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  • ZHANG Qiangjing, MA Yulu, SUN Xiaoqiang
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250340
    Accepted: 2025-09-27
    Based on the development concept of "Lucid waters and lush mountains are invaluable assets",this paper takes the establishment of five provincial (autonomous region) green finance reform and innovation pilot zones in 2017 as a quasi-natural experiment, and uses the panel data of 286 prefecture-level cities from 2011 to 2022 to construct a difference-in-differences (DID) model to empirically examine the impact of green finance innovation on green total factor productivity. The results show that:(1)The establishment of the green finance reform and innovation pilot zone has significantly improved the level of green total factor productivity and achieved a win-win situation between economic development and ecological protection.(2)The mechanism analysis shows that industrial structure upgrading and government innovation preference are important channels for green finance innovation to play a role.(3)The heterogeneity analysis found that the policy effects of the pilot areas were significantly different due to different geographical locations, resource endowments and economic development levels. This study not only provides empirical evidence for the double dividends of the economic environment of green finance reform, but also provides an important reference for the expansion of the subsequent pilot zone and the design of differentiated policies.
  • SUN Ling-Li, YANG Gui-Jun, HUA Xia-Long, QIAO Ting-Ting
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms240970
    Accepted: 2025-09-24
    The China labor force survey uses a weighted summation method to estimate target variables, which has certain gap in estimation accuracy compared with the calibration composite estimation method. The calibration composite estimation method is the mainstream estimation approach for rotation sample surveys. This study aims to construct a calibration composite estimator for China.s labor force survey by introducing the calibration composite estimation method and fully tapping auxiliary information of rotation samples improve estimation accuracy. The main research work is as follows: (1)Propose a one-step calibration composite estimator based on the 2-10-2 rotation model of China.s monthly labor force survey and discuss the approximate unbiasedness, variance, and variance estimation of the new estimator. (2)Conduct a Monte Carlo simulation to compare the one-step calibration composite estimator with the calibration composite estimator and the weighted estimator used in labor force surveys, and test the superiority of the one-step calibration composite estimator. (3)Through applied research, the specific process of the one-step calibration composite estimation is fully demonstrated, clarifying the technical details of the estimation method for practitioners in the statistical department. The research content of this paper is expected to be applied to China’s labor force survey and promote the reform of government statistical survey systems and methods.
  • LI Jing, YUAN Xiaohui, WANG Chunjie
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250154
    Accepted: 2025-09-22
    To deeply investigate the challenges faced in handling big data, we extend the poisson subsampling algorithm into the classic Cox proportional hazards model in the field of survival analysis under the framework of big data. This algorithm eliminates the need to precompute the sampling probabilities for all sample points, signi cantly enhancing computational e ciency compared to traditional sampling with replacement. It e ectively addresses the challenge of statistical analysis of large-scale survival data when computational resources are limited. Rigorous proof demonstrates the consistency and asymptotic normality of parameter estimates based on poisson subsampling, ensuring the theoretical reliability of the method. For practical application, a two-step algorithm is proposed. Simulation and empirical studies show that the application of the poisson subsampling algorithm in the Cox proportional hazards model is not only theoretically feasible but also demonstrates remarkable practical e ects, providing a new and e cient statistical tool for the field of survival analysis.
  • CHEN Cong, WANG Fanxin, ZHAO Sisi, PAN Jiayin, XU Yinfeng
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250402
    Accepted: 2025-09-22
    In cloud computing environments, user-driven resource selection is increasingly prevalent, as users tend to choose servers based on their own needs (such as latency and cost) to execute multiprocessor tasks. However, this decentralized and self-interested decision-making can lead to imbalanced resource utilization, thereby prolonging the maximum completion time of all tasks (Makespan) and impairing overall system efficiency. To address this challenge, this paper investigates the scheduling game model for tasks occupying consecutive multiple servers and designs a ‘Widest First’ (WF) coordination mechanism. The mechanism guides user decisions through a simple local policy: servers prioritize processing tasks with a larger width (i.e., those requiring more servers). Theoretical analysis shows that the WF mechanism limits the Price of Anarchy (PoA) to a constant upper bound of 4-3/m, a significant improvement on the worst-case performance guarantee compared to the unbounded PoA in uncoordinated scenarios. Further numerical experiments validate the mechanism’s excellent average-case performance: with an improved tie-breaking rule, the efficiency loss of the resulting equilibrium can be controlled to around 5% (PoA ≈ 1.05), far outperforming the theoretical worst-case bound. This research offers a practical strategy for cloud platform managers to balance user autonomy with system efficiency, holding significant theoretical and practical value.
  • LIU Rong, HE Zerong
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250209
    Accepted: 2025-09-17
    This paper establishes a hybrid hierarchical age-structured model with encounters mechanism based on the reproductive laws of vermin to describe the optimal contraception control problem of vermin. The state system consists of a firstorder partial differential equation with a global feedback boundary condition and two ordinary differential equations. Firstly, the existence of a unique non-negative bounded solution to the model is established, and some continuity results are given. Then, the optimality conditions given by the feedback forms of state variable and adjoint variable are obtained by constructing a proper adjoint system and using tangent-normal cones techniques. Meanwhile, the existence of a unique optimal policy is proved via Ekeland’s variational principle and fixed-point theory. Finally, some numerical simulations have been performed to demonstrate the feasibility of the obtained results.
