# Research on the Predictive Analysis of Park Landscape Design and Cost Based on RNN Model

Authors: Guang Lyu; Dan Zhang; ZuoLin Liu
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

As people’s awareness of the environment gradually increases and their requirements for the comfort of living space become higher, landscape design has also ushered in a golden period of development. With the increasing investment in landscape construction in urban development, the area of park green space has been increasing. A park is a place that provides recreation and relaxation for the public. However, the mere pursuit of landscape quality and artistic effects without effective cost control will eventually lead to a rise in construction costs. Therefore, this study explores the main influencing factors that lead to high park landscape costs by analyzing the current development of park landscape design. Based on the comprehensive analysis, a park landscape cost prediction model based on recurrent neural networks is proposed in order to better control the construction costs of park landscapes. This study applies advanced deep learning technology to the project management of park landscapes, which effectively improves the accuracy of cost prediction. In addition, an artificial bee colony algorithm is introduced to update the weights of the recurrent neural network, resulting in a globally optimal ABC-RNN prediction model. The experimental results show that the proposed ABC-RNN prediction model has higher prediction accuracy and stability than the commonly used prediction models.


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## Body

## 1. Introduction

With the increasing investment in landscape construction in urban development, the area of green space in parks has been increasing. A park is a place that provides recreation and relaxation for the public. However, the pursuit of landscape quality and artistic effects alone, without effective cost control, will eventually lead to an increase in construction costs. The rise in the construction cost of park landscapes will impose a greater economic burden on developers and the government. Therefore, it is of great practical significance to carry out research on cost control of park landscape design to effectively reduce the cost of landscape design [1–6]. With the technology of landscape design also becoming more and more mature, how to improve the quality of landscape projects and control landscape costs is an urgent problem for the relevant enterprises to solve.Nowadays, parks in cities have become an important part of people’s lives and perform a certain social function. Park landscapes can provide people with a comfortable living environment and a place to relax. The factors that influence the park environment are many and, in general, can be summarized into two main categories [7–10]: the natural ecological environment and the sociocultural factors. The natural ecological environment can simply be regarded as the external environment, and the sociocultural environment can be regarded as the internal environment. As a design object, a landscape is a complex made up of spatial objects on the land. Landscape design generally goes through four stages [11–13]: conceptual design, preliminary design, expansion design, and construction drawing design. As an applied discipline, landscape design requires a designer with a wide range of knowledge so that the relationship between man and nature can be harmonized. Landscape costs are the design costs, construction costs, and postmaintenance costs incurred by the property developer during the development of the project.Nowadays, with the continuous development of the real estate industry, park landscapes are also gaining more and more attention from consumers. An excellent park landscape project has become the most eye-catching aspect of a real estate project. An excellent park landscape project can increase the value of the entire project. According to the existing cost control theory of construction projects, the design stage is the focus of cost control for the whole project construction [14, 15]. (1) Cost control can make the cost structure more reasonable and improve the efficiency of the use of funds. According to the analysis of project function and project cost supporting scheme, designers need to adjust the cost of the park landscape project in real time [16, 17]. (2) Cost control of the project at the design stage can effectively improve the efficiency of investment. Predicting and analyzing the costs at the design stage can provide a better understanding of the components of the project and the proportion of investment in each part. For the key parts with a relatively large proportion of investment, they should be the focus of control, so as to effectively improve the efficiency of investment management [18–20]. (3) Cost control at the design stage is conducive to grasping the initiative of subsequent project construction. In the construction industry, because of the characteristics of the more expensive construction products, once the cost difference occurs, the resulting loss is often huge. So at the early stage, we need to have control over costs [21, 22]. To achieve a perfect combination of landscape design and economic cost, the cost of the project must be controlled at the design stage.Therefore, the purpose of this study is to apply recurrent neural networks in deep learning techniques to the project cost prediction of park landscapes, so that the construction cost of park landscapes can be better controlled. With the proposal of the deep learning theory and the improvement of computing performance of hardware devices, recurrent neural network (RNN) technology has gained great success in the fields of computer vision and natural language processing with a high recognition rate [23–28]. Therefore, this paper attempts to introduce RNN into the cost prediction of the park landscape project in order to further improve the accuracy of cost prediction. A cost prediction index system containing 13 items is constructed by considering the factors influencing the cost of the park landscape projects and combining them with practical work experience. In this paper, a park landscape project cost prediction model is constructed using RNN and the weights in the RNN backpropagation process are optimized using the artificial bee colony (ABC) algorithm [29, 30]. The proposed ABC-RNN model can automatically find the optimal connection without human intervention and improve the efficiency of RNN parameter optimization. The analysis was tested with several real park landscape case projects, and the results verified the stability of the ABC-RNN model.The rest of the paper is organized as follows. Related works are presented in Section2. In Section 3, the landscape design and project cost predictive indexes were studied in detail, while Section 4 provides the project cost prediction mode based on ABC-RNN. Section 5 provides the instance testing and analysis. Finally, the paper is concluded in Section 6.


