A Novel Approach for Predicting CO₂ Emissions in the Building Industry Using a Hybrid Multi-Strategy Improved Particle Swarm Optimization–Long Short-Term Memory Model

Abstract

The accurate prediction of carbon dioxide (CO₂) emissions in the building industry can provide data support and theoretical insights for sustainable development. This study proposes a hybrid model for predicting CO₂ emissions that combines a multi-strategy improved particle swarm optimization (MSPSO) algorithm with a long short-term memory (LSTM) model. Firstly, the particle swarm optimization (PSO) algorithm is enhanced by combining tent chaotic mapping, mutation for the least-fit particles, and a random perturbation strategy. Subsequently, the performance of the MSPSO algorithm is evaluated using a set of 23 internationally recognized test functions. Finally, the predictive performance of the MSPSO-LSTM hybrid model is assessed using data from the building industry in the Yangtze River Delta region as a case study. The results indicate that the coefficient of determination (R²) of the model reaches 0.9677, which is more than 10% higher than that of BP, LSTM, and CNN non-hybrid models and demonstrates significant advantages over PSO-LSTM, GWO-LSTM, and WOA-LSTM hybrid models. Additionally, the mean square error (MSE) of the model is 2445.6866 Mt, and the mean absolute error (MAE) is 4.1010 Mt, both significantly lower than those of the BP, LSTM, and CNN non-hybrid models. Overall, the MSPSO-LSTM hybrid model demonstrates high predictive accuracy for CO₂ emissions in the building industry, offering robust support for the sustainable development of the industry.

1. Introduction

1.1. Background

Greenhouse gas emissions have become a widespread concern for the global community and pose a significant barrier to human progress and well-being [1]. China has demonstrated its commitment as a leading nation, aiming to mitigate global warming due to carbon dioxide (CO₂) emissions. In 2020, China introduced ambitious objectives to achieve a carbon peak by the year 2030 and carbon neutrality by 2060 [2]. During the pursuit of these objectives, it is crucial to focus on CO₂ emissions in the building industry, which plays a pivotal role as one of the key industries supporting the national economy. As stated in the 2023 China Building Energy Consumption and Carbon Emission Research Report, the aggregate CO₂ emissions generated by the building industry account for a substantial 47.1% of the national energy-related CO₂ emissions [3]. Therefore, prioritizing low-carbon advancements within the building industry is imperative for attaining dual-carbon objectives. This study aims to address this challenge by proposing a novel approach for predicting CO₂ emissions in the building industry using a hybrid model, thereby supporting the sustainable development of this industry.

1.2. Literature Review

Sustainable development is a global goal, prompting increased scholarly focus on predicting CO₂ emissions [4]. The prediction of CO₂ emissions is commonly classified into three main categories: conventional methods, non-hybrid methods, and hybrid methods.

Conventional methods, such as the STIRPAT model and the system dynamics (SD) method, focus on analyzing influencing factors and utilizing scenario analysis for CO₂ emission prediction [5]. For example, Su and Lee utilized the STIRPAT model along with optimal control methods to determine when China might reach its CO₂ emissions peak [6]. Yang et al. enhanced the STIRPAT model with ridge regression to address multicollinearity issues, leading to successful predictions of CO₂ emissions in the transportation industry [7]. Zhou et al. expanded the STIRPAT model to investigate the influence of news attention on CO₂ emissions [8]. Additionally, Xie et al. utilized the SD method and a residential CO₂ emissions indicator model to predict CO₂ emissions in Guangdong Province for the year 2030 [9]. Abolghasemzadeh et al. established an energy–water relationship model within an SD framework to evaluate green greenhouse gas emissions [10]. Xu et al. used the SD method to analyze economic and social factors affecting residential CO₂ emissions in Kunming, predicting household CO₂ emissions for the 2022 to 2030 period [11]. Although these studies highlight the applicability of the STIRPAT model and SD method in predicting CO₂ emissions, their limitations become apparent when addressing the complex, dynamic, and uncertain nature of CO₂ emissions. In the context of rapidly evolving environmental conditions and the diversity of CO₂ emissions drivers, these methods may require integration with more flexible and adaptable approaches to improve the accuracy and reliability of predictions.

Non-hybrid methods are mainly based on machine learning methods, which have superior capabilities in capturing complex relationships and intricate features in CO₂ emissions data, thereby surpassing the effectiveness of conventional methods [12]. For example, Dai et al. analyzed industrial carbon reduction barriers in Bengbu using a resistance model and employed the gray model (GM) for prediction, providing specific recommendations [13]. Dong et al. used trend extrapolation and a backpropagation neural network (BPNN) to predict CO₂ emissions in the top ten carbon-emitting nations [14]. Huo et al. enhanced a support vector machine (SVM) model with a genetic algorithm to predict transportation sector emissions across various scenarios [15]. Yan et al. developed a real-time residential CO₂ emission prediction model based on a convolutional neural network (CNN), validating it in a Beijing case study [16]. Additionally, Zhao et al. introduced a heterogeneous GM that incorporates environmental investment scenarios to predict CO₂ emissions in 30 Chinese provinces from 2022 to 2030 [17]. Although non-hybrid methods have made significant progress in predicting CO₂ emissions, particularly in managing complex relationships and capturing fine features, their limitations have become increasingly apparent in highly dynamic and rapidly evolving contexts. First, these methods often require large amounts of training data, which can be difficult to acquire and may not always accurately reflect future conditions. Second, non-hybrid models are susceptible to overfitting issues, meaning they generalize poorly to new data despite performing well on training data.

