Search Results (587)

This study proposes a multi-objective, multi-class explainable modeling framework to explain country performance profiles in PISA Mathematics (PISAM), Reading (PISAR), and Science (PISAS). Instead of treating PISA as a simple ranking, the study models each country’s Low/Medium/High-achieving class and asks which structural signals the model relies on when assigning a country to this class. To this end, the study combines governance quality (e.g., accountability, control of corruption, and political stability, etc.), economic and administrative capacity, and regional/institutional location in a single prediction pipeline and explains the resulting classifications with SHAP contributions conditional on class. While the findings do not point to a single, universal determinant, in mathematics, high-level profiles cluster around political stability, economic scale barriers, and regional location, along with governance indicators; in reading, economic capacity is explicitly integrated into this institutional core; and in science, in addition to these two dimensions, the shared institutional dynamics of regional blocs come into play. Furthermore, the study not only produces explanations but also quantitatively reports their reliability. The fit with the model output (Fidelity) and the traceability of the decision logic (Faithfulness) are 0.95/0.85 for PISAM, 0.89/0.92 for PISAR, and 0.89/0.89 for PISAS, which demonstrates high internal consistency and traceability of the decision process. Overall, the study reframes the PISA results not as isolated test scores but as structural profiles generated by the combination of governance, capacity, and region, revealing the policy-relevant levers behind “high performance” as a transparent and reproducible decision-making pipeline. This provides policymakers with an important roadmap for creating a sustainable education policy. Full article

With the growing emphasis on holistic management throughout the entire product lifecycle, multi-stage production models that integrate distributed manufacturing, transportation, and assembly processes have gradually attracted research attention. However, studies in this area remain relatively scarce. This paper addresses the fuzzy distributed assembly hybrid flow shop scheduling problem (FDAHFSP), comprehensively considering the entire production flow from manufacturing and transportation to final assembly. A mathematical model is first established with the objectives of minimizing the fuzzy total weighted earliness/tardiness and the fuzzy total energy consumption. To effectively solve this problem, a Q-learning-based adaptive NSGA-II (Q-ANSGA) is proposed. The algorithm incorporates a hybrid strategy combining multiple rules to enhance the quality of the initial population. Additionally, a Q-learning-based adaptive parameter adjustment mechanism is designed to dynamically optimize genetic algorithm parameters, thereby improving the algorithm’s search efficiency and convergence performance. Furthermore, eight neighborhood search operators are developed, and an iterative greedy strategy is integrated to guide the local search process. Finally, comprehensive experiments on 45 test instances are conducted to evaluate the effectiveness of each improvement component and the overall performance of Q-ANSGA. Experimental results demonstrate that the proposed algorithm achieves superior performance in solving the FDAHFSP due to its systematic enhancements. Full article

In high-precision optical systems such as laser optics, astronomical observation, and semiconductor lithography, anti-reflection coatings are crucial for light transmittance, imaging quality, and stability, but traditional designs face modeling challenges in balancing ultralow reflectivity, high wavefront quality, and manufacturability amid multi-dimensional parameter coupling and multi-objective constraints. This study addresses these by proposing a unified mathematical modeling framework integrating a Symmetric five-layer high-low refractive index alternating structure (V-H-V-H-V) with dual-scale nanostructures, employing a constrained quasi-Newton optimization algorithm (L-BFGS-B) to minimize reflectivity, wavefront root-mean-square (RMS) error, and surface roughness root-mean-square (RMS) in a six-dimensional parameter space. The Sellmeier equation is adopted to calculate wavelength-dependent material refractive indices, the model uses the transfer matrix method for the Symmetric five-layer high-low refractive index alternating structure’s reflectivity, incorporates nano-surface height function gradient correction, sub-wavelength modulation, and radial optimization, applies Zernike polynomials for low-order aberration correction, quantifies surface roughness via curvature proxies, and optimizes via a weighted objective function prioritizing low reflectivity. Numerical results show the spatial average reflectivity at 632.8 nm reduced to 0.13%, the weighted average reflectivity across five representative wavelengths in the 550–720 nm range to 0.037%, the reflectivity uniformity to 10.7%, the post-correction wavefront RMS to 11.6 milliwavelengths, and the surface height standard deviation to 7.7 nm. This framework enhances design accuracy and efficiency, suits UV nanoimprinting and electron beam evaporation, and offers significant value for high-power lasers, lithography, and space-borne radars. Full article