## 2. Related Work

Research on project cost prediction has gone through three stages in total. The first stage was the BCIS model, which was proposed in the late 1950s and early 1960s. This model takes a similar project and breaks it down into six subsections. The accuracy of the model heavily relied on the similarity of similar projects, resulting in poor calculation accuracy. The second stage was the construction cost regression model proposed in the mid-1970s. This model takes into account the influence of various factors on the cost of construction projects and is, therefore, more stable but still less accurate. The third stage was the emergence of computer-based cost prediction models in the early 1980s, which were mainly divided into two types of models. The first model uses computer technology to simulate the construction process of a building project. This model needs to consider the probability distribution of all the variables and. Therefore, requires a large amount of statistical sample data before its distribution function can be determined. Second, the application of this model requires the project to be designed to a certain level of accuracy before the simulation can be carried out.The second model applies artificial intelligence and knowledge base technology to achieve project cost prediction. This model mainly relies on the knowledge and experience of experts and then makes predictions on project costs. Its accuracy depends mainly on the reliability and completeness of the experts’ experience. This expert knowledge base, therefore, needs to be frequently updated to ensure that its prediction results are reliable. Artificial intelligence is an advanced technology represented by the artificial neural network, fuzzy mathematics, grey system, etc. It is an important direction for modern project cost prediction model research. Cheng et al. [31] proposed a project cost prediction model based on the least squares support vector machine (LS-SVM) and differential evolution (DE). The LS-SVM was first applied to mine the functional mapping relationship between the construction cost index and its influencing factors, and then, the parameters of LS-SVM were optimized using the DE algorithm. Jafarzadeh et al. [32] improved the artificial neural network method and applied it to the significance prediction of construction costs. The study showed that the performance of the prediction model was influenced by the number of neurons in the hidden layer. Gunduz and Sahin [33] applied the multiple regression and artificial neural network method to establish a large-scale construction cost prediction model, which could effectively make decision analysis on the feasibility of project investment. Waziri et al. [34] proposed a construction cost prediction model based on a backpropagation artificial neural network (BPNN). The input variables are construction project characteristics, and the output variables are cost and duration. The training data were used several times to determine the weight parameters. The results show that the model’s predictions can contribute to a 3.91% reduction in cost and a 5% reduction in construction duration. After analyzing the existing research related to project cost management, this paper compares several mainstream project cost prediction methods, as shown in Table 1.Table 1
Comparison of project cost prediction methods.
Prediction methodsAdvantagesDisadvantagesAccuracyFuzzy mathematicsVery good logical reasoning and intellectual presentation skillsHighly subjective; lack of automatic access to rulesLowGrey theoryNo requirement for sample sizeFailure to consider the dynamic nature of project costsLowRegression analysisSimple modelsUncertain factors are not consideredLowBayes predictionGreater flexibilityHighly subjectiveLowTime-series predictionNo requirement for sample sizeHigh requirements for data reliabilityHighSupport vector machinesFast predictionDifficulties in training large samplesHighNeural networksHigh precisionStronger data dependencyHighRecurrent neural networks (RNNs) in deep learning techniques show some advantages when dealing with problems with a large number of input variables and more complex sample training. This is because RNNs are able to acquire information from the inputs more freely and dynamically without being limited by the number of input variables. Therefore, RNNs are introduced in this paper to perform the sample training task in the project cost prediction model. In addition, to effectively improve the accuracy of the cost prediction, the weight parameters of the RNN are optimized in this paper.The main innovations and contributions of this paper include the following:(1)
For the first time, RNN is applied to park landscape project cost prediction and explored the main influencing factors that lead to high park landscape cost, so as to better control the construction cost of park landscape.(2)
The performance of RNN is very dependent on the weighting parameters. The selection of the weight parameters directly affects its final prediction accuracy and stability. Therefore, in order to further improve the adaptability of the RNN to cope with a large number of predictive indexes, the ABC algorithm is used to optimize the weights of the RNN. The weight matrix was optimized by backpropagation to obtain a stable project cost prediction model. The experimental results show that the prediction accuracy of the proposed ABC-RNN is higher compared with commonly used prediction algorithms, verifying its effectiveness.


## 3. Landscape Design and Project Cost Predictive Indexes

### 3.1. Design Principles of the Park Landscape

The first and foremost issue in the planning and design of a park landscape is the need to meet the recreational needs of the residents. On the premise of satisfying the recreational function, a large area of natural ecological space should be reserved for the residents. The original topography and plants should be preserved as far as possible, and large-scale topographical changes should be avoided. The design of the park landscape needs to meet the aesthetic sensibilities of the general public and to be truly practical and aesthetically pleasing. There is a certain proportion of land for park landscapes, as shown in Table2.Table 2
The proportion of land in the park landscape.
ClassificationClass A (m2)Class B (m2)Class C (m2)Class D (m2)Area of green space>80275>70>65Garden floor area<2<2<3<3Paved site area6–126–1510–1812–20Road area<77<8<8In park landscape design, the following four main paving materials are used for event venues: concrete, natural stone, brick, and synthetic resin, as shown in Table3. They can be chosen appropriately according to their different characteristics.Table 3
Main surfacing materials for event venues.
ClassificationDurabilityInitial costPostmaintenance costsConcreteHighMediumLowNatural stoneHighHighLowBrickHighLowMediumSynthetic resinsMediumHighHighIn terms of plant configuration, park landscape design needs to focus on ecological issues. First, the original topography and vegetation must be fully preserved. This helps to save the cost of construction and protect the ecological environment, while reducing maintenance costs at a later stage. From an ecological point of view, the properties, habits, and functions of trees need to be fully considered. Under a unified style, attention should also be paid to the diversity of trees, thus creating a multilayered sense of plants. Second, the colorfulness of the plants should be enriched and a certain degree of artistry should be pursued. In the configuration of park landscape plants, the colors of the surrounding environment should be taken into account as far as possible, so that the configuration of plants is closer to the surrounding environment and the tone of the buildings. Coordinated color configurations can create a visual extension and enhance the sense of space. In terms of plant selection, trees that are more resistant to pests and diseases and easy to maintain should be planted. It is also important to choose species that are adapted to the local climate. The choice of vegetation should be based on fast-growing plants, such as shrubs with a distinctive plant fragrance. Shrubs attract birds and butterflies, thus allowing the residents to experience the atmosphere of being close to nature.


