Multi-objective optimization method for substation engineering based on intelligent algorithm and environmental constraints

Abstract

This invention discloses a multi-objective optimization method for substation engineering based on intelligent algorithms and environmental constraints. It addresses the problem that traditional solutions fail to consider practical factors and environmental requirements, necessitating new methods to find feasible optimization solutions. The key technical point is to construct an optimization model with four objectives—schedule, cost, quality, and environment—based on engineering practice. This involves establishing three basic objective models for schedule, cost, and quality. Based on evaluation and scoring results, a priority chain for environmental indicators is generated using a grey-scale association method. Considering resource constraints, a corresponding environmental indicator model is constructed. Finally, the SOA algorithm is used to find feasible solutions that meet the decision-makers' needs. This multi-objective optimization method for substation engineering based on intelligent algorithms and environmental constraints can obtain required solutions faster and with higher accuracy, better meeting actual needs.

Description

Technical Field

[0001] The invention relates to engineering project management technology, and in particular to a multi-objective optimization method for a substation project based on an intelligent algorithm and environmental constraints. Background Art

[0002] Regarding the management of substation projects, domestic and foreign scholars mainly study the optimization problems based on three indicators, namely, construction period, cost, quality and safety, and most of them use population algorithms such as particle swarm optimization to solve and obtain the optimized management plan. In order to achieve the full process and all-round development of the project goals, the management of traditional substation projects seeks a balance between the three goals of construction period, cost and quality, constructs mathematical models and gives corresponding algorithms to solve. However, as the requirements for substation management gradually increase, meeting environmental protection requirements has become a factor and goal that must be considered in the construction of engineering projects, and more optimized methods are urgently needed to obtain feasible management solutions. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-objective optimization method for substation engineering based on intelligent algorithms and environmental constraints, which can obtain demand solutions faster and with higher accuracy and is more in line with actual needs.

[0004] The above technical objectives of the present invention are achieved through the following technical solutions:

[0005] A multi-objective optimization method for a substation project based on an intelligent algorithm and environmental constraints includes the following steps:

[0006] S1. Establish an optimization target model with the duration T, cost C and quality Q of the substation project as the target;

[0007] S2, introduce environmental indicators to build the optimization target model of environment E and construction period T, and use the gray correlation method to generate the engineering priority chain about environmental indicators;

[0008] S3. Construct a mathematical model of environmental indicators based on resource constraints;

[0009] S4. Use SOA algorithm to solve and obtain the required results.

[0010] In summary, the present invention has the following beneficial effects:

[0011] Combined with the actual project, an optimization model with four objectives, namely, construction period, cost, quality and environment, is constructed, and an improved optimization algorithm is given to solve the model. On the basis of the traditional three basic index optimization model, environmental influencing factors are quantified, and the mathematical model of environment and construction period is obtained under the condition of resource constraints by using Lagrange multiplier method. The model is then introduced into the three basic models to become a four-objective optimization model, which better meets the needs and management requirements of modern substation project decision makers.

[0012] Compared with the traditional optimization model, this method is closer to actual engineering and more complex, and the solution set obtained is also diverse, which can meet the indicator preferences of decision makers. At the same time, as the model becomes more complex, a more flexible and inclusive algorithm is used to solve the model, and the solutions obtained are more diverse and more in line with reality. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a schematic diagram of the process of this method;

[0014] Figure 2 is a schematic diagram of an example of this embodiment;

[0015] Figure 3 This is the simulation result diagram of this example. DETAILED DESCRIPTION

[0016] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0017] According to one or more embodiments, a multi-objective optimization method for a substation project based on an intelligent algorithm and environmental constraints is disclosed, comprising the following steps:

[0018] S1. Establish an optimization target model with the duration T, cost C and quality Q of the substation project as the target;

[0019] S2, introduce environmental indicators to build the optimization target model of environment E and construction period T, and use the gray correlation method to generate the engineering priority chain about environmental indicators;

[0020] S3. Construct a mathematical model of environmental indicators based on resource constraints;

[0021] S4. Use SOA algorithm to solve and obtain the required results.

[0022] Specifically, Figure 1 As shown:

[0023] A model is established with the construction period T, cost C and quality Q of the substation project as the main optimization objectives.

[0024]

[0025] Environmental indicators are introduced to build a model of environment E and construction period T.

[0026] First, experts are required to evaluate and score the environmental indicators of each project, and then use the gray correlation analysis method to find the priority of each project and obtain the priority chain of each project.

