中国科学院数学与系统科学研究院期刊网

06 February 2026, Volume 46 Issue 2
    

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  • Supply Chain Decision Problem with Out-of-Stock Penalty Under Supply Disruptions
    ZUO Zhuan, YAN Jingbei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 337-347. https://doi.org/10.12341/jssms240705
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    This paper considers the supply interruption of a supply chain composed by two suppliers and one retailer, where one supplier is an integrated supply and marketing supplier and the other supplier is a pure supplier, and the retailer makes replenishment from the latter supplier and makes and emergency order from the former when the supply is interrupted. For this system, we mainly investigate the retail price decision and the emergency replenishment from the supply and retailing integrated supplier in the case of a supply interruption with a random end time from the second supplier. Based on maximizing the benefits of each member in the supply chain, we establish an optimization model, and its solution is obtained via a theoretical analysis which gives the optimal decision for each member of the supply chain. Some numerical experiments are made which give the impact analysis of main parameters on the optimal decision of each member of the supply chain and their benefits for the supply interruption period.
  • Research on Generalized Trend Filtering Model with Composite $\ell_0$ Constraint and Its Solution Method
    PAN Shanshan, DAI Qianqian, SHANG Pan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 348-363. https://doi.org/10.12341/jssms240586
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    Trend filtering is a widely used method for extracting long-term trends and eliminating short-term noise from time series data. In order to accurately capture the global change pattern and local fluctuation of the potential trend, this paper proposes the generalized trend filtering model with composite $\ell_0$ constraint (L0CTF) based on the primitive function representing sparsity, and the optimality theory is analyzed. However, solving the L0CTF model is a challenging task because of the combinatorial property and indivisibility of the composite $\ell_0$ function. Therefore, based on the properties of composite $\ell_0$ function, this paper reformulates the L0CTF model as a mixed integer programming problem with special ordered sets of type 1 and analyzes its equivalence with L0CTF in the sense of global optimal solution. Finally, experimental results on simulated and real data sets show that the proposed method is superior to some mainstream trend filtering methods in extracting potential trends.
  • How Can AI-HI Collaboration Improve the Quality of Emergency Plan Generation?— A Study Based on the Stackelberg Game Model
    WU Jiao, LIU Dehai, LI Yiying
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 364-387. https://doi.org/10.12341/jssms250237
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    With the development of natural language generative AI big model technology, AI with superb semantic understanding such as DeepSeek has become the infrastructure of the digital economy and society. The synergy between AI and HI has the characteristics of optimising time-intensive processes, reducing decision-making bias and mitigating all kinds of systematic risks, which is conducive to the enhancement of timeliness of emergency plan generation in highly dynamic environments, the effectiveness of and the operability. In emergency management practice, government departments need to weigh the costs and benefits of introducing AI. In this paper, we first consider the benefits and budgetary costs of human-computer collaboration between government departments and social organisations, and construct the Stackelberg game base model of AI-HI collaboration for emergency information sharing and emergency plan generation system, and obtain the equilibrium decision-making and optimal benefits of government departments and social organisations. Subsequently, the robustness of the model is enhanced by further extending the base model into three scenarios (customised AI, emergency plan amendment and data trust). The findings suggest that AI investment is not always beneficial and government departments need to choose whether to invest in AI technology based on their own budget. For government departments, customized AI should only be adopted when the marginal cost of AI technology investment is less than a certain critical value, and if the accuracy of an emergency plan is low, it is better to use manual preparation rather than human-computer collaboration followed by correction. For social organisations, the adoption of customised AI is always more beneficial than generic AI, and the amendment of the contingency plan has no impact on the optimal benefit of the social organisation. In addition, government departments should only adopt the data trust model if the benefits of improved digital governance capabilities outweigh the losses of human-computer collaboration.