Hybrid methods, which merge the strengths of both conventional and non-hybrid methods, consistently demonstrate superior accuracy, flexibility, and adaptability, which has led to their extensive adoption in academic research [18]. For example, Dai et al. introduced a CO₂ emission prediction model combining the GM and least squares support vector machine (LSSVM), enhanced by the modified shuffled frog-leaping algorithm (MSFLA), resulting in highly accurate predictions of China’s CO₂ emissions for the period 2018 to 2025 [19]. Ye et al. projected industrial CO₂ emissions by integrating an auto-regressive integrated moving average (ARIMA) and SVM models in a hybrid predicting method [20]. Cui et al. utilized a model based on the improved whale optimization algorithm and gradient-boosting decision tree (MWOA-GBDT) to predict China’s CO₂ emissions from 2020 to 2035, demonstrating considerable improvements over traditional methods [21]. Ren and Long developed an algorithm termed the fast learning network (FLN), utilizing chicken swarm optimization (CSO) to predict CO₂ emissions in China from 2020 to 2060 [22]. Luo et al. combined GM with the mind evolutionary algorithm (MEA) to enhance the BP model, aiming to predict CO₂ emissions in Jiangsu Province from 2022 to 2026 [23]. Niu et al. employed the improved fireworks algorithm (IFWA) to enhance the general regression neural network (GRNN) for predicting CO₂ emissions from 2016 to 2040 [24]. Zhang et al. used the sparrow search algorithm (SSA) to optimize the fractional accumulation gray model (FAGM) and support vector regression (SVR) for predicting CO₂ emissions in the G20 nations over the next decade [25]. These hybrid models not only demonstrate the advantages of combining multiple approaches but also provide highly reliable predictions for complex and long-term CO₂ emissions scenarios.

Summarizing the above literature, it is evident that the use of hybrid models for predicting CO₂ emissions has emerged as a dominant trend. To demonstrate the superiority of hybrid methods over conventional and non-hybrid methods, it is necessary to prove that hybrid methods have better performance in terms of prediction accuracy, flexibility, and adaptability. Several studies mentioned in the literature review clearly show that hybrid methods outperform non-hybrid methods. This study will build on this understanding by focusing on the building industry to develop a CO₂ emission prediction model, highlighting the enhanced performance of hybrid methods over non-hybrid methods.

2. Methods

2.1. PSO Algorithm

The particle swarm optimization (PSO) algorithm was selected in this study based on the following key factors:

• The PSO algorithm is especially well-suited for optimization problems in high-dimensional spaces. It effectively balances exploration and exploitation to determine the best or near-optimal solution. Its inherent ability to avoid local optima through strong global search capabilities makes it a reliable tool for complex optimization tasks [26];
• The PSO algorithm is straightforward to implement and can be seamlessly integrated with other deep learning models to form a powerful hybrid model [27];
• The PSO algorithm remains widely employed in predicting CO₂ emissions, and its strong track record highlights its effectiveness and reliability [28].

Therefore, although many machine learning algorithms are available, this study selected the PSO algorithm for its application in consideration of the aforementioned key factors. The PSO algorithm draws inspiration from the foraging behavior of bird flocks. It is based on the idea of collaboration and information sharing among individuals in a flock [29]. It conceptualizes birds as particles and food as the optimal solution to be searched. Assuming a target search space with $N$ dimensions and a swarm consisting of $M$ particles, the search process of the particles in the $t$ iteration is as follows:

$$X_i\left(t\right)=\left\{x_{i1}\left(t\right),x_{i2}\left(t\right),\cdots ,x_{iN}\left(t\right)\right\}$$

(1)

$$V_i\left(t\right)=\left\{v_{i1}\left(t\right),v_{i2}\left(t\right),\cdots ,v_{iN}\left(t\right)\right\}$$

(2)

$$p_{best}\left(t\right)=\left\{p_{i1}\left(t\right),p_{i2}\left(t\right),\cdots ,p_{iN}\left(t\right)\right\}$$

(3)

$$g_{best}\left(t\right)=\left\{g_{i1}\left(t\right),g_{i2}\left(t\right),\cdots ,g_{iN}\left(t\right)\right\}$$

(4)

$$v_{ik}\left(t+1\right)=\omega v_{ik}\left(t\right)+c_1{r}_1\left[p_{ik}\left(t\right)-x_{ik}\left(t\right)\right]+c_2{r}_2\left[g_{ik}\left(t\right)-x_{ik}\left(t\right)\right]$$

(5)

In these equations, $X_i$ denotes the position of the particle; $V_i$ denotes the velocity of the particle; $p_{best}$ denotes the best position currently found by the particle; $g_{best}$ denotes the best position currently found by the swarm; $\omega$ denotes the inertia weight; $c_1$ and $c_2$ denote the cognitive and social coefficients, respectively; $r_1$ and $r_2$ denote random numbers between 0 and 1; and $k$ denotes the dimension.