[0027] Model establishment under resource constraints:

[0028] After sorting the indicators according to their weights, this paper established a mathematical model of environmental impact after reading relevant materials and literature:

[0029]

[0030] Where E represents the proportional coefficient of the total engineering project's impact on the environment; e j represents the pollution index of sub-project j to the surrounding environment; R represents the optimal resource allocation.

[0031]

[0032] Among them, u j represents the resource consumption level of sub-project j on the critical path; k j represents the position of sub-project j on chain π after sorting by priority; H j represents the human resources allocated to sub-project j; η is the deterioration factor.

[0033] In general projects, in order to improve the efficiency of the project, the maximum human resource coefficient of the project will be pre-selected during the drafting stage. Therefore:

[0034]

[0035] Among them, G represents the maximum human resource ratio coefficient, and B represents the set of sub-projects on the critical path. j related, With H j It is irrelevant, so under the constraint Next, you can put P j Consider it as a constant quantity, so, at this time, to minimize E is to minimize R.

[0036] Based on this constraint, the objective function is:

[0037]

[0038] Obviously, in Under this condition, the objective function R is minimized. Therefore, the problem becomes R satisfying the constraints The conditional extreme value problem when . For this problem, the Lagrange multiplier method is used to solve it, and its Lagrange function is:

[0039]

[0040] Where λ(λ≥0) is the Lagrange multiplier.

[0041] Because the objective function is a convex function, in the above formula, H [j] , find the partial derivative of λ, and set the derivative function to 0, we can get:

[0042]

[0043]

[0044] We can get:

[0045]

[0046] Then we can get

[0047]

[0048] Based on the above conditions, update the resource consumption level:

[0049]

[0050] So at this point, the final total amount of resources is:

[0051]

[0052] From the above, we can get the mathematical model of environmental indicators:

[0053]

[0054] Through the assumptions of the model, we know that cost, construction period and quality are the main influencing factors of the project. Combining the above theoretical derivation and adding the environmental objective function, we can establish the following four-objective optimization model of construction period - cost - quality - environment:

[0055]

[0056] Use SOA algorithm to solve:

[0057] SOA uses a set of random solutions as the initial population. Assuming that there are m individuals in the n-dimensional search space, the position of the i-th individual is expressed as

[0058] Xi=(x i 1 ,x i 2,…,x i k ,…,x i n ); i=1,2,…,m

[0059] Then the update of the individual k-th dimension position component at the t+1th iteration is

[0060]

[0061] Where: x rand k (t) is the k-th dimension position component of the random individual at the t-th iteration; x best k (t) is the k-th dimensional position component of the best individual in the population at the t-th iteration; Iteration is the maximum number of iterations; a is a constant; r2 is a random number between [0,2π], and r3 is a random number between [0,1].

[0062] The algorithm uses r1, r2, and r3 to balance the global search and local development in the optimization process. At the beginning of the iteration, r1 is large, and r1×sinr2 has a large fluctuation range, which can better perform global search; as r1 decreases, the position change of the individual is small, and the algorithm performs local development. The size of r3 determines the starting point of the individual's position movement in the next iteration. When the value of r3 is [0,0.5), the position of the random individual is modified to obtain the next position, so that a wider search area can be covered; when the value of r3 is [0.5,1], the position of the optimal individual is modified to obtain the next position, and local development near the optimal individual can be completed.

[0063] To make it clear, here is an example:

[0064] The 110kV substation of Project A planned and constructed by the government of City S is selected. It is located in a newly built industrial park. The planned area of ​​this area is small and the power load is relatively concentrated. Figure 2 shown.

[0065] The engineering data is as follows:

[0066]

[0067]

[0068] P n : Under normal conditions, the time required to complete this sub-project. This normal duration depends on the proficiency and technical level of the construction workers, the management supervision of the management personnel, the timely supply of materials, etc.

[0069] P e : The shortest time required to complete this sub-project;

[0070] P l : The maximum time required to complete this sub-project;

[0071] e j : The pollution index of sub-project j to the surrounding environment;

[0072] b i : The cost of completing the operation in normal duration;

[0073] γ i : marginal cost increasing factor;

[0074] ω i : The proportion of each sub-project in the entire project, also called the project quality weight;

[0075] Q basic : The minimum quality level value achieved to complete the process.

[0076] The critical path of solving the network diagram using network planning technology is:

[0077] A—B—C—D—G—J—M—N—P—S—T—V—W.