### 3.2. Project Cost Predictive Indexes

The cost of construction is the price at which a construction project product is built. The components of the construction cost are shown in Figure1.Figure 1
Components of the project cost.It can be seen that the perception and scope of construction costs will change depending on the object of construction. The construction cost prediction model is assumed to be a black box. First, a number of variables related to construction characteristics are input into the black box. After performing complex operations in the black box, the black box outputs unilateral cost prediction values. Therefore, a set of input variables relating to architectural features need to be provided to the model before project cost predictions can be made. The model inputs can be supported by constructing cost prediction indexes for park landscape projects. The predictive indexes need to have characteristics of the park landscape project and have an impact on the project cost. When constructing cost prediction indexes for park landscape projects, the principles of scientificity, comprehensiveness, selectivity, independence, appropriateness, and operability need to be followed. Taking scientificity as an example, we should adopt a combination of quantitative and qualitative analysis to reasonably construct the cost indexes of the park landscape project. The essence of the park landscape project can only be grasped through the linking of theory and practice. When considering the cost of project as an abstract open system, it is affected by both the external environment and the internal properties of the system. The external environment includes human factors, natural factors, and market factors, while the internal properties are the design parameters and characteristics of the construction project, as shown in Figure2.Figure 2
Factors influencing the cost of construction.Park landscape projects have long construction cycles and complex influencing factors. However, it is not possible to select all the factors that affect the project cost. Therefore, it is necessary to reasonably select the key factors affecting the project cost throughout the construction cycle of the park landscape project. After consulting a large amount of project cost-related information, following the principles of scientificity, comprehensiveness, selectivity, independence, and moderation, 13 factors with a large impact on project cost were summarized, as shown in Table4.Table 4
Project cost indexes for park landscape works.
Serial numberImpact factor (prediction index)Impact factor (subject of prediction)lConstruction siteUnilateral cost2Project start/completion time3Project cost index4Area of green space5Garden floor area6Paved site area7Road area8Rate of change in average prices of concrete9Rate of change in average prices of natural stone10Rate of change in average price of bricks11Rate of change in average prices of synthetic resin12Rate of change in average price of vegetation13Decoration standardsIn particular, the project cost index reflects the impact of price fluctuations on construction costs over a time period. Average price changes are measured at 2021 base prices. The unilateral cost indexes are quantified in “¥/m2.”


## 3.1. Design Principles of the Park Landscape

The first and foremost issue in the planning and design of a park landscape is the need to meet the recreational needs of the residents. On the premise of satisfying the recreational function, a large area of natural ecological space should be reserved for the residents. The original topography and plants should be preserved as far as possible, and large-scale topographical changes should be avoided. The design of the park landscape needs to meet the aesthetic sensibilities of the general public and to be truly practical and aesthetically pleasing. There is a certain proportion of land for park landscapes, as shown in Table2.Table 2
The proportion of land in the park landscape.
ClassificationClass A (m2)Class B (m2)Class C (m2)Class D (m2)Area of green space>80275>70>65Garden floor area<2<2<3<3Paved site area6–126–1510–1812–20Road area<77<8<8In park landscape design, the following four main paving materials are used for event venues: concrete, natural stone, brick, and synthetic resin, as shown in Table3. They can be chosen appropriately according to their different characteristics.Table 3
Main surfacing materials for event venues.
ClassificationDurabilityInitial costPostmaintenance costsConcreteHighMediumLowNatural stoneHighHighLowBrickHighLowMediumSynthetic resinsMediumHighHighIn terms of plant configuration, park landscape design needs to focus on ecological issues. First, the original topography and vegetation must be fully preserved. This helps to save the cost of construction and protect the ecological environment, while reducing maintenance costs at a later stage. From an ecological point of view, the properties, habits, and functions of trees need to be fully considered. Under a unified style, attention should also be paid to the diversity of trees, thus creating a multilayered sense of plants. Second, the colorfulness of the plants should be enriched and a certain degree of artistry should be pursued. In the configuration of park landscape plants, the colors of the surrounding environment should be taken into account as far as possible, so that the configuration of plants is closer to the surrounding environment and the tone of the buildings. Coordinated color configurations can create a visual extension and enhance the sense of space. In terms of plant selection, trees that are more resistant to pests and diseases and easy to maintain should be planted. It is also important to choose species that are adapted to the local climate. The choice of vegetation should be based on fast-growing plants, such as shrubs with a distinctive plant fragrance. Shrubs attract birds and butterflies, thus allowing the residents to experience the atmosphere of being close to nature.


