Search Results (167)

With the widespread integration of renewable energy, microgrid environmental economic dispatch (EED) faces challenges such as uncertainties in wind and solar power outputs and multi-objective conflicts. This paper proposes a stochastic expected dispatch framework based on an improved multi-objective dung beetle optimization algorithm (MO-CLDBO). First, considering both wind–solar uncertainties and demand response, a Gaussian Copula function is employed to characterize the 24-h temporal correlations among wind speed, solar irradiance, and load, and typical scenarios are generated via Monte Carlo sampling and simultaneous backward reduction; a time-of-use demand response model is also introduced. Second, taking expected operational cost and environmental emission as dual objectives, three improvements are proposed to address the issues of uneven initial population, easy local convergence, and Pareto front collapse in the standard dung beetle algorithm: a Folded Two-Dimensional Modified Coupled Logistic-Sine Map (Folded 2D-MCLSM) is used to initialize a high-quality population, a non-dominated sorting mechanism is introduced, and a dynamic lens imaging backward learning strategy is designed. Finally, the proposed algorithm is compared with several classical algorithms in the mathematical model of microgrid optimal dispatch through 50 independent runs. Experimental results show that the improved dung beetle optimization algorithm achieves not only the lowest average operating cost, but also the best hypervolume (HV) indicator, demonstrating excellent comprehensive performance in multi-objective search convergence and solution set diversity. Full article

Three-dimensional (3D) path planning for Unmanned Underwater Vehicles (UUVs) in typical marine operating conditions presents high-dimensional, non-convex optimization challenges due to undulating seabed topography, underwater threat sources, and coupled multi-physical constraints. Existing studies lack multi-strategy collaborative optimization mechanisms specifically designed for UUV 3D marine navigation constraints, thereby hindering the simultaneous achievement of real-time performance, safety, and energy efficiency in path planning. This paper first develops a comprehensive multi-dimensional cost function based on the dynamic characteristics of UUV underwater 3D navigation, operational rules for typical marine operating conditions, and safe navigation requirements through mathematical modeling, thereby formally transforming the UUV 3D path planning problem in typical marine operating conditions into a multi-constrained nonlinear global optimization problem. To address this challenge, an Adaptive Cooperative WMA (ACWMA) is proposed. The key improvements include: (i) an adaptive parameter switching and Lévy flight disturbance mechanism to balance exploration and exploitation capabilities; (ii) an optimal value leadership strategy to accelerate convergence; and (iii) a team collaborative learning mechanism to enhance population optimization efficiency. Algorithm benchmark performance is validated using the CEC 2017 standard test suite, while comparative and ablation experiments are conducted in multi-gradient complex marine 3D scenarios. The statistical significance of the algorithm performance improvement is verified using the Wilcoxon rank-sum test. The proposed ACWMA achieves a significant performance improvement of 8.71% over the suboptimal WMA in terms of core performance metrics and generates low-energy-consumption 3D paths that satisfy multiple constraints. These findings provide valuable engineering insights for 3D path planning in UUV autonomous operations within typical marine operating conditions. Full article

Wireless sensor network (WSN) coverage optimization is a challenging high-dimensional and nonlinear problem that directly affects network performance, including sensing quality, energy efficiency, and system reliability. Although metaheuristic algorithms have been widely applied to this problem, many existing methods still suffer from premature convergence, insufficient population diversity, and an imbalance between exploration and exploitation. To address these issues, this paper proposes a multi-strategy enhanced enterprise development optimization algorithm (MEEDOA) inspired by business management mechanisms. The proposed method integrates a hybrid population initialization strategy, an adaptive activity switching mechanism based on performance feedback, a multi-elite collaborative learning strategy, and a Lévy flight-based stagnation escape mechanism. These strategies are tightly coupled within a unified adaptive framework to improve global search capability, convergence speed, and robustness. Furthermore, a mathematical model for WSN deployment is constructed based on a binary sensing model and discrete coverage evaluation. From the perspective of symmetry, the sensing regions of sensor nodes exhibit significant geometric symmetry in both two-dimensional and three-dimensional deployment spaces. In the two-dimensional case, the sensing and communication regions are modeled as concentric circular structures, while in the three-dimensional case, the sensing regions are represented by isotropic spheres with symmetric spatial distributions. Such symmetry properties provide an effective basis for describing coverage behavior, reducing redundant overlap, and improving the uniformity of node deployment. Meanwhile, the proposed MEEDOA preserves population diversity and enhances search balance, enabling the algorithm to better capture symmetric coverage patterns and more effectively explore complex spatial deployment configurations. Extensive experiments on CEC2014, CEC2017, CEC2020, and CEC2022 benchmark functions demonstrate that MEEDOA achieves superior convergence accuracy, faster convergence speed, and stronger robustness compared with several state-of-the-art algorithms. Additional simulation results in WSN deployment applications verify its effectiveness in improving coverage performance under both symmetric and irregular spatial deployment scenarios. The results indicate that the proposed MEEDOA provides a reliable and efficient solution for complex global optimization problems and practical engineering applications. Full article