  • CHEN Feiyan, YANG Yifan, WU Tong
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250171
    Accepted: 2025-09-16
    In the Internet and digital era, recommendation algorithms serve as essential technologies for enabling users to extract useful information from massive volumes of data. Traditional recommendation algorithms typically prioritize user ratings as the core basis, while overlooking the emotional information embedded in online reviews and the phenomenon of potential changes in user preferences which results in low levels of recommendation accuracy and personalization. To analyze the hidden emotional information in film reviews and the variation law of user interests, this study proposes a dynamic movie recommendation algorithm considering sentiment dictionary construction and user interest drift. First, considering the perceptual bias of general sentiment dictionaries toward movie reviews, a domain-specific sentiment dictionary is constructed, tailored to distinguish between different movie genres. Then, sentiment analysis is performed on movie reviews using this specialized sentiment dictionary to correct user ratings. Additionally, user interest changes are modeled based on Ebbinghaus’s forgetting curve, leading to the development of a dynamic movie recommendation algorithm that accounts for user interest drift. Finally, the algorithm’s effectiveness is verified using the Douban Movie dataset, with evaluation based on recall, precision, and F1 score. Experimental results demonstrate that the sentiment dictionary built in this paper has significant domain adaptability and emotional recognition advantages. The proposed dynamic movie recommendation algorithm is better able to capture hidden emotional information and user interest changes in reviews, providing recommendations that are more aligned with users’ current needs compared to traditional methods.
  • MA Yunfeng, YU Jing, Zhang Jiayi, Hou Wenjie, Ren Liang, Gao Dongpo
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250472
    Accepted: 2025-09-16
    The shuttle-based storage and retrieval system with two lifts exhibits remarkable features such as compactness and high efficiency. Dual-command operation, favored for its effectiveness in minimizing equipment idle time, is commonly employed in warehouse system scheduling. However, incorporating dualcommand operations while managing conflicts between the two lifts introduces significant complexity into the scheduling decisions. This paper addresses the scheduling challenges of the shuttle-based storage and retrieval system with two lifts by focusing on minimizing the makespan through a comprehensive consideration of dual-command operations and dual-lift constraints. A mixed-integer programming model is formulated to tackle these issues. Given the NP-hard nature of this problem, a two-stage algorithm is proposed by combining the adaptive large neighborhood search algorithm and dynamic programming. To align with real-world scenarios, three types of instances, namely small, medium, and large-scale, are designed, and the two-stage algorithm is benchmarked against the Gurobi solver, the Sequential Matching algorithm, and the Particle Swarm Optimization algorithm to evaluate its efficacy. The findings indicate that: (1) Lift speed exerts a significant impact on system efficiency, yet its marginal benefits decline with increasing speed; (2) For a given input/output point, there exists an optimal speed ratio between the upper and lower lifts; (3) Dual-command operations enhance efficiency by 42.72% compared to single-command operations, while dual-lift systems achieve a 47.09% improvement over single-lift systems. The study provides a scientific foundation and algorithmic basis for managers to develop effective scheduling strategies and offers theoretical support for optimizing the configuration of shuttle-based storage and retrieval systems with two lifts.
  • Jiang Chao, ZHANG Xinhua, An Chaofan
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250574
    Accepted: 2025-09-16
    During the critical period of transformation in the real estate industry, clarifying the optimal business layout strategy for real estate enterprises under multiple entities holds significant implications for implementing the principle that "houses are for living in, not for speculation", establishing a long-term mechanism for real estate development, and resolving deep-seated contradictions in the economic structure. Based on the framework of "policy regulation credit constraint", and in accordance with the theoretical systems of risk-return, credit constraint and social welfare, this paper constructs an evolutionary game model among real estate enterprises, banks and the government, and conducts simulation to explore the evolutionary game equilibrium state of the three participating entities and the specific impact of different parameter values on the stable equilibrium point. The research finds that, The scissors gap in investment returns between the real economy and the virtual economy is the key factor determining the strategic equilibrium of real estate enterprises. When the deep-seated contradiction of the separation of industry and finance is resolved, real estate enterprises can increase their layout in the financial market. Meanwhile, real estate enterprises are not sensitive to changes in the risk coefficient of financial investment, which will lead to the concealment and transfer of potential systemic risks. When the banking sector relaxes the entry threshold, that is, when competition among banks becomes the optimal strategy choice, it can alleviate the financing constraints faced by real estate enterprises, and the degree of friction in the credit market can determine the time it takes for the game to evolve to an equilibrium state. Regulatory costs and social welfare are key factors influencing the balanced strategies of government departments. The research of this article provides a useful reference for improving the real estate market and preventing the economy from deviating from the real economy to the virtual economy.
  • SONG Haijun, YU Jiangbo, ZHAO Yan, DING Xueying
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250391
    Accepted: 2025-09-15
    This paper addresses the finite-time anti-disturbance control problem for a class of chained nonholonomic systems subject to unknown parameters and mismatched disturbances. Leveraging a finite-time disturbance observer, a novel adaptive finite-time anti-disturbance control scheme is developed via the power integrator technique. To tackle the challenge that nonholonomic systems cannot be stabilized by continuous time-invariant feedback, a switching control strategy combined with the prescribed performance control concept is employed. Moreover, the restrictive assumptions on mismatched disturbances in existing literature are relaxed. The proposed approach effectively compensates for both unknown parameters and external mismatched disturbances, while ensuring practical finite-time stability of the closed-loop system. Rigorous theoretical analysis validates the convergence and robustness properties. Finally, numerical simulations are provided to demonstrate the superiority and effectiveness of the developed method, highlighting its potential for practical applications in robotic and vehicular systems.
  • PENG Jiangtao, YANG Jie, XIE Qiwei, SHEN Lijun, ZHOU Qiyin, YAN Qing
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250558
    Accepted: 2025-09-12
    Vision-language models (VLMs) can address the lack of interpretability caused by the black-box nature of end-to-end autonomous driving systems through natural language interaction, thereby improving the transparency and reliability of decision-making in such systems. Typical VLMs align visual and textual features using lightweight projection (‘glue’) layers, but due to their simple structure and random initialization, they often struggle to capture the complex relationships between modalities. When handling video question answering tasks, conventional VLMs rarely consider both fine-grained feature extraction and temporal modeling across video frames. Moreover, existing methods usually involve large-scale parameters, making practical deployment difficult. To tackle these issues, this paper proposes a lightweight driving VideoQA model based on fine-grained feature skip connections and spatiotemporal attention fusion, which effectively aligns video and textual features and fully exploits fine-grained visual information. The spatiotemporal attention gating module dynamically captures intra-frame fine-grained information and models inter-frame temporal dependencies by combining spatiotemporal attention with a gating mechanism, thereby adaptively fusing multi-frame features to enhance video representation. The alignment adapter and loss module guides the adapter to learn cross-modal feature mappings through an alignment loss function, achieving semantic alignment between visual and textual features. The fine-grained skip connection module introduces a residual connection variant and gating mechanism to inject detailed information into the encoder features of the large model, enabling better utilization of fine-grained features during decoding and mitigating the issue of detail loss caused by deep networks. Experimental results demonstrate the effectiveness of the proposed model, which achieves strong performance across key evaluation metrics.
