Method For Solution Of Problems Research Articles

Advances in partial disassembly line balancing: A state-of-the-art review

As sustainable manufacturing practices increasingly prioritize the efficient and environmentally conscious disassembly of products, understanding the nuances of partial disassembly line balancing (PDLB) becomes essential. In our study, we conducted an in-depth analysis of 53 PDLB studies, published from 2008 to 2024, to understand the current trends and gaps in this domain. Our research methodology involved a systematic collection of material, descriptive analysis, careful category selection, and rigorous material evaluation. This approach enabled us to construct a comprehensive taxonomy tailored to PDLB, distinguishing it from classical disassembly line balancing (DLB) literature. Our findings reveal a noticeable surge in PDLB research in the last three years, reflecting its growing relevance in sustainable manufacturing. The study highlights that deterministic disassembly conditions, economic performance indicators, and iterative heuristic approaches are the focal points in recent PDLB research. This insight is critical for guiding future investigations in the field. Our taxonomy not only categorizes existing research in PDLB but also sheds light on under-explored areas, offering a clear direction for upcoming studies. This paper contributes to the literature by providing a detailed review of PDLB-specific elements such as problem characteristics, disassembly levels, objectives, constraints, and solution methods, thus paving the way for further advancements in sustainable manufacturing practices.

On the construction of diagonally implicit two–step peer methods with RK stability

In this paper, diagonally implicit two–step peer methods for the numerical solution of initial value problems of order ordinary differential are divided into four types including the combination of explicit and implicit methods in a sequential or parallel environments. In this class of the methods, construction of implicit methods equipped with Runge–Kutta stability property together with A– or L–stability are investigated and examples of such methods are given up to order five. Finally, the efficiency and accuracy of the proposed methods are verified by applying them on some well–known stiff problems.

A ROBUST NUMERICAL METHOD FOR SINGULARLY PERTURBEDSOBOLEV PERIODIC PROBLEMS ON B-MESH

This article examines periodic Sobolev reports with a singular deviation, which causes significant difficulties in numerical approximation due to the presence of sharp or boundary layers. A stable quantitative method for the effective solution of such problems in the Bakhvalov lattice, a special grid for the deviant action of the solution, is proposed. Singularly perturbed periodic Sobolev problems create significant difficulties in numerical approximation due to the presence of sharp layers or boundary layers. Our proposed reliable numerical method for efficiently solving such problems on the Bakhvalov grid, a specialized grid, is designed to account for the singular behavior of the solution. First, an asymptotic analysis of the exact solution is performed. Then a finite difference scheme is created by applying quadrature interpolation rules to an adaptive network. The stability and convergence of the presented algorithm in a discrete maximum norm is analyzed. The results show that the proposed approach provides an accurate approximation of the solution for singular problems while maintaining computational efficiency.

Block Method for the Approximate Solution of Third-order Initial Value Problems.

This paper aims to develop a novel third derivative block method with two hybrid points for the direct approximation of third-order Initial Value Problems (IVP). The hybrid points, and , used for the development of the schemes are selected such that they lie in the interval . These derived hybrid schemes are implemented in a block form on some third-order IVPs. The properties of the proposed method including convergence, order, and zero-stability are established. Application of the derived block method on test problems confirms the superiority of the method when compared to exact solutions and existing methods. The numerical results show that the proposed method effectively integrates the third-order Initial Value Problems directly.

A solution method for stochastic multilevel programming problems. A systematic sampling evolutionary approach

Stochastic multilevel programming is a mathematical programming problem with some given number of hierarchical levels of decentralized decision makers and having some kind of randomness properties in the problem definition. The introduction of some randomness property in its hierarchical structure makes stochastic multilevel problems computationally challenging and expensive. In this article, a systematic sampling evolutionary method is adapted to solve the problem. The solution procedure is based on realization of the random variables and systematic partitioning of each hierarchical level’s decision space for searching an optimal reaction. The search goes sequentially upwards starting from the bottom up through the top hierarchical level problem. The existence of solution and convergence of the solution procedure is shown. The solution procedure is implemented and tested on some selected deterministic test problems from literature. Moreover, the proposed algorithm can be used to solve stochastic multilevel programming problems with additional complexity in their problem definition.

