Research Article
Shiva Karimi; Elyas Shivanian; Zahra Barikbin
Abstract
This paper presents a novel numerical method for solving variable-order fractional integro-differential equations using two-dimensional fractional-order Fibonacci wavelets. The proposed approach employs fractional-order Fibonacci wavelets together with their associated integral and derivative operational ...
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This paper presents a novel numerical method for solving variable-order fractional integro-differential equations using two-dimensional fractional-order Fibonacci wavelets. The proposed approach employs fractional-order Fibonacci wavelets together with their associated integral and derivative operational matrices. First, new integral and derivative operational matrices are derived. These matrices, which exhibit improved accuracy in the numerical examples reported herein, are then employed to transform the governing equation into a system of algebraic equations. The collocation method is subsequently applied to solve this system and determine the unknown coefficients. Finally, error analysis, convergence results based on relevant theorems, and numerical examples are provided to demonstrate the accuracy, reliability, and efficiency of the proposed method.
Applied Article
Javad Gerami; Alireza Davoodi
Abstract
Two-stage network Data Envelopment Analysis (DEA) models under variable returns to scale (VRS) suffer from a well-known pitfall: efficiency score decomposition and frontier projection can be mutually inconsistent, undermining both the theoretical foundations and practical interpretability of the results. ...
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Two-stage network Data Envelopment Analysis (DEA) models under variable returns to scale (VRS) suffer from a well-known pitfall: efficiency score decomposition and frontier projection can be mutually inconsistent, undermining both the theoretical foundations and practical interpretability of the results. A further limitation is the universal assumption of strong disposability for all inputs and outputs, which is unrealistic when variables are structurally or statistically interdependent—as is common in healthcare settings. This paper addresses both issues simultaneously by developing a novel two-stage network DEA model under hybrid disposability (HD) technology, which allows selective strong or weak disposability for subsets of closely related inputs, intermediate measures, and outputs. We formally derive the efficiency decomposition and frontier projection under HD technology, establish theoretical consistency between the envelopment and multiplier forms, and prove that the proposed model yields Pareto-efficient targets. The model captures synergistic scale effects across stages and preserves structural dependencies between them, thereby providing a more realistic representation of multi-stage production systems. The practical relevance and advantages of the proposed framework are demonstrated through an empirical case study involving 32 Iranian healthcare centers operating under a two-stage network structure with interdependent variables.
Research Article
Ramin Kazemi; Akram Kohansal
Abstract
We consider the estimation of model parameters and prediction of unobserved records based on record statistics for the Basic Gompertz distribution (BGD) with parameter $\lambda$ using frequentist and Bayesian analysis. In frequentist analysis, we give the moment generating function of the $m$th record, ...
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We consider the estimation of model parameters and prediction of unobserved records based on record statistics for the Basic Gompertz distribution (BGD) with parameter $\lambda$ using frequentist and Bayesian analysis. In frequentist analysis, we give the moment generating function of the $m$th record, the maximum likelihood estimation (MLE) of $\lambda$, the moment-based estimate (MBE) of $\lambda$, the confidence interval for $\lambda$, and the prediction of future records. Exactly, we show that $$\hat{\lambda}_{\text{MBE}}=\frac{m(m+1)}{2\sum_{i=1}^{m}(e^{Y_i}-1)}, \hat{\lambda}_{\text{MLE}}=\frac{m}{e^{y_m}-1},$$ where $m\geq 1 $ and $Y_m=\max(\min)\{ X_1,\ldots,X_m \}$. In Bayesian analysis, we obtain the Bayesian sample-based estimation and prediction. Exactly, we show that under the squared error loss (SEL) function, $$\hat{\lambda}_{BS}=\frac{m+a}{e^{y_m}+b-1}$$ and under the LINEX loss function, $$\hat{\lambda}_{BL}=-\frac{m+a}{c}\ln\bigg( \frac{e^{y_m}+b-1}{e^{y_m}+(b+c)-1}\bigg).$$ Based on Monte Carlo simulations, the performances of the different methods of estimation and prediction are compared via MSEs and Biases. Finally, a real dataset has been analyzed for illustrative purposes.
Research Article
Babak Masoudi
Abstract
Relational graph structures add a layer of complexity to multi-objective combinatorial optimization (MOCO) that often renders large-scale NP-hard instances computationally prohibitive. While traditional metaheuristics like NSGA-II remain the industry standard, their reactive nature prevents them from ...
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Relational graph structures add a layer of complexity to multi-objective combinatorial optimization (MOCO) that often renders large-scale NP-hard instances computationally prohibitive. While traditional metaheuristics like NSGA-II remain the industry standard, their reactive nature prevents them from learning policies that generalize to unseen tasks. To address this, an end-to-end Deep Reinforcement Learning (DRL) framework is introduced, integrated with a Graph Convolutional Network (GCN) specifically for the Multi-Objective Project Portfolio Selection Problem (PPSP). By mapping the structural interdependencies of projects, the GCN provides critical cues that allow a Proximal Policy Optimization (PPO) agent to construct high-quality portfolios. Training stability is ensured through a reward normalization strategy derived from weighted-sum Pareto scalarization theory. Benchmarks on Barab\'{a}si-Albert and fully-connected graph instances reveal that the proposed DRL agent achieves a Hypervolume indicator 2.4 times higher than NSGA-II on 50-project tasks. Notably, interpretability analysis shows the model learns to prioritize high-degree "hub" projects with strategic synergies. Regarding scalability, the agent maintained over 90% of its Hypervolume performance when transitioned from 50 to 200 projects in a zero-shot manner, requiring no further training. This efficiency is mirrored in its computational speed; an average inference time of 12.69 ms represents a 300-fold acceleration compared to the metaheuristic baseline. Such results underscore the potential of GNN-driven structural exploitation as a robust alternative for high-speed, multi-objective optimization.
Research Article
Majid Akbarian; Javad Zanganeh
Abstract
This paper proposes a novel observer-based adaptive neural command filter (CF) output-feedback tracking control scheme for uncertain nonlinear multiple-input multiple-output (MIMO) stochastic systems subject to constrained partial tracking errors (PTEs). The key contributions are threefold. First, a ...