  • JU Hongmei, ZHOU Fei, MENG Fan
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250264
    Accepted: 2025-09-11
    Noise, outliers, and class imbalance issues in real-world classification tasks can weaken the robustness of machine learning models. To address this, this paper proposes PSO-FTSVM, a hybrid framework combining the particle swarm optimization(PSO) algorithm with a fuzzy membership-driven twin support vector machine(TWSVM). The model combines methods based on class center distance and kernel density estimation, introducing a hybrid fuzzy membership function that dynamically assigns membership based on the global distribution and local density of samples, thereby enhancing the representativeness of critical samples. Additionally, PSO is utilized to adaptively optimize the model’s key parameters, thereby improving its generalization capability. Experiments on 10 datasets show that the PSO-FTSVM achieves an average accuracy of 92.011%?1.863, representing improvements of 14.080% and 10.587% over the baseline TWSVM and FTSVM, respectively. The model demonstrates outstanding performance in handling highly imbalanced datasets and maintains stable performance in noisy environments, showcasing exceptional robustness.
  • LV Zhuofan, WU Yun, ZHOU Kai, TANG Jingru, WANG Yijing, XU Xiaofeng, SHAN Xian
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250518
    Accepted: 2025-09-11
    Accurate natural gas consumption forecasting can help the effcient utilization of natural gas resources, and thus provide a reference basis for the operational decisions of natural gas sales enterprises. Existing studies have proved that combined forecasts show better forecasting accuracy than single forecasting models, among which the model averaging method represented by the Mallows et al. criterion is particularly outstanding in combined forecasts, which can significantly improve the forecasting accuracy. However, the traditional Mallows criterion does not consider the influence of time factor on the data in the process of determining the weights, ignoring the recent trend evolution of the data, which is inconsistent with the reality and may lead to a decrease in prediction accuracy. In this paper, we propose an improved Mallows criterion considering the weight of data timeliness by using the idea of exponential smoothing. By giving a higher weight to the recent error, we can accurately fit the current data distribution and realize the accurate prediction of natural gas consumption. In order to verify the effectiveness of the proposed method, this paper uses the dataset of monthly natural gas consumption in Hangzhou to analyze, and the results show that the RMSE, MAE, and MAPE of the proposed method are 0.2332, 0.2179, and 7.36%, and the prediction accuracy is significantly improved compared with the single-model prediction and the combination of the prediction under the other classical criteria.
  • WANG Ziming, ZHOU Baohuan, TAO Tao, LIANG Liang
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250443
    Accepted: 2025-09-10
    Ensuring vaccine safety remains a global public health priority, particularly given recent scandals highlighting the vulnerabilities of traditional vaccine supply chains, including opaque information flows and risks of data tampering. As an emerging technological solution, blockchain offers features such as decentralization, immutability, and traceability, which are highly relevant to enhancing vaccine supply chain transparency and reliability. This paper develops a theoretical model of a two-tier vaccine supply chain, comprising one vaccine manufacturer and two symmetric inoculation units, to explore the strategic impact of blockchain adoption, referred to as “on-chaining”, on supply chain participants’ pricing and participation decisions under competitive conditions. The results demonstrate that on-chaining enhances consumers’ trust in the safety and quality of vaccines, which in turn increases demand for vaccines provided by participating inoculation units. Consequently, both wholesale and retail prices tend to rise following blockchain adoption. However, the effects on each supply chain member’ s profit are asymmetric and highly sensitive to several contextual factors, including the proportion of qualified vaccines, market potential, vaccine production costs, and competitive intensity between inoculation units. Notably, while on-chaining leads to greater transparency, it can impose additional costs on inoculation units due to the need to discard unqualified vaccines, potentially reducing their profits. Meanwhile, non-adopting units may benefit from positive externalities created by their competitors’ on-chaining, thereby weakening the competitive advantage of early adopters. This article provides theoretical support for the practical application of blockchain technology in the vaccine supply chain, and provides useful reference for technology adoption and pricing decisions of supply chain members.
  • TANG Liping, JIANG Qian
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250521
    Accepted: 2025-09-10
    This paper investigates the characterization of (weakly) efficient solutions for nonsmooth multiobjective optimization problems from the perspective of fixed point. First, by using the upper semicontinuity of the Mordukhovich subdifferential mapping and the corresponding mean value theorem, it is shown that the a (weakly) efficient solution of nonsmooth multiobjective optimization problem corresponds to a Kakutani fixed point of a certain set-valued mapping. Subsequently, Fritz John necessary optimality conditions for (weakly) efficient solutions are established, and under suitable constraint qualification conditions, the Karush-Kuhn-Tucker type necessary optimality conditions are further derived. Finally, under the assumption of generalized convexity, it is provided that the Kakutani fixed points of the associated set-valued mapping are sufficient for (weakly) efficient solutions of the nonsmooth multiobjective optimization problem.
  • Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250296
    Accepted: 2025-09-09
    灾前规划和灾后抢修是提高城市道路交通系统韧性的关键策略.本文考虑道路受损异质性以及受损道路位置、恢复时间和受损类型的多维不确定性,以综合韧性指标最大为目标,构建城市道路交通系统设施选址与抢修调度两阶段随机规划模型.根据所构建模型的结构特征,设计基于浓度集的样本平均逼近(SAA)算法.实验结果表明,本文提出的韧性最优恢复策略优于传统随机、策略,且基于浓度集的SAA算法可以快速求解该问题.研究成果可为制定面向韧性提升的城市道路交通系统设施选址和应急抢修调度方案提供决策依据和算法支撑.