2.2. MSPSO Algorithm

This study utilized the PSO algorithm, optimizing it through the application of tent chaotic mapping, mutation for the least-fit particles, and a random perturbation strategy. This study successfully implemented a multi-strategy improved particle swarm optimization (MSPSO) algorithm.

2.2.1. Tent Chaotic Mapping

The quality of the population in the initialization phase directly determined the excellence of the algorithm, making the initial population quality crucial for the algorithm. The risk of diminishing population diversity and getting trapped in local optima was present due to the random population initialization method utilized in the particle swarm algorithm [30]. Tent chaotic mapping offered notable advantages in regularity, uniformity, and iteration speed. Its use in initializing the population helped maintain diversity and enhance the global search capability [31]. The initial expression for tent chaotic mapping is as follows:

$$x_{n+1}=\{\begin{array}{ll}u{x}_n& x_n<u\\ u(1-x_n)& x_n\ge u\end{array}$$

(6)

In this equation, $x_n$ denotes chaotic sequence, $x_n\in \left[0,1\right]$, and $u$ was assigned a value of 0.499.

2.2.2. Mutation for the Least-Fit Particles

In the PSO algorithm, premature convergence can weaken global search capability, leading to entrapment in local optima and negatively affecting the final result. Therefore, a least-fit particle mutation strategy was employed to mitigate this issue. The mutation expression for the least-fit particles is as follows:

$$k=1-r{(1-({\displaystyle \frac{t}{T_{\max }}}))}^2$$

(7)

$$x_{new}=x_{worst}+k\cdot n\cdot x_{worst}$$

(8)

In these equations, $r$ denotes a random number between 0 and 1, $t$ denotes the current iteration number, $T_{\max }$ denotes the maximum number of iterations, and $n$ denotes a set of random numbers with a mean of 0 and a dimension of $D$.

2.2.3. Random Perturbation Strategy

A random perturbation strategy was incorporated during the generation of the new population, expanding the dataset by introducing fluctuations within a certain range. This process increased the dataset volume and enhanced the robustness of the algorithm. The expression is as follows:

$$u=1-{({\displaystyle \frac{t}{T_{\max }}})}^{{\displaystyle \frac{1}{2}}}$$

(9)

$$x_{new}=\{\begin{array}{l}{x}_i+u(ub-lb)\cdot r\hspace{1em}r>0.5\\ x_i-u(ub-lb)\cdot r\hspace{1em}r\le 0.5\end{array}$$

(10)

In these equations, $x_{new}$ denotes the new individual after the perturbation update, $x_i$ denotes the current individual, $ub$ is the upper boundary, and $lb$ is the lower boundary.

2.3. LSTM Model

The following key factors were considered in selecting the long short-term memory (LSTM) model for this study:

• The LSTM model is particularly suited for processing time series data, which is essential for analyzing and predicting trends in CO₂ emissions over time. Its unique structure enables it to capture long-term dependencies in the data, making it an optimal choice for accurately predicting future emissions based on historical data [32];
• The LSTM model has been extensively validated across various applications such as building energy consumption prediction [33], text recognition [34], and fault diagnosis [35], demonstrating its versatility and effectiveness in handling complex, sequential datasets;
• The LSTM model can be seamlessly integrated with optimization algorithms such as PSO to form a hybrid model, leveraging the strengths of both approaches. This integration facilitates the development of more sophisticated models that improve prediction accuracy and generalization ability.

Therefore, despite the availability of numerous deep learning models, this study selected the LSTM model based on the aforementioned key factors. By implementing a gating mechanism, the LSTM model effectively regulates the retention and forgetting of information, addressing the issues of vanishing and exploding gradients in recurrent neural networks (RNNs) [36]. The LSTM model comprises an input gate, a forget gate, and an output gate, which collectively manage the cell state. The structure of LSTM is illustrated in Figure 1.

The implementation of running the LSTM model follows the equations outlined below:

$$f_t=\sigma \left(w_f\left[h_{t-1},x_t\right]+b_f\right)$$

(11)

$$i_t=\sigma \left(w_i\left[h_{t-1},x_t\right]+b_i\right)$$

(12)

$${\tilde{c}}_t=\tanh \left(w_c\left[h_{t-1},x_t\right]+b_c\right)$$

(13)

$$c_t=f_t\otimes c_{t-1}+i_t\otimes {\tilde{c}}_t$$

(14)

$$o_t=\sigma \left(w_o\left[h_{t-1},x_t\right]+b_o\right)$$

(15)

$$h_t=o_t\otimes \tanh \left(c_t\right)$$

(16)

In these equations, $\sigma$ denotes the $sigmoid$ activation function; $\omega$ denotes the weight matrix; $x_t$ denotes the input sequence at time $t$; $b$ denotes the bias term; $h_{t-1}$ denotes the hidden layer outputs at time $t-1$; $i_t,f_t,o_t$ denote the outputs of the input gate, forget gate, and output gate, respectively; and ${\tilde{c}}_t$ is a temporary variable for the computed $c_t$.

