99 Advances in Production Engineering & Management ISSN 1854-6250 Volume 20 | Number 1 | March 2025 | pp 99–115 Journal home: apem-journal.org https://doi.org/10.14743/apem2025.1.530 Original scientific paper Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Huang, L. a,* , Jiang, D.Y. a , Bai, T.Y. b a School of Economics and Management, Beijing Jiaotong University, Beijing, P.R. China b China Waterborne Transport Research Institute, Beijing, P.R. China A B S T R A C T A R T I C L E I N F O In response to the growing demand for accurate freight forecasting in sea-rail intermodal transportation, particularly under the constraints of stringent data protection regulations, we introduce a privacy-preserving, AI-based frame- work that focuses on the micro-level identification of container transport po- tential. The framework combines Vertical Federated Learning (VFL) with ad- vanced feature and sample selection techniques. It leverages privacy-preserv- ing methods, such as homomorphic encryption and random noise, enabling se- cure collaboration between ports and railways while safeguarding commer- cially sensitive data. Through extensive experiments, our framework demon- strates superior performance in predicting container transport demand, signif- icantly improving the accuracy of resource allocation and scheduling decisions for rail operators. The framework not only ensures compliance with data pro- tection regulations but also provides valuable insights into intermodal trans- portation planning, optimizing both railway operations and customer service quality. This approach offers a practical solution for improving strategic deci- sion-making in the sea-rail intermodal sector amid increasing privacy demands and complex logistical challenges. Keywords: Freight demand forecasting; Vertical federated learning; Privacy-preserving methods; Sample and feature selection; Machine learning; Homomorphic encryption; Resource allocation and scheduling *Corresponding author: lhuang@bjtu.edu.cn (Huang, L.) Article history: Received 20 October 2024 Revised 19 February 2025 Accepted 3 March 2025 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction With the continuous expansion of global trade, sea-rail intermodal transportation has emerged as a crucial part of modern logistics networks, effectively combining the advantages of different transportation modes and optimizing the utilization of diverse transportation resources[1]. Every day, major ports and railway systems worldwide process vast amounts of transport data, covering multiple stages from ship docking and cargo handling to final rail transportation [2]. Although this data is crucial for improving transport efficiency and optimizing logistics management, its frag- mented storage across various organizations (such as customs, ports, and railway companies) presents significant challenges for efficient utilization and integrated analysis [3]. This data frag- mentation not only limits information sharing and flow but also increases uncertainty throughout the transport chain. For example, delays in data exchange between port and rail departments can lead to prolonged container dwell times, ultimately reducing overall transport efficiency. Huang, Jiang, Bai 100 Advances in Production Engineering & Management 20(1) 2025 Due to the fragmented nature of the data, each party has a very limited view of the complete dataset, which not only affects information flow and collaboration efficiency but also increases operational complexity. More importantly, the growing demand for data privacy protection from data holders has made it increasingly difficult to integrate and analyse these datasets together, raising concerns about potential data leaks [4]. Therefore, developing an approach that allows for the efficient integration of fragmented data without violating privacy is now a critical challenge in sea-rail intermodal data analysis. Federated learning offers an innovative solution to these challenges by enabling multi-party data collaboration without sharing raw data [5]. The core principle of federated learning is that participants can collaboratively train models while keeping their respective data private. Vertical Federated Learning (VFL), in particular, is well-suited for scenarios where different organizations hold different data features but share the same samples [6]. The VFL framework ensures data privacy for all parties while utilizing the complementary data from multiple sources to improve model accuracy. Securing high-quality training datasets has always been a central challenge in machine learning and AI applications. The representativeness and quality of training data directly impact model performance. However, collecting and labelling sufficient high-quality data is costly. In a federated learning system, the selection of training samples and features plays a significant role in model performance. For instance, in horizontal federated learning, low-quality data—such as incorrect labels or skewed class distributions—can result in low and unstable model accuracy [7]. In verti- cal federated learning, where data features are distributed across different organizations and la- bel access is limited, the challenge of selecting effective training samples and features becomes even more complex [8]. To address these challenges, this paper introduces a VFL framework based on Gradient Upper Bound Norms and Feature Joint Information Gain. This framework aims to optimize the analysis process for identifying potential import container sources in sea-rail intermodal transportation while ensuring data privacy protection. The key concept is to assess the importance of each par- ticipant’s features to the overall model by calculating information gain, considering feature inter- actions via joint information gain. Sample importance is measured using Gradient Upper Bound Norms, determining which samples are best suited for model training. Additionally, the training and feature selection process incorporates homomorphic encryption and random noise to ensure privacy protection during model training. This innovative framework provides new insights and practical solutions for data analysis and decision-making in the sea-rail intermodal transportation system. The structure of this article is as follows: Section 2 presents a thorough literature review on Freight Demand Forecasting, Vertical Federated Learning (VFL), and Sample and Feature Selec- tion methods. Section 3 discusses the critical issue of data privacy protection within the scope of identifying potential containers for sea-rail intermodal transportation and formulates the core research problem. Section 4 provides a detailed explanation of the proposed framework, including the methodology and algorithms used to address the challenges of privacy-preserving container identification. Section 5 outlines the experimental setup and presents the results, comparing the performance of our method with existing state-of-the-art algorithms. Finally, Section 6 concludes by evaluating the effectiveness of the framework and discussing the business implications for rail- way container identification and intermodal transportation planning. 