Background: The albumin–bilirubin (ALBI) grade provides an objective assessment of hepatic reserve, but the need for calculation by means of a formula has hampered its use at the bedside. This study aimed to develop simple cut-off values for ALBI grade and validate its performance in a large multi-center real-world cohort. Methods: A mathematical simulation evaluated every possible ALBI pair that falls within the Child–Pugh classification (CP) A range, discretized to 0.1 increments. Cut points for patient stratification without equation-based calculation were derived. Validation was conducted with the Chang Gung Research Database (CGRD), which contains data from 10 hospitals in Taiwan. Patients with same-day albumin and bilirubin measurements in 2024 were included. Results: Mathematical modeling identified clinically applicable cutoffs—albumin ≥ 4.4 g/dL or ≤3.5 g/dL and bilirubin ≥ 2.4 mg/dL—with further refinement at albumin 4.0 g/dL and bilirubin ≥ 1.0 mg/dL. Among 7583 CP-A patients, 82% were directly classifiable without computation, with consistent applicability across chronic liver disease and hepatocellular carcinoma (HCC) subgroups. Equation dependence increased only slightly in the HCC group, confirming robustness across disease severities. Conclusions: Simplified cutoff rules derived from mathematical modeling and validated in a multi-center cohort enable rapid recognition of ALBI grade in most CP-A patients. This approach enhances the clinical usability of ALBI and supports its integration into patient care, clinical trials, and treatment allocation. Full article

In this paper, an anisotropic object electromagnetic image reconstruction system based on a two-stage multi-frequency extended network is developed by deep learning techniques. We obtain the scattered field information by irradiating the TM different polarization waves to uniaxial objects located in free space. We input the measured single-frequency scattered field into the Deep Residual Convolutional Neural Network (DRCNN) for training and to be further extended to multi-frequency data by the trained model. In the second stage, we feed the multi-frequency data into the Deep Convolutional Encoder–Decoder (DCED) architecture to reconstruct an accurate distribution of the dielectric constants. We focus on EMIS applications using Transverse Magnetic (TM) and Transverse Electric (TE) waves in 2D scenes. Numerical findings confirm that our method can effectively reconstruct high-contrast uniaxial objects under limited information. In addition, the TM/TE scattering from uniaxial anisotropic objects is governed by polarization-dependent Lippmann–Schwinger integral equations, yielding a nonlinear and severely ill-posed inverse operator that couples the dielectric tensor components with multi-frequency field responses. Within this mathematical framework, the proposed two-stage DRCNN–DCED architecture serves as a data-driven approximation to the anisotropic inverse scattering operator, providing improved stability and representational fidelity under limited-aperture measurement constraints. Full article

This paper aims to address the problem of the low success rate of seedling picking and throwing, and the high damage rate of pot seedling, caused by the unclear interaction and parameter mismatch between the seedling picking end effector and the pot seedling during the seedling picking and throwing process of automatic transplanters. An EDEM–RecurDyn coupled simulation was conducted, through which the disturbance of substrate particles in the bowl body during the inserting, extracting, and transporting processes by the seedling picking end effector was visualized and analyzed. The force and motion responses of the particles during their interaction with the seedling picking end effector were explored, and the working parameters of the seedling picking end effector were optimized. A seedling picking end effector using two fingers and four needles is taken as the research object, a kinematic mathematical model of the seedling picking end effector is established, and the dimensional parameters of each component of the end effector are determined. Physical characteristic tests are conducted on Shanghai bok choy pot seedlings to obtain relevant parameters. A discrete element model of the pot seedling is established in EDEM 2022 software, and a virtual prototype model of the seedling picking end effector is established in Recurdyn 2024 software. Through EDEM-Recurdyn coupled simulation, the force and movement of the substrate particles in the bowl body during the inserting, extracting, and transporting processes of the seedling picking end effector under different operating parameters were explored, providing a theoretical basis for optimizing the working parameters of the end effector. The inserting and extracting velocity, transporting velocity, and inserting depth of the seedling picking end effector were used as experimental factors, and the success rate of seedling picking and throwing, and the loss rate of substrate, were used as evaluation indicators; single-factor tests and three-factor, three-level Box–Behnken bench tests were conducted. Variance analysis, response surface methodology, and multi-objective optimization were performed using Design-Expert 13 software to obtain the optimal parameter combination: when the inserting and extracting velocity was 228 mm/s, the transporting velocity was 264 mm/s, the inserting depth was 37 mm, the success rate of seedling picking and throwing was 97.48%, and the loss rate of substrate was 2.12%. A verification experiment was conducted on the bench, and the success rate of seedling picking and throwing was 97.35%, and the loss rate of substrate was 2.34%, which was largely consistent with the optimized results, thereby confirming the rationality of the established model and optimized parameters. Field trial showed the success rate of seedling picking and throwing was 97.04%, and the loss rate of substrate was 2.41%. The error between the success rate of seedling picking and throwing and the optimized result was 0.45%, indicating that the seedling picking end effector has strong anti-interference ability, and verifying the feasibility and practicality of the established model and optimized parameters. Full article