2.4. MSPSO-LSTM Model

This study developed a hybrid model combining the MSPSO algorithm and LSTM for CO₂ emission prediction in the building industry. The MSPSO algorithm incorporates multiple strategies to dynamically adjust the PSO algorithm, thereby enhancing search efficiency in high-dimensional parameter space and mitigating the tendency of the traditional PSO algorithm to become trapped in local optima. As a deep learning model well-suited for processing time series data, the LSTM model effectively captures long-term dependencies and complex temporal dynamic characteristics in the data. The use of the MSPSO algorithm to optimize the hyperparameters of the LSTM model significantly enhances the prediction performance and generalization ability compared to non-hybrid models. Figure 2 offers a detailed illustration of the step-by-step procedure involved.

2.5. Random Forest Feature Importance

In this study, feature importance is assessed by calculating the reduction in Gini impurity attributed to each feature during node splitting in the random forest algorithm [37]. This calculation reflects the degree of influence that the selected influencing factor features exert on the model. Features with high scores are crucial for partitioning the datasets, indicating their critical importance in predicting CO₂ emissions in the building industry, while features with low scores have a relatively minor impact on the model. The equations for calculating the reduction in Gini impurity are as follows:

$$G=1-{\displaystyle \sum _{i=1}^C{p}_i^2}$$

(17)

$$\mathsf{\Delta }G=G-\left({\displaystyle \frac{N_{left}}{N}}\times G_{left}+{\displaystyle \frac{N_{right}}{N}}\times G_{right}\right)$$

(18)

In these equations, $G$ denotes the Gini impurity of a node; $C$ is the total number of feature categories; $p_i$ denotes the proportion of samples with feature $i$ in this node; $G_{left}$ and $G_{right}$ denote the Gini impurity of the left and right child nodes, respectively; $N_{left}$ and $N_{right}$ denote the number of samples in the left and right child nodes, respectively; and $N$ is the total number of samples in the parent node.

2.6. Evaluation Indicators

To evaluate the predictive performance of the model and compare it with the actual values, this study employed the coefficient of determination (R²), mean square error (MSE), and mean absolute error (MAE) as evaluation indicators.

Table 1. Evaluation indicators.

Indicator	Definition	Equation
R2	Coefficient of determination	${\mathrm{R}}^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(y_i-y_i^{\prime }\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2}}}$
MSE	Mean square error	$\mathrm{MSE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left(y_i-y_i^{\prime }\right)}$
MAE	Mean absolute error	$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^1\left|y_i-y_i^{\prime }\right|}$

presents the specific equations for these three indicators.

In these equations, $y_i$ denotes the true value, $y_i^{\prime }$ denotes the predicted value, ${\overline{y}}_i$ denotes the mean of the true value, and $n$ denotes the number of samples.

R² measures the proportion of variance in the dependent variable that can be predicted from the independent variables, with values ranging from 0 to 1. The closer R² is to 1, the better the predictive performance [38]. MSE quantifies the average squared difference between the predicted and actual values, and MAE evaluates the average absolute difference between the predicted and actual values. In both cases, lower values indicate higher predictive accuracy, meaning that the predictions are closer to the actual observed values [39].

3. Results and Discussion

3.1. Datasets Preparation

3.1.1. CO₂ Emissions Calculation

This study selected the Yangtze River Delta (YRD) region as the study area, one of the most economically prosperous regions in China, characterized by rapid development in the building industry and significant CO₂ emissions. Based on the relevant literature, CO₂ emissions from the building industry were categorized into direct and indirect emissions, considering their relevance for data collection [40]. Direct CO₂ emissions included the consumption of ten different types of energy: raw coal, coke, kerosene, diesel, gasoline, natural gas, liquefied petroleum gas, fuel oil, electricity, and heat, with their respective CO₂ emission factors shown in

Table 2. CO₂ emission coefficients of the various energy sources.

Energy Type	Carbon Emission Coefficient	Energy Type	Carbon Emission Coefficient
Raw coal	0.5394 (kg C/kg)	Natural gas	0.5956 (kg C/kg)
Coke	0.8303 (kg C/kg)	Liquefied petroleum gas	0.8635 (kg C/kg)
Kerosene	0.8446 (kg C/kg)	Fuel oil	0.8827 (kg C/kg)
Diesel oil	0.8620 (kg C/kg)	Electricity	0.3564 (kg C/kg)
Gasoline	0.8140 (kg C/kg)	Thermal energy	0.0086 (kg C/kg)

. Indirect CO₂ emissions encompassed the consumption of five building materials: steel, timber, cement, glass, and aluminum, with their respective CO₂ emission factors listed in

Table 3. CO₂ emission coefficients of the different building materials.