2. Literature review This study stands at the intersection of the research streams on Freight Demand Forecasting, Ver- tical Federated Learning, Sample and Feature Selection methods. We comprehensively review the previous literature in each research stream as follows. Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 101 2.1 Freight demand forecasting In the field of freight demand forecasting, methodologies have evolved from traditional statistical approaches to more advanced models that combine multiple techniques for improved accuracy and adaptability. Early approaches, such as time series models like ARIMA, primarily focused on leveraging his- torical data trends to make future predictions. Regression models followed, incorporating exter- nal variables such as economic indicators. For instance, Khan and Khan [9] applied multivariate time series methods, including the Johansen co-integration and error correction model, to capture both short- and long-run dynamics of rail freight demand. Over time, these models have been sup- plemented with more sophisticated machine learning techniques, such as LSTM networks, which have proven effective in handling sequential data and capturing long-term dependencies [10]. As the complexity of freight data increased, machine learning models like Random Forests and Neural Networks gained prominence. Salais-Fierro and Martínez [11] demonstrated the superior accuracy of Artificial Neural Networks (ANNs) over traditional statistical models, particularly in forecasting freight demand using historical transportation management system (TMS) data. More recently, hybrid approaches that blend machine learning with other techniques have emerged as powerful tools for freight demand forecasting. Hassan et al. [12] introduced a reinforcement learning framework that combines time series models and machine learning algorithms in a roll- ing horizon to improve prediction accuracy over various time periods. Other hybrid models have sought to improve interpretability and predictive power by incor- porating domain-specific insights. For instance, Liu et al. [13] combined Grey Relational Analysis (GRA) with Deep Autoencoder Neural Networks (DNN) to enhance railway freight demand pre- diction. Ling et al. [14] introduced the Spatio-Temporal Heterogeneous Graph Attention Network (STHAN), which captures both spatial and temporal relationships within freight transportation data, demonstrating the growing complexity of models designed to account for multiple data di- mensions. Econometric models also remain a staple in freight demand forecasting. Lu et al. [15] used input-output models to examine the effects of economic growth and structural changes on freight demand, emphasizing the continued relevance of economic indicators in freight modelling. To date, most studies have focused on macro-level freight demand forecasting, often overlook- ing micro-level analysis that could optimize logistics at the individual container level. This gap in the literature is particularly important for sea-rail intermodal transportation, where predicting the transport potential of individual containers is critical for optimizing resource allocation and planning. The current study addresses this gap, offering new insights into identifying freight de- mand for sea-rail intermodal carriers at the micro level. 2.2 Vertical federated learning Vertical Federated Learning (VFL) is designed for scenarios where different organizations hold disjoint sets of features for the same users or entities [16]. VFL enables organizations to jointly train machine learning models while keeping their raw data private, which is essential for privacy protection. VFL operates primarily through two architectures: Aggregation-based VFL (aggVFL) and Split- based VFL (splitVFL) [17]. In aggVFL, each party trains its local model, and the server aggregates the results to produce a global model. Tree-based models such as SecureBoost [18] and Se- cureGBM [19] often operate in this framework, utilizing techniques like homomorphic encryption to ensure privacy. Meanwhile, splitVFL uses a more dynamic approach where a trainable global model is split across parties, with neural network-based models being common [20]. This allows the parties to collaborate on training without exchanging sensitive label information, with only the server retaining access to the global model [21]. Neural network-based approach has proven effective across various applications, from financial systems [22, 23] to healthcare [24], ensuring data privacy while maximizing the utility of distributed datasets. In VFL, both sample and feature selection play crucial roles in improving communication effi- ciency and ensuring model performance. However, traditional methods face challenges due to pri- vacy constraints and the large communication overhead involved. In feature selection, approaches Huang, Jiang, Bai 102 Advances in Production Engineering & Management 20(1) 2025 like SFFS [25] struggle with contextual dependencies and heavy parameter transmission. To ad- dress this, methods such as FedSDG-FS [26], LESS-VFL [27] focus on reducing the impact of noisy features through advanced filtering mechanisms, maintaining privacy while ensuring feature im- portance, though it lacks consideration of feature correlations. For sample selection, VF-PS [28] focuses on selecting a subset of important participants. The LEARN framework [29] proposes a solution by selecting representative samples without requiring full-sample training. 