  • YAN Hui, XU Yangdong
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms240911
    Accepted: 2025-09-06
    As a classical imprecise line search method in multiobjective optimization, the Armijo line search can fully guarantee the reduction of all objective functions. However, empirical results show that the Armijo line search often results in a very small stepsize along the steepest descent direction, which seriously prolongs the time required for the algorithm to converge. To address this limitation, this paper proposes a Barzilai-Borwein descent method for multiobjective optimization problems with weak Armijo line search. The stepsize updating in weak Armijo line search needs to satisfy all inequalities simultaneously, which makes it possible to reduce only one objective function value in some iterations. Thus, it is a nonmonotone line search. In addition, the convergence property of the algorithm is proved. Finally, numerical examples show that the multiobjective Barzilai Borwin algorithm with weak Armijo line search strategy significantly outperforms the existing ones with Armijo line search strategy and other nonmonotone line search strategies.
  • ZENG Shouzhen, WAN Huanyu, GAO Luhong
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250403
    Accepted: 2025-09-04
    To address the Pythagorean fuzzy multi-criteria group decision-making problem, this study proposes an integrated method that incorporates newly developed Pythagorean fuzzy entropy and distance measures. First, a novel Pythagorean fuzzy entropy is proposed to overcome the limitations of existing entropy measures in specific contexts, thereby enabling a more accurate computation of criterion weights. Second, addressing the deficiency of existing Pythagorean fuzzy distance measures that fail to satisfy the property of triangular inequality, a new Pythagorean fuzzy distance measure is proposed to enhance the theoretical foundation of such measures. On this basis, a GRA-TOPSIS multi-criteria group decision-making method is developed by integrating grey relational analysis (GRA) and TOPSIS method with the new entropy measure and distance measure. Finally, the feasibility and effectiveness of the proposed method are validated through a comparative evaluation of the development level of "zero-waste cities".
  • PAN Haifeng, LI Chenchen, CHEN Junhao, FEI Weiyin
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250311
    Accepted: 2025-09-02
    By integrating the time-varying parameter vector autoregression (TVPVAR) model with the Diebold-Yilmaz (DY) spillover index model, this paper explores the dynamic relationships among climate policy uncertainty (CPU), global stock markets, bond markets, and commodity markets. It measures the intensity of cross-market risk spillovers, analyzes the time-varying characteristics of risk linkages and spillovers among these markets, particularly their dynamic fluctuation characteristics under the influence of major events. Furthermore, optimal portfolio weights are constructed under different objectives, such as minimum variance, minimum correlation, and minimum connectedness. Their performance is evaluated in terms of hedging effectiveness and Sharpe ratios. The results indicate that the spillovers across financial markets under CPU exhibit significant time-variation and dynamics, which are strongly influenced by major events and policy uncertainties. Heterogeneity exists in the dynamic net connectedness of different assets. The S&P 500 and the STOXX 50 act as key systemic risk transmission nodes in global financial markets. U.S. Treasuries show a net spillover effect, while German and Chinese Treasuries demonstrate a net spill-in effect. In the commodity market, copper and crude oil display large fluctuations in net connectedness. The dynamic paths of portfolio returns are broadly aligned across strategies, but structural differences exist, requiring dynamic adjustments in allocation to optimize portfolio performance. CPU plays an important role in portfolio optimization strategies. Incorporating CPU into crossmarket portfolios can effectively improve both mean returns and Sharpe ratios of the portfolios.
  • SHEN Hanlei, GE Shaohua, ZHANG Hu
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250543
    Accepted: 2025-09-02
    Short-term market trading is a core element of financial decision-making. However, the complexity and dynamism of financial markets pose significant challenges for forecasting short-term trading volume. To address this issue, this paper proposes a Graph neural network with Heterogeneous ATtention (GHAT) model. The model specifically integrates the high-noise characteristics, unique U-shaped pattern, and cyclical features of short-term trading volume to construct a tailored graph neural network, incorporating a heterogeneous attention mechanism. The research findings demonstrate that, within the complex environment of the Chinese stock market, the GHAT model significantly outperforms benchmark models, including ARMA, CMEM, GAMMA, SVR, LSTM, and Graph Convolutional Networks (GCN), in terms of predictive performance. Ablation studies further reveal that the introduction of the attention mechanism and adjacent nodes with a one-period lag effectively enhances the predictive accuracy for current-period stock trading volume. Heterogeneity analysis indicates that the GHAT model demonstrates superior performance in forecasting the short-term trading volume of stocks characterized by high market capitalization, high liquidity, and pronounced market trends. The GHAT model effectively addresses complex issues in short-term trading volume forecast, such as multivariate, nonlinear, and non-stationary characteristics, providing a novel methodological framework for research in areas such as financial trading, traffic flow, and crowd dynamics forecasting.
  • QU Guohua, PENG Yuqing, LI Chunhua
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250158
    Accepted: 2025-09-01
    The active and steady promotion of carbon peaking and carbon neutrality in the Yellow River Basin has become a major issue of continuous domestic concern. During the process of promotion, the participation of the government and enterprises is particularly important. Based on the connotation logic of promoting carbon peaking and carbon neutrality in the Yellow River Basin by new quality productivity, this paper analyzes the mechanism of the government’s role in promoting enterprises to achieve carbon peaking and carbon neutrality in the Yellow River Basin under the background of new quality productivity, and constructs an evolutionary game model of the government and enterprises under the background of new quality productivity for theoretical and simulation analysis. The research results show that the evolutionary path of the government and enterprises presents a bistable characteristic. That is, the system has two stable equilibrium points: (0,0) (government subsidy enterprises actively develop new quality productivity) and (1,1) (no subsidy enterprises passively respond), verifying the symbiotic relationship between policy incentives and enterprise responses. Dynamic subsidies have a significant leverage effect. When the government subsidy C is dynamically adjusted with the enterprise’s enthusiasm (1-y), the system nearly converges 100% to a win-win situation, indicating that precise policy measures can break the "subsidy dependence" dilemma. The cost sensitivity of enterprises dominates the strategy choice, while multi-dimensional heterogeneity requires differentiated governance in the Yellow River Basin. Based on this, this article suggests that the government should urge enterprises to actively develop new quality productivity through creating a differentiated policy environment, maintaining information symmetry and sharing between the government and enterprises, and establishing a supervision and management system, with the aim of achieving carbon peaking and carbon neutrality in the Yellow River Basin as soon as possible.