Construction Materials Type	Steel	Wood	Cement	Glass	Aluminum
Carbon emission coefficient	1.789 (kg/kg)	−0.842 (kg/m3)	0.815 (kg/kg)	0.966 (kg/kg)	2.600 (kg/kg)

. The CO₂ emissions of the building industry in the YRD region were calculated using the IPCC CO₂ emission factor method [41], as detailed below:

$$E_{x,y}=Z{E}_{x,y}+J{E}_{x,y}=44/12{\displaystyle \sum _m\left(N_m\times {\alpha }_m\right)}+{\displaystyle \sum _n{C}_n\times {\beta }_n\times \left(1-{\lambda }_n\right)}$$

(19)

In this equation, $E_{x,y}$ denotes the CO₂ emissions attributed to the building industry, $Z{E}_{x,y}$ denotes the direct CO₂ emissions, $J{E}_{x,y}$ denotes the indirect CO₂ emissions, $N_m$ represents the consumption of energy source $m$, $C_n$ represents the consumption of building material $n$, ${\alpha }_m$ signifies the CO₂ emission coefficient associated with energy source $m$, ${\beta }_n$ signifies the CO₂ emission coefficient associated with building material $n$, and ${\lambda }_n$ represents the recycling coefficient of the building material.

Additionally, the recycling coefficient of steel is 0.800, the recycling coefficient of aluminum is 0.850, and the recycling coefficients of the remaining building materials are all 0 [42].

All data were obtained from the China Statistical Yearbook [43], the China Energy Statistical Yearbook [44], and the China Construction Statistical Yearbook [45] and underwent rigorous data normalization to ensure the reliability of the study results. Figure 3 illustrates the CO₂ emissions from the building industry in the YRD region from 2005 to 2020.

Firstly, the result showed that from 2004 to 2011, CO₂ emissions exhibited a significant upward trend. During this period, CO₂ emissions increased from 220.2777 Mt in 2004 to 652.5111 Mt in 2011, with a significant annual growth rate. This phenomenon reflected the accelerating building industrialization process and increased energy consumption, which contributed to the rise in CO₂ emissions. However, starting in 2012, the growth trend of CO₂ emissions slowed down and even declined in certain years. For example, CO₂ emissions in 2012 were 606.8390 Mt, lower than in 2011. In the following years, CO₂ emissions fluctuated slightly, maintaining around 600 Mt. This change might have been related to the environmental protection policies, energy structure adjustments, and technological advancements implemented by China. According to the data from 2020 and 2021, CO₂ emissions were 652.1466 Mt and 577.2721 Mt, respectively, showing significant fluctuations. This dramatic change during this period might have been closely related to the impact of the COVID-19 pandemic. During the pandemic, building production and building material transportation activities decreased, leading to a reduction in CO₂ emissions.

3.1.2. Influencing Factors Selection

Selecting appropriate factors as input parameters is crucial for the predictive model. Considering the characteristics of CO₂ emissions in the building industry, the following three criteria were considered:

• The factors should be representative;
• The factors should be appropriate in type, as the sample size of CO₂ emissions in the building industry is relatively small, and numerous factors could easily lead to model underfitting or overfitting;
• The factors should be easily accessible and authoritative to enhance the credibility of the predictive results.

Therefore, based on the above analysis, this study identified six key factors as input variables. These factors included X₁: energy consumption; X₂: gross output value of the building industry; X₃: year-end resident population; X₄: gross production value; X₅: number of building enterprises; and X₆: CO₂ intensity. The random forest model offers robust analysis for variables with nonlinear relationships [46]. The detailed data on influencing factors are presented in

Table 4. Influencing factors data.

Year	X1 (Million Tons of Standard Coal)	X2 (Billion CYN)	X3 (Million People)	X4 (Billion CYN)	X5 (Units)	X6 (Ton/Ten Thousand CYN)
2005	660	11,940.48	205.89	46,614.20	14,159	1.862
2006	718	14,534.08	208.01	57,180.52	15,156	1.735
2007	763	18,023.43	210.60	64,627.14	16,163	1.580
2008	824	21,857.99	212.50	75,366.19	18,411	1.589
2009	898	25,923.95	214.27	82,556.92	18,721	1.411
2010	923	31,578.95	215.76	98,673.10	19,360	1.338
2011	1007	37,925.80	219.21	115,925.46	19,430	2.512
2012	1057	44,830.18	221.82	126,117.32	19,795	1.351
2013	1197	52,365.07	224.12	138,557.44	20,394	1.160
2014	1233	58,243.99	226.35	149,677.80	20,717	1.066
2015	1199	60,113.81	227.69	160,331.95	20,584	0.962
2016	1214	62,874.62	229.53	177,225.91	20,535	0.936
2017	1276	68,448.62	231.16	195,289.01	20,536	0.923
2018	1362	66,656.85	232.70	211,479.24	22,458	0.909
2019	1478	69,805.11	234.17	237,242.56	23,484	0.934
2020	1480	73,832.41	235.38	244,713.53	27,061	0.782

, and the random forest feature importance ranking is shown in Figure 4.

The X₁, energy consumption, measured in million tons of standard coal, exhibited a steady increase from 660 million tons in 2005 to 1480 million tons in 2020. This significant increase can be attributed to the growing industrial activities and economic development over the years.