  • Research on Carbon Emission Reduction Decision-Making Considering Enterprise Environmental Awareness Under Carbon Cap-and-Trade Mechanism
    WANG Mengyao, WANG Wenbin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 388-405. https://doi.org/10.12341/jssms240671
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    Considering the carbon cap-and-trade mechanism, this paper studies the emission reduction decision-making problems of coal power supply chain dominated by coal enterprises. A dynamic game model is constructed to explore the impact of environmental awareness and emission reduction difficulty on enterprise pricing and carbon emission reduction under decentralized decision-making and centralized decision-making respectively. Based on centralized decision-making, the profits and carbon emission reduction of coal and electricity companies are compared. In view of the efficiency loss of decentralized decision making, profit-sharing contracts are designed to coordinate the coal power supply chain. The results show that: 1) When the environmental protection consciousness of coal enterprises is not strong enough, the profit of coal enterprises is higher than that of electricity enterprises; When the environmental protection consciousness of coal enterprises is generally strong, the profit of coal enterprises is lower than that of electricity enterprises. 2) Emission reduction difficulty can change the relationship between power unit price and carbon emission reduction under decentralized decision-making and centralized decision-making; When the emission reduction difficulty is less than a specific value, the power unit price of decentralized decision-making power enterprises is lower, and it is also more conducive to increasing the carbon emission reduction of coal enterprises and power enterprises. 3) When the difficulty of emission reduction is greater than a specific value, the profit of centralized decision-making is higher than that of decentralized decision-making; 4) With the increase of profit sharing ratio of electricity enterprises, the wholesale price of coal will increase, the carbon emission reduction of electricity enterprises will increase, and the carbon emission reduction of coal enterprises will decrease.
  • Carbon Reduction and Financing Strategies for Dual Channel Supply Chains Considering Manufacturer's Fairness Concern Under Capital Constraints
    GUO Jinsen, ZHOU Yongwu, YU Chunyan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 406-424. https://doi.org/10.12341/jssms240177
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    The “carbon peaking and neutrality” goal puts forward new requirements for the coordinated emission reductions in the supply chain. Based on game theory, a dual channel supply chain carbon reduction and financing decision-making model is constructed under different financing models when manufacturer has financial constraints and fair concerns. The paper analysis the impact of manufacturer fairness concern on supply chain product pricing and carbon reduction strategies, and explores the preferences of manufacturer and retailer for different financing models. The research shows that manufacturer’s fair concern behavior reduces online channel product pricing and carbon reduction levels, while wholesale price and offline channel retail price are also influenced by manufacturers’ carbon reduction cost factor. The fair concern behavior of manufacturer increases the profits of manufacturer and supply chain, but reduces the retailer’s profits. Capital constraints lead to a decrease in the profits of manufacturer, but the profits of retailer may not necessarily decrease. When manufacturer has relatively low sensitivity of early payment wholesale price, the retailer prefers to choose the prepayment financing model. Otherwise, the retailer prefers to choose the bank loan+prepayment combination financing model. For the manufacturer and overall supply chain, when the sensitivity of early payment wholesale price is relatively low, they prefer to choose the prepayment financing model. Otherwise, the bank loan financing model is dominant.
  • On the Basics and Extensions of Regular Vine-Based Joint Density Modeling
    DUAN Xiaogang, FANG Weihua
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 425-443. https://doi.org/10.12341/jssms240361
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    This paper aims to provide a solid reference for basic theories concerning regular vine-based joint density modelling. Regular vine (rvine for short below), a powerful concept proposed by Cooke (1997), is a nesting sequence of trees satisfying a special proximity condition. For “nesting”, it refers to node set of next tree being identical to edge set of the neighbouring last tree. While for “proximity”, it means that two nodes in the next tree are connectable if and only if, as two edges in the neighbouring last tree, they have one common element. As a geometrical object, regular vines play essential roles in many applications including joint density decompositions and their statistical modelling. In this paper, we summarize and extend important properties of regular vine and its roles in joint probability density decomposition and construction, as well as systematic proofs for each of the main results. We also present a new understanding for regular vine matrix from a recursively building perspective.