2.3 Sample selection and feature selection In machine learning, sample selection and feature selection are essential for improving model per- formance, reducing computational costs, and avoiding overfitting. In centralized learning, feature selection methods are usually divided into three categories: filter, wrapper, and embedded meth- ods [30]. Filter methods calculate statistical relationships between features and the target varia- ble, e.g., Gini impurity [31], mutual information. Wrapper methods evaluate different feature sub- sets by iteratively training models, though this can be computationally expensive [32]. Embedded methods, such as Lasso regression, integrate feature selection within the training process [33], offering a more balanced approach between accuracy and efficiency. Mlinarič et al. [34] compared various classifiers (Decision Tree, Random Forest, Bagging, and Gradient Boosting) for feature selection in automated end-of-line quality inspection of electric motors. Sample selection focuses on selecting the most representative or important data samples for training, especially useful in scenarios with large datasets or limited labels [35]. It is particularly critical in situations where computational resources are constrained or data labelling is expen- sive. Traditional sample selection methods include uncertainty-based selection, where the model selects samples the most uncertain about for further labelling [36], and representativeness-based selection, where clusters or core sets are used to select samples that represent the overall data distribution [37]. However, in VFL scenarios, the lack of global data visibility adds significant complexity to both sample and feature selection. Each party holds a portion of the data (either features or samples) and cannot directly share raw data due to privacy constraints, rendering centralized selection ap- proaches impractical. While emerging methods like LESS-VFL [27] and LEARN [29] address these challenges by introducing secure and efficient communication protocols that enable local compu- tations and selective data sharing, there is still considerable room for further research. 3. Problem formulation 3.1 Data sharing status and problems Current data sharing in container sea-rail intermodal transportation heavily relies on the point- to-point exchange model, particularly through Electronic Data Interchange (EDI) between ports and railway stations. While this model provides a standardized and streamlined approach, it im- poses strict requirements for data transmission based on specific message standards for different data types. As a result, the format of data exchanges is highly regulated, and participants must closely adhere to these standards when transmitting key data fields through interface protocols. The data exchange process in sea-rail intermodal transport involves multiple key stakeholders, such as ports, customs, freight forwarders, shipping companies, railway operators, and final cargo recipients. As containers transition between modes of transport, such as from sea to rail, real-time information sharing becomes increasingly crucial. However, the current lack of a unified data- sharing infrastructure, combined with delays in exchanging critical information, can lead to sev- eral challenges. These include prolonged container dwell times, miscommunication, and opera- tional inefficiencies, all of which may result in shipment delays, information asymmetry, or even cargo loss. In summary, current data sharing in sea-rail intermodal transportation provides essential sup- port for the basic operations of various stakeholders and plays a crucial role in ensuring coordina- tion between operations and organizations. However, due to the need to protect commercial secrets, comply with data privacy regulations, and ensure data security, the scope and effectiveness of Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 103 existing data-sharing mechanisms are limited. Participants in the sea-rail intermodal chain are un- able to share all their data unconditionally. This selective data sharing, while safeguarding commercial interests, customer privacy, and data security, greatly restricts the potential for data mining. It limits the ability to fully leverage data for improving the overall efficiency of the transportation system, forecasting logistics de- mand, and optimizing resource allocation. Furthermore, the current reliance on message ex- changes and data interfaces poses additional security risks, such as potential interception or tam- pering during transmission. The delays in information transfer prevent real-time updates on the transport process, hindering timely decision-making. Additionally, challenges such as non-uniform data formats, inconsistent data quality, and com- patibility issues between different information systems further complicate the data-sharing pro- cess. These problems often require extensive data cleaning and validation to ensure accuracy, in- creasing both the cost and complexity of data sharing. 3.2 Potential container identification scenario In the sea-rail intermodal import process, the railway transportation workflow includes several key stages: freight forwarder application, daily train requests, railway acceptance, scheduling ap- proval, plan preparation, and departure confirmation. Before these steps, the railway freight mar- keting department typically conducts freight demand mining, which is crucial for efficient re- source allocation, maximizing transport efficiency, and minimizing costs. Currently, railway freight departments conduct market research-based freight demand min- ing. This process involves identifying transport demand across various regions and industries. The departments engage directly with shippers, offering freight rate subsidies to encourage them to choose rail transport for container shipments from ports. However, this method is time-con- suming and labour-intensive, resulting in slow progress in increasing the sea-rail intermodal ratio and facing bottlenecks. Additionally, the current approach does not utilize big data and related technologies for data analysis, limiting the accuracy and effectiveness of freight demand mining. As illustrated in Fig. 1, the traditional railway transport process is optimized by analysing data such as port schedules, container storage, documentation, operational records, and customs in- formation. Based on the results of potential container identification, preliminary railway transport plans—such as block trains and direct services—are formulated. The railway freight marketing department then uses these plans and transport products to conduct targeted market- ing to customers. Once the freight sources are secured, the pre-compiled plans are seamlessly in- tegrated into the existing workflow for final plan preparation. However, identifying potential con- tainer demand in real-time and ensuring privacy requires more advanced data-sharing solutions, which are discussed in the following section. Fig. 1 Optimized railway transportation process Huang, Jiang, Bai 104 Advances in Production Engineering & Management 20(1) 2025 3.3 Privacy computing needs The core of current data sharing in sea-rail intermodal transportation lies in supporting opera- tional collaboration and process coordination between railway and ports, rather than indiscrimi- nately sharing all data between both parties. The sharing mechanism