Introduction

Regional logistics encompasses the organized and coordinated efforts within a specific geographical region of a country, encompassing various logistics activities. It serves as a crucial factor in promoting economic expansion, enhancing logistical efficiency, facilitating industrial transformation, and it enhances the comprehensive competitiveness of the area. Consequently, the careful design and advancement of regional logistics frameworks are essential for nurturing enduring, robust, and expedited economic progress within the region (Huang et al., (2023)). Predicting regional logistics requirements entails the intricate assessment and anticipation of commodity movements. By leveraging this forecast data, regions can anticipate and adapt to evolving logistics challenges more effectively, optimizing their logistics networks to support economic growth, societal well-being, and the efficient movement of goods (Li et al., (2020)). Enhancing the precision of regional logistics demand forecasting models and identifying the optimal approach for such forecasting to more effectively underpin the strategic planning of the logistics sector constitutes a pivotal concern addressed in this paper.

However, the environmental implications of logistics industry development cannot be overlooked; however, the pathway to advancing its green competitiveness remains insufficiently explored. According to the research by Peng, Y. et al. (Peng et al., (2022)), the green competitiveness of the logistics sector is influenced by numerous factors and cannot be adequately accounted for by a solitary determinant. The study by Nan, Y. et al. (Nan et al., (2024)) indicates that the rate of green innovation within the logistics sector is consistently increasing with the fastest growth occurring in the less economically developed western regions. Zhu, X. et al. (Zhu et al., (2023)) have demonstrated that the implementation of green logistics is vital for attaining the 2060 carbon neutrality objective. Therefore, the prediction of logistics demand and analysis of its influencing factors in the CC-DEC are crucial for boosting the eco-competitiveness of the logistics sector. How to adjust the logistics demand forecasting model to consider low-carbon dimensions, such as energy consumption intensity and CO2 emission intensity, to support sustainable development is also a key issue that this paper aims to address.

The Economic Circle encompassing Chengdu and Chongqing in China is situated at the juncture of the “One Belt, One Road” Initiative and the Yangtze River Economic Zone. It serves as the origin of the new land-sea corridor situated in the western region and possesses distinctive benefits in linking China’s southwestern and northwestern territories, as well as East Asia, Southeast Asia, and South Asia. Building the CC-DEC and establishing a pivotal growth hub that fosters nationwide high-quality development represents a significant strategic plan to enhance the regional economic configuration in the contemporary era. It also constitutes a pivotal endeavor to expedite the establishment of a novel development paradigm, where the domestic cycle holds prominence, and the domestic and international cycles mutually reinforce one another. The promotion of the CC-DEC in China holds strategic significance in fostering coordinated regional development and constructing a regional economic configuration distinguished by mutually beneficial advantages and superior-quality progress. In this context, accurately forecasting the logistics demand of the CC-DEC in China becomes exceedingly important.

Among the diverse prediction methodologies employed, the support vector regression model distinguishes itself through its superior efficacy in comparison to alternative forecasting models. The applications of this machine learning technique in diverse fields are outlined below. Support Vector Regression (SVR) is commonly used for time series forecasting, wind power forecasting and electricity load forecasting, among others. Different SVR algorithms have been utilized for time series forecasting in various fields, and their performance has been compared to radial basis function (RBF) neural networks and backpropagation (BP) neural networks (Müller et al., (1997); Francis, Lijuan (2001)). The results indicate that SVR outperforms RBF neural networks and BP neural networks.

In 2016, Yang, X., along with colleagues (Yang, Lo (2016)), introduced a wind speed prediction model utilizing SVR and assessed its accuracy with real-world data. Li, L.L. (Li et al. 2021) integrated an enhanced dragonfly algorithm with a support vector machine to devise a hybrid model for predicting short-term wind power output. In the study conducted by Fan and his team (Fan et al. 2021), a short-term load forecasting model was put forward, which combines support vector regression (SVR), a grey mutation model (GM(1,1)), and random forest (RF) machine learning methodologies. In the work by Li and his colleagues (Li et al. 2021), a hybrid version of the improved cuckoo search algorithm (HICS) was introduced to fine-tune the hyperparameters of support vector regression (SVR), ultimately aiming to enhance short-term wind power output predictions (dubbed as HICS-SVR). In their 2019 research, Duan, J., and his team (Duan et al., (2019)) introduced a prediction model utilizing support vector regression (SVR) that is grounded in a hybrid maximum entropy criterion. utilized least squares support vector machines (LSSVM) for the purpose of forecasting short-term electricity load. Guillermo, S.B. et al. (Guillermo et al., (2016)) introduced a combined approach for forecasting wind speed, which is grounded in support vector regression, utilizing genetic algorithms to fine-tune the parameters of support vector regression. Suykens, J.A.K. et al. (Suykens et al., (2001)) introduced a method for optimizing the control of least squares support vector machines. Santamaría-Bonfil, G. et al. (Santamaría-Bonfil et al., (2016)) presented a hybrid technique utilizing Support Vector Regression (SVR) for predicting wind speed, wherein the genetic algorithm is employed to optimize the SVR parameters. These studies highlight the significant progress made in applying SVR to various prediction tasks, including time series, wind speed, wind power, and electricity load forecasting. The findings consistently demonstrate the effectiveness and potential of SVR in these domains.

Research on Logistics Demand Prediction has reached a mature stage, with numerous scholars employing different models and indicator systems to predict logistics demand. The following summarizes the research findings of several scholars in the field. Yan, P. et al. (Yan et al., (2019)) introduced a forecasting model that incorporates a combined approach, integrating the grey model. This model takes into account the trends and periodicity of logistics demand, resulting in relatively accurate forecasting results. Huang, L. (Huang et al., (2023)) employed a backpropagation (BP) neural network technique for the purpose of forecasting regional logistics demand. Cao, Z.Q. et al. (Cao et al., (2018)) utilized a genetic algorithm in conjunction with a support vector regression (SVR) model for the prediction of regional logistics demand. The parameters of the support vector regression model were optimized utilizing a genetic algorithm approach, leading to enhanced prediction accuracy. The research findings demonstrated that this method effectively forecasts regional logistics demand. Qi, F. et al. (Qi et al., (2010)) proposed a hybrid method combining grey model, artificial neural network, and other learning and analysis techniques for the purpose of predicting the logistics demand within ZheJiang Province. The findings indicated that the introduced model surpasses individual models, demonstrating superior accuracy and robustness in forecasting logistics demand. Wang J. et al. proposed a comprehensive fuzzy membership function integrated with the SVR model (Wang et al., (2016)), incorporates both distance and time data of the samples, thereby improving the precision of the model. The literature (Pei (2008); Sun, Pan (2014)) utilized the concept of Support Vector Data Description (SVDD) to construct a hyper-sphere with the minimum radius that contains as many sample data points as possible, thereby improving the fuzzy membership function and enhancing the precision of the Fuzzy Support Vector Regression Machine. These studies highlight the advancements in Logistics Demand Prediction, with each model offering unique benefits and improved prediction accuracy. The integration of different models and algorithms has proven effective in capturing the complexities of logistics demand and providing more reliable forecasts.