## 3.2. Project Cost Predictive Indexes

The cost of construction is the price at which a construction project product is built. The components of the construction cost are shown in Figure1.Figure 1
Components of the project cost.It can be seen that the perception and scope of construction costs will change depending on the object of construction. The construction cost prediction model is assumed to be a black box. First, a number of variables related to construction characteristics are input into the black box. After performing complex operations in the black box, the black box outputs unilateral cost prediction values. Therefore, a set of input variables relating to architectural features need to be provided to the model before project cost predictions can be made. The model inputs can be supported by constructing cost prediction indexes for park landscape projects. The predictive indexes need to have characteristics of the park landscape project and have an impact on the project cost. When constructing cost prediction indexes for park landscape projects, the principles of scientificity, comprehensiveness, selectivity, independence, appropriateness, and operability need to be followed. Taking scientificity as an example, we should adopt a combination of quantitative and qualitative analysis to reasonably construct the cost indexes of the park landscape project. The essence of the park landscape project can only be grasped through the linking of theory and practice. When considering the cost of project as an abstract open system, it is affected by both the external environment and the internal properties of the system. The external environment includes human factors, natural factors, and market factors, while the internal properties are the design parameters and characteristics of the construction project, as shown in Figure2.Figure 2
Factors influencing the cost of construction.Park landscape projects have long construction cycles and complex influencing factors. However, it is not possible to select all the factors that affect the project cost. Therefore, it is necessary to reasonably select the key factors affecting the project cost throughout the construction cycle of the park landscape project. After consulting a large amount of project cost-related information, following the principles of scientificity, comprehensiveness, selectivity, independence, and moderation, 13 factors with a large impact on project cost were summarized, as shown in Table4.Table 4
Project cost indexes for park landscape works.
Serial numberImpact factor (prediction index)Impact factor (subject of prediction)lConstruction siteUnilateral cost2Project start/completion time3Project cost index4Area of green space5Garden floor area6Paved site area7Road area8Rate of change in average prices of concrete9Rate of change in average prices of natural stone10Rate of change in average price of bricks11Rate of change in average prices of synthetic resin12Rate of change in average price of vegetation13Decoration standardsIn particular, the project cost index reflects the impact of price fluctuations on construction costs over a time period. Average price changes are measured at 2021 base prices. The unilateral cost indexes are quantified in “¥/m2.”


## 4. ABC-RNN-Based Project Cost Prediction Model

At present, there are relatively few relevant research results on the cost control of the park landscape projects. Throughout the process of park landscape construction, the management and control of all types of costs for the project can be a good way to help developers identify deficiencies in various areas. The most problematic stage of cost control is the landscape design stage. Landscape design is a profession with relatively high requirements. It requires people with extensive experience in project design and project management. This type of designer needs to have a good grasp of the visual presentation of the landscape, and professional knowledge of construction and costing. However, there is a scarcity of people who can meet these requirements at the same time. In addition, the overall cycle time for park landscape design is short. As a result, cost control is directly constrained by time. Overall, therefore, cost control in the landscape design phase of parks is relatively weak. Therefore, in order to solve the above problems, this paper attempts to invoke artificial intelligence technology into the cost control of the park landscape project.


### 4.1. Determination of Input Variables

As construction location and project opening/completion time prediction indexes will greatly increase the redundant structure of the RNN model, the above 2 index factors are removed and the remaining 11 are retained. We selectn representative samples of completed park landscape projects and set 11 index factors as inputs to the prediction model according to the above project cost prediction indexes, as shown in Table 5. The unilateral cost X0 is the reference sequence.Table 5
Characteristic series of input indexes.
IndexesProject 1Project 2…ProjectnProject cost indexX1X11X12…X1nArea of green spaceX2X21X22…X2nGarden floor areaX3X31X32…X3nPaved site areaX4X41X42…X4nRoad areaX5X51X52…X5nRate of change in average prices of concreteX6X61X62…X6nRate of change in average prices of natural stoneX7X71X72…X7nRate of change in average prices of bricksX8X81X82…X8nRate of change in average prices of synthetic resinX9X91X92…X9nRate of change in average price of vegetationX10X10,1X10,2…X10,nDecoration standardX11X11,1X11,2…X11,n


### 4.2. Data Normalization

It can be seen that the input indexes for the park landscape project contain two types of indexes: quantitative and qualitative. For example, the decoration standardX11 is a qualitative index and the rest are quantitative indexes. In order to be able to input the features of the park landscape project into the RNN prediction model, the project feature indexes need to be normalized. In other words, we need to transform the qualitative indexes into quantitative indexes. In this paper, the qualitative indexes are normalized using the assignment method and the quantitative indexes are normalized using the outlier normalization method.(1)Xi′=Xi−XminXmax−Xmin,where Xmax is the maximum value of the input sequence and Xmin is the minimum value of the input sequence.