The X₂, gross output value of the building industry, measured in billion CYN, also demonstrated significant growth, increasing from CYN 11,940.48 billion in 2005 to CYN 73,832.41 billion in 2020, indicating robust economic expansion during this period.

The X₃, year-end resident population, measured in million people, grew steadily from 205.89 million in 2005 to 235.38 million in 2020. This gradual population increase suggests a proportional rise in the labor force and potential market size.

The X₄, gross production value, measured in billion CYN, saw a remarkable increase from CYN 46,614.20 billion in 2005 to CYN 244,713.53 billion in 2020. This rise mirrors the extensive infrastructure development and capital expenditure in various sectors.

The X₅, number of building enterprises, measured in units, increased from 14,159 units in 2005 to 27,061 units in 2020, highlighting the expansion of the building industry and the entry of new businesses into the market.

The X₆, CO₂ intensity, measured in tons per ten thousand CYN, declined from 1.862 tons per ten thousand CYN in 2005 to 0.782 tons per ten thousand CYN in 2020. This declining trend in CO₂ intensity indicates enhancements in energy efficiency and the adoption of more sustainable practices over the years.

3.2. MSPSO Algorithm Testing

3.2.1. Test Functions

The fundamental optimization performance of the algorithm was evaluated through optimization experiments using test functions. This study assessed the MSPSO algorithm by employing 23 internationally recognized test functions, including F1–F7 unimodal functions, F8–F13 multimodal functions, and F14–F23 composite benchmark functions [47]. Unimodal functions were used to evaluate the convergence speed and accuracy of the algorithm. These functions were essential for understanding how quickly and precisely an algorithm can approach the optimal solution in a relatively simple landscape. Conversely, multimodal functions were employed to assess the global search capability of the algorithm. These functions featured multiple local optima, which test the capacity to avoid becoming trapped in local minima and its effectiveness in exploring the entire search space. Additionally, composite benchmark functions were employed to evaluate the overall efficiency of the algorithm. These functions integrate elements of both unimodal and multimodal functions, providing a comprehensive assessment of the performance across different types of landscapes, including its robustness, adaptability, and computational efficiency in handling complex real-world problems [48].

3.2.2. Test Results

To validate the improvements of the MSPSO algorithm, this study compared it with the PSO [49], grey wolf optimizer (GWO) [50], and whale optimization algorithm (WOA) [51]. The GWO simulates the social hierarchy and hunting tactics of grey wolves, employing a leadership-based strategy to navigate the search space. The WOA mimics the bubble-net hunting strategy of humpback whales, utilizing spiral-shaped movements and shrinking encirclement to find optimal solutions. All algorithms were subjected to 30 independent tests to minimize random errors and enhance the objectivity of the results. Performance indicators included the average fitness value and standard deviation. Parameters for the MSPSO and PSO algorithms were set as follows: acceleration factors ($c_1=c_2=1.5$), inertia weight coefficients (${\omega }_{\max }=0.8$), (${\omega }_{\min }=0.2$), population size of 50, and 500 iterations. The optimization results of the test functions are presented in

Table 5. Comparison of algorithm performance on 23 international test functions.