focuses on improving joint operational efficiency, ensuring that data exchange enhances cargo transport efficiency, optimizes scheduling, and improves customer service. It primarily targets the exchange of essential opera- tional data, such as train requests from ports, railway confirmations of train availability and esti- mated arrival times, loading confirmations, and intermediate stops. However, the current data-sharing system is not suitable for deeper freight demand mining in sea-rail intermodal transport. Railway needs to dynamically analyse a broader range of data in real time, including ship schedules, operations, yard conditions, and destination flows of all con- tainers. These types of raw data, however, are considered sensitive by organizations such as ports and customs and are large in volume. Under the current data-sharing framework, effective real- time sharing of this information is not possible. The primary goal of freight demand mining in sea-rail intermodal transport is to enable railway freight marketing departments to accurately identify potential container freight demand while ensuring the security of data across multiple parties. Based on this demand, railway can dynami- cally optimize transport organization and train schedules. The existing data-sharing mechanism is inadequate for this purpose, requiring the development of a new solution. Techniques such as federated learning and privacy computing are necessary to allow efficient and secure information sharing, enabling the mining of potential freight demand while safeguarding sensitive data across all stakeholders in sea-rail intermodal transportation. 4. The GUBN-FJIG framework Since the participants in sea-rail intermodal transportation, namely ports and railway, hold dif- ferent features of the training samples, a vertical federated learning model is required. Existing feature selection methods typically need direct access to training data, the model training process, and labels, but this is not allowed in vertical federated learning due to privacy protection require- ments. Additionally, the features held by the clients in vertical federated learning may interact with each other, and current methods tend to overlook these interactions and their joint impact on the target variable. We proposed a vertical federated learning sample and feature selection framework based on Gradient Upper Bound Norm and Feature Joint Information Gain (GUBN-FJIG framework). It con- sists of three submodules: feature importance initialization, sample importance calculation, and important sample and feature selection. Fig. 2 illustrates the flowchart of this sample and feature selection framework. In the vertical federated learning framework, the dataset of 𝑁𝑁 samples is divided into 𝑀𝑀 parts, denoted as 𝐷𝐷 = { 𝐷𝐷 1 , ⋯ , 𝐷𝐷 𝑀𝑀 }, where each client holds a unique feature set � 𝑓𝑓 𝑚𝑚 , 1 , ⋯ , 𝑓𝑓 𝑚𝑚 , 𝑑𝑑 𝑚𝑚 � and the local sample 𝑥𝑥 𝑛𝑛 , 𝑚𝑚 ∈ ℝ 𝑑𝑑 𝑚𝑚 , 𝑛𝑛 ∈ [ 𝑁𝑁 ]. Typically, the server S holds the sample labels 𝑦𝑦 𝑛𝑛 ∈ ℝ, 𝑛𝑛 ∈ [ 𝑐𝑐 ]. With the server’s coordination, all clients 𝑚𝑚 ∈ [ 𝑀𝑀 ]collaboratively contribute to the global model by sharing encrypted data to protect privacy. It allows clients to collaboratively train a global model by selecting important features and samples, while minimizing the global risk 𝑅𝑅 ( 𝜃𝜃 𝑠𝑠 ). 𝑅𝑅 ( 𝜃𝜃 𝑠𝑠 ) = 𝔼𝔼 𝑥𝑥 , 𝑦𝑦 𝐿𝐿 � ℎ � 𝜃𝜃 𝑧𝑧 1 , 𝑧𝑧 1 , … , 𝑧𝑧 𝑚𝑚 , 𝑦𝑦 𝑛𝑛 � � (1) Each client 𝑚𝑚 trains a local parameter ℎ 𝑚𝑚 , representing the local dataset 𝑥𝑥 𝑛𝑛 𝑚𝑚 ∈ ℝ 𝑑𝑑 𝑚𝑚 , which is mapped to a lower-dimensional space 𝑧𝑧 𝑛𝑛 𝑚𝑚 : = ℎ 𝑚𝑚 ( 𝜃𝜃 𝑚𝑚 , 𝑥𝑥 𝑛𝑛 𝑚𝑚 ⊙ 𝑠𝑠 𝑚𝑚 ) ∈ ℝ 𝑑𝑑 𝑓𝑓 𝑚𝑚 , where 𝑑𝑑 𝑓𝑓 𝑚𝑚 ≪ 𝑑𝑑 𝑚𝑚 , and 𝑠𝑠 𝑚𝑚 = {0,1} 𝑑𝑑 𝑚𝑚 indicates the selected features. The server coordinates the process by optimizing a joint model, with parameters 𝜃𝜃 0 : = { 𝑤𝑤 1 , ⋯ , 𝑤𝑤 𝑀𝑀 , 𝛼𝛼 0 }, where 𝑤𝑤 𝑚𝑚 ∈ ℝ 𝑑𝑑 𝑚𝑚 ′ are the parameters of the interaction layer. These parameters are combined with the lower-dimensional embeddings 𝑧𝑧 𝑛𝑛 𝑚𝑚 sent by each client. 𝛼𝛼 0 represents the parameters other than interaction layer. Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 105 Fig. 2 GUBN-FJIG vertical federated learning framework for sample selection and feature selection Following the Gaussian stochastic dual-gate used in FedSDG-FS [26], we utilize the 𝑙𝑙 0 norm to constrain the number of non-zero parameters in the model, minimizing the risk 𝑅𝑅 ( 𝜃𝜃 , 𝑠𝑠 , 𝑞𝑞 ) to con- struct the global model. Due to the large variance in the Bernoulli variables 𝑠𝑠 𝑚𝑚 and 𝑞𝑞 𝑚𝑚 during fea- ture selection optimization, a continuous relaxation based on the Gaussian distribution is applied, approximating each Bernoulli variable in 𝑠𝑠 𝑚𝑚 and 𝑞𝑞 𝑚𝑚 with parameters 𝜇𝜇 𝑚𝑚 , 𝑖𝑖 and 𝜔𝜔 𝑚𝑚 , 𝑗𝑗 . 𝑅𝑅 ( 𝜃𝜃 , 𝑠𝑠 , 𝑞𝑞 ) = 𝔼𝔼 𝑥𝑥 , 𝑦𝑦 𝐿𝐿 � ℎ � 𝜃𝜃 0 , 𝑟𝑟 𝑛𝑛 , 1 , … , 𝑟𝑟 𝑛𝑛 , 𝑀𝑀 � ; 𝑦𝑦 𝑛𝑛 � + 𝜆𝜆 �(| 𝑠𝑠 𝑚𝑚 | 𝑙𝑙 0 + | 𝑞𝑞 𝑚𝑚 | 𝑙𝑙 0 ) 𝑚𝑚 (2) 4.1 Feature importance initialization based on information gain For the client m , if feature 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 is categorical, with possible values � 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 ( 1) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 ( 2) , … , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 ( 𝑘𝑘 ) � . The condi- tional entropy is defined as: 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 � = � 𝑝𝑝 � 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 = 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) (3) where 𝑝𝑝 � 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � is the probability of feature 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 taking the value 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , and 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 = 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � is the entropy of 𝑌𝑌 given that 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 takes the value 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) . The calculation of conditional entropy is as follows: 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 = 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � = − � 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � log 2 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � 𝑐𝑐 ∈ 𝒞𝒞 (4) For continuous features, methods like binning or box plots can be used to discretize the feature. The information gain of a feature is calculated as 𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑘𝑘 , 𝑖𝑖 � = 𝐻𝐻 ( 𝑌𝑌 ) − 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑘𝑘 , 𝑖𝑖 � . For two features 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 and 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 of client 𝑚𝑚 , their joint conditional entropy is calculated as 