The widespread application of robots in complex and dynamic environments demands that Visual SLAM is both robust and accurate. However, dynamic objects, varying illumination, and environmental complexity fundamentally challenge the static world assumptions underlying traditional SLAM methods. This review provides a comprehensive investigation into the mathematical foundations of V-SLAM and systematically analyzes the key optimization techniques developed for dynamic environments, with particular emphasis on advances since 2020. We begin by rigorously deriving the probabilistic formulation of V-SLAM and its basis in nonlinear optimization, unifying it under a Maximum a Posteriori (MAP) estimation framework. We then propose a taxonomy based on how dynamic elements are handled mathematically, which reflects the historical evolution from robust estimation to semantic modeling and then to deep learning. This framework provides detailed analysis of three main categories: (1) robust estimation theory-based methods for outlier rejection, elaborating on the mathematical models of M-estimators and switch variables; (2) semantic information and factor graph-based methods for explicit dynamic object modeling, deriving the joint optimization formulation for multi-object tracking and SLAM; and (3) deep learning-based end-to-end optimization methods, discussing their mathematical foundations and interpretability challenges. This paper delves into the mathematical principles, performance boundaries, and theoretical controversies underlying these approaches, concluding with a summary of future research directions informed by the latest developments in the field. The review aims to provide both a solid mathematical foundation for understanding current dynamic V-SLAM techniques and inspiration for future algorithmic innovations. By adopting a math-first perspective and organizing the field through its core optimization paradigms, this work offers a clarifying framework for both understanding and advancing dynamic V-SLAM. Full article

Achieving precise prediction and intelligent control remains a pivotal challenge in cutting processes. This need is addressed through a comprehensive survey of three critical enabling technologies: cutting force/temperature modeling, tool path planning, and vibration suppression. First, the evolution of cutting force and temperature modeling is analyzed, tracing its progression from traditional analytical methods and finite-element numerical simulations to data-driven models such as machine learning (ML) and physics-informed neural networks. This analysis highlights multiphysics coupling and model–data fusion as key to enhancing prediction accuracy. Subsequently, the evolution of tool path planning is examined, showing its development from a geometric interpolation problem into a multi-objective optimization challenge incorporating dynamic constraints, involving computational geometry, graph theory, and meta-heuristic algorithms. Finally, stability analysis based on time-delay differential equations, state identification via signal processing and ML, and active control strategies for vibration suppression are discussed. In conclusion, mathematical methods are shown to be fundamentally integrated throughout the ‘perception–prediction–decision–control’ closed-loop of the cutting process. This integration provides a solid theoretical foundation and technical support for building high-performance manufacturing systems dedicated to complex curved critical components. Full article