  • Pricing and Subsidy Strategies of Low-Carbon Supply Chain Considering Green Design from the Perspective of ESG
    YAO Fengmin, DU Wenli, SUN Jiayi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 444-461. https://doi.org/10.12341/jssms240460
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    Under China’s “dual carbon” strategic goals, actively practicing ESG (environmental, social and governance) concept has become the key to realize the sustainable development of enterprises and their stakeholders. In the context of manufacturer’s implementation of green design, four game models of low-carbon supply chain were constructed when the manufacturer not considering/considering ESG based on two different subsidy modes: Production subsidy and cost subsidy, and the impact of government subsidies and manufacturer’s ESG behavior on low-carbon supply chain operation, environment and social welfare are analyzed. The research shows that the increase of consumer sensitivity coefficient of green design and cost reduction coefficient of green design can stimulate manufacturer’s ESG practice motivation and stimulate the government to increase subsidies. The increase of government subsidies is conducive to improving the green design level of low-carbon products, and manufacturer’s ESG behavior will strengthen the positive effect of subsidies to some extent. Moreover, manufacturer’s ESG behavior is always conducive to improving the performance of retailer and the whole low-carbon supply chain, and improving the total welfare of society, but it may not be conducive to reducing environmental impact. From the perspective of ESG, government implementation of cost subsidy is more effective.
  • A Study on Risk Propagation in New Energy Vehicle Supply Chain Based on SEIR Modeling
    XIANG Pengcheng, ZHAO Xiaping, YANG Yingliu
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 462-479. https://doi.org/10.12341/jssms240542
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    To enhance the scientific nature of risk prevention and control in the supply chain network of new energy vehicle (NEV), and to strengthen safety production and operational management in China’s NEV industry, we integrate complex network theory with SEIR (susceptible-exposed-infectious-recovered) modeling to simulate the process of risk propagation in the NEV supply chain network, aiming to uncover the mechanisms of risk propagation. Firstly, typical NEV companies such as Tesla and XPeng are selected as case studies, with suppliers as nodes and supplier cooperation relationships as edges to construct the topological networks of their automotive supply chains. Secondly, topological parameters such as average degree, clustering coefficient, and average path length are used to explore the characteristics of the supply chain networks of these two companies. Finally, based on the characteristics of the topological networks, an SEIR epidemic model is constructed for the supply chain networks to simulate the impact of different immunization strategies on the speed and scope of risk propagation in the supply chain. The results indicate: 1) The supply chain networks of both NEV companies exhibit scale-free network structures, with comparable network densities (average degrees of 2.293 for Tesla’s and 1.845 for XPeng’s supply chain networks). 2) Comparing the simulation results of risk prevention strategies between the two companies shows that their performances are largely similar. The proposed model effectively explores the characteristics of risk propagation in the NEV supply chain. Specifically, extending the incubation period of risks can significantly slow down the spread of risks, providing nearly three months of adjustment time for the companies, with Tesla experiencing a shorter delay of about 2 weeks to the peak risk period compared to XPeng; Shortening the duration of infection can notably reduce the scale of risk spread by approximately 20%, with Tesla showing a 4% greater reduction in the scope of risk impact compared to XPeng. Additionally, increasing the complexity of the supply chain network may accelerate the propagation of risks. The research findings can provide a reference for NEV companies to formulate effective risk response measures, ensuring the stability and safety of the supply chain.
