City; Figure 4 A three-dimensional optimal solution diagram of the total project duration, total project cost and total resource allocation changes for solving actual problems of construction engineering by the method proposed by the present invention; DETAILED DESCRIPTION
[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.
[0019] The present invention is further described in detail below with reference to the accompanying drawings. The present invention proposes an improved subtraction average optimization algorithm that takes into account the design problems of construction projects, including the following steps: 1. Analyze and process actual construction projects to establish a mathematical model; 2. Generate the initial value of the initial population and the search path during the dynamic update process through Tene chaos mapping; 3. Prevent the algorithm from falling into local optimality through the golden sine function; 4. Compare WOA, GWO, DBO, and SABO algorithms according to the CEC2005 benchmark test function; 5. Verify the effectiveness of the algorithm of the present invention based on the actual mathematical model of the construction project. The specific process is as follows: Figure 1 shown.
[0020] Step 1: Analyze and process the actual construction project and establish a mathematical model; Step 2: Generate the initial value of the initial population and the search path during the dynamic update process through Tene chaotic mapping; Step 3: Use the golden sine function to prevent the algorithm from falling into the local optimum; Step 4: Compare WOA, GWO, DBO, and SABO algorithms based on the CEC2005 benchmark function; Step 5: Verify the effectiveness of the algorithm of the present invention based on the actual mathematical model of the construction project.
[0021] In step 1, the actual construction project is analyzed and processed to establish a mathematical model. The specific process is as follows: S11: Objective function: In actual construction projects, in addition to the consumption of time, it is also necessary to comprehensively consider a variety of factors to ensure the smooth progress and ultimate success of the project. The fundamental task of multi-objective optimization problems is to balance the optimization of construction period, quality, and cost targets, find a relatively satisfactory solution, and achieve the optimal solution for one of the three major targets while the other targets are relatively satisfactory. In order to effectively solve the optimization problem of construction projects, the present invention proposes an improved optimization algorithm based on subtraction averaging. The goal of optimization is to improve the overall efficiency and sustainability of construction projects by minimizing key indicators such as cost, construction period, and resources.
[0022] The duration objective function aims to minimize the total duration of the project. Suppose the total duration of the project is , then the construction period objective function can be expressed as: (1) The cost objective function mainly considers direct costs and indirect costs Assume the total project cost is , then the cost objective function can be expressed as: {f}_{2}=minC=min(DC+IC)=\sum\left [ {{C}^{{1}^{min}}_{ij}+\frac {{C}^{{1}^{max}}_{ij}-{C}^{{1}^{min}}_{ij}} {\left ( {{t}^{min}_{ij}-{t}^{max}_{ij}} \right )^{2}}\cdot \left ( {{t}_{ij}-{t}^{max}_{ij}} \right )^{2}} \right ]+{T}_{o}{C}_{o} (2) The resource objective function considers the total amount of resources of each sub-project during the project construction process. Let the total project resources be , then the resource objective function can be expressed as: (3) in, It is the collection of all lines in the double-code network plan diagram of the engineering project; It is the collection of all processes on a critical path in the network planning diagram; They are total number of processes, total minimized project time, total resource types, and number of resources per day; For process the actual duration of Process the minimum and maximum direct costs; Process the minimum and maximum duration of The date agreed upon in the contract; is the indirect cost rate during the contract period; The total project time is The amount of resources that the day's plan uses.
[0023] S12: Constraints: In order to ensure the feasibility of the optimization results, the present invention introduces the following constraints on the basis of the objective function: 1) Time constraint: In order to ensure that the project is completed within the specified time, the time constraint stipulates that the completion time of each process cannot exceed the maximum allowable duration of the project, and cannot be less than the minimum allowable duration of the project. The completion time of the process is The maximum and minimum allowable durations of the project are , then the time constraint can be expressed as: (4) 2) Cost constraint: In construction project optimization, cost control is one of the key constraints. Cost constraint aims to ensure that the total cost of the project does not exceed the budget. Set the total budget of the project , No. The cost of the process is In order to ensure that the total cost of the entire project is within the budget, the cost constraint can be expressed as: (5) 3) Resource constraints: In order to ensure the reasonable allocation and use of project resources, the resource constraints stipulate that the total usage of each resource cannot exceed its maximum available amount. The maximum available amount of this resource is , No. The subproject uses The resources are , then the resource constraint can be expressed as: (6) By introducing the above constraints, we can ensure that various resources are reasonably allocated during the optimization process, the project can be completed within the specified time, and the technical requirements can be met, thereby ensuring the feasibility and effectiveness of the optimization results.