The support vector regression machine offers several advantages over other methods, including its ability to handle high-dimensional data, strong generalization capabilities, suitability for small sample sizes, capacity to address nonlinear problems, and robustness and interpretability. Given that the Logistics Demand Prediction problem in the CC-DEC in China is nonlinear and involves small sample data, the predictive model chosen is the support vector regression machine in this paper. This study aims to create a logistics demand forecasting model by integrating fuzzy logic and the Adam optimization algorithm, with the goal of enhancing the predictive accuracy of conventional models. Additionally, it will analyze the factors influencing logistics demand within the CC-DEC, with a focus on the impact of low-carbon indicators, providing insights for policy and strategic decisions in the logistics sector and how to achieve green logistics.

Compared to other studies on logistics demand forecasting methods, the innovations of this paper are threefold. First, our research presents an innovative method by combining fuzzy logic with the Support Vector Regression (SVR) model, subsequently refined through the application of the Adam optimization algorithm. This integration is a significant departure from traditional SVR models, enhancing the prediction accuracy by accounting for the inherent uncertainty and complexity in logistics demand data. Second, this paper establishes a unique Logistics Demand Prediction index system. Notably, it includes the intensity of energy consumption in logistics and the intensity of carbon dioxide emissions in logistics, which are closely linked to carbon peak and carbon neutrality. This approach allows for the establishment of a Logistics Demand Prediction index system for the CC-DEC in China from a low-carbon perspective. Third, the use of the Adam optimization algorithm to optimize the FSVR model represents a significant methodological advancement. Adam’s ability to dynamically adjust learning rates based on historical gradients leads to faster convergence and improved performance, which represents a fresh application within the realm of logistics demand forecasting.

The organization of this paper is delineated as follows. In Section 2, a brief overview of Support Vector Regression (SVR), Backpropagation neural networks (BPNN), and the Fuzzy Support Vector Regression Machine optimized by the Adam algorithm is provided. In section 3, the Logistics Demand Prediction index system in the CC-DEC in China is presented. Section 4 elaborates on the empirical research process. Section 5 discusses the research findings and elaborates on the practical applications of the model as well as the directions for future research. Finally, Section 6 provides the conclusion of the paper.

Research Methodology

Given the outstanding efficacy of the Support Vector Regression (SVR) relative to other predictive models, along with its applicability in solving non-linear problems and handling small sample data, this study utilizes the Fuzzy Support Vector Regression Machine model based on the Adam optimization algorithm to forecast logistics demand in the CC-DEC in China. The FSVR-AD integrates a fuzzy membership function into the conventional support vector regression machine, resulting in a fuzzy support vector regression machine. Additionally, the Adam optimization algorithm is employed to optimize the fuzzy support vector regression machine. In this section, the FSVR-AD, SVR, and BP neural network are employed for Logistics Demand Prediction in the CC-DEC in China. The SVR and BP neural network are compared with the FSVR-AD proposed in this paper. This part of the paper will offer a summary of the theoretical background underpinning these three methodologies.

Traditional support vector regression machine

It is assumed that the training sample set consists of \({\rm{m}}\) samples \(({{\rm{x}}}_{{\rm{i}}},{{\rm{y}}}_{{\rm{i}}})\in {{\rm{R}}}^{{\rm{n}}}\times {\rm{R}}\) (\({\rm{i}}=1,2,\,\cdot \cdot \cdot\,,{\rm{m}}\)), where \({{\rm{x}}}_{{\rm{i}}}\) is the input variable and \({{\rm{y}}}_{{\rm{i}}}\) is the corresponding output variable. Following the \({\rm{\varepsilon }}\) linear insensitive loss function, Vapnik proposed a support vector regression machine (SVR) based on the SVM method. The linear regression function in the high-dimensional feature space can be expressed as:

$${\rm{f}}({\rm{x}})={\rm{wx}}+{\rm{b}}$$
(2.1)

In practice, it is often difficult to directly determine the appropriate \({\rm{\varepsilon }}\) to ensure that most of the data will fall within the interval bands, so the slack variable \({{\rm{\xi }}}_{{\rm{i}}}\) and \({{\rm{\xi }}}_{{\rm{i}}}^{* }\) is introduced and the regression problem is transformed into an optimization problem:

$$\begin{array}{c}\mathop{\min }\nolimits_{{\rm{w}},{\rm{b}}}\,\frac{1}{2}{\Vert {\rm{w}}\Vert }^{2}+{\rm{c}}\mathop{\sum}\limits_{{\rm{i}}=1}^{{\rm{m}}}{\xi }_{{\rm{i}}}+{\xi }_{{\rm{i}}}^{\ast }\\ {\rm{s}}.\,{\rm{t}}.\,\left\{\begin{array}{c}{{\rm{y}}}_{{\rm{i}}}-{{\rm{wx}}}_{{\rm{i}}}-{\rm{b}}\le \varepsilon +{\xi }_{{\rm{i}}}\\ -{{\rm{y}}}_{{\rm{i}}}+{{\rm{wx}}}_{{\rm{i}}}+{\rm{b}}\le \varepsilon +{\xi }_{{\rm{i}}}^{\ast }\\ {\xi }_{{\rm{i}}}\ge 0,{\xi }_{{\rm{i}}}^{\ast }\ge 0,\,{\rm{i}}\,=1,2,\cdots ,{\rm{m}}.\end{array}\right.\end{array}$$
(2.2)

where \({\rm{C}}\) is the penalty factor, the larger the value, the larger the penalty for samples with training error greater than \({\rm{\varepsilon }}\). \({\rm{\varepsilon }}\) specifies the training error requirement for the regression function, where a smaller \({\rm{\varepsilon }}\) corresponds to a smaller training error for the regression function.