  • Research on Equipment Fault Diagnosis and Life Prognosis Based on Improved Hidden Semi-Markov Models
    LIU Qinming, XIANG Haodong, LIU Wenyi, HE Jiwei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 480-499. https://doi.org/10.12341/jssms240044
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    A data-model dual-driven stochastic process model is proposed for equipment health diagnosis and remaining life prediction problems. Firstly, a new signal scalarization method is proposed for non-vibration signals, so that continuous signals can be scalarized to form a data type that can be input to the hidden semi-Markov model. Secondly, a new deterioration kernel-based modified hidden semi-Markov model (DK-MHSMM) is proposed to realize the process of mapping the observation scales of mechanical equipment to the potential states, and to dynamically screen the equipment state patterns. Then, the adhesion coefficient is introduced into DKMHSMM, and the genetic algorithm and the co-evolutionary algorithm of the Sea Sheath swarm algorithm are used to estimate the model parameters instead of the conventional EM parameter estimation method, and the corresponding remaining life prediction method is proposed according to the characteristics of the whole life distribution of the equipment and the current state values of the equipment. Finally, the method is validated using the turbofan engine dataset, which verifies the effectiveness and feasibility of the method.
  • Green Manufacturer's Strategy of Channel Encroachment Based on Different Business Models
    LIN Zhibing, GUO Geng, CHEN Leiwen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 500-516. https://doi.org/10.12341/jssms240352
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    To explore the channel encroachment strategies of a green manufacturer when a retailer adopts different business models, a green supply chain model, consisting of a single manufacturer and a single retailer, is constructed. The optimal operational strategies of the supply chain enterprises are analyzed using Stackelberg game theory. Finally, the model is extended to a scenario where the manufacturer can also adopt different business models for channel encroachment. The research findings are as follows: 1) Unless the product’s energy consumption is high or energy prices are exceptionally high, the manufacturer can always improve its profits through channel encroachment, with the chosen business model for encroachment depending on the product’s energy consumption and energy prices. 2) Channel encroachment increases the extent to which supply chain members’ decisions are influenced by energy prices. However, a retailer who prefers a sharing business model can avoid these effects. Moreover, the manufacturer’s channel encroachment behavior always contributes to improving the overall profit of the supply chain. 3) When facing the potential threat of channel encroachment by the manufacturer, the retailer prefers the traditional business model if product energy consumption or energy prices are high. Conversely, when energy consumption or prices are lower, the retailer favors the sharing business model. Furthermore, retailers who prefer the sharing business model raise the threshold for the manufacturer’s channel encroachment. 4) Under certain conditions, an increase in energy prices does not always harm the profits of supply chain members or the energy-saving performance of green products.
  • Accelerated Attribute Reduction Algorithm Based on Heterogeneous Neighborhood Relationships and Inconsistency Degree
    YANG Dianqing, HUANG Jiwei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 517-532. https://doi.org/10.12341/jssms240026
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    Under the framework of classical neighborhood rough set, various fast attribute reduction algorithms based on fast positive region calculation have the following characteristics: 1) Neighborhood is the basic perspective of algorithm design; 2) Label information of datasets is not fully utilized; 3) Neighborhood and positive region are calculated by traversal method. These characteristics mean that these algorithms have redundant and inevitably repeated distance calculations and adopt inefficient calculation modes, which leads to low efficiency in calculating attribute reduction results, especially on large-scale datasets. In addition, these fast algorithms have good acceleration effects only when the dependency degree is used as the attribute evaluation function, which may lead to low classification ability of the attribute subset in the attribute reduction result. Therefore, we design an accelerated algorithm for attribute reduction from the basic perspective of heterogeneous neighborhood relationships and propose the inconsistency degree as the attribute evaluation function based on heterogeneous neighborhood relationships. The experimental results on 11 standard datasets show that the proposed method can save 88.0% of the total average computing time compared with the best-performing comparison algorithms (GRRS), and 97.1% of the total average computing time compared with the worst-performing comparison algorithm (EasiFFRA) while ensuring or improving the classification ability of the attribute reduction results.