[0078] According to the grayscale correlation analysis method, weights are assigned to each indicator of the sub-project. After evaluation and investigation by the expert group, the following indicators are selected to assign weights to the sub-projects;

[0079]

[0080] According to the Matlab programming algorithm, the weight parameters can be obtained;

[0081]

[0082] Then, according to the assigned weights, the TOPSIS method is used to determine the coefficients of each sub-project indicator:

[0083]

[0084]

[0085] Using the software SPSS to perform grayscale correlation analysis, we get the priority chain of sub-projects:

[0086] G—R—Q—F—I—L—B—T—J—P—C—N—S—A—M—E—D—H—W—V.

[0087] The algorithm programming is implemented on the computer using Matlab2020a software. This problem is based on the duration P of each process in the substation construction project. iis the decision vector X. In this example, there are 20 processes, so P is a 20-dimensional vector. Therefore, the dimension D of the feasible solution of the multi-objective particle swarm algorithm is set to 20, the initial population size is set to 100, the maximum number of loop iterations is 500, and the number of external set storages is 30.

[0088] Parameter settings: Maxlt=500; %maximum number of iterations; nPop=100; %population number; nRep=50; %storage number; ω=0.6; %inertia weight; c1=1; %individual learning factor; c2=2; %global learning parameter; η=1; %deterioration factor; G=100; %maximum human resource ratio coefficient.

[0089] Run the multi-objective particle swarm algorithm program in Matlab2020a. After one run, 50 Pareto optimal solutions are obtained. The calculation process is iterated about 500 times to obtain 30 Pareto optimal solution sets. The simulation results are as follows: Figure 3 shown.

[0090] When the project is actually implemented, the actual situation often differs from the expected situation during the design. In the actual project, the emphasis on the final construction level of construction period, cost, quality and environment is also different. As a manager, you may tend to optimize the cost, but the constructors tend to minimize the construction period. Based on the different emphasis of each optimization quantity, four groups of results with the best relative indicators were selected from the 30 solutions (as shown in the following table)

[0091] Pareto optimal solution Construction period (days) Cost (Yuan) quality(%) Environment (index) 1 196 9023719.41 0.9314 95.7599 2 195 9029731.273 0.931 96.5243 3 199 9079212.308 0.9477 97.9482 4 197 9055321.41 0.934 95.7599

[0092] As can be seen from the table, the combination of Pareto optimal solutions obtained by this method can prevent decision makers from adopting a single solution, and can be used to solve the requirements of substation engineering projects in various goals. Solution 1 is suitable for the pursuit of the lowest cost, Solution 2 is suitable for the requirements of short construction period and fast construction, Solution 3 is more suitable for high-quality engineering requirements, and Solution 4 has the least degree of environmental damage and is suitable for projects with higher environmental protection requirements. Decision makers can choose the appropriate engineering solution based on the actual engineering and project requirements.

[0093] The present invention takes the construction period as the independent variable, quantifies the cost and quality model, and quantifies the environmental impact in combination with various uncertain factors in the actual project: firstly, various indicators and requirements are quantified and evaluated in combination with the actual project, and weighted by the gray association analysis method, and a priority chain is constructed under the requirements of the project environmental indicators; secondly, considering the resource constraints of the project, the optimal resource allocation of the project on the critical path of the network diagram is achieved based on limited resources; finally, a mathematical model of the environment and construction period is constructed, and combined with the three major optimization goals, a feasible idea and reference for the multi-objective optimization problem of the substation is provided.

[0094] At the same time, based on the given model, the sinusoidal optimization SOA (Sinusoidal Optimization Algorithm) algorithm is introduced to solve the proposed multi-objective optimization problem. This method uses a new position update strategy based on the SCA (Sine Cosine Algorithm) algorithm, which has faster convergence speed and higher optimization accuracy than the SCA algorithm.

[0095] This specific embodiment is merely an explanation of the present invention and is not a limitation of the present invention. After reading this specification, those skilled in the art may make non-creative modifications to the present embodiment as needed. However, as long as they are within the scope of the claims of the present invention, they are protected by the patent law.