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This paper proposes a novel observer-based adaptive neural command filter (CF) output-feedback tracking control scheme for uncertain nonlinear multiple-input multiple-output (MIMO) stochastic systems subject to constrained partial tracking errors (PTEs). The key contributions are threefold. First, a linear Luenberger-type state observer is designed to handle unmeasured states, and radial basis function neural networks (RBFNNs) are employed to approximate unknown nonlinear functions. Second, a dynamic surface control (DSC) strategy augmented with compensating signals simultaneously eliminates the "explosion of complexity" inherent in conventional backstepping and rectifies filter-output errors in the DSC framework. Third, a minimal learning parameter (MLP) technique — based on Young's inequality — reduces the number of online-tunable parameters to a single scalar per subsystem, yielding a computationally efficient adaptive law. The closed-loop system is rigorously proven to be semi-globally uniformly ultimately bounded (SGUUB) in probability via Lyapunov-based stochastic stability analysis, and all PTEs remain within prescribed performance bounds throughout transient and steady-state operation. Comparative simulations on a second-order MIMO stochastic benchmark demonstrate that the proposed approach achieves significantly lower root mean square and integral absolute tracking errors than existing methods, while maintaining bounded and smooth control effort. Current limitations, including the restriction to strict-feedback topologies and the assumption of bounded external disturbances, motivate future extensions to multi-agent and event-triggered control frameworks.
Research Article
Nabil Sellami; Romaissa Mellal; Basim A. Hassan
Abstract
This paper introduces two hybrid nonlinear conjugate gradient algorithms, NRB1 and NRB2, for solving unconstrained optimization problems. Both methods are constructed as a convex combination of the AlBayati–AlAssady (BA) and Conjugate Descent methods (CD). The first variant, denoted NRB1, employs ...
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This paper introduces two hybrid nonlinear conjugate gradient algorithms, NRB1 and NRB2, for solving unconstrained optimization problems. Both methods are constructed as a convex combination of the AlBayati–AlAssady (BA) and Conjugate Descent methods (CD). The first variant, denoted NRB1, employs an adaptive combination parameter designed to align its search direction more closely with Newton’s method, improving curvature approximation and acceleration of convergence. The second variant, NRB2, independently satisfies the conjugacy condition without relying on line search mechanisms, enhancing numerical stability. Both methods guarantee sufficient descent and global convergence properties under the strong Wolfe line search criteria. Extensive numerical experiments, using the performance profile of Dolan and Moré, demonstrate that NRB1 and NRB2 consistently outperform some classical conjugate gradient methods, including BA, CD, and Dai–Yuan, particularly for large-scale problems. Furthermore, NRB1 is applied to image restoration under salt-and-pepper noise, achieving competitive or superior peak signal-to-noise ratios (PSNR) compared to the Fletcher–Reeves (FR) algorithm with significantly fewer iterations, especially at high noise intensities.
Research Article
Muayyad Mahmood Khalil; Najim Abdullah Ibrahim
Abstract
The Bagley--Torvik equation, which governs the motion of a rigid plate immersed in a Newtonian fluid with viscoelastic damping, represents one of the canonical benchmark problems in fractional calculus. This paper presents a systematic comparative numerical analysis of four established methods for solving ...
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The Bagley--Torvik equation, which governs the motion of a rigid plate immersed in a Newtonian fluid with viscoelastic damping, represents one of the canonical benchmark problems in fractional calculus. This paper presents a systematic comparative numerical analysis of four established methods for solving this equation: the Fractional-Order Hybrid Jacobi Functions method (FOHJF), the Polynomial Least Squares Method (PLSM), the Vieta-Lucas Spectral Method (VLSM), and the Cubic Spline Collocation Method (CSCM). Three benchmark test problems with qualitatively distinct forcing functions---polynomial, oscillatory (cosine), and exponential---and varying initial conditions are used to evaluate absolute approximation errors at resolution levels N = 8, 16, 32, and 64. Detailed error tables and graphical convergence analyses are provided. The results consistently demonstrate that VLSM achieves the highest accuracy, with maximum absolute errors below 2.3×10⁻⁸ at N = 32, followed by FOHJF. PLSM and CSCM offer simpler implementation at the cost of reduced accuracy. Practical recommendations are provided for selecting a method based on the required precision level and the type of forcing function. The study identifies key limitations and directions for future work, including extension to nonlinear formulations, variable-order derivatives, and adaptive hybrid approaches.
Research Article
Ghania Idiri
Abstract
In this paper, a systematic design approach for the parametric optimization of uncertain dynamical systems with bounded parameter uncertainties is proposed. The methodology proceeds in two stages. In the first stage, the control input is expressed as a finite linear combination of polynomial basis functions, ...
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In this paper, a systematic design approach for the parametric optimization of uncertain dynamical systems with bounded parameter uncertainties is proposed. The methodology proceeds in two stages. In the first stage, the control input is expressed as a finite linear combination of polynomial basis functions, and an approximate analytical solution of the state equation is derived using the Variational Iteration Method, which is a semi-analytical iterative technique that avoids discretization and linearization. Substituting this approximate trajectory into the performance index yields a robust min–max optimization problem parameterized by the control coefficients. In the second stage, the robust optimization problem is converted into a tractable scenario optimization problem by drawing a finite number of independent and identically distributed samples from the uncertainty set. The resulting problem is solved using a genetic algorithm. The effectiveness of the proposed approach is demonstrated through two application examples. The first example concerns an uncertain linear-quadratic regulator, and the second addresses an uncertain nonlinear optimal control problem. Optimal control and state trajectories are provided for a set of samples. In addition, the optimal value of the performance index is reported, showing that this value does not exceed the threshold imposed by the proposed approach. The paper concludes by discussing limitations, including dependence on the accuracy of the Variational Iteration Method approximation and the assumption of a known probability distribution over the uncertainty set, and identifies directions for future research.