Functions	MSPSO		PSO		GWO		WOA
	Average	Standard	Average	Standard	Average	Standard	Average	Standard
F1	6.15 × 10−236	0.00 × 100	1.57 × 103	6.29 × 102	1.56 × 10−9	1.58 × 10−9	1.73 × 10−8	3.43 × 10−8
F2	6.85 × 10−109	2.06 × 10−108	4.86 × 101	1.02 × 101	5.39 × 10−6	6.29 × 10−6	1.71 × 10−7	1.32 × 10−7
F3	7.20 × 10−223	0.00 × 100	5.31 × 103	2.19 × 103	7.64 × 100	7.28 × 100	7.30 × 101	1.55 × 102
F4	1.84 × 10−124	5.52 × 10−124	2.63 × 100	6.45 × 10−1	5.66 × 10−3	5.07 × 10−3	2.67 × 10−3	1.82 × 10−3
F5	4.35 × 10−2	3.09 × 10−2	6.06 × 105	3.90 × 105	2.85 × 101	3.95 × 10−1	2.87 × 101	2.72 × 10−1
F6	1.67 × 10−3	1.59 × 10−3	1.65 × 103	5.80 × 102	3.47 × 100	3.44 × 10−1	3.75 × 100	5.22 × 10−1
F7	7.92 × 10−3	3.48 × 10−3	1.74 × 100	7.53 × 10−1	1.04 × 10−2	6.24 × 10−3	3.61 × 10−3	2.93 × 10−3
F8	−1.25 × 104	1.76 × 102	−6.96 × 103	4.74 × 102	−5.42 × 103	6.71 × 102	−5.67 × 103	4.80 × 102
F9	0.00 × 100	0.00 × 100	1.92 × 102	2.32 × 101	1.45 × 101	9.11 × 100	8.62 × 10−7	2.55 × 10−6
F10	4.44 × 10−16	0.00 × 100	1.22 × 101	1.46 × 100	7.19 × 10−6	2.86 × 10−6	7.29 × 10−6	7.11 × 10−6
F11	0.00 × 100	0.00 × 100	8.43 × 100	2.28 × 100	3.59 × 10−2	2.52 × 10−2	1.62 × 10−3	4.87 × 10−3
F12	4.47 × 10−3	1.43 × 10−3	4.50 × 103	9.18 × 103	3.78 × 10−1	2.03 × 10−1	6.82 × 10−1	2.85 × 10−1
F13	6.65 × 10−4	6.87 × 10−4	1.29 × 102	3.70 × 101	1.70 × 100	1.70 × 10−1	2.29 × 100	9.24 × 10−2
F14	9.98 × 10−1	1.07 × 10−6	6.76 × 100	4.68 × 100	6.56 × 100	4.80 × 100	5.79 × 100	2.71 × 100
F15	7.83 × 10−4	5.39 × 10−4	9.22 × 10−3	1.00 × 10−2	1.02 × 10−2	1.73 × 10−2	7.34 × 10−4	3.63 × 10−4
F16	−1.03 × 100	4.51 × 10−6	−1.03 × 100	2.11 × 10−16	−1.03 × 100	1.49 × 10−6	−1.03 × 100	1.30 × 10−3
F17	3.98 × 10−1	6.33 × 10−6	3.98 × 10−1	0.00 × 100	3.98 × 10−1	3.11 × 10−6	3.98 × 10−1	5.14 × 10−4
F18	3.00 × 100	3.44 × 10−4	3.00 × 100	1.49 × 10−15	3.00 × 100	6.53 × 10−4	3.01 × 100	2.65 × 10−2
F19	−3.00 × 10−1	0.00 × 100	−3.00 × 10−1	0.00 × 100	−3.00 × 10−1	0.00 × 100	−3.00 × 10−1	0.00 × 100
F20	−3.24 × 10	6.58 × 10−2	−3.19 × 100	1.00 × 10−1	−3.22 × 100	1.68 × 10−1	−1.28 × 100	6.16 × 10−1
F21	−1.01 × 101	1.38 × 10−2	−8.90 × 100	2.57 × 100	−8.15 × 100	3.12 × 100	−8.54 × 10−1	3.82 × 10−1
F22	−1.04 × 101	4.55 × 10−2	−7.68 × 100	3.39 × 100	−1.04 × 101	2.02 × 10−3	−7.65 × 10−1	2.31 × 10−1
F23	−1.05 × 101	1.60 × 10−2	−6.89 × 100	3.72 × 100	−8.51 × 100	3.15 × 100	−7.87 × 10−1	3.97 × 10−1

, and the average fitness curves are illustrated in Figure 5.

According to the experimental results, the MSPSO algorithm demonstrated exceptionally high solution accuracy and stability across various test functions. For example, on functions F1, F2, F9, F10, and F11, the average values achieved by the MSPSO algorithm were nearly identical to or even reached the theoretically optimal solutions, significantly outperforming the other three algorithms. This performance indicated that the MSPSO algorithm possessed a significant advantage in addressing optimization problems that demand high precision.

In addition to its high solution accuracy, the MSPSO algorithm also demonstrated superior stability. The standard deviations on several functions were extremely low, even approaching zero (such as F1, F9, and F10), indicating that the MSPSO algorithm consistently maintained high performance across multiple runs and was less susceptible to random factors. In contrast, other algorithms exhibited larger standard deviations on certain functions, indicating significant performance fluctuations that could lead to uncertainties in practical applications.

The MSPSO algorithm excelled not only in simple or low-dimensional optimization problems but also demonstrated strong competitiveness in complex or high-dimensional optimization problems. For example, on functions F5, F6, and F8, the performance of the MSPSO algorithm was significantly better than that of other algorithms, suggesting higher efficiency and reliability in handling complex problems.

The advantages of the MSPSO algorithm in multiple aspects could be attributed to its internal improvement mechanisms. Compared to traditional PSO algorithms, the MSPSO algorithm incorporated tent chaotic mapping, mutation for the least-fit particles, and a random perturbation strategy. These strategies enabled the MSPSO algorithm to better balance exploration of the solution space and exploitation of existing information, thereby enhancing both its solution accuracy and stability.

In summary, the MSPSO algorithm demonstrated significant advantages in solution accuracy, stability, broad applicability, and the effectiveness of its improvement mechanisms. This made the MSPSO algorithm highly promising for optimizing the initial weights and thresholds of LSTM models, thereby improving their performance in prediction tasks.

3.3. CO₂ Emission Prediction for the Building Industry

The datasets in this study were divided into a 70% training set and a 30% testing set for the experiments. All data were strictly normalized using Equation (20).

$$x^{\ast }={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(20)

To evaluate the difference in prediction accuracy between the MSPSO-LSTM hybrid model and non-hybrid models, this study compared it to three widely used non-hybrid models: BP [52], LSTM [53], and CNN [54]. Data from 2005 to 2015 were used as the training set. The model was then tested using data from 2016 to 2020, with accuracy assessed through the established evaluation indicators. Results of the evaluation indicators are presented in

Table 6. Results of non-hybrid models evaluation indicators.