  • GU Nannan
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250635
    Accepted: 2025-08-31
    Graph-based semi-supervised dimensionality reduction is one of the most effective techniques in its field, yet some issues remain inadequately addressed. For example, how to leverage unlabeled samples to enhance class discriminability in the low-dimensional feature space, and how to effectively handle data with varying noise levels or even outliers. To tackle these problems, this paper proposes a self-paced semi-supervised dimensionality reduction method based on a sparse structured graph. The proposed method firstly implements label propagation on a sparse structured graph to get the pseudo-labels of unlabeled data. Then, it utilizes the self-paced learning regime to get the feature projection by incorporating data sequentially from simple to complex ones, where the easiness/importance of each unlabeled sample is measured by the smoothness loss of the feature projection at the sample, and the intra-class distance between the low-dimensional representation of the sample and the corresponding class anchor. In this way, a more and more mature model can be obtained in the robust self-paced manner. The proposed method can evaluate the importance of samples, which helps to differentiate the effects of samples on feature projection learning and suppress the negative effect of unreliable pseudo-labels. The method is also robust to data with noise or outliers. Besides, the method utilizes both unlabeled and labeled data to promote class discrimination in the low-dimensional feature space. Finally, the method is nonlinear and inductive. Experimental results demonstrate the effectiveness of the proposed method.
  • ZHANG Wanli, YANG Degang, LIN Wenting
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms240934
    Accepted: 2025-08-27
    This paper investigates finite-time control and bipartite synchronization of complex networks with quantized delayed couplings. The connections of networks are described by using signed graph and couplings. The parameters are introduced to characterize the different rates of the states for the nodes. The discontinuity of activation function and proportional delay coupling are also considered. Via 1-norm, non-delay-dependent controllers are designed. Those controllers don’t include sign function and they can be used to overcome the chattering of control signals. Based on the fact that the classical finite-time stability theorem is invalid to deal with delayed systems, the 1-norm analytical method is developed to realize finite-time synchronization of the considered networks. Moreover, the influences of proportional delays are overcome by using 1-norm Lyapunov functions. Some useful results of finitetime synchronization are also obtained by considering the simple forms of complex networks. Finally, numerical simulations are given to present the effectiveness of the theoretical results.
  • MU Weiyan, ZHANG Yuqing, QIAO Ziheng, XIONG Shifeng
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250367
    Accepted: 2025-08-27
    Multi-factor mixed-level experiments are commonly encountered in engineering and other fields. There is no universal method for designing such experiments, and iterative search algorithms are often required for their construction. This paper proposes an Enhanced Stochastic Evolution (ESE) algorithm to construct multi-factor mixed-level experimental designs. The algorithm integrates the advantages of the Stochastic Evolution Algorithm and the Simulated Annealing Algorithm, forming a dual-loop optimization framework. The inner loop performs local fine-tuning through directed element swaps in the design matrix, while the outer loop adjusts the global exploration intensity using an adaptive threshold. This approach effectively balances global search and local optimization efficiency. The algorithm exhibits strong flexibility, being compatible with various optimization criteria including maximin distance and discrepancy measures, and can be readily adapted to generate designs that satisfy specified constraints. Numerical experiments demonstrate that the ESE algorithm significantly outperforms traditional algorithms in terms of optimization efficiency and computational speed.
  • WANG Haijun, LI Xian, LI Ziyi, SU Danhua
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250319
    Accepted: 2025-08-26
    Household debt risk is a critical determinant of systemic financial risk, significantly impacting financial stability and social welfare. This study utilizes data from the China Family Panel Studies (CFPS) spanning 2012-2022 to construct a comprehensive database comprising 62 variables and 23,578 observations that integrates macroeconomic indicators with micro-household characteristics. This paper employs seven machine learning algorithms encompassing traditional econometric models, deep learning approaches, and ensemble learning methods to predict household debt risk. Through systematic comparison and fusion optimization using both Blending and Stacking fusion strategies, this paper examines the predictive performance of these models. The empirical results demonstrate that ensemble learning models significantly outperform traditional econometric approaches, with accuracy, precision, and AUC values exceeding 0.92. The Stacking fusion model achieves the highest AUC of 0.9852, representing a 47% improvement over the baseline Logit model. Using SHAP analysis, we identify that household asset variables, income-debt characteristics, and demographic-social structure factors exhibit significant nonlinear effects on debt risk. Our findings suggest that machine learning fusion models offer superior predictive capability for household debt risk assessment, providing valuable insights for financial regulation and policy formulation in managing systemic financial risks.
  • HAN Chen, TANG Xijin
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250173
    Accepted: 2025-08-26
    With the development of artificial intelligence, the dissemination of disinformation has accelerated, and its content has become increasingly complex, posing new challenges to social cognition and the information ecosystem. As a critical channel for information dissemination, technology news not only reports developments related to disinformation but also shapes public perceptions of the issue. However, existing research lacks a systematic analysis of how technology news reports on disinformation.This study examines the coverage of disinformation in technology news by analyzing the news articles published by ACM TechNews from 1999 to 2025. Employing keyword extraction, dynamic topic modeling, named entity recognition, and co-occurrence network analysis, this research explores the characteristics of disinformation in the technology domain. The findings indicate that since 2016, technology news on disinformation has increased significantly, with a shift in topics from cybersecurity to social media, artificial intelligence, and political elections. Additionally, the forms of disinformation dissemination have evolved from traditional text-based content to audios and videos. Furthermore, co-occurrence network analysis reveals that U.S. politicians, major international countries, and technology companies have become central actors in the discourse on disinformation.