An exact solution method for seru scheduling problems considering past-sequence-dependent setup time and adjustment activities

An exact solution method for seru scheduling problems considering past-sequence-dependent setup time and adjustment activities

An exact solution method for seru scheduling problems with multiple rate-modifying activities and learning effect

An exact solution method for seru scheduling problems with multiple rate-modifying activities and learning effect

Resource Assignment and Performance Optimisation in Intelligent Supply chain

The article gives the problem of resource assignment and performance optimisation in intelligent supply chain (ISC). The task of the resource assignment for intelligent supply chain is multi-product and multi-criterion task. Scale of the ISC determines the allocation of the suppliers and consumers of product. The customer demands for certain kind of product in ISC can be deemed as stochastic process. As goal of performance optimization task we should to evaluate parameters of ISC through assignment of production resources. The article presents the resource assignment model of ISC and its performance measures. On the base of simulation the verification and validation of presented model is carried out. The problem statement, solution method, numerical example and validation of model via simulation are represented for resource assignment and performance optimization model.

Solving the stochastic machine assignment problem with a probability-based objective: problem formulation, solution method and practical applications

Solving the stochastic machine assignment problem with a probability-based objective: problem formulation, solution method and practical applications

Solving the Stochastic Machine Assignment Problem with Probability-based Objectives: Problem Formulation, Solution Method, and Practical Applications

Solving the Stochastic Machine Assignment Problem with Probability-based Objectives: Problem Formulation, Solution Method, and Practical Applications

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

A FAMILY OF 82Q EXPONENTIAL HYBRID METHODS FOR SOLVING IVPS IN ODES

In a recent paper, a new class of exponential general linear methods of second stage seventh order for the numerical solution of first order initial value problems in ordinary deferential equations was derived. In this paper, we derive the new class of higher order extended exponential general linear methods for the numerical solution of first order initial value problems in ordinary deferential equations. The numerical results obtained by the new method for some problems show its superiority in efficiency and accuracy for solving problems for which the proposed general linear method is appropriate

Hybrid Deep Learning and Sensitivity Operator-Based Algorithm for Identification of Localized Emission Sources

Hybrid approaches combining machine learning with traditional inverse problem solution methods represent a promising direction for the further development of inverse modeling algorithms. The paper proposes an approach to emission source identification from measurement data for advection–diffusion–reaction models. The approach combines general-type source identification and post-processing refinement: first, emission source identification by measurement data is carried out by a sensitivity operator-based algorithm, and then refinement is done by incorporating a priori information about unknown sources. A general-type distributed emission source identified at the first stage is transformed into a localized source consisting of multiple point-wise sources. The second, refinement stage consists of two steps: point-wise source localization and emission rate estimation. Emission source localization is carried out using deep learning with convolutional neural networks. Training samples are generated using a sensitivity operator obtained at the source identification stage. The algorithm was tested in regional remote sensing emission source identification scenarios for the Lake Baikal region and was able to refine the emission source reconstruction results. Hence, the aggregates used in traditional inverse problem solution algorithms can be successfully applied within machine learning frameworks to produce hybrid algorithms.

A solution method for mixed-variable constrained blackbox optimization problems

A solution method for mixed-variable constrained blackbox optimization problems

A quantum-enhanced solution method for multi classification problems

With the increasing data size of multi classification problems, the running efficiency of classical algorithms is seriously affected. In the paper, in order to improve the implementation efficiency of the algorithm, we propose a quantum-enhanced solution method for multi classification problems. The method mainly introduces the quantum-enhanced technology into the classical algorithm. Aiming at the two steps of solving Euclid distance and kernel function in the classical algorithm, the paper relates the classical inner product principle with the amplitude evolution of quantum states. On the basis of quantizing the sample data, a general quantum circuit that can calculate the inner product is designed and constructed. The circuit can make full use of the advantages of quantum parallel computing to achieve exponential acceleration of computing efficiency. Aiming at solving linear equations in the classical algorithm, a quantum circuit based on the quantum singular value estimation is designed and constructed. The circuit makes use of the acceleration advantage of quantum computing in matrix computing to achieve polynomial acceleration of matrix computing. The experimental results show that the method can not only find the optimal solution for multi classification problems, but also greatly improve the operation efficiency of the algorithm. Compared with the classical methods, the method has at least polynomial improvement in time complexity and spatial complexity.