BP neural network model

The BP (Back Propagation) neural network, proposed by a group of scientists led by Rumelhart D.E. (Rumelhart et al., (1986)), is a multi-layer feedforward network trained using the error backpropagation algorithm. It stands as one of the most prevalently employed neural network architectures. Its learning rule utilizes gradient descent and continuously adjusts the network’s weights and thresholds through backpropagation to minimize the sum of squared errors. The topology of the BP neural network model includes an input layer, hidden layer(s), and an output layer. The algorithm flowchart of the BP (Back Propagation) neural network is shown as Fig. 1.

Fig. 1: BP neural network algorithm flowchart. It contains the detailed operation process of the BP neural network.
figure 1

Where x is the input variable, y is the output variable, and w and b are the weights and thresholds respectively.

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The detailed operational process of the BP (Backpropagation) neural network encompasses the following steps: ①Initialize the weights and thresholds randomly; ②Provide input values to the input layer; ③Forward propagate the inputs through the network, calculating the output values of each neuron in the hidden layers and the output layer; ④Calculate the error between the desired output and the actual output; ⑤Backpropagate the error through the network, adjusting the weights and thresholds based on the gradient descent algorithm; ⑥Repeat steps ③ to ⑤ for a specified number of iterations or until the desired level of accuracy is achieved; ⑦Evaluate the performance of the trained network using test data; ⑧If the performance is satisfactory, the training is complete; otherwise, go back to step ① and repeat the process.

To introduce nonlinearity into the model, an activation function will be integrated into the backpropagation neural network algorithm. The BP neural network algorithm frequently employs either the Sigmoid function or the linear activation function. The computation of a basic log-Sigmoid function can be performed utilizing formula (2.3):

$$f\left(x\right)=\frac{1}{1+{e}^{-x}}$$
(2.3)

The domain of \(x\) encompasses all real numbers. The value of the function falls within the interval from 0 to 1. In specific applications, additional parameters can be incorporated to regulate the curve’s position and configuration.

The Backpropagation Neural Network (BPNN) has found extensive application across diverse predictive modeling tasks, including stock market forecasting, traffic flow prediction, disease prediction, and more. Considering the broad applicability and proven reliability of this model within the realm of forecasting, we will employ the Backpropagation Neural Network (BPNN) for predicting the scale of logistics demand in the CC-DEC in China, in order to compare its performance with the proposed FSVR-AD.

GM(1,1) model

The GM(1,1) model, often referred to as the Grey Model, is a mathematical model used for forecasting the behavior of a system based on incomplete or partial data. It falls within the category of Grey System Theory, a framework established by Chinese scholar Deng J.L. in 1982 (Deng 1982). The GM(1,1) model is a first-order, single-variable model. It uses a small number of data points to generate predictions by fitting a differential equation to the data. If the original data column is \({{\rm{x}}}^{(0)}=({{\rm{x}}}^{\left(0\right)}\left(1\right),{{\rm{x}}}^{\left(0\right)}\left(2\right),\,\cdot \cdot \cdot\,{,{\rm{x}}}^{\left(0\right)}\left({\rm{n}}\right)).\) The one-time cumulative generated sequence is \({{\rm{x}}}^{(1)}=({{\rm{x}}}^{\left(1\right)}\left(1\right),{{\rm{x}}}^{\left(1\right)}\left(2\right),\,\cdot \cdot \cdot\, {,{\rm{x}}}^{\left(1\right)}\left({\rm{n}}\right)),\) where \({{\rm{x}}}^{\left(1\right)}\left({\rm{k}}\right)={{\rm{x}}}^{\left(1\right)}\left({\rm{k}}-1\right)+{{\rm{x}}}^{\left(0\right)}\left({\rm{k}}\right)\). \({{\rm{z}}}^{(1)}=({{\rm{z}}}^{\left(1\right)}\left(2\right),{{\rm{z}}}^{\left(1\right)}\left(3\right),\,\cdot \cdot \cdot\, {,{\rm{z}}}^{\left(1\right)}\left({\rm{n}}\right))\) is a generated sequence for the adjacent of \({{\rm{x}}}^{(1)}.\) The GM(1,1) grey differential formula is

$${x}^{\left(0\right)}\left(k\right)+a{z}^{\left(1\right)}(k)=b$$
(2.4)

It’s a whitening formula is

$$\frac{d{x}^{(1)}}{{dt}}+a{x}^{(1)}=b$$
(2.5)

Calculate \(a,b\) and it’s time response sequence can be got as:

$${\hat{x}}^{\left(1\right)}\left(k+1\right)=\left({x}^{\left(0\right)}\left(1\right)-\frac{b}{a}\right){e}^{-{ak}}+\frac{b}{a},$$
$$k=1,2,\cdots ,n-1$$
(2.6)

So the predicted value is

$${\hat{x}}^{(0)}(k+1)={\hat{x}}^{\left(1\right)}\left(k+1\right)-{\hat{x}}^{\left(1\right)}\left(k\right),$$
$$k=1,2,\cdots ,n-1.$$
(2.7)

The GM(1,1) model is particularly useful in scenarios where traditional statistical methods may not be applicable due to limited data availability or insufficient information (Jia et al., (2020)).

Fuzzy support vector regression machine approach based on Adam optimization

This section begins with an introduction to the notion of fuzzy membership grade. The model known as the Fuzzy Support Vector Regression Machine (FSVR) is constructed through adding an association function to illustrate the significance of each sample in relation to the error component of the conventional SVR. The choice of the affiliation function \({S}_{i}\) is very important for the FSVR. The advantage of incorporating a fuzzy membership function into the Support Vector Regression (SVR) model is that it enables the model to handle uncertainties and nonlinear relationships in the data more effectively. Compared to traditional SVR, this improvement enhances the prediction accuracy. To optimize the FSVR model, we employ the Adam optimization algorithm to fine-tune the weight vector \(w\) and bias \(b\) of the model, establishing the FSVR-AD. The Adam algorithm is a widely-used optimization technique that converges faster and learns more effectively than other adaptive learning rate algorithms, while simultaneously mitigating issues like sluggish convergence and diminishing learning rates, or mitigating high variability in parameter adjustments, which can cause substantial oscillations in the loss function. This section delves into a comprehensive explanation of the algorithmic workflow of the FSVR-AD.