  • SHI Guiqiang, LI Xiao, SHEN Dehua
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250321
    Accepted: 2025-08-26
    Investor attention allocation plays a pivotal role in micro-market research. This paper constructs an artificial Bitcoin market comprising whale traders, trend traders, and noise traders to examine how attention allocation shapes volumeprice dynamics. The results demonstrate that the volume-price relationship in the artificial market aligns with the Sequential Information Arrival Hypothesis but contradicts the Mixture of Distribution Hypothesis. By defining the most extreme 1% returns of the S&P 500 Index as exogenous attention shocks, the analysis reveals that these shocks enhance the contemporaneous correlation between trading volume and prices while diminishing their lead-lag relationship. This effect accelerates price adjustments to new information. In sensitivity analyses, we systematically examine the robustness of these results by: (1) adjusting the proportion of whale traders, (2) varying the threshold for exogenous shocks, (3) substituting the proxy variable from the S&P 500 Index to the DJIA, and (4) modifying the share of noise traders. The core conclusions remain robust across all these alternative specifications. The study not only extends cross-market research on investor attention allocation but also offers fresh insights into interpreting market volume-price dynamics.
  • TAN Bing, LI Yi-feng, YANG You, ZHAO Guang-ming, SUN Xiao-chi, LIU Xue-wen
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250109
    Accepted: 2025-08-22
    Yard cranes (YCs) are the primary loading and unloading equipment in container terminal yards, and their scheduling efficiency is a critical factor influencing the overall operational efficiency of the terminal. This paper studies YC scheduling in multi-crane and partitioned zones, based on task priority and YC occupancy level. Firstly, the execution priority of YC tasks is defined, and YC occupancy level is introduced to characterize the balance of YC operations. It is worth noting that most existing literature measures YC balance solely based on the number of tasks, while YC occupancy level depends not only on the quantity of tasks but also on their difficulty. Secondly, considering different types of tasks, a mixed-integer programming model is constructed with the objective of minimizing the sum of YC idle time and the variance of YC occupancy level, based on the concepts of task priority and YC occupancy level. Finally, a genetic algorithm is employed to solve the proposed model, and a case study is provided to demonstrate the effectiveness of the proposed method. Compared to existing research, the YC scheduling method based on task priority and YC occupancy level proposed in this paper is applicable to more general operational scenarios, while also improving the parallelism and efficiency of YC operations.
  • CHEN Jiali, PANG Zhiqiang, LING Ling, ZHANG Chongqi
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250469
    Accepted: 2025-08-22
    To better investigate practical research and development scenarios where responses are simultaneously influenced by mixture component proportions and their order of addition, this study employs optimality criteria for designs within mixture design regions defined by basic and additional constraints. We systematically examine saturated design problems covering no interaction, first-order interaction, and second-order interaction cases between component proportions and order-of-addition variables. Explicit closed-form solutions are derived for the D- and A-optimality criterion functions, the corresponding saturated optimal designs, and their associated D- and A-efficiencies under the order-of-addition-dependent q-component secondorder Scheffé centroid polynomial models. Analysis of these efficiencies reveals that A-optimal designs consistently demonstrate superior robustness compared to D-optimal designs when evaluated under combined optimality criteria. Case studies validate the theoretical findings.
  • HAN Meng-ying, GAO Kai-ye, YAN Rui, QIU Qing-an
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms240708
    Accepted: 2025-08-22
    The abnormal behaviors of protection systems, such as misoperation and refusal operation, can result in significant economic losses and pose safety threats to individuals and even the nation. In this paper, a condition-based and action-based maintenance strategy is proposed for a multi-state protection system with competing failure processes. A random shock model is employed to describe the action demand arrival process, where invalid shocks indicate that no protective actions are required, while valid shocks represent the arrival of actual action requirements, necessitating protective actions. The action behaviors depend on the system’s state: when an invalid shock arrives, a defective system may lead to misoperation; when an valid shock arrives, a defective system may exhibit refusal operation, whereas a failed system inevitably experiences refusal operation. The states of the system can only be detected by inspections. Based on the inspection outcomes, the system undergo defect-based or failure-based replacement if it is identified as defective or failed, respectively. Additionally, misoperation-based or refusal-operation-based replacement are required if misoperation or refusal operation occurs. Subsequently, a maintenance model aimed at minimizing the expected cost rate is constructed based on the probabilities of different renewal scenarios. The correctness of the proposed model is verified using a discrete-event simulation algorithm, and the practical applicability of the strategy is demonstrated through a numerical example. The results indicate that probabilities of misoperation and refusal operation in a defective system significantly influence the optimal inspection strategy, and the proposed model provides a theoretical basis and decision support for the maintenance of relevant systems in engineering practice.
  • GUO Fengjia, JIA Lifen, CHEN Wei
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250053
    Accepted: 2025-08-21
    This paper proposes a multi-attribute reverse auction (MARA) winner determination method for fourth-party logistics integrators (4PLI) selecting thirdparty logistics suppliers (3PLS). The method addresses incomplete and heterogeneous information while considering 4PLI risk preferences. It employs heterogeneous decision information, including real numbers, interval numbers, and probabilistic linguistic term sets (PLTS), to describe 3PLS price and non-price attributes. A trust transmission model and a trust aggregation model are built to establish a complete social trust network. Based on this network and information similarity, a model completes incomplete bid evaluation information. Furthermore, a hyperbolic absolute risk aversion (HARA) utility function is integrated into regret theory to characterize 4PLIs’ differentiated risk preferences. To handle attribute correlation, weights are determined using the Spearman correlation coefficient combined with the Criteria Importance Through Intercriteria Correlation (CRITIC) method. An improved probabilistic linguistic distance measure is then defined to quantify evaluation information differences. Combining this distance measure, the attribute weighting model, and the Evaluation based on Distance from Average Solution (EDAS), an alternative selection procedure for heterogeneous decision-making information is presented. Numerical examples verify the method’s effectiveness and superiority. This work extends MARA winner determination theory and provides practical methods for 4PLIs selecting partners.