### 4.3. ABC-RNN Model

Although there is more research on project cost prediction methods, it can be seen through the research that single prediction algorithms all have certain limitations. For example, although traditional methods such as regression analysis and fuzzy mathematics have the advantages of simple algorithms and strong logical reasoning, the accuracy of prediction is not high. Support vector machines have a fast prediction speed but cannot be applied to large-scale samples. Neural networks have high prediction accuracy and can be trained on data of various sizes. Recurrent neural networks (RNNs) in deep learning techniques have shown some advantages when dealing with problems with a large number of input variables and more complex samples to train. Therefore, this paper introduces RNN to complete the sample training task in the project cost prediction model.The RNN model requires weight coefficients and bias constants to express the mapping relationships of the input nodes.(2)fx=w1x1+w2x2+⋯+wnxn+b=∑i=1nwixi+b,where wii=1,2,⋯,n is the weight factor corresponding to each node and b is the bias constant.After the weighting and biasing processes, an activation function is required to process the individual nodes of the neural network.(3)gx=G∑i=1nwixi+b.The core idea of RNN is the loop structure of the hidden layer. Letx and o be the input and output of the RNN, respectively; s be the result of the hidden layer activation; and the specific loop structure is shown in Figure 3.Figure 3
RNN structure.The values ofot are not only related to xt, but also related to st−2 and st−1. st−2 and st−1 are derived from the output of the hidden layer corresponding to xt−2 and xt−1, respectively. The output at the moment t is influenced not only by the input at moment but also by the output of the hidden layer at several moments before t. U, V, and W denote the connection weight matrix of each hidden layer, respectively. The sample xt is influenced by the excitation function after it has passed through the hidden layer.(4)st=fUxt+Wst−1+ht,where f⋅ and ht are the hidden layer’s excitation and bias, respectively. st After the excitation of the output ⋅, the output ot is obtained.(5)ot=gVst+bowhere bo is the bias constant.The iterations are carried out from timet, while tht and bo are not involved as constants during the iteration.(6)ot=gVst=VfUxt+Wst−1=VfUxt+WfUxt−1+Wst−2=VfUxt+WfUxt−1+WfUxt−2+Wst−3=VfUxt+WfUxt−1+WfUxt−2+WfUxt−3+L.The RNN requires continuous loop iteration to achieve the solution operation. We weight the data before timet to improve the temporal memory of the output. With weighted cyclic solving, RNNs can improve the effectiveness of deep network training.During the circular iteration of the RNN, the output of thek-th node is yk and the error is δk.(7)δk=dk−ykyk1−yk,where dk is the actual value.The RNN’s weights are updated in the manner shown as follows:(8)Δwjkn=η1+NΔwjkn−1+1δkhj,where η is the learning rate, and hj indicates the output.(9)wjkn+1=wjkn+Δwjkn,where wjkn+1 is the updated weighting.The biasΔbkn is updated as shown as follows:(10)Δbkn=α1+NΔbkn−1+1δk,where α is the update step and is normally set to α = 1.(11)bkn+1=bkn+Δbkn,where bkn+1 is the updated bias.(12)E=12∑k=1Mdk−yk2,where E is the error of all nodes. When E satisfies the set threshold, the iteration stops, and thus, a stable RNN model is obtained.The above analysis shows that the performance of RNN is very dependent on the weight parameters. The selection of the weight parameters directly affects its final prediction accuracy. Therefore, in order to further improve the adaptability of the RNN to cope with a large number of predictive indexes, the ABC algorithm is used to optimize the weights of the RNN. A stable project cost prediction model is obtained by optimizing the weight matrix through backpropagation. The ABC algorithm is mainly based on the search path of the honeybee to find the optimal solution [35–38]. Let the target be i, and the initial random position of the bee be Xid.(13)Xid=Ld+rand0,1Ud−Ld,where Ud and Ld are the upper and lower boundaries of the search range on the dimension d, respectively.The bee launches a target search atXid, and the new target is Vid.(14)Vid=Xid+φXid−Xjd,where φ is in the range [−1, 1], and Xjd is any position within the search range except Xid.When the bee detects a new target, it compares the quality of the new target with the old one. The comparison is performed by calculating the fitness values of both. The fitness of the new target isfiti.(15)fiti=11+fi,fi≥0,1+absfi,otherwise.If the fitness value ofVi is better than Xi, we replace the original target with the new one.Bees communicate target data to other bees and select preferred target probabilitiespi.(16)pi=fiti∑i=1SPfiti.When the maximum number of iterations is reached, the process is rejumped to equation (13); otherwise, the search for the optimal target continues.(17)Xit+1=Ld+rand0,1Ud−Ld,trial≥Itrmax,Xit,trial<Itrmax.The updating of time-series weights in the backpropagation process of RNN networks usually uses the gradient descent algorithm [39], which has the disadvantage of being very easy to fall into local minima and cannot obtain a globally optimal training target. Therefore, in this paper, the ABC algorithm, which has a strong global optimization capability, is used to optimize the weights of the RNN network. The key element of the optimization is to compare the output value of the RNN network with the predicted value, and the mean squared error (MSE) is chosen as the fitness function of ABC.(18)mini=1nMSEi=mini=1n1p∑s=1P∑j=1Ndisj−yisj2,where np is the number of swarms in ABC, N is the number of nodes in the output layer of the RNN, djs is the prediction result of the RNN, yjs is the true value corresponding to the output samples, and MSEi is the mean square error of target i in the whole training dataset.


### 4.4. Project Cost Prediction Process

First, a sample of cost predictions was obtained based on the index data of the park landscape project. Then, the indexes of all samples were preprocessed according to equation (1). Finally, the cost prediction model was obtained by ABC-RNN training, as shown in Figure 4.Figure 4
ABC-RNN-based project cost prediction process.


## 4.1. Determination of Input Variables

As construction location and project opening/completion time prediction indexes will greatly increase the redundant structure of the RNN model, the above 2 index factors are removed and the remaining 11 are retained. We selectn representative samples of completed park landscape projects and set 11 index factors as inputs to the prediction model according to the above project cost prediction indexes, as shown in Table 5. The unilateral cost X0 is the reference sequence.Table 5
Characteristic series of input indexes.
IndexesProject 1Project 2…ProjectnProject cost indexX1X11X12…X1nArea of green spaceX2X21X22…X2nGarden floor areaX3X31X32…X3nPaved site areaX4X41X42…X4nRoad areaX5X51X52…X5nRate of change in average prices of concreteX6X61X62…X6nRate of change in average prices of natural stoneX7X71X72…X7nRate of change in average prices of bricksX8X81X82…X8nRate of change in average prices of synthetic resinX9X91X92…X9nRate of change in average price of vegetationX10X10,1X10,2…X10,nDecoration standardX11X11,1X11,2…X11,n


## 4.2. Data Normalization

It can be seen that the input indexes for the park landscape project contain two types of indexes: quantitative and qualitative. For example, the decoration standardX11 is a qualitative index and the rest are quantitative indexes. In order to be able to input the features of the park landscape project into the RNN prediction model, the project feature indexes need to be normalized. In other words, we need to transform the qualitative indexes into quantitative indexes. In this paper, the qualitative indexes are normalized using the assignment method and the quantitative indexes are normalized using the outlier normalization method.(1)Xi′=Xi−XminXmax−Xmin,where Xmax is the maximum value of the input sequence and Xmin is the minimum value of the input sequence.