This paper adopts a comprehensive fuzzy membership function (Wang et al., (2016)), including the distance and timing information of the sample, so that the fuzzy SVR can more accurately describe the importance of each sample, consequently enhancing the prediction accuracy. In the support vector machine data domain method, for the given training set \(X=\left\{{x}_{1},{x}_{2},\cdots ,{x}_{m}\right\}\), \({x}_{i}\in {R}^{n}\) in the input space. According to the literature (Pei (2008); Sun, Pan (2014)), apply the concept of Support Vector Data Description (SVDD) to construct a hyper-sphere with the minimum radius that contains as many sample data points as possible, establishing a new fuzzy membership function. The definition of the Euclidean distance from any point \({x}_{i}\) in the input space to the center of the hypersphere is:

$$D({x}_{i})=\Vert {x}_{i}-{x}_{R}\Vert$$
(2.8)

where \({x}_{R}=\frac{{\sum }_{i=1}^{m}{x}_{i}}{m}\) is the the center of the hypersphere, \(R=\frac{\mathop{\sum }\nolimits_{i=1}^{m}D({x}_{i})}{m}\) is the radius of the hypersphere. Let \({D}_{\max }=\max \left(D\left({x}_{i}\right)\left|{x}_{i}\in X\right.\right)\) and \({D}_{\min }=\min (D({x}_{i})|\)

\({x}_{i}\in X)\) be the maximum and minimum distances from the samples to the center of the hypersphere, respectively. Therefore, the fuzzy membership function containing distance information is obtained as:

$${\omega }_{1i}=\left\{\begin{array}{c}{\left(1-\frac{D\left({x}_{i}\right)-{D}_{\min }}{{D}_{\max }-{D}_{\min }}\right)}^{Q}+\tau ,R \,<\, D({x}_{i})\,\le\, {D}_{\max }\\ 1-\frac{D\left({x}_{i}\right)-{D}_{\min }}{{D}_{\max }-{D}_{\min }},{D}_{\min }\,\le\, D({x}_{i})\,\le\, R\end{array}\right.$$
(2.9)

where \(\tau \,<\, 1\) is a adequately small positive number, and \(Q\ge 2\). The representation of temporal information in the samples is as follows.

$${\omega }_{2i}=\frac{1}{1+\exp \left(\alpha -2\times \alpha \times \frac{i}{n}\right)}$$
(2.10)

where \(\alpha \,>\, 0\) is the parameter that controls the rate of weight rise. The final fuzzy affiliation function is denoted as \({S}_{i}=\lambda {\omega }_{1i}+\mu {\omega }_{2i}\), where \(\lambda +\mu =1\), so that the resulting affiliation function contains both the distance information of the samples and the temporal information of the samples.

FSVR is based on support vector regression by introducing the affiliation function \({S}_{i}\left(0 \,<\, {S}_{i}\le 1\right)\), which is used to indicate the importance level of the \(i-{th}\) sample. The set of training samples is transformed into training samples with the factors of the affiliation function and \({S}_{i}{\xi }_{i}\) into relaxation factors with different weights, thus forming a fuzzy support vector machine. At this point the optimization problem for solving the optimal hyperplane is transformed into:

$$\begin{array}{c}\mathop{{\min }}\limits_{w,b}\,\frac{1}{2}{\Vert w\Vert }^{2}+C\mathop{\sum }\limits_{i=1}^{m}{S}_{i}({\xi }_{i}+{\xi }_{i}^{\ast })\\ {\rm{s}}.\,{\rm{t}}.\,\left\{\begin{array}{c}{y}_{i}-w{x}_{i}-b\le \varepsilon +{\xi }_{i}\\ -{y}_{i}+w{x}_{i}+b\le \varepsilon +{\xi }_{i}^{\ast }\\ {\xi }_{i}\ge 0,{\xi }_{i}^{\ast }\ge 0\end{array}\right.\end{array}$$
(2.11)

Let \(L\left(w,{x}_{i},{y}_{i}\right)=\max (\left|{w}^{T}{x}_{i}+b-{y}_{i}\right|-\varepsilon ,0)\) denote the loss function of the SVR. The optimization objective function of FSVR used in this study is shown as formula (2.12).

$$\mathop{\min }\limits_{w,b}f\left(w,b\right)=\frac{1}{2}{w}^{T}w+\mathop{\sum }\limits_{i=1}^{m}C{S}_{i}*$$
$$\max \left(\left|{w}^{T}{x}_{i}+b-{y}_{i}\right|-\varepsilon ,0\right)$$
(2.12)

To optimize the weight vector \(w\) and bias \(b\) of the FSVR, we employ the Adam optimization algorithm to tackle the optimization challenge presented in equation (12). And we can get the optimal classification decision function \(f\left(x\right)={wx}+b\) to predict.

The Adam optimization algorithm is used inthe above FSVR in this paper to predict the CC-DEC in China. The proposed model in this paper is the FSVR, which is based on the Adam optimization algorithm. The flowchart of the FSVR-AD is shown in Table 1.