Research Article
Yaprak Güldoğan Dericioğlu
Abstract
The Extended Block Arnoldi–Backward Differentiation Formula (EBA–BDF) is a projection-based integrator for solving large-scale Matrix Differential Riccati Equations (DREs). Like many Krylov subspace methods, its performance depends on the choice of the subspace dimension. In practice, this ...
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The Extended Block Arnoldi–Backward Differentiation Formula (EBA–BDF) is a projection-based integrator for solving large-scale Matrix Differential Riccati Equations (DREs). Like many Krylov subspace methods, its performance depends on the choice of the subspace dimension. In practice, this parameter is often determined through empirical tuning. In this work, we introduce a lightweight, data-driven pre-solver to estimate this dimension \emph{a priori}. The approach uses a Random Forest model trained on spectral norms and discretization parameters, and predicts the required subspace size without modifying the numerical core or stability properties of the original method. Numerical experiments show that the proposed approach can automate parameter selection and reduce the need for manual tuning. The effect is more noticeable in diffusion-dominated regimes, where spectral properties lead to more regular Krylov convergence. By simplifying the initialization stage, the approach supports the practical use of EBA–BDF solvers in large-scale problems.
Research Article
Alpha Peter Lukonde; Homan Emadifar
Abstract
This study presents a numerical technique for solving Volterra--Fredholm integral equations of the second kind. The solution is approximated via two independent polynomial bases, namely the Pell--Lucas polynomials and the Clique polynomials, each paired with a collocation discretisation. Both approaches ...
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This study presents a numerical technique for solving Volterra--Fredholm integral equations of the second kind. The solution is approximated via two independent polynomial bases, namely the Pell--Lucas polynomials and the Clique polynomials, each paired with a collocation discretisation. Both approaches are evaluated under two distinct sets of collocation points: standard equally spaced points and Chebyshev--Gauss--Lobatto points, the latter included for comparative purposes. Solution accuracy is assessed through the L2 and L∞ norms, the absolute error, and the root mean squared error (RMSE), while an upper bound error analysis is provided to establish convergence. Numerical experiments confirm that both methods achieve progressively higher accuracy as the degree N of the approximating polynomial series increases. Where applicable, the results are benchmarked against those reported in the existing literature. All numerical findings are presented in tabular and graphical form.
Research Article
Islem Bennadja; Omar Kebiri; Djamal Chaabane
Abstract
Human immunodeficiency virus (HIV) gradually depletes CD4+ T-cells, weakening the immune system and potentially leading to AIDS without effective treatment. To counter this immune decline, antiretroviral therapy (ART) has greatly improved the clinical management of HIV by suppressing viral replication ...
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Human immunodeficiency virus (HIV) gradually depletes CD4+ T-cells, weakening the immune system and potentially leading to AIDS without effective treatment. To counter this immune decline, antiretroviral therapy (ART) has greatly improved the clinical management of HIV by suppressing viral replication and preserving immune function. However, because treatment is often required over long periods, its use may be limited by cumulative toxicity, drug resistance, and adherence challenges. These limitations have encouraged the study of structured treatment interruptions, in which therapy is temporarily stopped and resumed according to a planned schedule to reduce drug exposure while maintaining viral control. In this context, this work proposes a clinically motivated block-wise multi-objective optimization framework for HIV treatment scheduling, based on a nonlinear six-state dynamical model with two binary control variables corresponding to protease inhibitor (PI) and reverse transcriptase inhibitor (RTI) therapies. Rather than determining a single treatment schedule over the entire time horizon, the proposed framework incorporates sequential re-optimization over consecutive 30-day blocks to reflect periodic clinical reassessment and treatment adaptation. The study also compares asynchronous and synchronous binary control strategies under identical conditions. Within each block, daily treatment decisions are optimized using the Non-dominated Sorting Binary Genetic Algorithm II (NSBGA-II), with the aim of preserving CD4+ T-cell levels, suppressing viral load, and reducing total drug administration. This formulation provides a more clinically realistic basis for constructing adaptive and personalized HIV treatment schedules.
Research Article
Guemmaz Abderrahim
Abstract
This paper introduces a novel parameterized kernel function for primal–dual interior-point methods (IPMs) applied to the linear optimization (LO) problem. The proposed kernel, governed by two parameters — a base u > 1 and a term-count ℓ ∈ N \ {0} — employs a multi-exponent ...
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This paper introduces a novel parameterized kernel function for primal–dual interior-point methods (IPMs) applied to the linear optimization (LO) problem. The proposed kernel, governed by two parameters — a base u > 1 and a term-count ℓ ∈ N \ {0} — employs a multi-exponent power-sum structure (i.e., a sum of power terms with geometrically spaced exponents (u, u2, ..., uℓ) that decouples local curvature near the central path from asymptotic growth far from it. This decoupling is impossible with single-parameter kernels such as self-regular or trigonometric variants. Under mild, verifiable conditions, the resulting IPM attains a worst-case iteration complexity of O(uℓ n((uℓ +1)/2uℓ ) log(n/ϵ )) for large-update strategies, and O(u2ℓ √n log(n/ϵ )) for small-update strategies. Choosing u = (log n/2 )1/ℓ recovers the best-known large-update bound O(√n log(n) log(n/ϵ )). Numerical experiments on benchmark LP instances with dimensions up to n = 1000 confirm that the ℓ = 1, u = 3.5 variant consistently outperforms the classical self-regular kernel of Peng et al. in both iteration count and CPU time. The study demonstrates that self-regularity is sufficient but not necessary for optimal complexity, broadening the theoretical foundations of kernel-based interior-point frameworks.
Research Article
Masoud Ghods; Negar Kheirkhahan
Abstract
This research evaluates the integration of graph-theoretic topological indices (TIs) with machine learning (ML) frameworks to forecast the physicochemical attributes of anxiolytic drugs. By representing molecular structures as graphs, the study extracted TIs to serve as primary features for four distinct ...