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � = − ∑ 𝑝𝑝 ( 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � ) 𝑐𝑐 ∈ 𝒞𝒞 log 2 𝑝𝑝 ( 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � ) . The information gain of joint features is 𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � = 𝐻𝐻 ( 𝑌𝑌 ) − 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � . The feature interaction information gain is calculated as 𝐼𝐼𝐼𝐼𝐼𝐼 � 𝑌𝑌 ; 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � = 𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � − 𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 � − 𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � . The above calculations are completed through client-server collaboration, as shown in Algo- rithm 1. In this work, we use Paillier as homomorphic encryption method to encrypt the data re- quiring privacy protection during computation. This method supports addition of encrypted val- ues and multiplication of ciphertexts by constants. Huang, Jiang, Bai 106 Advances in Production Engineering & Management 20(1) 2025 Algorithm 1: Information gain-based feature importance initialization algorithm Input: Client 𝑚𝑚 ，Server 𝑆𝑆 Output: Feature importance (Initialized) Server 𝑆𝑆 1 Compute the class entropy 𝐻𝐻 ( 𝑌𝑌 ) 2 Create an indicator matrix 𝐴𝐴 and encrypt: ⟦ 𝐴𝐴 ⟧ ← Enc( 𝐴𝐴 ) 3 Send the encrypted indicator matrix ⟦ 𝐴𝐴 ⟧ to all clients Client 𝑚𝑚 4 Based on feature 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 discretize sample 𝑈𝑈 into 𝑈𝑈 1 , ⋯ , 𝑈𝑈 𝑘𝑘 5 For feature 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 calculate 𝑝𝑝 � 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � ← | 𝑈𝑈 𝑘𝑘 | | 𝑈𝑈 | 6 Compute � 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � ← � ⟦ 𝐴𝐴 ⟧ 𝑛𝑛 , 𝑐𝑐 𝑛𝑛 ∈ 𝐼𝐼 � 𝑈𝑈 𝑘𝑘 � | 𝑈𝑈 𝑘𝑘 | 7 If there is a joint feature 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 ，discretize sample 𝑈𝑈 into 𝑈𝑈 1 , ⋯ , 𝑈𝑈 𝑘𝑘 ′: 8 Compute 𝑝𝑝 � 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � ， � 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � ， 9 Add the encryption factor: � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � ← � 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � ⋅ 𝜖𝜖 𝑚𝑚 ， � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � ← � 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � ⋅ 𝜖𝜖 𝑚𝑚 10 Send � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � ， � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � to the server Server 𝑆𝑆 11 Compute 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � ← 𝐷𝐷 𝐷𝐷𝑐𝑐 � � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � � 12 Decrypt 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � ← 𝐷𝐷 𝐷𝐷𝑐𝑐 � � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � � 13 Compute log 2 � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � , log 2 � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � and send to the client Client 𝑚𝑚 14 Remove noise log 2 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � ← log 2 � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) � � − log 2 𝜖𝜖 𝑚𝑚 Log 2 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � ← log 2 � 𝜖𝜖 𝑚𝑚 𝑝𝑝 � 𝑐𝑐 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 ( 𝑘𝑘 ) , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑘𝑘 ′ � � � − log 2 𝜖𝜖 𝑚𝑚 15 Calculate 𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � ，𝐻𝐻 � 𝑌𝑌 ∣ 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 � and send to the Server Server 𝑆𝑆 16 Compute information gain 𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 � ，𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � and send to the client Client 𝑚𝑚 17 Compute joint information gain 𝐼𝐼𝐼𝐼𝐼𝐼 � 𝑌𝑌 , 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � , and initialize 𝜇𝜇 𝑚𝑚 , 𝑗𝑗 18 𝜇𝜇 𝑚𝑚 , 𝑗𝑗 ∝ 𝐼𝐼𝐼𝐼 � 𝑌𝑌 ; 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � + � 𝐼𝐼𝐼𝐼𝐼𝐼 � 𝑌𝑌 ; 𝑓𝑓 𝑚𝑚 , 𝑖𝑖 , 𝑓𝑓 𝑚𝑚 , 𝑗𝑗 � 𝑖𝑖 ≠ 𝑗𝑗 4.2 Sample importance estimation The Gradient Upper Bound Norm is used as a sample importance indicator. Its calculation is shown below, mainly involving the input and output of the model’s top layers. The computation of this norm requires only one forward pass, reducing computational costs. It provides a reason- ably accurate estimate of sample importance, whereas conventional norms require both forward and backward passes through the network, making them more expensive to compute. 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ) = � � � 𝛽𝛽 𝑛𝑛 𝑡𝑡 𝛻𝛻 𝛼𝛼 𝑛𝑛 𝑡𝑡 𝐿𝐿 � ℎ � 𝜃𝜃 0 , 𝑧𝑧 𝑛𝑛 , 1 , ⋯ , 𝑧𝑧 𝑛𝑛 , 𝑀𝑀 � ; 𝑦𝑦 𝑛𝑛 � 𝑡𝑡 � 2 (5) Here, 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ) represents the importance of sample 𝑥𝑥 𝑛𝑛 at iteration 𝑡𝑡 , and 𝛽𝛽 𝑛𝑛 𝑡𝑡 , 𝛼𝛼 𝑛𝑛 𝑡𝑡 are the input and output of the top layer for sample 𝑥𝑥 𝑛𝑛 at the 𝑡𝑡 -th iteration. For samples with higher gradient norms in the global model’s output, the sample is assigned greater importance. Conversely, to avoid selecting samples that display unusually high values, a predefined threshold parameter 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ) ≤ 𝛿𝛿 𝑡𝑡 is set, where 𝛿𝛿 𝑡𝑡 is a user-defined parameter (e.g., the median of the sample norm dis- tribution). The calculation of sample importance is completed through the forward propagation process, as described in Algorithm 2. By adding random noise, the server ensures privacy protection for client data. First, the client selects a batch of samples and calculates the importance score 𝑠𝑠 𝑚𝑚 , 𝑖𝑖 Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 107 based on the feature importance initialization. Encrypt intermediate results 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 using Paillier be- fore send to the Server. Then the Server adds random noise to the model's parameters 𝜖𝜖 𝑎𝑎 and sends the encrypted result to the client. The client decrypts the data, removes the added noise, and sends the adjusted result 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 back to the server. The server then removes the final noise 𝜖𝜖 𝑠𝑠 , calculates the gradient for the top layer and completes the sample importance calculation 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ). If 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ) ≥ 𝛿𝛿 𝑡𝑡 , the sample is included for training, and a sample selection indicator ma- trix P is generated. Algorithm 2 ：Privacy-Preserving Forward Propagation Process Input: Client 𝑚𝑚 , Server 𝑆𝑆 Output: Loss 𝐿𝐿 𝑛𝑛 , Sample importance 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ) Client 𝑚𝑚 1 Select a batch of samples 𝑥𝑥 𝑛𝑛 , 𝑚𝑚 based on the set batch size 2 Sample 𝜌𝜌 𝑚𝑚 , 𝑖𝑖 , 𝛾𝛾 𝑚𝑚 , 𝑗𝑗 from 𝒩𝒩 (0, 𝜎𝜎 2 ), 𝑖𝑖 ∈ [ 𝑑𝑑 𝑚𝑚 ], 𝑗𝑗 ∈ [d ′ ] 3 Calculate s 𝑚𝑚 , 𝑖𝑖 = 𝑚𝑚𝑚𝑚 𝑥𝑥 � 0, 𝑚𝑚𝑖𝑖 𝑛𝑛 � 1, 𝜇𝜇 𝑚𝑚 , 𝑖𝑖 + 𝜌𝜌 𝑚𝑚 , 𝑖𝑖 � � , q 𝑚𝑚 , 𝑗𝑗 = 𝑚𝑚𝑚𝑚 𝑥𝑥 � 0, 𝑚𝑚𝑖𝑖 𝑛𝑛 � 