检索结果-内蒙古大学图书馆

Non-Linear Matrix Correlation for Multiphase Temperature-Composition Coupling in Modeling of Solidification and Macrosegregation

学校读者我要写书评

暂无评论

SSRN 2024年

作者： Jafari-Ramiani, Amin Mojab, S. Amirmohamad Karimi, Zahra Amirkabir University of Technology Tehran Polytechnic Faculty of Materials and Metallurgical Engineering Tehran Iran

A reassessment was done on the state-of-the-art mathematical description of solidification to cope with the critical issues about the restricting assumption of equilibrium and uncertainties in the composition fields. Two hypotheses were suggested: (1) A phase fraction field that involves phase-change kinetics would be expressed via a source-based transport equation that tracks deviations of temperature and composition from equilibrium. (2) Local multiphase equilibria and solute mass balance can be combined by a Non-Linear programming (NLP) strategy to form a consistent correlation between temperature, composition, and phase fraction fields. Accordingly, a mathematical model was presented based on volume-averaged mass, momentum, energy, and species transports for a general three-phase binary alloy solidification. A new Multiphase-Thermodynamic-Coupling (MTC) was proposed based on NLP to link the phase diagram with the transport equations. The model was tested numerically through two benchmarks of directional solidification of an Al-Cu alloy. The proposed approach resulted in a lever-rule-like final solution with deviations from equilibrium during the iterations and near the chill boundary. The computed macrosegregation profile showed agreement with a semi-analytical solution (0.3% error) and available experimental data (1.5% error). The distributions of Phase-Change-Rate (PCR) were obtained in the form of bell-shaped curves. The proposed MTC approach provided an extendable formulation that allows one to read a phase diagram directly and run a source-based phase-change-kinetics which can deviate from equilibrium. © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

LINEAR AND NON-LINEAR MODELS FOR MASTER SCHEDULING OF DYNAMIC RESOURCES PRODUCT MIX

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Mohammed, Ayman R. Abu Sleem, Ahmad Abdel-Aal, Mohammad A.M. Industrial & Systems Engineering Department King Fahd University of Petroleum and Minerals Dhahran31261 Saudi Arabia Interdisciplinary Research Center of Smart Mobility & Logistics King Fahd University of Petroleum and Minerals Dhahran31261 Saudi Arabia

The literature on master production scheduling for product mix problems under the Theory of Constraints (TOC) was considered by many previous studies. Most studies assume a static resources availability. In this study, the raw materials supplied to the manufacturer is considered as dynamic depending on the results of the problem. Thus, an integer linear heuristic, an integer non-linear optimization model, and a basic non-linear model are developed to find a good solution of the problem. The results of the three models were compared to each other in terms of profit, raw materials costs, inventory costs and raw materials utilization. Recent studies in the field are reviewed and conclusions are drawn. Copyright © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

Revisiting Theoretical Guarantees of Direct-Search Methods

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Dzahini, K.J. Rinaldi, F. Royer, C.W. Zeffiro, D. Argonne National Laboratory 9700 S. Cass Avenue LemontIL60439 United States Dipartimento di Matematica "Tullio Levi-Civita" Università di Padova Padua Italy LAMSADE CNRS Université Paris Dauphine-PSL Place du Maréchal de Lattre de Tassigny Paris75016 France Dipartimento di Matematica 'Tullio Levi-Civita' Università di Padova Padua Italy

Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization and may thus seem intractable other than by using heuristics. However, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct search, is particularly popular thanks to its simplicity of implementation, even though its theoretical underpinnings are not always easy to grasp. In this work, we survey contemporary direct-search algorithms from a theoretical viewpoint, with the aim of highlighting the key theoretical features of these methods. Our study goes beyond the classical, textbook cases and tackles the presence of nonsmoothness, noise, and constraints in the problem at hand. In addition to reviewing classical results in the field, we provide new perspectives on existing results, as well as novel proofs that illustrate the versatility of direct-search schemes. © 2024, CC BY.

关键词： nonlinear programming

Mass Conservative Limiting and Applications to the Approximation of the Steady-State Radiation Transport Equations

学校读者我要写书评

暂无评论

SSRN 2024年

作者： Guermond, Jean-Luc Wang, Zuodong Department of Mathematics Texas A&M University 3368 TAMU College StationTX77843 United States CERMICS Ecole des Ponts Marne-la-Vallee77455 Cedex 2 France INRIA Paris Paris75589 France

A limiting technique for scalar transport equations is presented. The originality of the method is that it does not requires solving nonlinear optimization problems nor does it rely on the construction of a low-order approximation. The method has minimal complexity and is numerically demonstrated to maintain high-order accuracy. The performance of the method is illustrated on the radiation transport equation. © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