Linear Hybrid Multistep Block Method for Direct Solution of Initial Value Problems of Third Order Ordinary Differential Equations

In this article, we focus on linear hybrid multistep method for direct solution of initial value problems of third order ordinary differential equations without reduction to system of first-order ordinary differential equations. The derivation of the method involved using collocation and interpolation techniques with power series as basis function to produce a system of linear equations. The unknown parameters in the system of equations were obtained through the Gaussian elimination technique. The values of the determined parameters were then substituted and evaluated at different grid and off-grid points to produce the required continuous block method. The discrete scheme obtained from the method is self-starting with improved accuracy and a larger interval of absolute stability. Basic properties of the method were investigated. The results showed that the method is zero stable, consistent , convergent and of order seven. The performance of the method was tested by solving linear and nonlinear problems of general third order ordinary differential equations. The result were found to compare favourably with some existing methods in literature.

PLASTIC DEFORMATION WITH OPEN STITCHING. FORMULATION OF THE PROBLEM

A new method for the analytical solution of complex variational problems in the mechanics of a deformable solid body is proposed. Its effectiveness will be demonstrated in a series of articles on firmware. The first article systematizes the regularities of this process and performs a theoretical analysis of the billet upsetting stage.

On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems

Runge–Kutta algorithms with adaptive step size control provide reliable tools for the solution of initial value problems. Most widespread within the vast family of Runge–Kutta methods are the diagonally implicit Runge–Kutta (DIRK) methods. In particular, the new low-order explicit last-stage diagonally implicit Runge–Kutta (ELDIRK) methods are investigated, combining implicit schemes with an additional explicit evaluation as an explicit last stage. This results in Butcher tableaus with two solutions of different convergence orders suitable for embedded methods, where the higher-order solution is achieved by additional explicit evaluations. Thus, the iterative solution of non-linear systems is omitted for the additional stage, presenting a major reduction in computational cost for the determination of a local error estimate. The key contribution is the application of the novel Butcher tableaus to phase-field problems, solved with the finite-element method, leading to substantial numerical investigations with an efficient approach for diagonally implicit Runge–Kutta schemes. The most important aspects are the extension towards fourth-order methods, the study of the convergence orders for the ELDIRK schemes, their respective stability regions and computational efficiency. A local error estimator is presented capturing the evolution of the phase-field problems, such that adaptive step size control for the new low-order embedded schemes based on an empirical approach for error estimation is achieved. A suitable parallel algorithm is presented with conclusive two-dimensional phase-field simulations based on a Kobayashi–Warren–Carter model including benchmarks for computational efficiency. The higher-order convergence suggested by the novel schemes is confirmed, and their effective results are demonstrated, resulting in a valuable semi-explicit addition to the family of Runge–Kutta time integration schemes.

Numerical solution of third order singular boundary value problems with nonclassical SE-sinc-collocation and nonclassical DE-sinc-collocation

In this paper, we use the nonclassical SE-sinc-collocation and nonclassical DE-sinc-collocation methods for the numerical solution of singular third-order boundary value problems. The novelty of the approach is based on using the new non-classical weight function for sinc method instead of the classic ones. The convergence and error estimation of our methods is discussed. Several examples are solved and numerical results are compared with the existed methods, the obtained results demonstrate the validity of the obtained theoretical results and the efficiency of the our methods.

Application of linear ordinary differential equations to the stability control of long time lag networks

Abstract Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.