https://mathco.journals.pnu.ac.ir/ Control and Optimization in Applied Mathematics en daily 1 Thu, 21 May 2026 00:00:00 +0330 Thu, 21 May 2026 00:00:00 +0330 https://mathco.journals.pnu.ac.ir/article_12574.html In this study, we examine solutions to Optimal Tracking Control (OTC) problems for both Linear Quadratic (LQ) and nonlinear systems. Classical approaches to OTC rely on formulating and solving the Hamilton-Jacobi-Bellman (HJB) equation, which typically requires numerical solutions of the state, co-state, and stationary equations using the forward-backward method. Such methods often involve intricate mathematical analysis and substantial computational effort. To address these challenges, we explored the use of Physics Informed Neural Networks (PINN) as an alternative framework for solving OTC problems. The PINN approach is implemented by constructing a problem-specific loss function that directly incorporates the governing dynamics and control objectives. This method is comparatively simpler and more flexible to implement. The performance of PINNs is evaluated through quantitative error analysis and benchmarked against the classical Runge-Kutta (RK) method. A detailed comparison is presented using tabulated error metrics and time-domain plots of absolute errors. Numerical results demonstrate that PINNs achieve lower approximation errors than Runge-Kutta method for both LQ and nonlinear tracking problems, indicating their effectiveness as a viable alternative solution strategy for OTC problems.  https://mathco.journals.pnu.ac.ir/article_12621.html  This paper introduces and analyzes, for the first time, the \emph{fractional Pauli operator}, a non-local generalization of the fundamental quantum mechanical operator describing spin-1/2 particles in magnetic fields. The operator is defined through the spectral theory of the magnetic fractional Laplacian $(H_{\vecA})^s$, with s ∈ (0,1), and acts on spinor-valued wavefunctions. We formulate the associated eigenvalue problem on a bounded domain Ω ⊂ ℝ^2 subject to exterior Dirichlet conditions. The intrinsic non-locality of the model is addressed via a variational formulation in suitable magnetic fractional Sobolev spaces. Under appropriate assumptions on the vector potential $\vecA$ and the magnetic field B, we establish the existence of a discrete spectrum. For a constant magnetic field on \R^2, we derive explicit eigenvalues exhibiting a nonlinear B_0^s scaling of the Landau levels. In addition, a finite element–based numerical scheme is developed to compute the spectrum on a disk, illustrating the combined effects of spatial confinement and non-locality. The physical implications of fractional kinetic effects on Landau quantization and spin-dependent phenomena are discussed, highlighting the relevance of the fractional Pauli operator for modeling anomalous transport in bounded quantum systems. https://mathco.journals.pnu.ac.ir/article_12693.html  Multi-criteria decision-making (MCDM) often involves situations characterized by uncertainty, ambiguity, and vagueness. To address such complexities, MCDM techniques play a crucial role. This paper presents a comparative analysis of two widely used methods—Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR)—within a hesitant fuzzy environment. Hesitant fuzzy sets allow decision-makers to express hesitation by assigning multiple possible membership values to an element rather than a single value. In this framework, the TOPSIS ranks alternatives based on their closeness to the positive and negative ideal solutions, while the VIKOR identifies a compromise solution by balancing individual and collective regret measures. The effectiveness of the comparison is demonstrated through illustrative numerical examples. Moreover, some real life applications of these methods are discussed. https://mathco.journals.pnu.ac.ir/article_12779.html Classical inverse location models aim to modify problem parameters such that pre-specified facility locations become optimal with respect to a given objective. This paper addresses a fundamentally different variant: the inverse balanced    facility location problem in the Euclidean plane, in which parameters are adjusted so as to achieve an equitable distribution of client demand between two given facilities. Specifically, given a set of n weighted points in the plane and two predetermined facility locations, the objective is to minimally modify either the weights or the coordinates of the client points such that the absolute difference in total demand assigned to each  facility-referred to as the unbalancing number-is minimized. For the weight-modification case, we establish that the planar problem is structurally equivalent to its network counterpart and is therefore solvable in O(n Log n) time under any Lp norm, via an existing linear programming formulation. For the coordinate-modification case under the Euclidean norm, we exploit the isometric property of orthogonal rotations to prove that thetwo-dimensional problem reduces, without loss of generality, to a one-dimensional problem along the perpendicular bisector of the segment joining the two facilities. Leveraging this reduction, we design three novel greedy algorithms-IFLP1, IFLP2, and IFLP3-that prioritize minimization of the unbalancing number, minimization of the total transfer cost, and a hybrid criterion balancing both objectives, respectively. Under uniform weights and identical modification costs, all three algorithms are proven to yield optimal solutions and operate within O(n2) time  complexity. Extensive computational experiments on standard benchmark datasets and randomly generated instances demonstrate that IFLP1 achieves the lowest