1, 𝜔𝜔 𝑚𝑚 , 𝑗𝑗 + 𝛾𝛾 𝑚𝑚 , 𝑗𝑗 � � 4 Record 𝑅𝑅 𝑚𝑚 = � Φ � 𝜇𝜇 𝑚𝑚 , 𝑖𝑖 𝜎𝜎 � 𝑖𝑖 ∈[ 𝑑𝑑 𝑚𝑚 ] + � Φ � 𝜔𝜔 𝑚𝑚 , 𝑗𝑗 𝜎𝜎 � 𝑗𝑗 ∈ � 𝑑𝑑 𝑚𝑚 ′ � 5 𝑧𝑧 𝑛𝑛 , 𝑚𝑚 ← ℎ 𝑚𝑚 � 𝜃𝜃 𝑚𝑚 ; 𝑥𝑥 𝑛𝑛 , 𝑚𝑚 ⊙ 𝑠𝑠 𝑚𝑚 � , 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 = 𝑧𝑧 𝑛𝑛 , 𝑚𝑚 ⊙ 𝑞𝑞 𝑚𝑚 6 Encrypt � 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � ← Enc � 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � 7 Send � 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � to the Server 𝑆𝑆 Server 𝑆𝑆 8 Add random noise to the interact layer parameters: 𝑤𝑤 𝑚𝑚 ′ ← 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑎𝑎 9 � 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ′ � ← � 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � ∙ 𝑤𝑤 𝑚𝑚 ′ , add random noise 𝜖𝜖 𝑠𝑠 10 Send � 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ′ + 𝜖𝜖 𝑠𝑠 � to client 𝑚𝑚 Client 𝑚𝑚 11 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ′ + 𝜖𝜖 𝑠𝑠 ← 𝐷𝐷 𝐷𝐷𝑐𝑐 � � 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ′ + 𝜖𝜖 𝑠𝑠 � � 12 Remove the random noise 𝜖𝜖 𝑎𝑎 ，𝑔𝑔 𝑛𝑛 , 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 ← 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ′ + 𝜖𝜖 𝑠𝑠 − 𝜖𝜖 𝑎𝑎 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 13 Send 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 back to the Server 𝑆𝑆 Server 𝑆𝑆 14 Remove the noise 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 = 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 − 𝜖𝜖 𝑠𝑠 15 Compute 𝐿𝐿 𝑛𝑛 ← 𝐿𝐿 � ℎ � 𝛼𝛼 0 , 𝑔𝑔 𝑛𝑛 , 1 , ⋯ , 𝑔𝑔 𝑛𝑛 , 𝑀𝑀 � ; y n � 16 Obtain top layer input 𝛽𝛽 𝑛𝑛 𝑡𝑡 , calculate ∇ 𝛼𝛼 𝑛𝑛 𝑡𝑡 𝐿𝐿 � ℎ � 𝛼𝛼 0 , 𝑔𝑔 𝑛𝑛 , 1 , ⋯ , 𝑔𝑔 𝑛𝑛 , 𝑀𝑀 � ; y n � 17 Calculate 𝜆𝜆 ( 𝑥𝑥 𝑛𝑛 , 𝑡𝑡 ) 4.3 Backpropagation update Based on the sample selection indicator matrix, the selected data participates in training and un- dergoes forward propagation, followed by model updates through backpropagation. As shown in Algorithm 3, to prevent data leakage, the server adds noise 𝜖𝜖 𝑠𝑠 to the gradient � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 � during trans- mission. The client decrypts the result and adjusts the gradient by a scaling factor 𝜂𝜂 𝑠𝑠 before send- ing it back to the server. The cumulative noise 𝜖𝜖 𝑚𝑚 is recorded during this process. Server updates interaction layer parameters 𝑤𝑤 𝑚𝑚 ′ = 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑚𝑚 with noisy gradients. The update of client-side model requires no noise, as the server uses encrypted cumulative noise for gradient calculations 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ⋅ 𝑤𝑤 𝑚𝑚 ′ − ⟦ 𝜖𝜖 𝑎𝑎 ⟧ ⋅ 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 . The server sends the updated gradient back to the client, where the client uses backpropagation to update parameters such as 𝜇𝜇 𝑚𝑚 , 𝜔𝜔 𝑚𝑚 , 𝜃𝜃 𝑚𝑚 , thereby completing feature se- lection with 𝑠𝑠 𝑚𝑚 , 𝑞𝑞 𝑚𝑚 and updating the client model. Huang, Jiang, Bai 108 Advances in Production Engineering & Management 20(1) 2025 Algorithm 3: Privacy-Preserving Backpropagation Process Input: Sample loss 𝐿𝐿 𝑛𝑛 , Server learning rate 𝜂𝜂 𝑠𝑠 , Client learning rate 𝜂𝜂 𝑚𝑚 Output: Global model Server 𝑆𝑆 1 Compute the gradient � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 � ← 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ⋅ � 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � , � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � ′ ← 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 ⋅ 𝑤𝑤 𝑚𝑚 ′ , 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝛼𝛼 0 2 Add random noise 𝜖𝜖 𝑠𝑠 , and send � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 � to client 𝑚𝑚 Client 𝑚𝑚 3 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 ← 𝐷𝐷 𝐷𝐷𝑐𝑐 � � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 � � 4 Add random noise 𝜖𝜖 𝑚𝑚 , � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 � ′ ← 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 − 𝜖𝜖 𝑚𝑚 𝜂𝜂 𝑠𝑠 5 Encrypt the noise ⟦ 𝜖𝜖 𝑎𝑎 ⟧ ← 𝐸𝐸 𝑛𝑛𝑐𝑐 ( 𝜖𝜖 𝑎𝑎 ) and accumulate noise 𝜖𝜖 𝑎𝑎 ← 𝜖𝜖 𝑎𝑎 + 𝜖𝜖 𝑚𝑚 6 Send � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 � ′ , ⟦ 𝜖𝜖 𝑎𝑎 ⟧ to the server Server 𝑆𝑆 7 Remove the noise � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 � ′ ← � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 + 𝜖𝜖 𝑠𝑠 � ′ − 𝜖𝜖 𝑠𝑠 8 Update the interaction layer parameters 𝑤𝑤 𝑚𝑚 ′ ← 𝑤𝑤 𝑚𝑚 ′ − 𝜂𝜂 𝑠𝑠 � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑤𝑤 𝑚𝑚 � ′ , 𝛼𝛼 0 ← 𝛼𝛼 0 − 𝜂𝜂 𝑠𝑠 ∇ 𝛼𝛼 0 𝐿𝐿 𝑛𝑛 9 Compute gradients, update other layer parameters 10 Remove the noise � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � ← � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � ′ − ⟦ 𝜖𝜖 𝑎𝑎 ⟧ ⋅ 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑔𝑔 𝑛𝑛 , 𝑚𝑚 , and send to client 𝑚𝑚 Client 𝑚𝑚 11 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 = 𝐷𝐷 𝐷𝐷𝑐𝑐 �� 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝑟𝑟 𝑛𝑛 , 𝑚𝑚 � � , compute gradients 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝜇𝜇 𝑚𝑚 , 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝜔𝜔 𝑚𝑚 , 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝜃𝜃 𝑚𝑚 12 Update the client model 𝜇𝜇 𝑚𝑚 ← 𝜇𝜇 𝑚𝑚 − 𝜂𝜂 𝑚𝑚 � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝜇𝜇 𝑚𝑚 + 𝜆𝜆 𝜕𝜕 𝑅𝑅 𝑚𝑚 𝜕𝜕 𝜇𝜇 𝑚𝑚 � , 𝜔𝜔 𝑚𝑚 ← 𝜔𝜔 𝑚𝑚 − 𝜂𝜂 𝑚𝑚 � 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝜔𝜔 𝑚𝑚 + 𝜆𝜆 𝜕𝜕 𝑅𝑅 𝑚𝑚 𝜕𝜕 𝜔𝜔 𝑚𝑚 � 𝜃𝜃 𝑚𝑚 ← 𝜃𝜃 𝑚𝑚 − 𝜂𝜂 𝑚𝑚 𝜕𝜕 𝐿𝐿 𝑛𝑛 𝜕𝜕 𝜃𝜃 𝑚𝑚 5. Framework evaluation using practical data In this section, we apply the proposed framework in a practical scenario to identify potential con- tainers at a port in China. We choose the metrics of accuracy and to evaluate the performance of the proposed framework. We also compare our results against baseline models. 5.1 Data description and preprocessing The integration of the framework faces several challenges. First, there is the issue of data integra- tion. Since the data formats used in port and railway management systems vary, significant effort will be required for data standardization and preprocessing. Secondly, many existing systems rely on outdated infrastructure, which may not be compatible with the proposed framework and may require upgrades. Finally, collaboration among multiple stakeholders is key to ensuring smooth integration. The data for this study were gathered from several sources. Container-related data, including basic information, shipping schedules, stack storage, and operational records, were obtained from the port's container management system. The railway transport data was collected from the China Railway Research Institute, covering two transport stations at the port, with data on daily de- mands, waybills, and trajectory information. Road transportation data for container trucks was sourced from Baidu Maps, utilizing truck route planning services based on primary truck models and destinations. Data collection spanned from June 2022 to July 2023. Table 1 provides a sum- mary of the datasets, including descriptions, record counts, and ownership. Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 109 Table 1 Data sources Dataset Fields Numbers Data Owner Container Basic Information Dataset Container ID, Type, Size, Weight, Goods Description, Trade Type, etc. 7322158 Port System Shipping Schedules Dataset Estimated & Confirmed Arrival Times, Work Start & Completion Times, Departure Time, etc. 1048575 Port System Stack Storage Dataset Stack Entry & Departure Times, etc. 9414876 Port System Container Operation Dataset Destination, Dispatch Time, Mode of Transportation, etc. 485792 Port System Container Truck Road Transportation Dataset Transportation Distance, Fuel cost, Toll Fee, Freight Charges, Duration of Transportation, etc. 150 Baidu Maps Container Railway Transportation Dataset Departure & Arrival Stations, Distance Covered, Freight Charges, Discount Policy, Transportation Duration, etc. 76840 China Railway Research Institute The proposed framework is designed to be highly adaptable to different geographic regions and logistics networks with varying data structures. It employs a flexible preprocessing pipeline that can accommodate diverse data formats and structures, allowing it to integrate and process data from different sources, such as ports and railways. The framework is capable of handling differences in data granularity, such as variations in feature sets or missing values, by applying localized feature augmentation and alignment methods. This enables the framework to function effectively across regions with distinct logistical setups or data sources. Fig. 3 Data preprocessing process in multi-party systems Huang, Jiang, Bai 110 Advances in Production Engineering & Management 20(1) 2025 All data from these three sources were integrated, as illustrated in Fig. 3. The data prepro- cessing in this study involves four steps: data cleaning, data integration, data filtering, and feature augmentation. The same preprocessing was applied to the port and railway datasets, though they were handled separately. After sample alignment, containers transported by road lacked railway data (distance, cost, and duration), and those transported by rail lacked road transport data. To address this, feature augmentation was applied. Missing railway features were supplemented us- ing destination information and historical transport data, while missing road transport features were added based on destination and basic container information. Since customs hold domestic destination data, both the port and railway used pre-calculated tables for transport distance, cost, and duration for all origin-destination pairs. These were indexed using destination hashes for ef- ficient lookup. Finally, the augmented port and railway features were aligned for consistency. After completing the above procedures, data from multiple sources were integrated into a sin- gle dataset in logic. The dataset can be vertically divided into two parts based on the ownership of data features: port-owned features and railway-owned features, as outlined in Table 2. Table 2 Data features and examples Feature Values Type Data Owner Cargo weight 25.5 t, 26.3 t, … Numeric Port Arrival interval 8.95 h, 6.61 h, … Numeric Port Wait interval 3.13 h, 1.38h, … Numeric Port Work interval 14.14 h, 6.70 h, … Numeric Port Leave interval 2.80 h, 1.73 h, … Numeric Port Transport interval 4.37 min, 8.20 min, … Numeric Port Stack interval 249.44 h, 98.29h, … Numeric Port Container type HC, RH, FR, RF, RH, TK, … Factor Port Container size 20 ft, 40 ft, … Factor Port Road transportation distance 580.26 km, 149.08 km, … Numeric Port Road transportation time 7.16 h, 1.93 h, … Numeric Port Road fuel cost 303.58 CNY, 77.99 CNY, … Numeric Port Road tolls 1047 CNY, 215 CNY, … Numeric Port Road total cost 3261.04 CNY, 763.26 CNY, … Numeric Port Empty container E, F, … Factor Port Trade type D, F, … Factor Port Rail transportation distance 825 km, 174 km, … Numeric Rail Rail transportation time 10.31 h, 2.18 h, … Numeric Rail Rail total cost 3067.6 CNY, 994.2 CNY, … Numeric Rail 95306 rail freight cost 3744.5 CNY, 853 CNY, … Numeric Rail Discount 1439 CNY, 430.5 CNY, … Numeric Rail 5.2 Experimental setup Considering that the GUBN-FJIG framework aims to identify similar transportation containers as potential freight demand, the data used for this case study was in-bureau container transport data, which has shown steady growth. The GUBN-FJIG framework's model was trained until the prediction accuracy reached the max- imum allowable iteration of 2,00. The Paillier method was used for privacy homomorphic encryp- tion (PHE), and the Adam optimizer was applied with the learning rate and weight decay, were tuned from a grid of {0.01,0.005,0.002,0.001} , and a batch size of 128, with 𝜆𝜆 = 0.1. All other hy- perparameters within the network remain at their default settings. First, the overall model’s performance was compared in terms of accuracy and on the test set, to evaluate the effectiveness of feature importance initialization based on information gain within the framework, and its comparison with other feature selection methods such as all-features, Sto- chastic Gates (STG) and Gini impurity using similar data protection mechanisms. The same net- work architecture and hyperparameters were used for all methods, with the ReLU activation func- tion and 𝑅𝑅 2 . Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 111 After completing the evaluation of feature selection methods, the effectiveness of the sample selection strategy based on the gradient upper bound norm in the framework was validated by comparing the model's training efficiency and accuracy on the test set with and without a sample selection strategy. 