  • Dynamic Pricing and Service Strategies in Sustainable Service Supply Chains Under Manufacturer Competition and Cooperation
    YAN Lizhao, HONG Pengfei, LI Zi, LIU Jian
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 533-554. https://doi.org/10.12341/jssms240531
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    As global market competition intensifies and the service economy rapidly develops, businesses face the challenge of transitioning from traditional singular product or service offerings to integrated product-service supply chains. This paper, delves into the optimization strategies of dual-channel sustainable service supply chains under manufacturer competition and cooperation environments from a dynamic perspective. The research findings reveal: 1) The goodwill growth rate and final stable level in competitive scenarios surpass those in cooperative scenarios. Competitive environments more effectively stimulate supply chain members to enhance service levels, with manufacturers and retailers’ service efforts showing rapid upward trends, potentially leading to more enduring competitive advantages in the long term. 2) While manufacturer cooperation can reduce costs, it may lead to decreased service levels, impacting long-term competitiveness. The effects of cooperative strategies on supply chain members are uneven; Manufacturer profits may increase, while retailer profits may be negatively affected, necessitating thorough consideration of all parties’ interests in decision-making. 3) Service efficiency disparities are a crucial factor influencing manufacturers’ choice between competitive or cooperative strategies, wherein larger efficiency gaps incline the weaker party towards cooperation to alleviate competitive pressure, while similar efficiency levels enable cooperation to bring more significant profit improvements for both parties.
  • Research on Online Product Recommendation Model Based on Prospect-Regret Theory and Decision-Making Preference
    WANG Yuhong, PAN Yangyang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 555-573. https://doi.org/10.12341/jssms2024-0132
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    Online reviews, as an objective reflection of product performance, have a significant impact on consumer decision-making. However, the ambiguity of information and the irrational consumption behavior often pose challenges to the decision-making process. This paper proposes an innovative online product recommendation model. Firstly, based on the psychological behavior of consumer purchasing decisions, considering the influence of the order and quantity of comment texts on consumer decisions, designed a temporal weight function and applied to thematic sentiment analysis. Then, used the intuitionistic fuzzy topsis and intuitionistic fuzzy grey relational analysis methods to calculate the score of the comment text. Finally, based on the information that consumers are concerned about and the decision-making preferences of e-commerce platforms, the final product ranking is determined. By analyzing 28,611 pieces of data from 9 brands of microwave ovens on JD.com, it is found that different decision preferences can lead to changes in rankings, and the fluctuation trend is similar to the satisfaction ranking results published by Chnbrand. In addition, classic multi criteria decision-making methods were selected for comparative analysis to verify the effectiveness and scientificity of the model.
  • A Deep Reinforcement Learning-Based Composite Optimization Algorithm for Garment Cut Order Planning
    WU Xiang, Lü Jinyang, LIN Wenjie, DONG Hui, GUO Fanghong, ZHANG Dan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 574-592. https://doi.org/10.12341/jssms240185
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    A composite optimization algorithm based on deep reinforcement learning and multi-objective particle swarm optimization (MOPSO) is proposed to solve the problem of large-scale and irregular multi-color cut order planning (MCOP). Firstly, the MCOP multi-objective optimization model is established with the production error and production cost as optimization objectives, combined with the constraints such as the number of equipment and the number of layers. Secondly, the global optimization solution strategy based on twin delayed deep deterministic policy gradient (TD3) is designed, the Markov decision process of TD3 algorithm is constructed, and the global solution set is obtained by designing the reward function based on error and cost. Furthermore, the local optimization algorithm of MOPSO cut order planning on linear decoupling is proposed, and the decoupling strategy of linear programming is designed to realize the fast decoupling calculation of the size combination matrix and the fabric layer matrix, which effectively improves the solving accuracy and speed. At the same time, the Pareto optimal solution of MCOP problem is obtained through elite file strategy. Finally, the feasibility and superiority of the proposed method are verified through the actual case and the algorithm comparison experiment, which can provide a good reference value for garment enterprises.