CPU time and smallest unbalancing number, while IFLP3 yields superior performance in termsof total transfer cost and is recommended for practical applications https://mathco.journals.pnu.ac.ir/article_12797.html This paper develops and analyzes a class of double pre-test shrinkage estimators for the reliability function of the Pareto distribution based on progressively Type-II censored samples. The proposed approach combines a preliminary test of the shape parameter against a prior target value with shrinkage toward the corresponding prior reliability, yielding four reliability estimators with fixed and data-dependent shrinkage weights. Closed-form analytical expressions are derived for the bias and bias ratio of the proposed reliability estimators, as well as for their risk functions under the Precautionary Loss Function (PLF) and the associated relative risk with respect to the classical pooled estimator. Numerical results are obtained by direct numerical evaluation of the derived analytical expressions, including one- and two-dimensional integrals and special functions, implemented in Python. Across a wide range of design settings and reliability levels, the proposed estimators reduce PLF-risk and improve relative efficiency, with the most pronounced gains typically occurring when the prior ratio λ = θ₀/θ  is close to unity. In addition, the proposed framework can be viewed as an optimization problem under uncertainty, where the PLF-risk acts as the objective function and the design parameters, including the shrinkage weight, significance level, and stage sample sizes, define the feasible decision space. https://mathco.journals.pnu.ac.ir/article_12650.html In this paper, we address the problem of covering a given bounded domain in the plane using simple geometric figures. The proposed approach is based on a discretization of the domain, which leads to a corresponding discrete optimization problem. To solve this problem, we introduce a novel iterative algorithm that minimizes a given objective function by generating successive neighboring nodal points. As the covering elements, circular sectors with centers located outside the domain are considered. The objective is to determine the locations of the sector centers and their radii in such a way that the entire domain is completely covered, while the ratio of the total area of the covering sectors to the area of the domain is minimized. Finally, the algorithm is demonstrated on a representative example, and the resulting coverings are illustrated. https://mathco.journals.pnu.ac.ir/article_12620.html This study develops a mathematically informed optimization framework for decision-making in reverse supply chain management, with an application to Apple’s MacBook product line. The proposed framework integrates Failure Mode and Effects Analysis (FMEA) with deep learning, based sentiment analysis in a multi-stage structure designed to quantify risk factors and predict consumer-driven outcomes. The dataset consists of 91 days of Twitter user feedback on Apple notebooks, processed using supervised learning algorithms to extract sentiment scores and thematic indicators of product performance. The analysis identifies “power and battery” and “storage” as the most critical components contributing to user dissatisfaction and elevated risk severity. These data-driven insights are incorporated into an optimization model that supports decisions on product recycling, refurbishment, and reuse. The hybrid framework enhances decision stability and accuracy compared with conventional reverse logistics models, while improving operational efficiency and environmental performance. The results demonstrate the model’s suitability as a scalable, machine-learning-supported optimization tool for reverse supply chain systems. https://mathco.journals.pnu.ac.ir/article_12665.html This paper presents a novel hybrid orthogonal polynomial method for solving optimal control problems governed by fractional parabolic PDEs. By strategically weighting and combining these polynomial bases, the method adaptively leverages their respective strengths to achieve superior approximation properties. The proposed approach combines the spectral accuracy of Legendre polynomials, the minimax properties of Chebyshev polynomials, and the flexibility of Jacobi polynomials to create a robust numerical framework. The hybrid orthogonal polynomial method is applied to discretize the fractional parabolic PDEs, and an efficient numerical scheme is developed to solve the resulting optimal control problem. Numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed approach, showing significant improvements over traditional radial basis function methods. The results highlight the potential of the hybrid orthogonal polynomial method for solving complex optimal control problems in science and engineering. https://mathco.journals.pnu.ac.ir/article_12778.html Homogeneous second-order Aw-Rascle-type models have demonstrated greater effectiveness than their non-homogeneous counterparts in traffic flow modeling. This study addresses the numerical solution of hyperbolic conservation laws governing these models by coupling the second-order HLLE Riemann solver, a Godunov-type finite volume approach, with the wave propagation algorithm. A novel wave-speed selection strategy is proposed by comparing characteristic velocities with Roe speeds, yielding solutions with guaranteed positive density and speed. The proposed IWP-HLLE method is applied to simulate shock, rarefaction, and contact discontinuity waves under homogeneous long-road conditions, eliminating the influence of external source terms and ensuring the homogeneity of the governing