The coffee berry borer (Hypothenemus hampei) is the primary pest of coffee crops worldwide. Sustainable management strategies increasingly rely on the integration of biological control and interventions activated by population thresholds. In this work, a comparative framework based on dynamical systems is presented, integrating three complementary mathematical models to analyze different management strategies for the coffee berry borer. First, a biologically structured three-dimensional model describes the interaction between adult and immature borers and predatory ants. Second, a two-dimensional formulation allows the maximum per capita consumption rate of the predator to be studied as a bifurcation parameter, identifying critical parameter values that delimit regions of coexistence or effective pest control. Finally, a piecewise-smooth dynamical system incorporates ethological control activated when infestation exceeds a predefined threshold, whose effectiveness depends on the capture intensity associated with the traps. Using stability theory, bifurcation analysis, and techniques from piecewise-smooth dynamical systems, parametric regions associated with persistence, coexistence, or significant pest reduction are characterized. The results show that biological control alone may be insufficient if a predation threshold is not exceeded, whereas its combination with early threshold-based interventions considerably enlarges the dynamical regions favorable to producers. This study provides a dynamical interpretation of the agricultural concept of intervention threshold and offers a quantitative framework to strengthen integrated management and the sustainability of coffee production. Full article

To address the severe multiple-seed pickup problem during the seed-filling process of an air-suction seed metering device for small-seed crops with multiple seeds per hill, a combined seed-cleaning mechanism consisting of an upper seven-tooth seed-cleaning device and a lower seed-cleaning blade was developed based on an analysis of the causes of multiple pickup. Mathematical models of seed motion and force were established to describe the interaction between the seven-tooth seed-cleaning device and the seed population during the cleaning process. The installation position and adjustment mechanism of the device on the seed chamber housing were determined, and its tooth-profile parameters and major operating positions were theoretically analyzed. Accordingly, the design method and calculation models for the key parameters of the seven-tooth seed-cleaning device were established. A quadratic regression orthogonal rotational combination experiment was conducted using three factors affecting cleaning performance: the distance between the apex of the first tooth and the corresponding suction hole, the operating speed of the seed metering device, and the negative pressure. Regression equations were established and response surface analysis was performed. With the seed-cleaning qualification rate as the optimization objective, the optimal parameter combinations were obtained as follows: for millet, 3.36 mm, 3.59 km/h, and 1.43 kPa; for broomcorn millet, 3.49 mm, 4.22 km/h, and 2.11 kPa; and for rapeseed, 3.15 mm, 3.73 km/h, and 1.52 kPa. To reduce the influence of random error, 200 repeated bench tests were conducted for each seed type under its corresponding optimal parameter combination at operating speeds of 2.0–5.0 km/h. The seed-cleaning qualification rates for millet, broomcorn millet, and rapeseed were all above 90%, meeting the design requirements of the seed-cleaning mechanism. This study provides a theoretical basis and technical reference for seed-cleaning mechanisms for air-suction precision seed metering devices for small-seed crops with multiple seeds per hill. Full article