## 4.3. ABC-RNN Model

Although there is more research on project cost prediction methods, it can be seen through the research that single prediction algorithms all have certain limitations. For example, although traditional methods such as regression analysis and fuzzy mathematics have the advantages of simple algorithms and strong logical reasoning, the accuracy of prediction is not high. Support vector machines have a fast prediction speed but cannot be applied to large-scale samples. Neural networks have high prediction accuracy and can be trained on data of various sizes. Recurrent neural networks (RNNs) in deep learning techniques have shown some advantages when dealing with problems with a large number of input variables and more complex samples to train. Therefore, this paper introduces RNN to complete the sample training task in the project cost prediction model.The RNN model requires weight coefficients and bias constants to express the mapping relationships of the input nodes.(2)fx=w1x1+w2x2+⋯+wnxn+b=∑i=1nwixi+b,where wii=1,2,⋯,n is the weight factor corresponding to each node and b is the bias constant.After the weighting and biasing processes, an activation function is required to process the individual nodes of the neural network.(3)gx=G∑i=1nwixi+b.The core idea of RNN is the loop structure of the hidden layer. Letx and o be the input and output of the RNN, respectively; s be the result of the hidden layer activation; and the specific loop structure is shown in Figure 3.Figure 3
RNN structure.The values ofot are not only related to xt, but also related to st−2 and st−1. st−2 and st−1 are derived from the output of the hidden layer corresponding to xt−2 and xt−1, respectively. The output at the moment t is influenced not only by the input at moment but also by the output of the hidden layer at several moments before t. U, V, and W denote the connection weight matrix of each hidden layer, respectively. The sample xt is influenced by the excitation function after it has passed through the hidden layer.(4)st=fUxt+Wst−1+ht,where f⋅ and ht are the hidden layer’s excitation and bias, respectively. st After the excitation of the output ⋅, the output ot is obtained.(5)ot=gVst+bowhere bo is the bias constant.The iterations are carried out from timet, while tht and bo are not involved as constants during the iteration.(6)ot=gVst=VfUxt+Wst−1=VfUxt+WfUxt−1+Wst−2=VfUxt+WfUxt−1+WfUxt−2+Wst−3=VfUxt+WfUxt−1+WfUxt−2+WfUxt−3+L.The RNN requires continuous loop iteration to achieve the solution operation. We weight the data before timet to improve the temporal memory of the output. With weighted cyclic solving, RNNs can improve the effectiveness of deep network training.During the circular iteration of the RNN, the output of thek-th node is yk and the error is δk.(7)δk=dk−ykyk1−yk,where dk is the actual value.The RNN’s weights are updated in the manner shown as follows:(8)Δwjkn=η1+NΔwjkn−1+1δkhj,where η is the learning rate, and hj indicates the output.(9)wjkn+1=wjkn+Δwjkn,where wjkn+1 is the updated weighting.The biasΔbkn is updated as shown as follows:(10)Δbkn=α1+NΔbkn−1+1δk,where α is the update step and is normally set to α = 1.(11)bkn+1=bkn+Δbkn,where bkn+1 is the updated bias.(12)E=12∑k=1Mdk−yk2,where E is the error of all nodes. When E satisfies the set threshold, the iteration stops, and thus, a stable RNN model is obtained.The above analysis shows that the performance of RNN is very dependent on the weight parameters. The selection of the weight parameters directly affects its final prediction accuracy. Therefore, in order to further improve the adaptability of the RNN to cope with a large number of predictive indexes, the ABC algorithm is used to optimize the weights of the RNN. A stable project cost prediction model is obtained by optimizing the weight matrix through backpropagation. The ABC algorithm is mainly based on the search path of the honeybee to find the optimal solution [35–38]. Let the target be i, and the initial random position of the bee be Xid.(13)Xid=Ld+rand0,1Ud−Ld,where Ud and Ld are the upper and lower boundaries of the search range on the dimension d, respectively.The bee launches a target search atXid, and the new target is Vid.(14)Vid=Xid+φXid−Xjd,where φ is in the range [−1, 1], and Xjd is any position within the search range except Xid.When the bee detects a new target, it compares the quality of the new target with the old one. The comparison is performed by calculating the fitness values of both. The fitness of the new target isfiti.(15)fiti=11+fi,fi≥0,1+absfi,otherwise.If the fitness value ofVi is better than Xi, we replace the original target with the new one.Bees communicate target data to other bees and select preferred target probabilitiespi.(16)pi=fiti∑i=1SPfiti.When the maximum number of iterations is reached, the process is rejumped to equation (13); otherwise, the search for the optimal target continues.(17)Xit+1=Ld+rand0,1Ud−Ld,trial≥Itrmax,Xit,trial<Itrmax.The updating of time-series weights in the backpropagation process of RNN networks usually uses the gradient descent algorithm [39], which has the disadvantage of being very easy to fall into local minima and cannot obtain a globally optimal training target. Therefore, in this paper, the ABC algorithm, which has a strong global optimization capability, is used to optimize the weights of the RNN network. The key element of the optimization is to compare the output value of the RNN network with the predicted value, and the mean squared error (MSE) is chosen as the fitness function of ABC.(18)mini=1nMSEi=mini=1n1p∑s=1P∑j=1Ndisj−yisj2,where np is the number of swarms in ABC, N is the number of nodes in the output layer of the RNN, djs is the prediction result of the RNN, yjs is the true value corresponding to the output samples, and MSEi is the mean square error of target i in the whole training dataset.