hyperbolic equations. Its performance is benchmarked against the MacCormack scheme supplemented by two standard stabilization techniques, namely artificial viscosity (AV) and central differencing (CD). Spatiotemporal distributions and density profiles are examined across four representative traffic scenarios: free flow, congested traffic flow, queue dissolution, and congested flow with non-equilibrium velocity and uniform density. The results demonstrate that the IWP-HLLE approach substantially suppresses numerical oscillations compared to both AV and CD methods while maintaining stability across all test cases. https://mathco.journals.pnu.ac.ir/article_12800.html This paper presents a systematic comparative study of two widely used numerical solvers --- HOFiD_bvp (high-order finite difference scheme) and bvp4c (collocation-based) --- for solving singular second-order ordinary differential equations (ODEs) with first-kind (regular) boundary singularities. Four representative benchmark problems drawn from fluid dynamics, materials science, and radially symmetric diffusion models are used to evaluate solver performance across key metrics: maximum residual, maximum error, mesh point count, and ODE/BC function call counts. Results show that HOFiD_bvp consistently achieves lower residuals and errors with fewer function evaluations, making it computationally more efficient. Conversely, bvp4c demonstrates superior robustness for nonlinear singular problems and offers better adaptive mesh refinement capabilities. These findings provide practical guidance for selecting the appropriate numerical technique in applied science and engineering contexts, with implications for optimization of computational simulation workflows. https://mathco.journals.pnu.ac.ir/article_12478.html This paper offers the idea of (anti) (m‎, ‎n)-fuzzy BL-subalgebras as a novel extension of classical BL-algebras within the fuzzy mathematical framework. ‎The proposed structures generalize various types of fuzzy subalgebras, including (anti) intuitionistic, (anti) Pythagorean, (anti) Fermatean, and (anti) q-rung orthopair fuzzy BL-subalgebras for q >= 1. Fundamental algebraic properties and equivalent characterizations of (m,n)-fuzzy BL-subalgebras are established through the notion of value-cuts. Furthermore, the concept of power-implication preserving (PIP) BL-algebras is introduced, and it is shown that a PIP BL-algebra exists for every prime number. Several closure properties of (m,n)-fuzzy BL-subalgebras under combination operations are also derived within this framework. From an applied perspective, the developed theoretical results can serve as a mathematical foundation for modeling and reasoning in fuzzy control systems and optimization processes, particularly in decision-making environments characterized by uncertainty and graded information. https://mathco.journals.pnu.ac.ir/article_12689.html Efficient layout design in healthcare facilities is critical for operational effectiveness and patient care. This study addresses the healthcare facility layout problem using a multi-objective optimization approach. We propose a novel methodology based on graph theory, specifically planar adjacency graphs, to generate and evaluate department layouts. Nodes in the graph represent departments, while weighted edges represent the desired closeness based on patient flow and functional relationships. We introduce five strategies based on different weightings of these objectives and evaluate them using a real-world hospital case study. Our results show that a hybrid strategy, prioritizing patient flow while incorporating departmental relationships, yields the optimal layout. This approach provides a systematic and data-driven framework for healthcare planners to create efficient layouts that enhance workflow, reduce travel distances, and improve overall service quality. https://mathco.journals.pnu.ac.ir/article_12846.html 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. https://mathco.journals.pnu.ac.ir/article_12972.html 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. https://mathco.journals.pnu.ac.ir/article_12973.html 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. https://mathco.journals.pnu.ac.ir/article_12974.html 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. https://mathco.journals.pnu.ac.ir/article_12975.html 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. https://mathco.journals.pnu.ac.ir/article_12976.html 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. https://mathco.journals.pnu.ac.ir/article_12983.html 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. https://mathco.journals.pnu.ac.ir/article_12992.html 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. https://mathco.journals.pnu.ac.ir/article_13012.html 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. https://mathco.journals.pnu.ac.ir/article_13073.html 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. https://mathco.journals.pnu.ac.ir/article_13074.html 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.  https://mathco.journals.pnu.ac.ir/article_13083.html 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. https://mathco.journals.pnu.ac.ir/article_13114.html 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. https://mathco.journals.pnu.ac.ir/article_13126.html 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. https://mathco.journals.pnu.ac.ir/article_13151.html  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. https://mathco.journals.pnu.ac.ir/article_13175.html 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. https://mathco.journals.pnu.ac.ir/article_13243.html 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.