Table 1 FSVR-AD Algorithm.
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Based on the Adam optimization algorithm, the algorithm steps for the FSVR-AD are as shown in the table above. The Adam algorithm, i.e., Adaptive Moment Estimation method, is a stochastic optimization method proposed by Kingma, D.P. (Kingma, Ba (2014)). The Adam optimization algorithm is a stochastic optimization technique that builds upon the idea of the gradient descent algorithm. It integrates aspects from both the Adagrad and RMSProp algorithms by employing both first-order momentum and second-order momentum. Adam’s algorithm computes based on the first-order derivative of the objective function, which ensures relatively low computational volume. In this research paper, we utilize Adam’s algorithm for optimizing the weight vector \(w\) and bias \(b\) in the SVR. We now give the gradient of \(w\) with respect to the objective function as

$${\nabla }_{W}f\left(w,b\right)=\frac{\partial f\left(w,b\right)}{\partial w}=w+\mathop{\sum }\limits_{i=1}^{m}C{S}_{i}\frac{\partial L\left(\varPhi \left({x}_{i}\right),{y}_{i}\right)}{\partial w}$$
(2.13)

where

$$\frac{\partial L({x}_{i},{y}_{i})}{\partial w}=\left\{\begin{array}{l}0,\,if\,|{w}^{T}{x}_{i}+b-{y}_{i}|-\varepsilon \,\le\, 0\\ {x}_{i},\,if\,|{w}^{T}{x}_{i}+b-{y}_{i}|-\varepsilon \,>\, 0\end{array}\right.$$

and the gradient of \(b\) with respect to the objective function as

$${\nabla }_{{\rm{b}}}f\left(w,b\right)=\frac{\partial f\left(w,b\right)}{\partial b}=\mathop{\sum }\limits_{i=1}^{{\rm{m}}}C{S}_{i}\frac{\partial L\left({x}_{i},{y}_{i}\right)}{\partial b}$$
(2.14)

where

$$\frac{\partial L({x}_{i},{y}_{i})}{\partial b}=\left\{\begin{array}{c}0,\,if\,|{w}^{T}{x}_{i}+b-{y}_{i}|-\varepsilon \,\le\, 0\\ 1,\,if\,|{w}^{T}{x}_{i}+b-{y}_{i}|-\varepsilon \,>\, 0\end{array}\right.$$

The optimization process of Adam’s algorithm in gradient descent is given as Table 2. In Table 2, \({\rm{t}}\) is the number of steps to be updated, \({\rm{\rho }}\) is the learning rate, which is used to control the step size, \({\rm{f}}\left({\rm{w}},{\rm{b}}\right)\) is the random objective number with \({\rm{w}}\) and b, which is generally referred to as the loss function, \({{\rm{g}}}_{{\rm{t}}}\) represents the gradient derived from the objective function \({\rm{f}}\left({\rm{w}},{\rm{b}}\right)\), \({{\rm{\beta }}}_{1}\), \({{\rm{\beta }}}_{2}\) are the first-order moment attenuation coefficients and second-order moment attenuation coefficients, respectively, and the requirement of \({{\rm{\beta }}}_{1},{{\rm{\beta }}}_{2}\in \left[0,1\right)\), \({{\rm{m}}}_{{\rm{t}}}\) is the first-order moments of the gradient \({{\rm{g}}}_{{\rm{t}}}\), \({{\rm{v}}}_{{\rm{t}}}\) is the first-order moments of the gradient, the initial value of \({{\rm{m}}}_{{\rm{t}}}\), \({{\rm{v}}}_{{\rm{t}}}\), and \({\rm{t}}\) is all \(0\), and the bias corrections of \({{\rm{m}}}_{{\rm{t}}}\) are \({\hat{{\rm{v}}}}_{{\rm{t}}}\) and is the bias correction of \({{\rm{v}}}_{{\rm{t}}}\).The default settings for the hyperparameters \({\rm{\rho }},{{\rm{\beta }}}_{1},{{\rm{\beta }}}_{2},{\rm{\xi }}\) are \({\rm{\rho }}\) = 0.001, \({{\rm{\beta }}}_{1}\) = \(0.9\), \({{\rm{\beta }}}_{2}\) = 0.999, and \({\rm{\xi }}=1{0}^{-8}\).

Table 2 Adam optimization algorithm.
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Construction of indicator system for Logistics Demand Prediction

In order to utilize the Fuzzy Support Vector Machine Regression method based on the Adam optimization algorithm for forecasting the logistics demand of the CC-DEC in China, this section requires the establishment of an indicator system for forecasting logistics demand. Drawing upon data sourced from the China Energy Statistics Yearbook, the logistics industry in China accounted for 8.29% of total energy consumption and emitted 1.016 billion tons of carbon dioxide in 2020. These statistics underscore the significant energy consumption and carbon dioxide emissions attributed to the logistics sector, leading to significant environmental impact. Consequently, achieving the goals of “carbon peak” and “carbon neutral” in China’s economy necessitates the transition towards low-carbon and green sustainable develop-ment within the logistics industry. Serving as a conduit linking manufacturing enterprises with consumers, the logistics sector is a vital component of daily life and plays a pivotal role in the economic growth of China.

Referring to the studies of several scholars (Tang (2022); Li et al., (2015); Yu et al., (2015); Jiang et al., (2018)) and the actual situation of CC-DEC in China, this paper, based on the principles of scientificity, comprehensiveness, measurability and accessibility, selects a total of 16 indexes from the two dimensions of logistics and economy, including two indexes closely related to the low-carbon goal, namely, logistics energy consumption intensity (X1) and logistics carbon dioxide emission intensity (X2), and establishes a Logistics Demand Prediction indicator system for CC-DEC in China from the perspective of low-carbon. The data in this paper are sourced from China Statistical Yearbook, Sichuan Statistical Yearbook, Chongqing Statistical Yearbook and China Energy Statistical Yearbook. In this paper, freight transportation volume (Y) is taken as the output indicator to measure the regional logistics demand, and other 15 indicators are taken as the input indicators.

The seven input indicators are logistics energy consumption intensity (X1), logistics carbon dioxide emission intensity (X2), freight turnover (X3), postal and telecommunication business volume (X4), logistics fixed investment (X5), the number of people working in the logistics industry (X6), and the number of highway mileage (X7). For the economic aspect, 8 input indicators are selected, namely, Gross Regional Product (X8), Total Retail Sales of Consumer Goods (X9), Total Imports and Exports (X10), Per Capita Disposable Income of Urban Residents (X11), Per Capita Consumption Expenditures of Urban Residents (X12), the proportion of the primary industry (X13), the proportion of the secondary industry (X14), and the proportion of the tertiary industry (X15). The indicators for predicting logistics demand in the dual-city economic circle are listed in Table 3.