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This research evaluates the integration of graph-theoretic topological indices (TIs) with machine learning (ML) frameworks to forecast the physicochemical attributes of anxiolytic drugs. By representing molecular structures as graphs, the study extracted TIs to serve as primary features for four distinct predictive algorithms: basic and optimized support vector regression (SVR-Basic and SVR-Tuned), random forest (RF), and linear regression (LR). To address the constraints of a small sample size, the authors utilized Leave-One-Out cross-validation (LOOCV) and bootstrap resampling to ensure robust performance metrics, including confidence intervals and coefficients of variation (CV\%) for stability assessment. The findings indicate that the combination of hyperparameter refinement and rigorous validation significantly elevates the precision and reliability of ML models in chemical property prediction.
Research Article
Mehdi Ramezanifard; Naser Pariz; Mohammad Bagher Naghibi Sistani; Majid Akbarian
Abstract
Non-holonomic mobile robots are widely deployed in industrial and service environments, yet designing controllers for moving-target tracking under nonholonomic constraints remains a challenging open problem. In this paper, we present a Mamdani-type fuzzy logic tracking controller specifically designed ...
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Non-holonomic mobile robots are widely deployed in industrial and service environments, yet designing controllers for moving-target tracking under nonholonomic constraints remains a challenging open problem. In this paper, we present a Mamdani-type fuzzy logic tracking controller specifically designed for non-holonomic mobile robots pursuing dynamic targets with arbitrary movement patterns. Although tailored to differential-drive platforms, the proposed architecture can be extended to other types of mobile robots and autonomous systems. A key feature of the controller is the explicit enforcement of a predefined safe distance between the robot and the target, preventing collision while simultaneously supporting covert or low-detection tracking applications. A significant advantage of this model-free architecture is its computational efficiency: the system operates on minimal sensor inputs, requires no dynamic model of the robot,and can be seamlessly deployed on low-cost sensing hardware, making it well-suited for energy-constrained platforms. Lyapunov-based stability analysis is provided for the closed-loop system, and the methodology is validated through simulation on a differential-drive robot model across multiple complex scenarios in a virtual environment, including cases with high measurement noise. The comprehensive simulation results confirm that the controller achieves robust stability and high tracking precision, demonstrating its practical acceptability for real-time target tracking applications.
Research Article
Mohammad Eshaghnezhad; Niloufar Kamkar; Javad Banihassan; Jalal A. Nasiri; Amin Mansoori
Abstract
Data envelopment analysis (DEA) is a widely used non-parametric method for evaluating the relative efficiency of peer decision-making units (DMUs). To address the computational demands of conventional solvers, this study develops a neurodynamic optimization framework derived from the Karush--Kuhn--Tucker ...
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Data envelopment analysis (DEA) is a widely used non-parametric method for evaluating the relative efficiency of peer decision-making units (DMUs). To address the computational demands of conventional solvers, this study develops a neurodynamic optimization framework derived from the Karush--Kuhn--Tucker (KKT) optimality conditions of the CCR-based, input-oriented DEA model. To date, only a few studies have applied neurodynamic approaches to DEA, and all of them rely on double-layer structures. Our primary contribution is the construction of a KKT-based dynamic system tailored to the CCR-based DEA formulation. Furthermore, we provide a rigorous theoretical foundation by establishing the Lyapunov stability of the proposed system, thereby ensuring its global convergence to an exact optimal solution. The model's practical effectiveness is validated through a comprehensive case study analyzing the efficiency of participating nations in the Asian Games. The results, obtained using our neurodynamic framework and evaluated in terms of CPU time, demonstrate its robustness and computational efficiency for real-world performance benchmarking.
Research Article
Anıl Burcu Özyurt Serim; Mustafa Akan
Abstract
This paper investigates the structural divergence in investment behavior that arises from the temporal misalignment between shareholders and managers within a principal-agent framework. We develop a continuous-time optimal control model in which the agent's contract horizon serves as the fundamental ...
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This paper investigates the structural divergence in investment behavior that arises from the temporal misalignment between shareholders and managers within a principal-agent framework. We develop a continuous-time optimal control model in which the agent's contract horizon serves as the fundamental determinant of investment incentives, rather than information asymmetry or moral hazard. The analysis establishes that the gap between shareholder and managerial investment objectives is not incidental but structurally embedded in the finite nature of managerial tenure: even under perfect information and symmetric monitoring, managers systematically underinvest relative to the socially optimal level. Three contract scenarios are examined to characterize this dynamic fully. In the infinite-horizon case, the agent's objectives converge to those of the shareholder, yielding a benchmark steady-state equilibrium. In the fixed-horizon case, the approaching contract expiration date progressively erodes investment incentives, driving managerial effort toward zero at the terminal date. In the free-horizon case, where the agent endogenously determines the exit time, the same myopic pattern emerges through the transversality conditions governing the optimal stopping decision. Across all three scenarios, the analysis identifies the precise parametric conditions under which principal and agent objectives either align or persistently diverge. It demonstrates that long-term contracting is the necessary — though not always sufficient — mechanism for closing the structural investment gap.
Research Article
Mohammad Javad Pahlevanzadeh; Mohammad Reza Fathi; Amirhossein Saffarinia
Abstract
This study presents a multi-objective mixed-integer linear programming (MILP) model for optimizing rotational shift scheduling of personnel at gas pressure reduction stations (CGSs) and administrative offices of the Gas Company of Qom Province, Iran. The model simultaneously addresses organizational ...
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This study presents a multi-objective mixed-integer linear programming (MILP) model for optimizing rotational shift scheduling of personnel at gas pressure reduction stations (CGSs) and administrative offices of the Gas Company of Qom Province, Iran. The model simultaneously addresses organizational requirements and human-centric factors, including employee shift preferences, coworker compatibility, sensitivity to mercaptan gas, public communication skills, commuting distances, and regulatory workload constraints. A two-phase solution framework is employed: the multi-objective problem is first scalarized using the ε-constraint method, and the resulting single-objective subproblems are then solved using the Gray Wolf Optimizer (GWO) and the Crow Search Algorithm (CSA). An MILP-solver-based ε-constraint baseline is also reported for benchmarking. A real-world case study involving 49 employees, 9 service locations, and a 30-day planning horizon is used to evaluate the framework. Results from 30 independent runs show that CSA obtains lower average overtime (44.2 h versus 48.6 h), higher shift-preference satisfaction (90.1% versus 87.3%), higher coworker-preference satisfaction (86.4% versus 83.6%), and shorter average runtime (109.8 s versus 121.4 s) than GWO. Wilcoxon signed-rank tests indicate statistically significant differences at the 5% level. Sensitivity analysis reveals the trade-off between individual shift preferences and coworker compatibility under alternative weight settings. The framework therefore provides a practical and adaptable decision-support approach for workforce planning in continuous and safety-critical gas distribution operations.