Aggregate production planning (APP) helps medium-term production, manpower, inventory, and subcontracting decisions match expected demand. Deterministic planning models are generally ineffective in manufacturing due to demand and operational variability. Fuzzy linear programming (FLP) has been frequently used to describe imprecision using membership functions and satisfaction levels. Despite its versatility, accurate approaches for solving multi-objective FLP-based APP models become computationally expensive as issue size and complexity increase. Thus, metaheuristic algorithms are widely used, although many still have premature convergence, parameter sensitivity, and restricted scalability. This study investigates the Narwhal Optimization Algorithm (NO) as a population-based metaheuristic framework. It proposes two hybrid variants to improve convergence reliability and constraint-handling capability: NO combined with the Super Modified Simplex Method (SMS) for local refinement and NO integrated with a Runge–Kutta-based optimizer (RK) for search stability. These hybrid techniques are tested for solution quality, convergence behavior, and robustness using eight response-surface benchmark functions and four constrained optimization problems. A real-parameter fuzzy APP problem with three goods and a six-month planning horizon uses the best variations. The Elevator Kinematic Optimization (EKO) algorithm, chosen for its compliance with the same mathematical framework and consistent parameter values, is used to compare the offered solutions fairly and controlled. Fuzzy programming uses a max–min satisfaction framework with linear membership functions from positive and negative ideal solutions. Computational experiments assess solution quality, stability, and efficiency for nominal and ±10% demand disturbances. The hybrid NO variants better resist premature convergence, stabilize solutions, and satisfy users more than the original NO and benchmark approaches. For small and medium-sized organizations in dynamic situations, hybrid narwhal-based optimization appears to be a reliable and scalable decision-support solution for APP problems under uncertainty. Full article

Measles remains a significant public health threat despite widespread vaccination, with recent resurgences driven by vaccine hesitancy and coverage gaps. Existing mathematical models often fail to capture the substantial temporal heterogeneity in incubation periods, vaccine-induced protection, and recovery processes that characterize measles transmission. We develop and analyze an SVEIR epidemic model incorporating four independent distributed time delays with exponential survival factors, capturing the realistic variability in these epidemiological processes. The model features compartment-specific mortality rates, disease-induced mortality, and imperfect vaccination with failure probability $\theta$. Using next-generation matrix methods adapted for delay kernels, we derive the delay-dependent reproduction number ${\mathcal{R}}_0^d$ and prove, via systematic construction of Volterra-type Lyapunov functionals, that it constitutes a sharp threshold: the disease-free equilibrium is globally asymptotically stable when ${\mathcal{R}}_0^d\le 1$, while a unique endemic equilibrium emerges and is globally stable when ${\mathcal{R}}_0^d>1$. Normalized forward sensitivity analysis reveals that the transmission rate $\beta$ and recruitment rate $\Lambda$ exhibit maximal positive elasticity, while the vaccination rate p, vaccine failure probability $\theta$, and incubation delay ${\tau }_3$ possess the largest negative elasticities. Critically, ${\tau }_3$ exerts exponential influence via $e^{-n_3{\tau }_3}$, making interventions that delay infectiousness—such as post-exposure prophylaxis—unusually potent. We derive an explicit expression for the critical delay ${\tau }_3^{\mathrm{cr}}$ at which ${\mathcal{R}}_0^d=1$, demonstrating that prolonging the effective incubation period sufficiently can shift the system from endemic persistence to extinction. Numerical simulations using Dirac delta kernels confirm all theoretical predictions. These findings provide three actionable insights for public health: (1) maintaining high vaccination coverage among new birth cohorts remains paramount; (2) improving vaccine quality (reducing $\theta$) yields substantial returns; and (3) the incubation delay represents a quantifiable, measurable target for evaluating the population-level impact of time-sensitive interventions. The framework is broadly applicable to infectious diseases characterized by significant temporal heterogeneity. Full article

In this study, we propose a compartmental mathematical model that considers two interacting populations (citrus plants and insect vectors) and investigate the transmission dynamics of Huanglongbing in citrus crops. This disease is caused by the bacterium Candidatus Liberibacter asiaticus and is vectored by the psyllid Diaphorina citri. The disease is modeled under the following three main assumptions: there is vital dynamics with constant recruitment rates of citrus plants, the force of infection in both populations is a spatially dependent function varying with geographic location, and there is a spatial displacement of the vectors. In the main results of the paper, we formulate a coupled ordinary and partial differential equation system with initial and zero flux boundary conditions, establish the existence and uniqueness of solutions to the proposed model by applying semigroup theory, and introduce a numerical approximation of the system. Moreover, we develop a stability and persistence analysis. From the analytical point of view, we calculate the basic reproduction number $R_0$ and prove three facts: the disease-free equilibrium is globally asymptotically stable when $R_0<1$; the disease-free equilibrium is globally asymptotically stable when $R_0>1$; and the hybrid system exhibits uniform persistence of infection when $R_0>1$. In addition, we present some numerical examples. Full article