Table 3 Chengdu-Chongqing region logistics demand indicator system table.
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The cities of Chongqing and Chengdu account for about 90% of the population and economic total of the Sichuan-Chongqing region, while the data indicators for the single city of Chengdu are not available, so the data for Sichuan and Chongqing are chosen to replace the data for the CC-DEC in China based on the availability of data. As per the data released by the National Bureau of Statistics and the National Standards Bureau in 1994, the logistics industry belongs to the warehousing, transportation, and postal industries in the tertiary sector, and the GDP of the transportation, storage and postal industry is used to reflect the total output value of production in the logistics industry.

Based on the energy consumption figures documented in the China Energy Statistical Yearbook concerning the logistics industry, the indicators of logistics energy intensity(\({X}_{1})\) and logistics CO2 emission(\({X}_{2})\) intensity can be calculated., the process of calculating the indicators of logistics energy consumption intensity and logistics CO2 emission intensity is as follows:

$${\rm{Logistics}}\; {\rm{energy}}\; {\rm{intensity}}=\,\frac{{\rm{Logistics}}\; {\rm{energy}}\; {\rm{concumption}}}{{\rm{Value}}\; {\rm{added}}\; {\rm{of}}\; {\rm{the}}\; {\rm{logistics}}\; {\rm{industry}}}$$

The energy consumption of regional logistics corresponds to the cumulative quantity of various energy inputs utilized within the logistics system of the respective area. According to China Energy Statistical Yearbook, the logistics system in CC-DEC in China consumes nine types of energy: raw coal, gasoline, kerosene, diesel, coke, natural gas, liquefied natural gas, fuel oil and electricity. In order to determine the aggregate amount of energy consumed by the logistics sector in the CC-DEC, it is necessary to convert the quantities of these 9 types of energy sources into the quantities of standard coal in accordance with their respective conversion coefficients, which are referenced in Appendix 4 of the China Energy Statistics Yearbook 2018.

$${\rm{Logistics}}\; {\rm{CO}}2\,{\rm{emission}}\; {\rm{intensity}}=\,\frac{{\rm{CO}}2\,{\rm{consumption}}\; {\rm{in}}\; {\rm{the}}\; {\rm{logistics}}\; {\rm{sector}}}{{\rm{Value}}\; {\rm{added}}\; {\rm{of}}\; {\rm{the}}\; {\rm{logistics}}\; {\rm{industry}}}$$

Regional logistics carbon dioxide consumption refers to the total CO2 emissions from the various energy sources consumed during logistics operations. The overall carbon emissions generated by the logistics industry are computed by multiplying the consumption of the nine primary energy sources utilized by the logistics sector by their corresponding carbon dioxide emission coefficients. The formula for calculating CO2 emissions is:

$${\rm{Q}}=\mathop{\sum }\limits_{{\rm{i}}=0}^{{\rm{n}}}{{\rm{Q}}}_{{\rm{i}}}=\mathop{\sum }\limits_{{\rm{i}}=0}^{{\rm{n}}}{{\rm{E}}}_{{\rm{i}}}* {\rm{NC}}{{\rm{V}}}_{{\rm{i}}}* {\rm{CE}}{{\rm{F}}}_{{\rm{i}}}* {\rm{CO}}{{\rm{F}}}_{{\rm{i}}}* 44/12$$
(3.15)

where Q represents the total amount of carbon dioxide emissions, i represents the type of energy, including raw coal, gasoline, kerosene, diesel, coke, natural gas, liquefied natural gas, fuel oil, and electricity, Ei represents the consumption of the ith type of energy, NCVi represents the average heat output at a lower temperature level, CEFi represents the carbon content per unit of heat value, COFi represents carbon oxidization factor, and 44/12 represents the molar mass of carbon dioxide. Among the nine main energy sources inputted into the logistics system, electricity is a secondary energy source, which requires the application of the internationally used conversion factor for coal power generation in the calculation process to estimate the CO2 emissions generated by electricity by converting the raw coal used for electricity into standard coal. The coefficients for converting standard coal for various energy sources and the CO2 emission coefficients are listed in Table 4.

Table 4 CO2 Emission Factors for Standard Coal from Various Energy Sources.
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Table 5 shows the values of all the indicators for the logistics demand forecast of the CC-DEC in China from 2005 to 2021, encompassing the metrics for logistics energy consumption intensity and logistics carbon dioxide emission intensity, which show the low-carbon perspective.

Table 5 All Indicator Values of Logistics Demand Forecast for CC-DEC in China.
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Research on the prediction of logistics demand in the CC-DEC in China

The objective of this research is to estimate the magnitude of the demand for logistical services within CC-DEC in China, emphasizing a low-carbon approach. The process of empirical research is illustrated in Fig. 2. Firstly, a Logistics Demand Prediction indicator system for the CC-DEC in China is established based on the collected data. Then, a fuzzy support vector regression (FSVR) model is constructed as the prediction model. The Adam optimization algorithm is employed to fine-tune the model’s weight vector and bias parameters. The FSVR-AD model is utilized for forecasting the logistics demand within the CC-DEC in China, and its predictions are compared against those of the SVR and BPNN models. The best-performing model is selected to forecast the logistics demand of the CC-DEC in China for the years 2022 to 2026.

Fig. 2: Empirical research process.
figure 2

It encompasses the entire experimental procedure conducted in this work.

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Comparison of logistics demand prediction models

In this paper, we have selected Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and the Coefficient of Determination (R²) as metrics to assess the performance of the model, and the specific formulas are as follows.

$${MAPE}=\frac{1}{m}\mathop{\sum }\limits_{i=1}^{m}\frac{\left|{y}_{i}-{y}_{j}\right|}{{y}_{j}}\times 100 \%$$
(4.16)
$${RMSE}=\sqrt{{\begin{array}{cc}\frac{1}{m} & {\sum }_{i=1}^{m}\left({y}_{i}-{y}_{j}\right)\end{array}}^{2}}$$
(4.17)
$${MAE}=\frac{1}{m}\mathop{\sum }\limits_{i=1}^{m}\left|{y}_{i}-{y}_{j}\right|$$
(4.18)
$${R}^{2}=1-\frac{{\sum }_{i=1}^{m}{\left({y}_{i}-{y}_{j}\right)}^{2}}{{\sum }_{i=1}^{m}{\left({y}_{i}-\bar{y}\right)}^{2}}$$
(4.19)

Among them, RMSE indicates the degree of dispersion in the errors, with smaller values signifying better performance; MAPE reflects the overall effectiveness of the prediction method, and the smaller its value, the better; MAE represents the average of the absolute values of the prediction errors, and its value reflects the magnitude of the model’s accuracy, and the smaller its value, the better; The regression fitting curve’s quality of fit is represented by R2, with higher values indicating a superior match.