  • Multi-Depot Multi-Objective Electric Vehicle Routing Problem Considering Charging Price Difference and Customer Satisfaction
    WANG Li, WU Qifeng, ZHOU Xiancheng, ZHAO Xinyu, LI Qi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 593-615. https://doi.org/10.12341/jssms240738
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    Under the market mechanism for charging services, some charging stations have designed discriminatory service pricing schemes. Rational logistics electric vehicle (EV) drivers are likely to travel farther to lower-priced charging stations for charging, which will affect delivery efficiency and customer satisfaction. In view of this, a multi-depot multi-objective electric vehicle routing problem considering charging price difference and customer satisfaction (MDMOEVRPCCPDCS) for intercity logistics scenario is studied in this paper. Firstly, an EV energy consumption model is established, given the influence of some factors on the energy consumption of EVs, i.e., vehicle load, driving speed and vehicle characteristic parameters. Next, an MDMOEVRPCCPDCS optimization model is constructed with the goal of total cost minimization and average customer satisfaction maximization. Specifically, the total cost includes fixed operating cost, delivery time cost and charging cost. In view of the fact of delivery time is the main factor affecting customer satisfaction, so the goal of average customer satisfaction maximization is transformed into delivery time window constraints. And then, the multi-objective optimization problem is simplified into a single-objective problem. In order to solve MDMOEVRPCCPDCS model, a hybrid genetic-adaptive large neighborhood search (GA-ALNS) algorithm based on 3D K-means spatio-temporal clustering is designed. The hybrid algorithm is based on 3D K-means spatio-temporal clustering to reallocate customer resources in the three-dimensional space composed of time and space, which can contributes to enhancing the breadth and depth of the solution space search process. Through several sets of arithmetic examples, the MDMOEVRPCCPDCSCS model is verified to achieve multi-objective balancing among logistics cost, and customer satisfaction, which can provide a theoretical basis for transportation and logistics enterprises to optimize the decision-making distribution scheme.
  • Analysis of Aggregate Lifetime Data via the Method of Moments
    SONG Kai
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 616-624. https://doi.org/10.12341/jssms240318
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    In engineering practice, exact failure times of individual components are generally not available. In contrast, only the number of component failures and the system’s cumulative operating time are known, which leads to the aggregate lifetime data. Inference of lifetime distributions based on the aggregate lifetime data is of great challenge. This paper proposes a moment-based point estimation method, and uses the bias-corrected Bootstrap method to construct confidence intervals for quantities of interest. The maximum likelihood method needs the likelihood function of the aggregate lifetime data, however, it is only applicable to a few distributions that have the closure property with respect to the operation of convolution. Differently, the proposed method does not utilize the likelihood function, thus it applies to more distributions. Finally, both the simulation study and the real data analysis are performed for demonstration and illustration.
  • A New Method for Differentiating Between Unit Root and Stationarity Based on Adaptive Bridge
    XIE Fubin, XU Feng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 625-641. https://doi.org/10.12341/jssms240229
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    This paper proposes a new method for differentiating between unit root and stationary series based on adaptive bridge where adaptive weights are imposed on different coefficients in the bridge penalty. Different from unit root tests, discrimination between unit root and stationarity becomes a variable selection problem by applying adaptive bridge in ADF regression. Meanwhile, adaptive bridge select “zero” parameter on the lagged dependent variable and the lags of the first order differenced dependent variables. In this way, we can select unit roots and determine the lag orders simultaneously. Theoretical analyses indicate that adaptive bridge can correctly identify the unit root process with probability approaching to 1 under the nonstationary case. And in the case of stationarity, the adaptive bridge estimators are consistent and asymptotically normally distributed. And for the lags of the first order differences, “zero” parameters are estimated to be zero with probability approaching to 1, and “nonzero” estimators possess asymptotic normal distribution. In addition, for the efficient use of adaptive bridge, we also propose a modified BIC criterion where the trace of the “hat” matrix is used for approximating the effective degrees of freedom. Simulation results show that the proposed method can accurately distinguish between the unit root and stationary series. Compared with the ADF unit root test and method proposed by Caner and Knight (2013), our method has better finite sample performance. Thus, it can be a good alternative for the unit root test.