Research Article
Iman Makhdoom; Shahram Yaghoobzadeh Shahrastani
Abstract
Parametric modeling of continuous data plays a fundamental role in reliability analysis, survival studies, and proportion modeling. This paper develops a unified optimization-based Bayesian and robust divergence estimation framework for continuous parametric models under both censored and complete data ...
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Parametric modeling of continuous data plays a fundamental role in reliability analysis, survival studies, and proportion modeling. This paper develops a unified optimization-based Bayesian and robust divergence estimation framework for continuous parametric models under both censored and complete data settings. The proposed approach integrates hierarchical Bayesian and E-Bayesian inference with divergence-based robust estimation---specifically the L2E method---to enhance efficiency and stability against model misspecification and potential data contamination. For lifetime data, the framework is applied to the two-parameter Weibull distribution under progressive Type-II censoring schemes; for proportion data, it is applied to the Beta distribution under complete sampling. For the Beta distribution, the proposed E-Bayesian methodology is investigated under the simplified setting in which the second shape parameter is assumed known and fixed (ß=1). This assumption is adopted to illustrate the proposed optimization-based inferential framework while keeping the methodological development analytically tractable. Bayesian and E-Bayesian estimators are derived under both symmetric and asymmetric loss functions, including squared error, entropy, and Linex losses. The divergence-based estimator is incorporated as a robust alternative within the same optimization structure. Extensive Monte Carlo simulations are conducted to evaluate estimator performance in terms of absolute bias and mean squared error across various scenarios. Numerical illustrations further demonstrate the practical applicability of the proposed framework. The results indicate that the integrated methodology provides accurate and robust parameter estimation across different data structures, offering a flexible inferential tool for continuous parametric modeling.
Applied Article
Maha Mohsin Mohammed Ali
Abstract
A core challenge in numerically solving partial differential equations (PDEs) is achieving accuracy without sacrificing computational tractability. Globally supported methods provide high-order precision but at a computational cost that grows prohibitively with problem size, while locally supported schemes ...
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A core challenge in numerically solving partial differential equations (PDEs) is achieving accuracy without sacrificing computational tractability. Globally supported methods provide high-order precision but at a computational cost that grows prohibitively with problem size, while locally supported schemes scale more efficiently, though often with a reduction in solution accuracy. The proposed localized meshless framework resolves this tension through the integration of Radial Basis Function (RBF) approximation with the Partition of Unity (PU) decomposition, with applications to elliptic, convection-diffusion, and Helmholtz boundary value problems and their corresponding PDE-constrained optimal control problems. The domain is partitioned into overlapping subdomains, each accommodating an independent RBF expansion that is subsequently blended by compactly supported PU weight functions. This localization strategy replaces the single ill-conditioned dense system of global RBF collocation with a collection of smaller, well-conditioned local systems, reducing the theoretical computational complexity from O(N3) to O(N log N). Three canonical benchmark problems validate the framework: Poisson’s equation, a singularly perturbed convection-diffusion equation, and the Helmholtz equation on a circular domain, each embedded in a distributed optimal control formulation. The proposed scheme achieves L2-norm errors of order 10-4 at N = 1,000 nodes, outperforming both standard finite difference methods and global RBF collocation by factors of 28 to 49 in accuracy. Optimal control problems are handled through a Lagrange multiplier formulation yielding coupled state and adjoint systems, both discretized within the same RBF-PU architecture. The framework is illustrated through a detailed engineering case study — optimal heat-source regulation in a thermally loaded plate — in which the complete optimality system is derived, physically interpreted, and numerically solved. Numerical stability, current limitations, and directions for future investigation are discussed.
Research Article
Mahnaz Abedini; Gorbanali Haghighatdoost; Hossein Kheiri
Abstract
This study develops and analyzes a four-compartment predator–prey model incorporating disease dynamics and optimal control. The first prey population follows logistic growth and is susceptible to infection, whereas the second prey population remains disease-free and exhibits greater competitive ...
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This study develops and analyzes a four-compartment predator–prey model incorporating disease dynamics and optimal control. The first prey population follows logistic growth and is susceptible to infection, whereas the second prey population remains disease-free and exhibits greater competitive ability. The model incorporates an epidemic process within the first prey population and considers two control measures: reducing disease transmission and treating or removing infected individuals. We investigate the resulting system theoretically to assess the effects of these interventions on disease prevalence, prey persistence, predator dynamics, and ecosystem stability. In particular, stability analysis, sensitivity analysis, and optimal control theory are employed to characterize the model dynamics and identify the most influential parameters. The results indicate that the carrying capacity (k), infection rate (γ), and disease-induced mortality rate (µ) play major roles in determining the persistence of infection. Moreover, the optimal isolation (u1) and treatment (u2) strategies substantially reduce disease prevalence, increase the healthy prey population, and promote predator stability compared with the uncontrolled scenario. Numerical simulations further demonstrate the effectiveness of the proposed control strategies in mitigating infection and maintaining ecological balance. These findings demonstrate that the model provides a unified framework for examining the interactions between heterogeneous prey populations, disease transmission, predation, and targeted control interventions.
Research Article
Parastoo Heiatian Naeini; Ahmad Rezaee
Abstract
We consider a finite-dimensional multiobjective optimization problem with locally Lipschitz objective functions and finitely many locally Lipschitz inequality constraints. We formulate an active-set Slater test in which σxˆ is selected from a structurally restricted admissible class or selection ...