Given that the data utilized in this study consists of a small sample size, the test set and training set are not divided, and all available data points are employed for training the prediction model to obtain the forecasted values, which are used to evaluate the accuracy of the prediction model. The model combining Adam optimization algorithm and fuzzy support vector regression machine (FSVR-AD) proposed in this paper is benchmarked against the SVR and BP neural network models to predict the freight volume of CC-DEC in China from 2005 to 2021 correspondingly, and the results of this comparison are presented in Table 6.

Table 6 Model Evaluation Indicators.
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As obtained from Table 6, the RMSE of the FSVR-AD is 7001.901, which is smaller compared to the SVR and BPNN models, revealing that the FSVR-AD exhibits a more stable fit. The MAPE of the FSVR-AD is 0.027%, which is smaller than the SVR and BPNN models, evidencing that the FSVR-AD has a better prediction. The MAE of the FSVR-AD is 6255.315, which is smaller than the SVR and BPNN models, demonstrating that the FSVR-AD is more accurate. The R2 of the FSVR-AD is 0.987, which is higher than that of the SVR and BPNN models, indicating that the FSVR-AD is better fitted. This shows that the FSVR-AD is more effective and better than the other two models.

The three models, FSVR-AD, SVR and BPNN, are utilized to forecast the freight volume of the CC-DEC in China from 2005 to 2021 respectively, and the predicted value of the freight volume obtained from the three models is plotted against the real value of the freight volume in Fig. 3.

Fig. 3: Comparison of true value of freight volume with model predictions.
figure 3

SVR and BPNN are the compared models. The data is sourced from the China Statistical Yearbook, Chongqing Statistical Yearbook, Sichuan Statistical Yearbook, and China Energy Statistical Yearbook.

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The three models, FSVR-AD, SVR and BPNN, respectively predict the freight traffic in the CC-DEC in China from 2005 to 2021, and the predicted values obtained are shown in the Table 7. As obtained from Fig. 3 and Table 7, the model that combines the Adam optimization algorithm and the FSVR proposed in this paper, i.e., the FSVR-AD model exhibits the best fitting performance and most accurately reflects the actual trend of the freight volume of the CC-DEC in China from 2005 to 2021. The real value of the freight volume of the CC-DEC in China showed an upward trend from 2005 to 2021, and in 2014 showed a slight decline, the real value of freight traffic in the CC-DEC in China continued to rise from 2014 to 2018, and again showed a downward trend from 2018 to 2019, and the freight traffic was more stable in the three years from 2019 to 2021.

Table 7 Comparison of the real value of freight volume with the model predicted value.
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Forecast of logistics demand in the CC-DEC in China from 2022 to 2026

The FSVR-AD model has shown superior performance in Logistics Demand Prediction, the FSVR-AD model will serve as a tool for forecasting logistics demand of the CC-DEC in China from 2022 to 2026.

In order to procure the forecasted values of logistics demand for the CC-DEC in China from 2022 to 2026 using the FSVR-AD model, it is essential to gather the values of all explanatory variables for the period spanning from 2022 to 2026. The GM(1,1) model leverages a limited amount of data to construct a forecasting model grounded in grey prediction theory, resulting in relatively high prediction accuracy. Therefore, the GM(1,1) model will be used to forecast the values of the explanatory variables for the next five years. First, the GM(1,1) model is used to forecast the values of the 15 explanatory variables in the logistics forecast indicator system proposed in this paper for the years 2022–2026. Then, based on the predicted values of the explanatory variables obtained from the GM(1,1) model, the freight volume of the CC-DEC in China for the years 2022–2026 is forecasted, resulting in the logistics demand forecast for the CC-DEC in China from 2022 to 2026. Based on the aforementioned forecasting steps, the predicted values for the freight volume in the CC-DEC in China from 2022 to 2026 are obtained and presented in Table 8 and Fig. 4.

Table 8 Forecasted values for all indicators from 2022 to 2026.
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Fig. 4: FSVR-AD model forecasted values for 2022–2026.
figure 4

SVR and BPNN are the compared models. The data is sourced from the China Statistical Yearbook, Chongqing Statistical Yearbook, Sichuan Statistical Yearbook, and China Energy Statistical Yearbook.

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Table 8 presents the predicted values from 2022 to 2026 for variables X1-X15 obtained using the GM(1,1) model. Furthermore, the table also includes the predicted values for the freight volume within China’s CC-DEC, covering the years from 2022 to 2026, based on the forecasted values of the 15 explanatory variables obtained using the GM(1,1) model, are included utilizing the FSVR-AD.

Fig. 4 offers a contrast between the estimated and observed values of freight volume for the CC-DEC in China from 2005 to 2021 obtained by FSVR-AD, SVR, and BPNN meths, as well as the predicted values of freight volume for the CC-DEC in China from 2022 to 2026 by the best-performing FSVR-AD.

Analysis of factors influencing the demand in the CC-DEC in China

Based on the weight vectors obtained from the FSVR-AD forecasted model run, the following histogram of indicator weights is shown as in Fig. 5. As evident from the figure presented above, the indicators with larger weights are freight turnover (X3), the number of logistics employees (X6), the proportion of the secondary industry (X14) and the number of highway mileage (X7), which indicates that freight turnover rate is the main factor influencing the logistics demand in the CC-DEC in China, the number of logistics employees, the share of the secondary industry and the number of highway mileage. The secondary sector primarily refers to the processing industry and manufacturing industry, including manufacturing, mining, heat, gas, water, electricity, production and supply industries, and construction, compared with the quota of the primary industry and the quota of the tertiary industry on the logistics demand of CC-DEC in China has a greater impact on the secondary industry for the transportation to provide energy, and closely related to logistics demand.

Fig. 5: Indicator weighting chart.
figure 5

It is the indicator weighting chart plotted from the feature index weight vector obtained by FSVR-AD.