[0024] In summary, the multi-objective function model of the project can be obtained through formula (1-6) as follows: {f}_{2}=minC=min(DC+IC)=\sum\left [ {{C}^{{1}^{min}}_{ij}+\frac {{C}^{{1}^{max}}_{ij}-{C}^{{1}^{min}}_{ij}} {\left ( {{t}^{min}_{ij}-{t}^{max}_{ij}} \right )^{2}}\cdot \left ( {{t}_{ij}-{t}^{max}_{ij}} \right )^{2}} \right ]+{T}_{o}{C}_{o} (7) In step 2, the initial value of the initial population and the search path in the dynamic update process are generated by Tene chaotic mapping. The specific process is as follows: Tene chaos mapping is a commonly used chaotic sequence generation method, which has good ergodicity and initial value sensitivity. The introduction of Tene chaos mapping can increase the randomness and diversity of the algorithm, thereby improving the optimization effect. The formula of Tene chaos mapping is as follows: (8) in, is the chaotic mapping parameter, usually taking a value between (0, 4).
[0025] In the optimization algorithm, Tene chaotic mapping is used to generate the initial value of the initial population and the search path during the dynamic update process. The nonlinear and chaotic characteristics of this mapping help the algorithm maintain sufficient diversity in the search space and avoid falling into the local optimal solution.
[0026] In step 3, the golden sine function is used to prevent the algorithm from falling into a local optimum. The specific process is as follows: The golden sine function is derived from the mathematical properties of the golden section and its expression is: (9) In order to enhance the global search capability of the algorithm, the present invention introduces the golden sine function. The golden sine function can provide an effective search method by combining the golden ratio and the periodicity of the sine function to avoid the algorithm falling into the local optimum. Its formula is as follows: (10) in, is the golden ratio; is the current iteration number.
[0027] In the step 4, the WOA, GWO, DBO, and SABO algorithms are compared according to the CEC2005 benchmark test function.
[0028] In combination with the embodiment, in order to verify the performance of the improved SABO algorithm, the CEC2005 test set is used to conduct a comparative test on the five algorithms. The comparison results are as follows: Figure 2 shown.
[0029] In step 5, the effectiveness of the algorithm of the present invention is verified based on an actual mathematical model of a construction project.
[0030] In combination with the embodiment, the construction site is arranged with a living area and an office area. The living area is arranged in the northeast corner of the site. The office building is arranged across a basketball court. The canteen, drying room and badminton court are arranged on the east side of the site, which has no impact on the construction site. Temporary construction roads are arranged on the construction site. Rebar processing rooms, wood processing rooms, warehouses, and material stacking yards are set up around the buildings. The tower crane covers the building to ensure the transportation of materials without affecting the living and office areas. A guard room is set up at the gate. Temporary living and production construction, equipment layout, and road layout. And the project includes 12 processes. The specific process work breakdown is shown in Table 1 below. Figure 3 Shown Table 1 Process No. Process Name Job Description Post-process 1 A Construction preparation B 2 B Large earth excavation C 3 C Basic structure construction D 4 D Underground main structure construction E 5 E Construction of above-ground structures below 9 floors F,H 6 F Construction of above-ground structures with 9 floors or above G 7 G External wall engineering N 8 H Masonry works L 9 I Interior wall engineering M 10 G Ground Engineering N 11 K Step water ramp O 12 L Completion acceptance - A construction project in S City involves many key points and difficulties. The headquarters and the work area have high expectations for the construction period, cost and resources. An expert group composed of the headquarters, relevant persons in charge of the construction project, supervisors and external experts, combined their own experience and referred to the data of related projects, comprehensively considered the influence of nature, personnel, materials and management, and gave the following parameters for each process, as shown in Table 2.
[0031] Table 2 Process Name Minimum time Actual time Maximum time Number of resources Maximum cost Minimum cost A 3 5 7 20 200,000 150,000 B 8 12 16 50 600,000 400,000 C 12 18 25 100 1,500,000 1,200,000 D 18 27 35 150 2,000,000 1,700,000 E 25 40 55 200 3,500,000 2,800,000 F 20 30 40 150 3,000,000 2,500,000 G 15 22 28 100 2,000,000 1,500,000 H 10 15 20 80 1,200,000 900,000 I 12 18 24 100 1,500,000 1,200,000 J 8 12 16 80 1,000,000 800,000 K 5 7 10 50 500,000 400,000 L 10 15 20 30 500,000 300,000 Based on the above data and multi-objective model, a multi-objective model of a construction project in S City is established, as follows: The total changes in project cost, total project duration, and total resource allocation in the project schedule solution of the Pareto optimal frontier in the three-dimensional space of project goals are shown in Figure 4 ,These Pareto optimal points show the total project cost, total project duration and the total ,change of resource allocation for the non-dominant project schedule solution. ,It can be seen that under the premise of the three objectives, the ,optimal solution of this case can be found in the three ,three graph by the improved SABO algorithm.
[0032] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.