This paper analyses the self-organization and spatio-temporal pattern formation in bacterial and human populations using chemotaxis-based mathematical models. The pattern formation in the following three chemotaxis-type systems is investigated: the self-organization of suspensions of luminous Escherichia coli bacteria, the capital-induced labor migration in a spatial Solow model, and the movement of urban criminals forming crime hotspots. The three models are selected as representative examples of chemotaxis mechanisms that capture distinct modeling assumptions and applications. Nonlinear two-dimensional as well as one-dimensional-in-space reaction–diffusion–chemotaxis models were used to simulate the pattern formation in all three chemotactic systems within a restricted area—a circle. The models are formulated in dimensionless form, and the corresponding dimensional parameters are estimated through the comparison of simulation results with experimental and statistical data. The numerical simulation under the transient conditions was carried out using the finite difference technique. This study highlights substantial differences between bacterial motility and the geographical movement of humans; however, human populations’ movement toward an attractant can be regarded as analogous to the chemotactic behavior of biological cells, differing primarily in scale. Full article

This paper addresses the question of how many autonomous aerial vehicles (UAVs or drones) can safely operate within a bounded three-dimensional airspace. First, we derive the absolute mathematical limits on drone density using geometric arguments from sphere packing and covering theory. Then, we verify these limits empirically by simulating a swarm controlled via model predictive control. We incrementally increase the number of drones until motion becomes impossible. Each drone is modeled as a double-integrator system with a bounded speed and acceleration and is surrounded by a radius spherical safety zone $r>0$. The drones are controlled via model predictive control with hard separation constraints. We formalize complete blockage as the loss of any feasible non-trivial trajectory set, either due to geometric crowding or dynamic limitations. Using tools from discrete geometry, we establish absolute upper bounds on a safe population via sphere-packing results and sufficient conditions for total immobilization via sphere-covering arguments. We extend these static bounds by incorporating dynamics through stopping-distance analysis, leading to an inflated exclusion radius that captures the effect of finite control authority. In addition, we prove min-cut style flow-capacity bounds that limit feasible throughput across bottlenecks and derive horizon-dependent conflict-graph conditions that capture MPC infeasibility at high densities. These results provide a rigorous theoretical framework for determining the transition from feasible multi-drone operation to inevitable gridlock, offering explicit quantitative thresholds that can inform airspace design, drone density regulation, and the tuning of predictive controllers. We evaluate our theoretical findings with a simulation environment. Full article

The Multi-Objective Flexible Job Shop Scheduling Problem (MOFJSSP) represents a core challenge in modern manufacturing: achieving synergistic optimization of multiple conflicting objectives while pursuing production efficiency and energy sustainability. To address this, this study proposes an enhanced hybrid heuristic algorithm—KNN–Tabu Search NSGA-II (KTNSGA-II)—for simultaneously optimizing completion time, machine load, and total energy consumption. First, a three-objective mathematical model is established. Subsequently, four key strategies are integrated: (1) workload balancing initialization rapidly generates high-quality initial solutions; (2) an adaptive job-level crossover mechanism dynamically adjusts subset sizes during iterations to balance global exploration and local exploitation; (3) K-nearest neighbor-based congestion distance calculation maintains population diversity; (4) tabu search applied to non-dominated solutions on the Pareto front for local refinement. Extensive experiments on standard benchmark instances demonstrate that KTNSGA-II significantly outperforms representative algorithms in terms of convergence and diversity. For large-scale Behnke benchmark instances, KTNSGA-II achieves an average hypervolume (HV) improvement of 32.32% compared to other comparison algorithms. Furthermore, this method substantially enhances solution diversity: the Spacing Performance (SP) metric improved by 39.72%, indicating more uniform distribution of Pareto optimal solutions; the Diversity Metric (DM) increased by 57.54%, reflecting broader coverage and more even distribution along the Pareto frontier boundary. These results confirm that KTNSGA-II generates higher-quality, better-distributed Pareto fronts, achieving a more optimal trade-off between completion time, machine load, and energy consumption. Full article