## 4.4. Project Cost Prediction Process

First, a sample of cost predictions was obtained based on the index data of the park landscape project. Then, the indexes of all samples were preprocessed according to equation (1). Finally, the cost prediction model was obtained by ABC-RNN training, as shown in Figure 4.Figure 4
ABC-RNN-based project cost prediction process.


## 5. Instance Testing and Analysis

To validate the performance of the ABC-RNN model in project cost prediction, several samples of the park landscape projects were subjected to example analysis. A sample of 344 park landscape projects from 2016 to 2021 was collected from the government’s cost index website (https://www.cecn.org.cn/). A total of 344 park landscape project samples can be divided into two categories: soft landscapes and hard landscapes, as shown in Figures 5 and 6 respectively. A total of 64 soft landscapes were divided into 48 training sets and 16 test sets. The 280 hard landscapes were divided into 210 training sets and 70 test sets. The division of the sample datasets is shown in Table 6. A total of 344 samples were normalized, and the data are shown in Table 7.Figure 5
Soft landscape.Figure 6
Hard landscape.Table 6
Division of the sample dataset.
TypeTraining setTest setTotalSoft landscapes481664Hard landscapes21070280Table 7
Normalized sample data.
No.X1X2X3X4X5X6X7X8X9X10X11Unilateral cost1−0.60−0.19−1.00−1.00−0.30−0.630.33811−0.98−0.980.002−1.000.45−0.82−0.330.740.810.61501−0.99−0.98−0.463−0.17−0.53−0.78−0.33−0.390.630.362−10−0.93−0.99−0.894−0.01−0.180.681.00−0.03−1.000.3860−1−0.92−0.98−0.4950.00−0.810.10−1.00−0.91−0.81−0.84710−0.95−0.990.036−0.01−0.14−0.84−0.330.390.810.23000−0.91−0.980.38…………………………………344−0.01−0.11−0.83−0.33−0.30−0.81−0.2311−0.93−0.980.23First, the project cost prediction model was tested on a test set. Second, the performance of project cost prediction with different time factors is simulated. Finally, the commonly used project cost prediction algorithms and the algorithms in this paper are compared.


### 5.1. Sample Training and Testing

First, ABC-RNN was used to train 258 training samples for prediction to obtain a stable RNN model. The output curve of the training data is shown in Figure7.Figure 7
Training data output curve.Project cost predictions were then made for the 86 test sets, and the test data output curves are shown in Figure8.Figure 8
Test data output curve.It could be seen that among the 86 test samples, the expected values of most samples were consistent with the predicted values, but eight samples with prediction errors also appeared. Taking the four test samples of park landscape works as an example, the results of comparing the predicted values with the actual values are shown in Table8.Table 8
Predicted and actual values.
Sample projectsActual value (¥/m2)Prediction value(¥/m2)Absolute error(¥/m2)Relative error(%)511036.221022.7−13.52−0.65521211.51238.5272.23531455.991469.313.310.91541407140810.07The statistics of the predicted results for soft and hard landscapes are shown in Table9.Table 9
Prediction results for different types.
TypeNumber of samplestestedPredictionaccuracy (%)Soft landscapes1681.25Hard landscapes7092.8It can be seen that the prediction accuracy for hard landscapes reached 92.8%, while the prediction accuracy for soft landscapes was only 81.25%, which indicates that the ABC-RNN model is not particularly accurate for soft landscapes. This may be due to the fact that soft landscapes involve more plant configurations. The flexibility and artistry of the plant configuration lead to a greater degree of subjectivity in the normalization of multiple predictors. In addition, the planting of vegetation receives a large influence from the time factor; therefore, a test sample of different time periods will be selected for testing below.


### 5.2. Predictive Performance at Different Time Periods

In order to verify the influence of different time periods on the ABC-RNN project cost prediction model, 86 test samples from different seasons were selected for prediction analysis, as shown in Table10.Table 10
Prediction results for different time periods.
Time periodType of sampleNumberof samplestestedPredictionaccuracy (%)SpringSoft landscapes1683.1Hard landscapes7092.3SummerSoft landscapes1688.6Hard landscapes7092.9AutumnSoft landscapes1680.9Hard landscapes7093.2WinterSoft landscapes1676.8Hard landscapes7092.1It can be seen that the test samples from different time periods have some influence on the prediction results of project cost, especially for soft landscapes. This suggests that for soft landscapes, the ABC-RNN prediction model is more sensitive to the temporal properties of the samples.


### 5.3. Comparison of the Performance of Different Prediction Models

In order to compare the performance of different prediction models in park landscape project cost prediction, BP neural network (BPNN) [40], convolutional neural network (CNN) [41], RNN[42], and ABC-RNN models were used to conduct comparative analysis on the test set, respectively; the time period was chosen as summer; and the results are shown in Figure 9.Figure 9
Prediction accuracy of the four models.It can be seen that the ABC-RNN model has the highest prediction accuracy, reaching stability at about 87%. The RNN model has a prediction accuracy of about 83%. The BPNN model has the worst performance, at 79%. However, in terms of prediction time, the BPNN model was the most efficient, taking only about 16 s. The ABC-RNN model took 20 s.The comparison of the area under the curve (AUC) of the four prediction models continues below. After 20 iterations, the AUC values obtained by the four models are shown in Figure10.Figure 10
AUC performances of the 4 models.It can be seen that the ABC-RNN model has the highest AUC value of approximately 0.95. In terms of the stability of the AUC, the multiple AUC values of the ABC-RNN model are more aggregated, while the AUC values of the BPNN model and the CNN model are both more dispersed. It should be noted that the RNN model has one outlier in the AUC values, indicating that the predictive stability of the model needs to be enhanced. This result validates the analysis in the introduction that the stability of typical RNNs needs to be improved. This is because the update of historical time-series weights in the backpropagation process of RNN networks usually uses a gradient descent algorithm, which has the disadvantage of being very prone to fall into local minima and cannot obtain globally optimal training results. However, the ABC-RNN proposed in this paper solves this problem by obtaining stable and accurate prediction results with the strong global optimality finding performance of ABC and by reasonably choosing the fitness function.