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The weights of logistics energy consumption intensity (X1) and logistics carbon dioxide emission intensity (X2) added from a low-carbon perspective are all negative, indicating that the greater the logistics demand in CC-DEC in China, the lower the intensity of energy consumption and carbon dioxide emissions in the logistics sector, and that the improvement of logistics operation efficiency can effectively minimize the consumption of energy and emissions of carbon dioxide resulting from logistics transportation. Promoting the construction of intelligent logistics system in CC-DEC in China is an effective way to boost the productivity of logistics processes. Smart logistics achieved through advanced hardware and software solutions, Internet of Things, big data analytics and other intelligent methodologies, so that the logistics of each link of refinement, dynamization and visualization of the management, and improve the logistics system intelligent analysis, decision-making and automation of the operation of the implementation of the ability to refine the operational efficiency of logistics, while decreasing the intensity of consumption of energy and production of carbon dioxide emissions (Aliev et al., (2021); Kang et al., (2024); Yang, Lo (2016)).

Accelerating the construction of intelligent logistics system can maximize the value of massive logistics data, promote energy saving, emission reduction and sustainable development within the logistics industry, and serve a positive function in “carbon neutrality”.

Results and Discussion

Our results demonstrate that the FSVR-AD model outperforms both the traditional SVR and BPNN models in the aspect of forecast precision. The Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Coefficient of Determination (R²) scores for the FSVR-AD model were significantly lower and higher, respectively, indicating a more precise and reliable forecast when compared to the other models.

This is due to the fact that we incorporated a fuzzy membership function into the SVR model and optimized the model parameters using the Adam optimization algorithm. The advantage of using fuzzy membership functions in our model is that it enables the FSVR-AD model to handle uncertainties and nonlinear relationships in the data more effectively. Compared to traditional crisp set methods, this improves prediction accuracy. Adam is a representative of adaptive moment estimation, which adapts the learning rate for each parameter during training. This is particularly useful in our model because it allows for faster convergence and better performance.

The weights assigned to different indicators in the FSVR-AD model provide insights into their relative importance in influencing logistics demand. The integration of carbon-related indicators in our model also has important sustainability implications. By highlighting the relationship between logistics demand and carbon emissions, our model can help companies identify opportunities to reduce their carbon footprint. This could involve adopting more energy-efficient transportation modes, optimizing routes to reduce empty miles, or investing in green technologies.

While the FSVR-AD model has demonstrated superior performance in forecasting logistics demand within the CC-DEC, it is essential to acknowledge its limitations. The accuracy and reliability of the FSVR-AD model are inherently reliant on the quality and completeness of the input data. In regions where data collection is less systematic or where certain indicators are not tracked, the model’s predictive power may be compromised. The FSVR-AD model, like any regression model, is sensitive to the input variables used. Changes in the underlying assumptions or the inclusion of new variables could affect the model’s performance.

Despite these limitations, we believe that the FSVR-AD model has the potential to be generalized to other contexts with appropriate modifications. The core framework that combines fuzzy logic with support vector regression and optimizes it with the Adam algorithm can be employed for predicting demand in other regions or sectors, such as finance or healthcare. This could involve cross-validation with data from different regions or sectors, as well as sensitivity analyses to comprehend how alterations in input variables influence the model’s predictions.

The practical applications of the FSVR-AD model are multifaceted. Our model can serve as a decision-support tool for logistics planners, enabling them to anticipate demand fluctuations and make informed decisions about resource allocation, warehousing, and transportation strategies. The model’s consideration of carbon-related indicators can guide logistics companies in assessing the environmental impact of their operations and inform strategies to reduce their carbon footprint, aligning with global sustainability goals.

Future research endeavors can delve into the incorporation of real-time data streams, such as trends on social media platforms or data from IoT sensors, to elevate the model’s predictive capabilities and provide more timely insights for logistics planning. Additionally, exploring other advanced optimization schemes, such as particle swarm optimization or genetic algorithms, in combination with fuzzy logic, could further improve the performance of the model. To expand the scope of this research, potential collaborations with other researchers or industries will be considered. For instance, partnering with data scientists from leading technology companies or logistics experts from the transportation industry could provide valuable insights and resources.

Conclusion

The primary goal of this study was to predict logistics demand of the CC-DEC using a Fuzzy Support Vector Regression Machine based on the Adam optimization algorithm (FSVR-AD). Our results demonstrate that the FSVR-AD model outperforms both the traditional SVR and BPNN models in terms of prediction accuracy. The Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Coefficient of Determination (R²) scores for the FSVR-AD model were significantly lower and higher, respectively, indicating a more precise and reliable forecast when compared to the other models.

The remarkable performance of the FSVR-AD model is attributable to its proficiency in managing non-linear data, coupled with its robust optimization features, which are particularly suited to the complex and dynamic nature of logistics demand. The integration of fuzzy logic into the support vector regression framework allows for a more nuanced understanding of the relationships between various factors influencing logistics demand, leading to improved prediction accuracy.

Our findings also highlight the importance of considering low carbon factor in logistics demand forecasting. The negative weights assigned to logistics energy consumption intensity (X1) and logistics carbon dioxide emission intensity (X2) in the FSVR-AD model suggest that as logistics demand increases, the consumption of energy and emissions of carbon dioxide per unit of logistics activity decrease. This indicates that growth in logistics demand does not necessarily lead to proportional increases in energy consumption and emissions, and that improvements in logistics operation efficiency can significantly diminish the ecosystem impact of logistics activities.

The results of our study have practical implications for policymakers and industry practitioners in the logistics sector. The ability to accurately forecast logistics demand is crucial for optimizing resource allocation, enhancing operational efficiency, and reducing environmental impact. Our FSVR-AD model provides a reliable tool for stakeholders to make informed decisions and plan for future logistics needs in the CC-DEC and potentially in other regions facing similar challenges.

In conclusion, our study provides a robust and accurate method for forecasting logistics demand that can aid in strategic planning and decision-making processes within the logistics sector. The FSVR-AD model’s effectiveness in capturing the complexities of logistics demand and its consideration of low carbon factor in make it a valuable asset for promoting sustainable and efficient logistics operations.