In this paper, the Multistage Bipolar method is developed. The paper presents a synthesis of three streams related to multiple criteria decision-making: the reference point-based approach, the interactive approach and multistage decision processes. A significant problem, the solution of which is a prerequisite for the application of the Multistage Bipolar method, is the determination of the sets of reference objects for subsequent stages. This paper addresses the question of how to utilize an interactive multi-criteria approach to select subsets of ‘good’ and ‘bad’ objects for each stage of the considered process, which the decision-maker will accept as sets of reference objects. Its objective is to propose an interactive procedure for generating these sets. The approach proposed in this paper is illustrated by the utilization of stage sets of reference points, generated via the proposed interactive procedure, within a mathematical model for resource allocation in a multistage regional development planning problem. The problem addressed constitutes a mathematical economics model, while simultaneously demonstrating that multi-criteria methods are widely applicable in management. Of fundamental importance here is the expenditure of public funds in a manner that yields maximum benefits for citizens. Full article

In two-sided disassembly lines, stations are symmetrically arranged on both sides of the conveyor, which is suitable for large-sized waste products. During the disassembly process, evenly assigning parts to workstations while satisfying various constraints and optimizing some disassembly objectives is a challenging task. Therefore, this study deals with a two-sided partial disassembly line balancing problem, and a multi-objective mathematical model for this problem is built. While satisfying various constraints, four objectives, namely, the hazard index, profit, smoothness index, and demand index, are optimized. Due to the NP-hard nature of the problem, an improved discrete whale optimization algorithm is proposed. According to the characteristics of the feasible solutions, an encoding method based on a one-dimensional integer array is designed, which can effectively decrease the memory space and simplify the design of neighbor structures. In the three stages of encircling prey, random wandering, and bubble-net attacking, based on the search features of each stage, different neighbor operators and search strategies are designed to enhance the local exploitation and global exploration capabilities. Finally, the performance of the proposed algorithm was tested against other algorithms for different types of instances and a disassembly case. The results show that the proposed algorithm can not only solve various types of disassembly line balancing problems but also shows superior performance. Full article

Hybrid AC/DC transmission expansion planning must balance investment cost, supply reliability and AC/DC stability, which challenges conventional mathematical programming and heuristic methods. This paper proposes a multi-objective planning framework based on an improved multi-step backtracking α-Q(λ) reinforcement learning algorithm with eligibility traces and an adaptive learning factor. A tri-objective model minimises annual economic cost, expected power shortage and a comprehensive electrical index that combines electrical betweenness, commutation-failure margin and effective short-circuit ratio. The mixed-integer planning problem is reformulated as an interactive learning process, where the state encodes candidate line construction decisions, the action builds or cancels lines, and the eligibility-trace matrix is used to quantify line importance. Case studies on the Garver-6 system, the IEEE 24-bus reliability test system and a 500 kV regional hybrid AC/DC grid show that, compared with classical Q-learning, the proposed method yields lower annual cost, reduced expected power shortage and improved AC/DC stability; in the 500 kV system, the expected annual power shortage is reduced from 70,810 MWh to 28,320 MWh. Full article

With the rapid transformation of the automotive industry towards electric vehicles, how to achieve efficient mixed-line production of electric vehicles and fuel vehicles has become a key challenge for modern assembly systems. This study investigated the balancing problem of a mixed-model multi-manned assembly line, considering workstation sharing (MMuALBP-WS), and developed a deterministic multi-objective model that integrates the heterogeneity of tasks and the coordination of shared workstations. An improved genetic algorithm was proposed, whose decoding mechanism enables different types of electric vehicle and fuel vehicle tasks to achieve dynamic collaboration within the shared workstations. A real case study from the chassis assembly line of Company W demonstrated the effectiveness of the proposed method, achieving a 25% reduction in the number of workstations, a 27% decrease in the total number of workers, and a 23.56% increase in average workstation utilization. The results confirmed that the workstation sharing mechanism significantly improved production balance, labor utilization, and flexibility, providing a practical and scalable optimization framework for the mixed-model assembly system in the era of the transition from electric vehicles to fuel vehicles. In addition to its practical significance, this study enhances the understanding of mixed-model multi-manned line balancing by incorporating workstation-sharing logic into both the mathematical modeling and optimization process, offering a theoretical basis for future extensions to more complex production environments. Full article