  • LUO Guowang, WANG Luhong, WU Yuyao
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250208
    Accepted: 2025-08-21
    This paper considers statistical inference for spatial autoregressive models with measurement errors in covariates under restricted conditions. Under the condition that the measurement error variance is known or can be estimated, a bias-corrected restricted two-stage least squares (RC2SLS) estimation method and a test method are proposed for the model parameters. The asymptotic properties of the proposed estimators and test statistics are established under certain regularity conditions. Finally, numerical simulations are carried out to verify the proposed estimation and test methods.
  • SUN Rong, YIN Hao
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250257
    Accepted: 2025-08-21
    In the field of financial investment, non-stochastic uncertainty is widespread, and traditional portfolio models based on probability theory are unable to reflect this type of uncertainty. Given that fuzzy set theory can effectively deal with nonstochastic uncertain information, the theory of fuzzy portfolio has emerged accordingly. Considering the heterogeneity of investors’ expectations, this paper employs coherent fuzzy numbers to characterize asset returns and introduces an adaptive index k to reflect differing return aspirations. To enhance portfolio diversity, a novel proportional-entropy function is devised. By integrating realistic constraints such as transaction costs, liquidity, purchase thresholds, and cardinality limits, we construct a coherent fuzzy meanõvarianceõproportional-entropy model. Using historical daily data for ten Shanghai Stock Exchange stocks from 16 September 2022 to 24 January 2025, we evaluate portfolios via the fuzzy Sharpe ratio (FSR) and conduct empirical tests with an improved NSGA-II algorithm. Results show that optimal portfolio configurations emerge under varying adaptive settings. Compared with alternative models, the coherent fuzzy meanõvarianceõproportional-entropy model demonstrates marked advantages in return, risk control, and diversification, offering investors a more effective decision-making tool for portfolio optimization.
  • CAI Mei, CHEN Hao
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250369
    Accepted: 2025-08-20
    In view of the limitations of classical probabilistic models in dealing with complex decisions and the interference of overlapping communities on decision-making, a group decision-making method based on quantum cognitive theory considering the overlapping community division is proposed. Taking consumers’ multiple social identities as the breakthrough point, we reveal the mechanism of preference formation and group preference integration under the interference effect. Firstly, a fuzzy C-means clustering algorithm is used to divide overlapping communities based on the differences in decision-makers’ preferences, and the membership degree of an individual in different communities is obtained and quantized to reflect the individual’s superposition state of multiple community belongings. Then, in the framework of quantum-like Bayesian networks, the belief entropy method is used to quantify the interference effect between communities, modify the weight of decision makers and integrate group preferences. Finally, the method is used to analyze the online reviews to verify the influence of the interference effect between communities on the group decision results. The study shows that the quantized overlapping community division method can effectively capture the complex belonging relationship of individual consumers to multiple communities. And the quantum-like Bayesian network has stronger explanatory power in predicting consumer preferences under the interference of overlapping communities.
  • XIA Jiejin, YANG Xinjia, DENG Kaixin, YIN Zhujia
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250203
    Accepted: 2025-08-20
    Based on the data of Chinese A-share listed companies from 2007 to 2023, this study explores whether and how the board diversify promotes high-quality innovation of enterprises. The research findings show that board diversity has a positive impact on high-quality innovation overall. The mechanism analysis reveals that board diversity can effectively enhance the supervisory and governance functions of the board, and improve the role of attracting investment and talents. In the heterogeneity analysis, the effect of board diversity on high-quality innovation is more pronounced in non-state-owned enterprises and high-tech enterprises. Additionally, from a multi-dimensional analysis, the diversity of board members’ education level, social background, and experience helps to enhance high-quality innovation, while the diversity of demographic characteristics may have an adverse impact on innovation. Therefore, companies should aim at the specific issues and \embrace strengths and avoid weaknesses" to promote board diversity to improve the level of high-quality innovation, and regulatory authorities should issue more targeted guidelines to guide the boards of companies to achieve reasonable diversification.
  • REN Yuhang, FENG Zhongwei, YANG Yuzhong, TAN Chunqiao
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250065
    Accepted: 2025-08-18
    Consider a system consisting of an electric automaker (EA) with the ability to produce batteries and an EA without the ability to produce batteries, who build extra charging stations. This paper constructs a Cournot competition model, and respectively constructs a co-opetition model with independence-based pricing and a co-opetition model with negotiation-based pricing through Stackelberg game and Nash negotiation game. This paper investigates the optimal strategy choice and decisions of building extra charging stations for EAs. It is shown that: 1) The optimal strategy choice (i.e., competition, co-opetition with independence-based pricing and co-opetition with negotiation-based pricing) depends on the bargaining power of the EAs, the degree of electric vehicle substitution, the network efficiency of charging stations and the battery cost difference. And whether the wholesale price of batteries is determined through bargaining mainly depends on bargaining power. 2) When the EA with the ability to produce batteries has relatively high bargaining power, compared with bargaining, the EA with the ability to produce batteries can always benefit from the pioneer advantage in the Stackelberg game, but the Stackelberg game undermines the overall profits of the two EAs during cooperation-competition.3) Compared with the competitive strategy, when co-opetition strategies realize the Pareto improvement of EAs, the electric vehicle prices are also lower than the competition strategy. 4) When the co-opetition strategy is implemented, co-opetition strategy will make the EA without the ability produce batteries to build more charging stations, while it will cause the EA with the ability to produce batteries to build less charging stations. And co-opetition contracting can also affect decisions of building extra charging stations for EAs.