[0033] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. An improved subtraction average optimization algorithm considering architectural engineering design problems, characterized in that: The method comprises the following steps: Step 1: Analyze and process the actual construction project and establish a mathematical model; Step 2: Generate the initial value of the initial population and the search path during the dynamic update process through Tene chaotic mapping; Step 3: Use the golden sine function to prevent the algorithm from falling into the local optimum; Step 4: Compare the WOA, GWO, DBO, and SABO algorithms based on the CEC2005 benchmark function; Step 5: Verify the effectiveness of the algorithm based on the actual mathematical model of the construction project. in: In step 1, the actual construction project is analyzed and processed to establish a mathematical model. The specific process is as follows: Step 1.1: Objective function: In actual construction projects, in addition to the consumption of time, it is also necessary to comprehensively consider a variety of factors to ensure the smooth progress and ultimate success of the project. It is the fundamental task of multi-objective optimization problems to balance and optimize the construction period, quality, and cost targets, find a relatively satisfactory solution, and achieve the optimal solution for one of the three major targets while the other targets are relatively satisfactory. In order to effectively solve the optimization problem of construction projects, an improved optimization algorithm based on subtraction average is proposed. The optimization goal is to improve the overall efficiency and sustainability of construction projects by minimizing key indicators such as cost, construction period, and resources. The duration objective function aims to minimize the total duration of the project. Suppose the total duration of the project is , then the construction period objective function can be expressed as: (1) The cost objective function mainly considers direct costs and indirect costs , assuming the total project cost is , then the cost objective function can be expressed as: {f}_{2}=minC=min(DC+IC)=\sum\left [ {{C}^{{1}^{min}}_{ij}+\frac {{C}^{{1}^{max}}_{ij}-{C}^{{1}^{min}}_{ij}} {\left ( {{t}^{min}_{ij}-{t}^{max}_{ij}} \right )^{2}}\cdot \left ( {{t}_{ij}-{t}^{max}_{ij}} \right )^{2}} \right ]+{T}_{o}{C}_{o} (2) The resource objective function considers the total amount of resources of each sub-project during the project construction process. Let the total project resources be , then the resource objective function can be expressed as: (3) in, It is the collection of all lines in the double-code network plan diagram of the engineering project; It is the collection of all processes on a critical path in the network planning diagram; They are total number of processes, total minimized project time, total resource types, and number of resources per day; For process the actual duration of Process the minimum and maximum direct costs; Process the minimum and maximum duration of The date agreed upon in the contract; is the indirect cost rate during the contract period; The total project time is The number of resources used by the daily plan; Step 1.2: Constraints: In order to ensure the feasibility of the optimization results, the following constraints are introduced based on the objective function: 1) Time constraint: In order to ensure that the project is completed within the specified time, the time constraint stipulates that the completion time of each process cannot exceed the maximum allowable duration of the project, and cannot be less than the minimum allowable duration of the project. The completion time of the process is The maximum and minimum allowable durations of the project are , then the time constraint can be expressed as: (4) 2) Cost constraint: In the optimization of construction projects, cost control is one of the key constraints. Cost constraint aims to ensure that the total cost of the project does not exceed the budget and set the total budget of the project. , No. The cost of the process is ,In order to ensure that the total cost of the entire project is within the budget, the cost constraint can be expressed as: (5) 3) Resource constraints: In order to ensure the reasonable allocation and use of project resources, the resource constraint stipulates that the total usage of each resource cannot exceed its maximum available amount. The maximum available amount of this resource is , No. The subproject uses The resources are , then the resource constraint can be expressed as: (6) By introducing the above constraints, we can ensure that various resources are reasonably allocated during the optimization process, the project can be completed within the specified time, and meet the technical requirements, thereby ensuring the feasibility and effectiveness of the optimization results. In summary, the multi-objective function model of the project can be obtained through formula (1-6) as follows: {f}_{2}=minC=min(DC+IC)=\sum\left [ {{C}^{{1}^{min}}_{ij}+\frac {{C}^{{1}^{max}}_{ij}-{C}^{{1}^{min}}_{ij}} {\left ( {{t}^{min}_{ij}-{t}^{max}_{ij}} \right )^{2}}\cdot \left ( {{t}_{ij}-{t}^{max}_{ij}} \right )^{2}} \right ]+{T}_{o}{C}_{o} (7) In step 2, the initial value of the initial population and the search path in the dynamic update process are generated by Tene chaotic mapping. The specific process is as follows: Tene chaos mapping is a commonly used chaotic sequence generation method, which has good ergodicity and initial value sensitivity. The introduction of Tene chaos mapping can increase the randomness and diversity of the algorithm, thereby improving the optimization effect. The formula of Tene chaos mapping is as follows: (8) in, is the chaotic mapping parameter, usually between (0, 4); In the optimization algorithm, Tene chaotic mapping is used to generate the initial value of the initial population and the search path in the dynamic update process. The nonlinear and chaotic characteristics of this mapping help the algorithm maintain sufficient diversity in the search space and avoid falling into the local optimal solution. In step 3, the golden sine function is used to prevent the algorithm from falling into the local optimum. The specific process is as follows: The golden sine function is derived from the mathematical properties of the golden section and its expression is: (9) In order to enhance the global search capability of the algorithm, the golden sine function is introduced. The golden sine function combines the golden ratio and the periodicity of the sine function to provide an effective search method to prevent the algorithm from falling into the local optimum. The formula is as follows: (10) in, is the golden ratio; is the current iteration number; In step 4, the WOA, GWO, DBO, and SABO algorithms are compared according to the CEC2005 benchmark test function; In step 5, the effectiveness of the algorithm is verified based on the actual mathematical model of the construction project.