As a multi-switching power electronic circuit with complex variable topology, the three-level active neutral point clamped (ANPC) converter is a complex system with strong coupling and low linearity. It has numerous high-speed switching devices, a large number of switch states, and a high matrix dimension. Modeling each switch will undoubtedly further increase the circuit size. While in real-time simulation, updating all states of the model to produce outputs within a single time step results in a significant computational load, causing an increasing consumption of FPGA hardware resources as the number of switches and circuit size grow. In order to solve this problem, the current common practice is to decompose the entire complex power electronic system into smaller serial subsystems for modeling. The overall modeling approach for small circuits can be achieved, but when the size of the circuit increases, the overall modeling complexity and difficulty are increased or even impossible to achieve. Decoupling power electronic circuits with this decomposition into subsystem modeling not only reduces the matrix dimension and simplifies the modeling process, but also improves the computational efficiency of the real-time simulator. However, this inevitably generates simulation delays between different subsystems, leading to numerical oscillations. In an effort to overcome this challenge, this paper adopts the method of parallel computation after subsystem partitioning. There is no one-beat delay between different subsystems, and there is no loss of accuracy, which can improve the numerical stability of the modeling and can effectively reduce the step length of real-time simulation and alleviate the problem of real-time simulation resource consumption. In addition, to address the problems of low accuracy due to the traditional forward Euler method as a solver and the possibility of significant errors at some moments, this paper uses a modified prediction correction method to solve the discrete mathematical model, which provides higher accuracy as well as higher stability. And, different from the traditional control method, this paper uses an improved FCS-MPC strategy to control the switching transients of the ANPC model, which achieves a very good control effect. Finally, a simulation step size of less than 60 ns is successfully realized by empirical demonstration on the Speedgoat test platform. Meanwhile, the accuracy of our model can be objectively evaluated by comparing it with the simulation results of the Matlab Simpower system. Full article

Production scheduling that involves distributed factories, machine maintenance, and resource constraints plays a crucial role in manufacturing. However, these realistic constraints have rarely been considered simultaneously in the hybrid flow shop (HFS). To address this issue, a distributed resource-constrained hybrid flow shop scheduling problem with machine breakdowns (DRCHFSP-MB) is studied. There are two optimization objectives, i.e., makespan and total energy consumption (TEC). To solve the strongly NP-hard problem, a mathematical model is established and a block–neighborhood-based multi-objective evolutionary algorithm (BNMOEA) is developed. In the proposed algorithm, an efficient hybrid initialization method is adopted to obtain high-quality individuals to participate in the evolutionary process of the population. Next, to enhance the search capability of the BNMOEA, three well-designed crossover operators are used in the global search. Then, the convergence of the proposed algorithm is improved by utilizing eight critical factory-based local search operators combined with block–neighborhood. Finally, the BNMOEA is compared with several of the most advanced multi-objective algorithms; the results indicate that the BNMOEA has an outstanding performance in solving DRCHFSP-MB. Full article

The exponential growth of the Internet of Things (IoT) has made it increasingly vulnerable to cyberattacks, where malicious manipulation of network and sensor data can lead to incorrect data classification. IoT data are inherently heterogeneous, comprising sensor readings, network flow records, and device metadata that differ significantly in scale and structure. This diversity motivates transforming tabular IoT data into image-based representations to facilitate the recognition of intrusion patterns and the analysis of spatial correlations. Many deep learning models offer robust detection performance, including CNNs, LSTMs, CNN–LSTM hybrids, and Transformer-based networks, but many of these architectures are computationally intensive and require significant training resources. To address this challenge, this study introduces an evolutionary-driven framework that mathematically formalizes the transformation of tabular IoT data into image-encoded matrices and optimizes feature selection through metaheuristic algorithms. Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Variable Neighborhood Search (VNS) are employed to identify optimal feature subsets for Random Forest (RF) and Extreme Gradient Boosting (XGBoost) classifiers. The approach enhances discrimination by optimizing multi-objective criteria, including accuracy and sparsity, while maintaining low computational complexity suitable for edge deployment. Experimental results on benchmark IoT intrusion datasets demonstrate that VNS-XGBoost configurations performed better on the IDS2017 and IDS2018 benchmarks, achieving accuracies up to 0.99997 and a significant reduction in Type II errors (212 and 6 in tabular form, reduced to 4 and 1 using image-encoded representations). These results confirm that integrating evolutionary optimization with image-based feature modeling enables accurate, efficient, and robust intrusion detection across large-scale IoT systems. Full article