  • CHEN Jing, TANG Xueping, CHEN Liwei, ZHAO Heng
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250422
    Accepted: 2025-08-14
    Addressing the issue of battery strategy selection in the production and R&D of new energy vehicles by traditional automakers, a two-tier and three-tier automotive supply chain model is constructed, led by manufacturers and involving suppliers and dealers. Utilizing differential games and optimal control theory, the study examined the impact of various battery selection strategies on the optimal emission reduction trajectory for fuel vehicles, the optimal goodwill trajectory, and long-term profits under scenarios where fuel consumption targets are met or not met. The results reveal that: First, as time progresses, there is an observable increase in the emission reduction and fuel efficiency levels of fuel vehicles, as well as an enhancement in their brand goodwill. In the long term, the in-house battery development strategy demonstrates superiority over the external procurement strategy in terms of emission reduction, brand goodwill trajectories, and stable revenue values. Second, the credit price exhibits a threshold effect across various strategies. At low credit prices, the in-house development strategy offers a significant advantage in reducing carbon emissions. In contrast, at high credit prices, the purchased strategy responds more quickly under fuel efficiency compliance conditions. Thirdly, under the in-house development strategy, an increase in credit price effectively incentivizes manufacturers to allocate more resources to enhancing the range capabilities of new energy vehicles.
  • BIN Ning, ZHU Huai-nian
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250256
    Accepted: 2025-08-11
    This paper studies the time-consistent non-zero-sum stochastic differential game strategies for n competitive insurance companies. Insurance companies adopt the proportional reinsurance, and the risk process follows a compound Poisson risk model. Considering the stochastic correlation between risky assets, a multivariate 4/2 stochastic covariance model is introduced to characterize the price processes of two risky assets. The objective of each insurer is to find the optimal investment-reinsurance strategy so as to maximize the expected value of its terminal relative wealth while minimizing the variance of the terminal relative wealth. By introducing an auxiliary deterministic process, this paper obtains a modified mean-variance objective function, and constructs an alternative time-consistent mean-variance control problem. Then, by solving the HJB equation, the time-consistent equilibrium investment-reinsurance strategies for insurers are obtained. Finally, some numerical examples are provided to analyze the effects of important parameters on the equilibrium strategies. The results show that the intensification of competition between insurers will prompt them to adopt more aggressive investment and reinsurance behaviors; and at the same time, the correlation between risky assets in financial markets will also influence the decision-making of insurers.
  • XU Yanmei, ZHANG Yanan
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250195
    Accepted: 2025-08-11
    Small and medium-sized manufacturing enterprises play an important role in the national economic development, and are an important driving force for economic growth, an important source of technological innovation, and an important cornerstone for social stability. Digital transformation is an important way to enhance the competitiveness of small and medium-sized enterprises. However, small and medium-sized enterprises often face the dilemma of ”not daring to turn” and ”not knowing how to turn” in digital transformation. Therefore, identifying the influencing factors of digital transformation and mining the linkage mechanism of digital transformation is the key to accelerating the digital transformation process of small and medium-sized manufacturing enterprises. This article uses the dynamic fuzzy set qualitative comparative analysis method, or dynamic QCA method, to study the panel data of small and medium-sized manufacturing listed companies from 2016 to 2022 based on the TOE theoretical framework, and explores the configuration path that drives the digital transformation of small and medium-sized manufacturing enterprises. The research found that, firstly, achieving high digital transformation requires the collaborative efforts of multiple factors, and a single factor cannot play a role alone in achieving high digital transformation; The application of high-digital technology plays an important role in enhancing digital transformation; The lack of digital technology, RD investment, managerial awareness, and digital infrastructure construction are the core factors that have caused some enterprises to have low digital transformation. Secondly, there are multiple paths and complex mechanisms for the digital transformation of small and medium-sized manufacturing enterprises. Three types of configuration paths can achieve high digital transformation, including technology-environment dual-driven, technology-organization dual-driven, and technology-organization-environment multi-collaborative. Finally, the digital transformation of small and medium-sized manufacturing enterprises has not shown significant time effects, but the enterprises do not follow a consistent configuration path in achieving high-level digital transformation, showing individual differences.
  • CAO T Y, ZHUANG A T, WANG Y G
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250458
    Accepted: 2025-08-10
    As a non-parametric Bayesian regression approach, Bayesian Additive Regression Trees (BART) model combines the precision of likelihood-based inference with the flexibility of machine learning algorithms. It provides superior predictive performance when there is a nonlinear relationships or complex interaction scenarios among the response variables and covariates. Longitudinal data, widely presents in fields such as medicine, economics, and environmental science, holds important research significance. To improve the predictive accuracy of longitudinal data analysis, this study proposes a new method for longitudinal data analysis based on BART, in which utilizes BART to estimate non-parametric parts in the semiparametric mixed-effects model. In numerical simulations, this study compares the new method with four other methods: mixed-effects gradient boosting method (MEGB), stochastic mixed-effects regression tree method (SMERT), stochastic random effects expectation-maximization regression tree method (SREEMtree), and stochastic mixed-effects random forest method (SMERF). The simulation results consistently show that the new method outperforms the other four methods. To illustrate its practical application, this study applies it to two real-world datasets.
  • ZHOU Yufeng, PAN Zimei
    Journal of Systems Science and Mathematical Sciences. https://doi.org/10.12341/jssms250267
    Accepted: 2025-08-09
    To address the challenges of digital healthcare services and meet the personalized needs of diverse patient types, this study investigates the optimization of scheduling and routing for home healthcare workers. Unlike previous studies, in the problem, both doctor and patient bilaterally have personal preferences, heterogeneous patients can choose three service modes: outpatient, door-to-door, and online services, healthcare workers have fatigue perception, and healthcare workers’ scheduling and routing decisions are reflected in hybrid scheduling and routing multi-objective optimization decision-making with the fusion of online and offline multi-service modes. A bi-objective mixed-integer programming (MIP) model is proposed to maximize the satisfaction of both healthcare workers and patients, subject to constraints such as shift limitations and worker-patient matching. To address the characteristics of the model, an improved Strength Pareto Evolutionary Algorithm-II (ISPEA-II) is developed. Using metrics such as HV, Spacing, and GD for algorithm evaluation, numerical experiments demonstrate that the proposed ISPEA-II outperforms traditional Strength Pareto Evolutionary Algorithm-II (SPEA-II), Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), Differential Evolutionary Algorithm (DE), and Immune Algorithm (IA). Finally, sensitivity analyses on key parameters, including skill levels of healthcare workers, shift lengths, and maximum consecutive working days, yield managerial insights, providing theoretical guidance for scheduling and routing decisions in home healthcare.