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We consider a finite-dimensional multiobjective optimization problem with locally Lipschitz objective functions and finitely many locally Lipschitz inequality constraints. We formulate an active-set Slater test in which σxˆ is selected from a structurally restricted admissible class or selection rule Σ(ψ, xˆ) prescribed before testing the qualification, rather than constructed from an MFCQ direction. Pointwise (σxˆ, rj)-invex inequalities with rj ≥ 0 imply the Clarke–Mangasarian–Fromovitz constraint qualification (ClarkeMFCQ). Standard maximum-function and normal-cone arguments then yield normalized Clarke–KKT multipliers at locally weakly efficient solutions, positive objective multipliers for positive weighted-sum solutions, and a perturbed-KKT inclusion at locally isolated efficient solutions. If Σ(ψ, xˆ) contains every locally Lipschitz map, the test is equivalent to Clarke-MFCQ. A nonsmooth nonconvex example illustrates the assumptions and multiplier inclusions.
Research Article
Hamid Rahimi; Reza Sheibani; Gelareh Veisi
Abstract
In this paper, a hybrid framework called E-SNM-CNN-LSTM was proposed for cellular traffic prediction and base station sleep-wake decision support in heterogeneous networks. First, traffic data were processed using an entropy-based refinement step to reduce noise and short-term spikes. Then, a combination ...
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In this paper, a hybrid framework called E-SNM-CNN-LSTM was proposed for cellular traffic prediction and base station sleep-wake decision support in heterogeneous networks. First, traffic data were processed using an entropy-based refinement step to reduce noise and short-term spikes. Then, a combination of CNN and LSTM with the adaptive memory gate (AMG) was employed to extract spatial-temporal patterns. Meta-parameter tuning was subsequently performed using a newly proposed Star-nosed mole (SNM) algorithm. The performance of the proposed method was evaluated on four datasets, Milan, Madrid LTE, Telecom Shanghai, and Trentino, and compared with baseline models and the Transformer--ConvLSTM reference framework. Results showed that the proposed model provided small and stable improvements in MAE, RMSE, and R\textsuperscript{2} for traffic prediction, while achieving higher accuracy and a lower false-off rate in sleep decision-making. In high-density scenarios such as Telecom Shanghai and sparse-data conditions such as Trentino, the framework improved both prediction accuracy and energy-based decision-making quality. Furthermore, simulations of a two-layer macro-small cell network showed that the proposed model increased energy savings and reduced the number of on/off switches. Independent evaluation of the SNM algorithm on the CEC BC 2017 benchmark functions also demonstrated competitive and stable performance in search capability and overall ranking. Overall, the findings indicate that the proposed framework is a practical and reliable solution for efficient energy management in 5G and beyond networks, supporting sustainable operation and intelligent resource utilization across heterogeneous wireless communication environments while maintaining robust performance under diverse network traffic conditions.
Research Article
Hossein Jahangiri; Pooria Rashvand; Ahmad Shokouhfar; Reza Farokhzad; Nima Amani
Abstract
Accurate forecasting of final construction costs is important for project planning and cost control in inflation-sensitive construction markets. This study develops a BIM-integrated artificial neural network (ANN) workflow that links item-level Fehrestbaha data and official construction adjustment indices ...
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Accurate forecasting of final construction costs is important for project planning and cost control in inflation-sensitive construction markets. This study develops a BIM-integrated artificial neural network (ANN) workflow that links item-level Fehrestbaha data and official construction adjustment indices to BIM components and forecasts unit costs at a user-specified completion date. Historical cost information for sixteen materials over 2013--2022 was used to develop the deterministic ANN predictor, and the resulting unit-cost forecasts were returned to the BIM quantity-takeoff workflow. The framework was evaluated on a single nine-story residential building in Tehran by comparing the April 2022 initial estimate, the ANN-based December 2023 forecast, and the actual final project cost. The December 2023 case lies beyond the 2013--2022 historical development horizon and is therefore used as the principal project-level temporal check, whereas the internal training/test diagnostics are interpreted only as model-fit diagnostics because the monthly resampling procedure can induce dependence among adjacent observations. For this case, the absolute project-level deviation was 11.30% for the ANN forecast compared with 23.89% for the initial no-update estimate. The contribution is the automated linkage of national item coding, time-indexed cost information, ANN forecasting, Revit plug-ins, and BIM quantity aggregation rather than a new optimization algorithm or a probabilistic uncertainty model. The results support the feasibility of the workflow as a proof of concept, subject to stricter chronological validation, improved categorical encoding, benchmark comparisons, and multi-project external validation.
Research Article
Asiyeh Ebrahimzadeh
Abstract
This paper presents a chickenpox-inspired mathematical modeling framework for analyzing varicella-like disease transmission dynamics, using a modified compartmental model that incorporates vaccination, isolation-induced contact reduction, treatment efficacy, and public awareness interventions. The objective ...
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This paper presents a chickenpox-inspired mathematical modeling framework for analyzing varicella-like disease transmission dynamics, using a modified compartmental model that incorporates vaccination, isolation-induced contact reduction, treatment efficacy, and public awareness interventions. The objective is to develop an optimal-control framework and compare scenario-based intervention policies aimed at decreasing infection rates while considering economic and public-health constraints. For scenario comparison, the numerical simulations use fixed representative control levels; they do not numerically solve for time-dependent optimal control trajectories. The research applies Pontryagin’s Maximum Principle to formulate a theoretical optimal control framework, including the most critical intervention measures such as vaccination, isolation-induced contact reduction, treatment efficacy, and public awareness. Sensitivity analysis is utilized to examine the impact of model parameters on disease transmission, focusing on the basic reproduction number ℜ0. Numerical computations under various control regimes reveal that an appropriate combination of vaccination, isolation-induced contact reduction, treatment improvement, and public awareness campaigns can effectively reduce infection rates and provide theoretical insights into community-level intervention planning. The findings are highly beneficial for policymakers by supporting the evaluation of epidemic intervention scenarios and resource allocation decisions in public health administration.