5.3 Results and discussion In the case study, 5-fold cross-validation was used to evaluate the impact of different feature se- lection methods on model performance. The dataset was divided into five subsets, with each sub- set used as a validation set while the remaining four were used for training. The average perfor- mance across all five folds was taken as the final evaluation metric to reduce bias introduced by data splitting and ensure the stability and reliability of the results. Fig. 4a shows the change in training loss for different feature selection methods during train- ing. The FJIG method achieved the fastest initial decline in training loss and eventually reached the lowest final training loss, indicating its high efficiency and good overall model performance. Its feature selection process effectively filtered out irrelevant features, allowing the model to focus on more valuable ones, improving training efficiency. Fig. 4b shows the average validation accu- racy of the five-fold cross-validation using different feature selection methods (including no fea- ture selection). STG, Gini, and FJIG methods are compared in terms of average accuracy. The re- sults show that the FJIG method achieved significantly better validation accuracy than the other methods, especially after epoch 100, where its accuracy remained stable with less fluctuation. In contrast, the testing accuracy of the all-features method was significantly lower than other meth- ods. Fig. 4 Training loss and test accuracy of different feature selection methods over training epochs Fig. 5 shows the average R² values across different feature selection methods during the 5-fold cross-validation. The results indicate that the FJIG method consistently maintained the highest R² value throughout the training process. In particular, towards the later stages of training, FJIG's R² value stabilized at a high level, significantly outperforming other feature selection methods. This suggests that the FJIG method, by removing noisy features, better fits the data and improves the model's predictive ability. Both STG and GINI also performed well in terms of R² but slightly lagged behind FJIG. The R² value for the all-features selection method was significantly lower than the other methods, indicating that it struggled to effectively utilize the features, especially in the pres- ence of many noisy features. Fig. 6 shows the changes in the number of selected features during training for different feature selection methods. The FJIG method quickly reduced the number of features early in the training process and stabilized at the minimum number of features towards the later stages. In contrast, the STG and GINI methods selected slightly more features than the FJIG method. The ability of the FJIG method to maintain high model performance with fewer features demonstrates its effective- ness in the feature selection process. Huang, Jiang, Bai 112 Advances in Production Engineering & Management 20(1) 2025 Fig. 5 R-squared of different feature selection methods over training epochs Fig. 6 Number of selected features by different feature selection methods over training epochs Fig. 7 Test Accuracy and Training Sample Selection Ratio of GUBN-FJIG Method over Training Epochs Fig. 7a shows the changes in test accuracy during training for the GUBN-FJIG method with and without sample selection. In the early stages of training (around the first 50 epochs), the test ac- curacy of the GUBN-FJIG method increased rapidly and gradually stabilized around 0.95. In con- trast, the FJIG method's test accuracy was slightly lower throughout the training process, stabiliz- ing between 0.90 and 0.95. The superior performance of the GUBN-FJIG method in terms of test accuracy indicates that its sample selection effectively improved the model's ability to generalize to unseen test data. Fig. 7b shows the proportion of selected training samples as the training progresses for the GUBN-FJIG method. In the early stages of training, the proportion of selected samples gradually decreased, likely because the model had not yet converged, making sample importance judgments Privacy-preserving AI-based framework for container transportation demand forecasting in sea-rail intermodal systems Advances in Production Engineering & Management 20(1) 2025 113 less stable, leading to more samples being excluded. As training progressed, the proportion of se- lected samples stabilized and slightly increased towards the later stages, with the final selection rate stabilizing at around 40 %. This demonstrates that the GUBN-FJIG method can dynamically adjust the number of training samples involved in the process. Reducing the number of training samples in the early stages may help accelerate model convergence. In the later stages, slightly increasing the number of selected samples ensures that the model is exposed to enough infor- mation near convergence, further optimizing performance. In conclusion, the GUBN-FJIG method enhances training efficiency and generalization performance by effectively selecting training sam- ples. The dynamic changes in the sample selection ratio reflect the method's advantage in evalu- ating and adapting to sample importance at different stages of training. 6. Conclusion In this study, we proposed the GUBN-FJIG framework, which combines Gradient Upper Bound Norms (GUBN) and Feature Joint Information Gain (FJIG) for effective sample and feature selec- tion in container transportation demand forecasting. Our approach addresses the challenges of identifying potential freight containers in the sea-rail intermodal transportation system while en- suring data privacy and computational efficiency. Through extensive experiments, we demonstrated that the GUBN-FJIG method significantly improves model performance in terms of both accuracy and efficiency. By dynamically selecting important samples during training and filtering out irrelevant features, the method accelerates model convergence, reduces overfitting, and enhances the model's generalization ability. Our re- sults showed that GUBN-FJIG consistently outperformed other feature selection methods, such as STG and GINI, especially in scenarios with noisy features and large datasets. Moreover, the GUBN-FJIG method’s dynamic adjustment of the number of training samples during different stages of training contributed to its superior performance. By selecting fewer samples in the early stages to speed up convergence and increasing the sample size near conver- gence, the model maintained a balance between training efficiency and final performance. In conclusion, the GUBN-FJIG framework offers a robust solution for container transportation demand forecasting in sea-rail intermodal systems. It not only optimizes model performance but also ensures data privacy protection through privacy-preserving techniques such as homomor- phic encryption and random noise. From a business perspective, the framework enhances the ability of railway operators to more accurately identify potential container freight demand, lead- ing to more informed decision-making for resource allocation and capacity planning. This results in improved operational efficiency, reduced transportation costs, and better coordination be- tween sea and rail modes, ultimately improving service reliability and customer satisfaction. Fu- ture work could explore other scenarios of intermodal transportation systems and further im- proving the feature and sample selection strategies for even more efficient training and predic- tion. 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