Indicators	MSPSO-LSTM	BP	LSTM	CNN
R2	0.9677	0.8537	0.8708	0.8478
MSE	2445.6866	11,065.2243	9773.7044	11,513.0002
MAE	4.1010	8.0218	8.2538	8.2105

, with a comparison of prediction results illustrated in Figure 6.

As shown in Table 6, the comparison of evaluation indicators demonstrates that the MSPSO-LSTM hybrid model significantly outperformed the BP, LSTM, and CNN non-hybrid models across various evaluation indicators. Specifically, the R² value for the MSPSO-LSTM hybrid model was more than 10% higher than that of BP, LSTM, and CNN non-hybrid models, indicating a substantial improvement in predictive performance. In terms of MSE, the MSPSO-LSTM hybrid model achieved values below 2500 Mt, while the BP, LSTM, and CNN non-hybrid models were around 10,000 Mt, demonstrating notably lower prediction errors for the MSPSO-LSTM hybrid model. Additionally, the MAE for the BP, LSTM, and CNN non-hybrid models was twice as high as that for the MSPSO-LSTM hybrid model, indicating the superior predictive accuracy of the MSPSO-LSTM hybrid model.

To further assess the gap in prediction accuracy between the MSPSO-LSTM hybrid model and other hybrid models, this study compared the MSPSO-LSTM hybrid model with the PSO-LSTM, GWO-LSTM, and WOA-LSTM models, which integrate LSTM with the PSO, GWO, and WOA, respectively, as discussed in the previous section. The evaluation indicator results are presented in

Table 7. Results of hybrid models evaluation indicators.

Indicators	MSPSO-LSTM	PSO-LSTM	GWO-LSTM	WOA-LSTM
R2	0.9677	0.9336	0.9378	0.9553
MSE	2445.6866	5020.5132	4702.2445	3376.5822
MAE	4.1010	6.7442	5.5917	4.3746

. The comparison of prediction results is illustrated in Figure 7.

As shown in Figure 7, the MSPSO-LSTM hybrid model demonstrated slightly superior performance compared to the other hybrid models in terms of evaluation indicators. The parameter optimization provided by the MSPSO algorithm proved to be more effective than that of the PSO, GWO, and WOA. When combined with the LSTM model, the MSPSO-LSTM hybrid model outperformed the PSO-LSTM, GWO-LSTM, and WOA-LSTM hybrid models in terms of performance, error, reduction, accuracy, and robustness, particularly in predicting CO₂ emissions in the building industry. This made the MSPSO-LSTM hybrid model particularly well-suited for predicting CO₂ emissions in the building industry, offering valuable data support and a robust theoretical foundation for industry decision-makers.

4. Conclusions and Discussions

This study developed and validated an MSPSO-LSTM hybrid model for predicting CO₂ emissions in the building industry, focusing on the Yangtze River Delta (YRD) region as a case study. The MSPSO algorithm was used to optimize the LSTM model, resulting in enhanced predictive accuracy, stability, and robustness compared to both non-hybrid models (BP, LSTM, and CNN) and other hybrid models (PSO-LSTM, GWO-LSTM, and WOA-LSTM). The key findings are as follows:

• The optimization effect of the MSPSO algorithm has been tested by 23 internationally recognized standard test functions, and compared with the PSO, GWO, and WOA algorithms, it has shown excellent optimization ability, higher convergence accuracy, and higher stability. This enhances the parameter selection of the LSTM model, thereby improving the prediction performance;
• The MSPSO-LSTM hybrid model achieved an R² of 0.9677, an MSE of 2445.6866 Mt, and an MAE of 4.1010 Mt, indicating high accuracy and high consistency between the predicted CO₂ emissions and the actual emissions. The model outperformed other non-hybrid and hybrid models in various evaluation indicators, especially in predicting CO₂ emissions in the complex environmental context of the construction industry;
• The MSPSO-LSTM model exhibits strong robustness and is suitable for application in complex and dynamic environments. The model is able to provide accurate and reliable predictions, making it a valuable tool for policymakers and industry stakeholders, laying a solid foundation for informed decision-making to mitigate CO₂ emissions.

Despite the strengths of this study, there are several limitations that warrant further investigation:

• Only the Yangtze River Delta region was selected for the case study. Although the model showed excellent prediction performance in this context, its applicability to other regions with different environmental and economic conditions should be explored;
• The performance of the model depends on the quality and availability of the data. In regions where historical data are sparse or inconsistent, the model may face challenges in maintaining its predictive accuracy;
• The integration of MSPSO and LSTM increases the computational complexity of the model. Future research can explore ways to optimize the efficiency of the model without affecting its accuracy.

To address these limitations, future work should focus on extending the model to other regions and testing its adaptability in different environments. In addition, research can explore the potential of integrating other optimization algorithms or adopting ensemble methods to further improve prediction accuracy. Finally, reducing the computational requirements of the model while maintaining its robustness remains an important area for future exploration.