Taganrog Bay is part of the Azov Sea, which has significant environmental value. However, in recent years, anthropogenic activity and climate change have increasingly impacted this coastal system. These factors have led to increased sea salinity. These factors also contribute to abundant blooms of potentially toxic cyanobacteria. One additional method for preventing the abundant growth of cyanobacteria may be the introduction of green algae into the bay. The aim of this study was to conduct a computational experiment on the biological rehabilitation of Taganrog Bay using mathematical modeling methods. For this purpose, the authors developed and analyzed a mathematical model of phytoplankton populations. A software model was developed based on modern mathematical modeling methods. The input data for the software module included grid points for advective transport velocities, salinity, and temperature, as well as phytoplankton population and nutrient concentrations. The software module outputs three-dimensional distributions of green algae and cyanobacteria concentrations. A computational experiment on biological rehabilitation of the Taganrog Bay by introducing a suspension of green algae was conducted. Green algae and cyanobacteria concentrations were obtained over 15 and 30-day time intervals. The concentration and volume of introduced suspension were empirically determined to prevent harmful cyanobacteria growth without leading to eutrophication of the bay by green algae. Full article

The progress of contemporary pharmacology is deeply linked to pharmacokinetics (PK) and its quantitative exploration through PK modeling. By offering a robust mathematical framework to describe and predict drug absorption, distribution, metabolism, and excretion (ADME), PK modeling is essential for designing and optimizing safe and effective dosing regimens and for advancing personalized medicine and model-informed drug development (MIDD). The reliability of population PK (popPK) and physiologically based PK (PBPK) models depends on high-quality experimental data to estimate PK parameters. Traditional PK data sources include clinical studies, preclinical animal models, and human-derived cell lines. Although considered gold standards, these sources have significant drawbacks. Clinical trials are often restricted by ethical, logistical, and financial challenges and often include homogenous populations that fail to reflect real-world interindividual variability. Similarly, animal and cell-based models lack the physiological complexity of humans, leading to discrepancies between preclinical predictions and clinical outcomes. These constraints have stimulated interest in alternative platforms that more faithfully recapitulate human physiology and interindividual diversity. This review explores the potential of organoids as a novel or complementary source of PK-relevant data. Organoids, three-dimensional (3D) stem cell-derived structures, mimic the cellular architecture, functional heterogeneity, and physiological responses of human tissues. In particular, intestinal, liver, and kidney organoids preserve essential cellular features of ADME processes, positioning them as promising tools for integration into popPK and PBPK modeling frameworks. 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

Background/Objectives: Myasthenia gravis (MG) is a rare autoimmune neuromuscular disease. Clinical trials with rigorously collected data provide valuable opportunities for mathematical modeling of patient outcomes over time. However, for rare diseases such as MG, combining data across multiple trials presents challenges due to heterogeneity in outcome measures. This study aims to address these challenges by investigating relationships among commonly used MG outcome measures to support the development of a standardized “Myasthenia Gravis Portrait.” Methods: We integrated three primary data types from multiple clinical studies: (i) laboratory and medication data, (ii) Electronic Health Record (EHR) data (e.g., age, sex, years since diagnosis, BMI), and (iii) disease severity scores. We examined the relationships among several MG-specific scoring systems, including Activities of Daily Living (MG-ADL), Quantitative Myasthenia Gravis (QMG), MG Composite (MG-CE), and MG Quality of Life-15 (MGQOL-15), to evaluate consistency and comparability across studies. Results: Preliminary analyses revealed variable correlations among the different scoring systems, indicating that, while some measures capture overlapping aspects of disease progression, others reflect distinct patient- or clinician-centered perspectives. These findings highlight the need for a harmonized framework that captures both functional and clinical dimensions of MG severity. Conclusions: The proposed “Myasthenia Gravis Portrait” provides a standardized approach for representing patient outcomes across diverse clinical datasets. This framework will facilitate the creation of virtual populations of digital twins, enabling a machine-learning-based modeling of MG progression and prediction of individualized disease trajectories. Full article