Research Article
Priti Mojad; Babasaheb Gavhane; Shrikisan Gaikwad; Kalyanrao Takale; Chetan Shirore
Abstract
This work addresses the numerical approximation of the time-fractional stochastic traveling wave equation (TFSTWE) with a Caputo fractional derivative of order α ∈ (1, 2] driven by multiplicative space-time white noise. An explicit finite difference method (FDM) is constructed by discretizing ...
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This work addresses the numerical approximation of the time-fractional stochastic traveling wave equation (TFSTWE) with a Caputo fractional derivative of order α ∈ (1, 2] driven by multiplicative space-time white noise. An explicit finite difference method (FDM) is constructed by discretizing the space domain. For the first time step, a mean-square stability bound and an error estimate of order O(∆t2-α + ∆x2) are derived under a restriction on ∆t that depends explicitly on ∆x, the diffusion coefficient K, and the fractional order α, while the noise intensity σ enters the mean-square growth constant; stability and convergence at later time levels are supported numerically. Comprehensive numerical experiments demonstrate the effectiveness and reliability of the proposed method, and the Python programming language is used to plot the approximate mean solution profiles in two and three dimensions. The outcomes confirm the suitability of the method for accurately solving TFSTWEs under stochastic perturbations and support the theoretical analysis.
Applied Article
Seyedeh Yasamin Hashemi; Omid Solaymani Fard
Abstract
As the Forex market becomes increasingly complex, accurate directional forecasting is essential for effective trading decisions. This study proposes a multi-timeframe framework to evaluate directional trend prediction for the EUR/USD exchange rate using Ichimoku Cloud-inspired feature engineering and ...
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As the Forex market becomes increasingly complex, accurate directional forecasting is essential for effective trading decisions. This study proposes a multi-timeframe framework to evaluate directional trend prediction for the EUR/USD exchange rate using Ichimoku Cloud-inspired feature engineering and CNN-based hybrid architectures, including CNN, CNN-LSTM, and CNN-GRU. The study optimizes model hyperparameters using the Starfish Optimization Algorithm (SFOA). Specifically, the study investigates multi-step trend prediction for the H1 and H4 timeframes, and one-step-ahead prediction for the daily (D1) timeframe. Historical EUR/USD data are used to train continuous forecasting models, whose outputs are transformed into discrete trend classification labels. The framework ultimately employs a voting mechanism to determine the final trend decision at the daily (D1) timeframe. To assess the model's zero-shot classification capability and generalization, eight additional currency pairs are evaluated using the same evaluation criteria at the relevant stages to assess both individual model performance and overall framework effectiveness. Regression performance is assessed using MSE, MAE, and MAPE, while classification performance is evaluated using Accuracy and F1-score. Statistical robustness is further examined using the Diebold--Mariano test and bootstrap analysis. Experimental results demonstrate that incorporating GRU layers into CNN architectures consistently improves forecasting performance across multiple timeframes and currency pairs, with the proposed IICGS architecture achieving the most competitive overall performance. Selected results and implementation code are publicly available on GitHub.
Research Article
Mohammad Hamidi; Shohreh Shirani Nazhvani
Abstract
Complex hypernetworks are important in real-world problems, and their regularity and balance are particularly significant; hence, suitable mathematical tools are needed. In this regard, this paper introduces the notion of refined Pythagorean fuzzy superhypergraphs (RPFSs) on an arbitrary non-empty set, ...
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Complex hypernetworks are important in real-world problems, and their regularity and balance are particularly significant; hence, suitable mathematical tools are needed. In this regard, this paper introduces the notion of refined Pythagorean fuzzy superhypergraphs (RPFSs) on an arbitrary non-empty set, for the clustering of complex hypernetworks. We introduce the complement of an RPFS, classify RPFSs as complementary, self-complementary, complete, and regular, and investigate their fundamental properties. The notion of isomorphic RPFSs is established, which leads to self-complementary RPFSs, and conditions under which an RPFS is self-complementary are considered. For any RPFS, we introduce density measures for Pythagorean fuzzy links and Pythagorean fuzzy superedges, which serve as measures of coherence for hypernetworks, and we analyze these measures for constant complete and self-complementary RPFSs. The notions of Pythagorean fuzzy link-degree and superedge-degree are established, yielding positive regular hyperstructures whose densities are computed. Finally, balanced RPFSs are introduced, characterized via density, and analyzed under isomorphism.
Research Article
Reza Rajabi; Farzin Modarres Khiabania; Saba Sadeghi Gavganib
Abstract
Candidate route sets in the Urban Transit Network Design Problem (UTNDP) must provide adequate network coverage and connectivity while complying with prescribed route-length and route-cardinality requirements. This study develops a demand-aware heuristic-initialized NSGA-II framework for the UTNDP. The ...
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Candidate route sets in the Urban Transit Network Design Problem (UTNDP) must provide adequate network coverage and connectivity while complying with prescribed route-length and route-cardinality requirements. This study develops a demand-aware heuristic-initialized NSGA-II framework for the UTNDP. The method uses demand and travel-time information to construct feasible initial route sets, then applies Pareto ranking, crowding-distance selection, crossover, problem-specific mutation, feasibility repair, and duplicate filtering during the evolutionary search. The optimization model minimizes two explicitly defined objectives: the demand-weighted passenger generalized travel time (F1) and the total route weight, which serves as an operator-cost proxy (F2). In the reported Mandl/Mumford-style benchmark evaluation, every transfer edge of the transfer-expanded graph carries a fixed 5-min penalty, consistent with the standard convention for the urban transit routing problem (UTRP). Candidate route sets that leave any positive-demand origin–destination pair disconnected are first subjected to feasibility repair and, if the repair fails, are rejected before environmental selection. The framework is assessed on established UTNDP benchmark networks ranging from small to large instances. Hypervolume and spacing are formally defined as Pareto-set performance indicators, whereas the reported numerical comparisons are restricted to benchmark objective values directly supported by the available computational records; no run-level inferential comparison is claimed. Duplicate filtering and parameter settings are treated as algorithmic design components rather than being assigned independent gains without a dedicated ablation study. On the reported benchmark data, the framework yields passenger-cost values of 21.34 min for Mumford0 (22.18 min in the original study by Mumford) and 52.18 min for Edinburgh200 (55.34 min in the original study by Mumford). We treat frequency and vehicle capacity as exogenous quantities so the experiments isolate route-set optimization. The resulting framework provides a reproducible basis for passenger–operator trade-off analysis and a clearly delimited platform for future extensions to joint frequency, capacity, uncertainty, and parallel-computing formulations.