Claims

1. A multi-objective optimization method for substation engineering based on intelligent algorithms and environmental constraints, characterized in that: The following steps are included: S1. Establish an optimization target model with the construction period T, cost C, and quality Q of the substation project as the target, wherein the optimization target model includes the minimum construction time, minimum cost, and best construction quality of all projects corresponding to the substation project; S2, introduce environmental indicators to build the optimization target model of environment E and construction period T, and use the gray correlation method to generate the engineering priority chain about environmental indicators; First, experts were asked to evaluate and score the environmental indicators of each project, and then the priority of each project was calculated using the gray correlation analysis method to obtain the priority chain of each project. Establishment of the model under resource constraints: After ranking the indicators according to their weights, a mathematical model of environmental impact and resource allocation is established to obtain the minimum impact ratio of the total project on the environment: Obtain optimal resource allocation based on the resource consumption level of sub-projects on the critical path, prioritize the sub-project resources on the critical path according to the optimal resource allocation, and extract the location of the sub-project according to the priority ranking; S3. Based on resource constraints, a mathematical model of environmental indicators is constructed; the mathematical model of environmental indicators is: S4, using SOA algorithm to solve and obtain the required results; The mathematical model of environmental indicators is added to the optimization target model to establish a four-target optimization model of construction period, cost, quality and environment. After solving the four-target optimization model with the SOA algorithm, the optimal trade-off solution among the four targets of construction period, cost, quality and environment for the substation project is obtained.

2. The multi-objective optimization method for substation engineering based on intelligent algorithm and environmental constraints according to claim 1 is characterized in that: The specific optimization target model in step S1 is:

3. The multi-objective optimization method for substation engineering based on intelligent algorithm and environmental constraints according to claim 2 is characterized in that: Step S2 is specifically as follows: Evaluate the environmental requirements of each project; Calculate the priority of each project based on the gray correlation analysis method and obtain the priority chain of each project; After ranking the indicators according to their weights, an optimization target model for environmental impact is established. Where E represents the proportional coefficient of the total engineering project's impact on the environment; e j represents the pollution index of sub-project j on the surrounding environment; R represents the optimal resource allocation; Among them, u j represents the resource consumption level of sub-project j on the critical path; k j represents the position of sub-project j on chain π after sorting by priority; H j represents the human resources allocated to sub-project j; η is the deterioration factor.

4. The multi-objective optimization method for substation engineering based on intelligent algorithm and environmental constraints according to claim 3 is characterized in that: Step S3 specifically includes: Pre-select the maximum human resource factor for the project Among them, G represents the maximum human resource ratio coefficient, and B represents the set of sub-projects on the critical path; Since there are only R and H in E j related, With H j It is irrelevant, so under the constraint Next, put P j Consider it as a constant quantity. At this time, finding the minimum E means finding the minimum R. Based on the constraints, the objective function is: exist When , the objective function R is minimized; A mathematical model for obtaining environmental indicators based on the objective function.

5. The multi-objective optimization method for substation engineering based on intelligent algorithm and environmental constraints according to claim 4 is characterized in that: The mathematical model for obtaining environmental indicators based on the objective function is as follows: Transform the objective function into R satisfying the constraints The conditional extreme value when ; The Lagrange multiplier method is used to solve it, and its Lagrange function is: Where λ(λ≥0) is the Lagrange multiplier; For H [j] , find the partial derivative of λ, and set the derivative function to 0, we can get: Then we can get: Update resource consumption levels: The final total amount of resources obtained is: The mathematical model of environmental indicators obtained is added to the optimization target model to establish the optimization model of the four targets of construction period, cost, quality and environment. The four-target optimization model is:

6. The multi-objective optimization method for substation engineering based on intelligent algorithm and environmental constraints according to claim 5 is characterized in that: Step S4 specifically includes: SOA uses a set of random solutions as the initial population. Assuming that there are m individuals in the n-dimensional search space, the position of the i-th individual is expressed as Xi=(x i 1 ,x i 2 ,…,x i k ,…,x i n );i=1,2,…,m; The update of the individual k-th dimension position component at the t+1th iteration is Among them, x rand k (t) is the k-th dimension position component of the random individual at the t-th iteration; x best k (t) is the k-th dimension position component of the best individual in the population at the t-th iteration; Iteration is the maximum number of iterations; a is a constant; r2 is a random number between [0,2π], and r3 is a random number between [0,1] r1, r2, and r3 are used to balance the global search and local development in the optimization process. Global search can be better performed at the beginning of the iteration. As r1 decreases, the position change of the individual is small, and the algorithm performs local development. The size of r3 determines the starting point of the individual's position movement in the next iteration. When the value of r3 is in [0,0.5), the position of the random individual is modified to obtain the next position, which can cover a wider search area. When the value of r3 is in [0.5,1], the position of the optimal individual is modified to obtain the next position, which can complete local development near the optimal individual.

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