## 5.1. Sample Training and Testing

First, ABC-RNN was used to train 258 training samples for prediction to obtain a stable RNN model. The output curve of the training data is shown in Figure7.Figure 7
Training data output curve.Project cost predictions were then made for the 86 test sets, and the test data output curves are shown in Figure8.Figure 8
Test data output curve.It could be seen that among the 86 test samples, the expected values of most samples were consistent with the predicted values, but eight samples with prediction errors also appeared. Taking the four test samples of park landscape works as an example, the results of comparing the predicted values with the actual values are shown in Table8.Table 8
Predicted and actual values.
Sample projectsActual value (¥/m2)Prediction value(¥/m2)Absolute error(¥/m2)Relative error(%)511036.221022.7−13.52−0.65521211.51238.5272.23531455.991469.313.310.91541407140810.07The statistics of the predicted results for soft and hard landscapes are shown in Table9.Table 9
Prediction results for different types.
TypeNumber of samplestestedPredictionaccuracy (%)Soft landscapes1681.25Hard landscapes7092.8It can be seen that the prediction accuracy for hard landscapes reached 92.8%, while the prediction accuracy for soft landscapes was only 81.25%, which indicates that the ABC-RNN model is not particularly accurate for soft landscapes. This may be due to the fact that soft landscapes involve more plant configurations. The flexibility and artistry of the plant configuration lead to a greater degree of subjectivity in the normalization of multiple predictors. In addition, the planting of vegetation receives a large influence from the time factor; therefore, a test sample of different time periods will be selected for testing below.


## 5.2. Predictive Performance at Different Time Periods

In order to verify the influence of different time periods on the ABC-RNN project cost prediction model, 86 test samples from different seasons were selected for prediction analysis, as shown in Table10.Table 10
Prediction results for different time periods.
Time periodType of sampleNumberof samplestestedPredictionaccuracy (%)SpringSoft landscapes1683.1Hard landscapes7092.3SummerSoft landscapes1688.6Hard landscapes7092.9AutumnSoft landscapes1680.9Hard landscapes7093.2WinterSoft landscapes1676.8Hard landscapes7092.1It can be seen that the test samples from different time periods have some influence on the prediction results of project cost, especially for soft landscapes. This suggests that for soft landscapes, the ABC-RNN prediction model is more sensitive to the temporal properties of the samples.


## 5.3. Comparison of the Performance of Different Prediction Models

In order to compare the performance of different prediction models in park landscape project cost prediction, BP neural network (BPNN) [40], convolutional neural network (CNN) [41], RNN[42], and ABC-RNN models were used to conduct comparative analysis on the test set, respectively; the time period was chosen as summer; and the results are shown in Figure 9.Figure 9
Prediction accuracy of the four models.It can be seen that the ABC-RNN model has the highest prediction accuracy, reaching stability at about 87%. The RNN model has a prediction accuracy of about 83%. The BPNN model has the worst performance, at 79%. However, in terms of prediction time, the BPNN model was the most efficient, taking only about 16 s. The ABC-RNN model took 20 s.The comparison of the area under the curve (AUC) of the four prediction models continues below. After 20 iterations, the AUC values obtained by the four models are shown in Figure10.Figure 10
AUC performances of the 4 models.It can be seen that the ABC-RNN model has the highest AUC value of approximately 0.95. In terms of the stability of the AUC, the multiple AUC values of the ABC-RNN model are more aggregated, while the AUC values of the BPNN model and the CNN model are both more dispersed. It should be noted that the RNN model has one outlier in the AUC values, indicating that the predictive stability of the model needs to be enhanced. This result validates the analysis in the introduction that the stability of typical RNNs needs to be improved. This is because the update of historical time-series weights in the backpropagation process of RNN networks usually uses a gradient descent algorithm, which has the disadvantage of being very prone to fall into local minima and cannot obtain globally optimal training results. However, the ABC-RNN proposed in this paper solves this problem by obtaining stable and accurate prediction results with the strong global optimality finding performance of ABC and by reasonably choosing the fitness function.


## 6. Conclusions

In order to be able to better control the construction cost of park landscapes, a park landscape cost prediction model based on recurrent neural networks is proposed. First, the design principles of the park landscape are analyzed and 13 project cost prediction indexes are given. Second, after reducing the 13 indexes to 11 indexes, data normalization was carried out on them. Then, in order to further improve the adaptability of the RNN to cope with a large number of predictive indexes, the ABC algorithm was used to optimize the weights of the RNN. An ABC-RNN model is proposed, and a project cost prediction process based on the ABC-RNN model is given. Finally, a case empirical study was conducted using 344 samples of the park landscape projects. The experimental results show that compared with BPNN, CNN, and RNN, the proposed ABC-RNN model has a certain improvement in prediction accuracy and stability, which verifies its feasibility. The subsequent study will further expand the 13 project cost prediction indexes, that is to say, add more quantifiable indexes as inputs to the model, so as to further improve the reliability of the model.



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