Applied & Interdisciplinary
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.
Applied & Interdisciplinary
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.
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 ...
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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.
Applied & Interdisciplinary
Omar Jabar Alial 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 ...
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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.
Applied & Interdisciplinary
Ahmad Jalili; Fatemeh Babakordi
Abstract
Energy constraint is the most critical challenge in Wireless Sensor Networks (WSNs), particularly in dynamic environments with mobile nodes. This paper proposes an intelligent clustering protocol based on Fuzzy Neural Networks (FNN) that adaptively optimizes energy consumption by ...
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Energy constraint is the most critical challenge in Wireless Sensor Networks (WSNs), particularly in dynamic environments with mobile nodes. This paper proposes an intelligent clustering protocol based on Fuzzy Neural Networks (FNN) that adaptively optimizes energy consumption by dynamically selecting cluster heads and determining optimal cluster configurations. The FNN integrates fuzzy logic's uncertainty handling with neural networks' learning capabilities, using key parameters including residual energy, node distance, neighbor density, and signal-to-noise ratio. Unlike static clustering approaches such as LEACH and HEED, our method continuously adapts to changing network conditions through real-time parameter evaluation. Extensive MATLAB simulations with 100 nodes demonstrate significant performance improvements: the proposed FNN extends network lifetime by 35% compared to LEACH, 28% compared to HEED, and 15% compared to ANN-based ELDC. The First Node Dies (FND) is delayed by 45%, 38%, and 22% respectively, while achieving 25% lower energy consumption. Results confirm the FNN approach's superior energy efficiency and network stability, making it highly suitable for dynamic WSN applications.
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