  • A Multiple Divide-and-Conquer Strategies Based Approach to Large Scale Multi-Depot Capacitated Arc Routing Problem
    ZHANG Yuzhou, MEI Yi, JIANG Jiansheng, ZHANG Haiqi, ZHAO Fen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 642-656. https://doi.org/10.12341/jssms240656
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    Multi-depot capacitated arc routing problem (MDCARP) is an important extension version of the basic capacitated arc routing problem (CARP). In MDCARP, each task can be assigned to any depot, so MDCARP is more complex than CARP. Large scale multi-depot capacitated arc routing problem (LSMDCARP) is extremely challenging on the problem structure and the vast solution space. Though, RoCaSH2 is a state-of-the-art approach which outperformed the other algorithms on the test data with a larger scale, it will encounter the straits when the problem scale ranges up to a certain level in which the scale of the sub-CARPs appears to be larger. In RoCaSH2, the operator for the sub-CARP ignores the scalability of the problem. In view of this, a multiple divide-and-conquer strategies based approach (MDCSbA) is proposed for LSMDCARP based on RoCaSH2, where the divide-and-conquer strategies are distributed in the decomposition of MDCARP, the collaborative optimization among sub-CARPs and the decomposition of sub-CARPs. As a result, the complexity of the problem is decreased at multiply stages. In order to verify the effectiveness of MDCSbA, it is evaluated on two test sets (i.e., mdHefei and mdBeijing) in which the number of the tasks is up to 3584. The results show that MDCSbA can outperform the compared algorithms significantly within runtime budget.
  • Nonparametric Confidence Interval of Quantile Under Ranked Set Sampling
    DONG Xiaofang, ZHANG Liangyong, FAN Xiangjia
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 657-669. https://doi.org/10.12341/jssms240639
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    For the problem of nonparametric interval estimation of population quantile, this paper proposes a nonparametric estimator of population quantile by using quantile ranking set sampling method, and proves the strong consistency and asymptotic normality of the new estimator. The confidence interval of the population quantile is constructed. According to lengths of confidence intervals, the relative precisions of the confidence intervals under proposed sampling and standard ranked set sampling to the confidence interval under simple random sampling are calculated. For the problem that the expression of confidence interval contains unknown probability density function value, the approximate confidence interval of population quantile is constructed by using the kernel density estimation method, and the coverage and precision of the interval are simulated. The results show that the coverage and precision of interval under quantile ranked set sampling are higher than those under ranked set sampling and simple random sampling, and the proposed sampling method makes up for the deficiency of the standard ranked set sampling method in extreme quantiles. Finally, the actual analysis results of coniferous tree data verify the correctness of the theoretical research results.
  • Test of Structural Change Points in Linear Regression Model with LMSV Errors
    CHEN Zhanshou, LIANG Yan, WEI Qiuyue
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 670-684. https://doi.org/10.12341/jssms240103
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    This paper investigates the testing of structural change points in linear regression model with long memory stochastic volatility errors that can simultaneously capture both the long memory and heteroscedasticity. We propose a self-normalized CUSUM statistic that does not require the estimation of scale parameters, constructed based on the residuals from least squares estimation. Under the null hypothesis, the limiting distribution of the test statistic is derived, and it is found that it is not affected by the long-memory parameter. Under the alternative hypothesis, the consistency of the statistic is proved. Numerical simulation results demonstrate that the proposed method not only effectively controls the empirical size but also achieves good testing performance. Finally, we illustrate the effectiveness of the proposed method by modeling and testing structural change points in a data set of PM2.5 concentration and SO2 concentration in the air in Xining City.
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