Research Article
Control Theory & Systems
Fidelis Nofertinus Zai; Rian Kurnia; Juan Prihanda Nainggolan
Abstract
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, ...
Read More
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.
Research Article
Applied & Interdisciplinary
Yusif Gasimov; Aynura Aliyeva
Abstract
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 ...
Read More
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.
Research Article
Optimization & Operations Research
Harmandeep Kaur; Sukhpreet Kaur Sidhu
Abstract
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 ...
Read More
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.
Research Article
Optimization & Operations Research
Sina Nemati; Jafar Fathali; Abolfazl Poureidi
Abstract
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 ...
Read More
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
Research Article
Applied & Interdisciplinary
Omar Jabar AlilLal Al-Qaragholi; Alaa Khlaif Jiheel
Abstract
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 ...
Read More
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.
Research Article
Optimization & Operations Research
Ali Shokri; Roman Rafig Maharramov; Mutallim Mirzaahmed Mutallimov; Elshan Giyas Hashimov; lkin Aladdin Maharramov
Abstract
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 ...
Read More
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.
Research Article
Optimization & Operations Research
Niousha Zeidyahyaee; Sajjad Shokouhyar; Alireza Motameni
Abstract
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 ...
Read More
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.
Research Article
Control Theory & Systems
Muhammed Hassanein Al-Hakeem; Mahmoud Mahmoudi; Ahmed Sabah Ahmed Al-Jilawi
Abstract
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. ...
Read More
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.
Research Article
Optimization & Operations Research
Alireza Ezzati; Mahdi Mollazadeh; Sadegh Moodi; Morteza Araghi; Hossein Mahdizadeh
Abstract
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, ...
Read More
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.
Research Article
Mathematics & Theoretical Foundations
Saad Qasim Abbas; Wasan Saad Ahmed
Abstract
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 ...
Read More
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.
Research Article
Control Theory & Systems
Roohallah Daneshpayeh; Sirous Jahanpanah
Abstract
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, ...
Read More
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.
Research Article
Optimization & Operations Research
Mohammad Mahyar Amiri Chimeh; Babak Javadi
Abstract
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, ...
Read More
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.
)
)
)
)
)
)
)
)
)
)
-Fuzzy BL-Subalgebras: Algebraic ... ', 'data/mathco/coversheet/701767635546.png'))
)