Research Article
Fatema Ali Albayati; Nadia Ali Abbas Almosa; Hayder F. Ghazi
Abstract
We formulate roadside greenbelt design in arid highway corridors as a constrained multi-objective mixed-integer nonlinear program on a discretized cross-section consisting of a median and two verges. Activating a cell installs a cluster of one species, and a per-zone irrigation variable fixes the realized ...
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We formulate roadside greenbelt design in arid highway corridors as a constrained multi-objective mixed-integer nonlinear program on a discretized cross-section consisting of a median and two verges. Activating a cell installs a cluster of one species, and a per-zone irrigation variable fixes the realized crown geometry. Three functionals are minimized: the daily sensible-heat release, the worst-case A-weighted level at residential receivers, and a roadside risk index that combines fixed-object hazard with aeolian shelter. The irrigation volume is bounded by an ε-constraint. We prove that the marginal risk response is non-monotone in lateral offset, with a unique interior minimizer beyond the clear zone; that the functionals select incompatible sides, so that every efficient design is transversely asymmetric; and that the scalarized problem is NP-hard. A converged evolutionary study on a 1 km corridor at 33.3◦N recovers both structural predictions: the designs place 63–100% of the activated verge cells on the receiver side, that is, the side carrying the modeled residences.
Research Article
Zargham Heydari; Hamed Gorginpour; Nariman Heidari
Abstract
High-power multiphase induction motors are attractive for safety-critical and power-intensive applications because of their inherent advantages, including superior fault tolerance, lower per-phase power requirements, and reduced torque pulsation. Under open-phase faults, however, the loss of phase symmetry ...
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High-power multiphase induction motors are attractive for safety-critical and power-intensive applications because of their inherent advantages, including superior fault tolerance, lower per-phase power requirements, and reduced torque pulsation. Under open-phase faults, however, the loss of phase symmetry couples the fundamental and harmonic subspaces, increasing torque ripple and current distortion. This paper develops a hierarchical control framework for a high-power seven-phase induction motor that combines online harmonic-reference optimization with enhanced nonlinear model predictive control (ENMPC). The upper layer estimates the machine state and slowly varying electrical parameters using an Extended Kalman Filter (EKF) and weighted recursive least squares (WRLS), and determines reference components in the third- and fifth-harmonic subspaces. The lower layer directly regulates the fundamental and harmonic current components subject to voltage, current, and terminal-state constraints. An explicit fault-constrained state-space representation is derived for one open phase and two adjacent open phases, and a terminal-set Lyapunov argument is given for nominal recursive feasibility and asymptotic closed-loop stability. MATLAB/Simulink simulations of the 1-MW plant consider a healthy interval, a single-phase open fault at 4 s, and an adjacent two-phase open fault at 8 s. For the reported cases, the compensated hierarchical controller maintains 5.76 kN·m and 4.68 kN·m of effective torque under the single- and two-phase fault conditions, respectively, while the corresponding torque-ripple factors are 4.8% and 8.5%. These results support the proposed architecture as a fault-tolerant control strategy while also defining the present study as simulation-based and motivating hardware-in-the-loop and experimental validation.
Research Article
Champak Nath; Ranu Paul
Abstract
This paper presents a deterministic nonlinear dynamical model to investigate the interactions among migration, unemployment, job availability, public resources, and environmental pollution. We establish that, under nonnegative initial data, the model solutions remain bounded, and we use analytical methods ...
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This paper presents a deterministic nonlinear dynamical model to investigate the interactions among migration, unemployment, job availability, public resources, and environmental pollution. We establish that, under nonnegative initial data, the model solutions remain bounded, and we use analytical methods to demonstrate the existence of feasible endemic equilibria and to establish conditions for local and regional asymptotic stability. For the selected parameter set, four feasible endemic equilibria are identified, of which only one is locally asymptotically stable. To mitigate the adverse effects of unregulated migration surges, such as rapid resource depletion and severe pollution, we formulate an optimal control problem and apply Pontryagin’s Maximum Principle to design intervention strategies that reduce migration intensity and pollution levels. Numerical simulations support the theoretical conclusions and show that a combination of socioeconomic and environmental measures provides the most effective and balanced outcome. The study emphasizes the importance of coordinated policy approaches for achieving long-term regional sustainability.
Research Article
Alireza Hamidieh; Bahareh Akhgari Rik
Abstract
Optimizing investment portfolios by assessing efficiency in competitive environments is a vital topic in investment management. The volatility of financial markets and increasing uncertainty make it difficult to use traditional models effectively. As a result, there has been growing interest in optimizing ...
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Optimizing investment portfolios by assessing efficiency in competitive environments is a vital topic in investment management. The volatility of financial markets and increasing uncertainty make it difficult to use traditional models effectively. As a result, there has been growing interest in optimizing financial models under uncertainty to better reflect real-world conditions. The present study develops a combined optimization model to evaluate risk under uncertainty in inputs and outputs. This model uses Network Data Envelopment Analysis (NDEA), robust optimization, and Lagrangian relaxation. The data for this study are the latest adjusted price data of 40 top cryptocurrencies from CoinMarketCap, used to estimate risk and create an optimal portfolio. A two-step approach is proposed to select and optimize the cryptocurrency portfolio, make the investment process more reliable, and comprehensively evaluate cryptocurrencies based on financial criteria. In the first step, the efficiency of the selected cryptocurrencies is evaluated using NDEA and robust programming. In the second step, Lagrangian relaxation is applied to handle the complicating constraints of the problem. This approach helps determine the selection of cryptocurrencies and the investment amounts, and provides a basis for allocating investment amounts. The computational results compare the direct solution of the model in GAMS with the Lagrangian relaxation algorithm on instances of increasing size.
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