Magnetic Dipole Target Two-Point Positioning Method Based on Tensor Invariants

学校读者我要写书评

暂无评论

IEEE Transactions on Instrumentation and Measurement 2025年 74卷

作者： Liu, Gaigai Zhang, Yingzi Liu, Wenyi Wang, Chen Li, Qiang Qin, Xiaoya North University of China State Key Laboratory of Dynamic Measurement Technology Taiyuan030051 China

Magnetic anomaly detection (MAD) technology based on magnetic gradient tensor (MGT) holds great potential for applications in unexploded ordnance (UXO) detection and underwater moving target tracking. The existing inversion methods are highly susceptible to the effects of geomagnetism, environmental noise, and measuring point distance. In order to address these problems, this article presents a novel two-point method for dipole target positioning based on tensor invariant theory. First, the geometric relationships between the target and measuring points are derived using the tensor invariants at two measuring points, and four equations containing the target position parameters are established. In order to improve the noise immunity, an objective function is constructed, and the solution of the target position is transformed into an optimization problem;moreover, to analyze the positioning effects and blind spots of the method, a simulation model is designed. Simulation results indicate that the method exhibits excellent positioning performance on the entire trajectory and eliminates the effects of the geomagnetic field and measuring point distances to the greatest extent. Finally, the applicability of the method in both stationary and moving target positioning scenarios was validated through field experiments. The average relative positioning errors for stationary and moving targets are 10.57% and 7.59%, respectively, which are lower than the state-of-the-art method. © 1963-2012 IEEE.

关键词： nonlinear programming

Non-Linear Matrix Correlation for Multiphase Temperature-Composition Coupling in Modeling of Solidification and Macrosegregation

学校读者我要写书评

暂无评论

SSRN 2024年

作者： Jafari-Ramiani, Amin Mojab, S. Amirmohamad Karimi, Zahra Faculty of Materials and Metallurgical Engineering Tehran Iran

关键词： nonlinear programming

Understanding and Reducing the Class-Dependent Effects of Data Augmentation with A Two-Player Game Approach

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Jiang, Yunpeng Weng, Paul Ban, Yutong Shanghai Jiao Tong University China Duke Kunshan University China

Data augmentation is widely applied and has shown its benefits in different machine learning tasks. However, as recently observed, it may have an unfair effect in multi-class classification. While data augmentation generally improves the overall performance (and therefore is beneficial for many classes), it can actually be detrimental for other classes, which can be problematic in some application domains. In this paper, to counteract this phenomenon, we propose CLAM, a CLAss-dependent Multiplicative-weights method. To derive it, we first formulate the training of a classifier as a nonlinear optimization problem that aims at simultaneously maximizing the individual class performances and balancing them. By rewriting this optimization problem as an adversarial two-player game, we propose a novel multiplicative weight algorithm, for which we prove the convergence. Interestingly, our formulation also reveals that the class-dependent effects of data augmentation is not due to data augmentation only, but is in fact a general phenomenon. Our empirical results over five datasets demonstrate that the performance of learned classifiers is indeed more fairly distributed over classes, with only limited impact on the average accuracy. © 2024, CC BY.

关键词： nonlinear programming

Joint Optimization of Water and Traffic Flow Discharge During Flood Evacuations

学校读者我要写书评

暂无评论

SSRN 2024年

作者： Bahrami, Sina Nourinejad, Mehdi Roorda, Matthew J. Yin, Yafeng Department of Civil and Environmental Engineering University of Michigan Ann Arbor United States Department of Civil and Environmental Engineering York University Toronto Canada Department of Civil and Mineral Engineering University of Toronto Toronto Canada Department of Industrial and Operations Engineering University of Michigan Ann Arbor United States

Flood evacuation plans prioritize discharging regions that are more vulnerable to getting flooded. More people can evacuate by delaying the flood's arrival at vulnerable regions through optimal placement and control of the water flow from the reservoirs. This paper proposes an optimization model to jointly control the reservoir system (in a water network) and the evacuation plan (in a transportation network) for maximizing the number of evacuees. We present the traffic flow as a cell transmission model and the water flow as a Muskingum-Cunge flood-routing model. We formulate the problem as a nonlinear program. To solve this problem, we solve a linear relaxation of the model using generalized Benders decomposition. The Town of High River in Canada is chosen as a case study. We show that the integrated flood management system regulates the reservoir discharge rates and evacuation rates to minimize the impact of the flood. © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

A Review of Neural Network Solvers for Second-order Boundary Value Problems

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Sau, Ramesh Chandra Yin, Luowei Department of Mathematics Indian Institute of Technology Bombay India Department of Mathematics The Chinese University of Hong Kong New Territories Shatin Hong Kong

Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into highly nonlinear optimization problems of neural network parameters. This work reviews several deep learning solvers proposed a few years ago, including PINN, WAN, DRM, and VPINN. Numerical results are provided to make comparisons amongst them and address the importance of loss formulation and the optimization method. A rigorous error analysis for PINN is also presented. Finally, we discuss the current limitations and bottlenecks of these methods. Copyright © 2024, The Authors. All rights reserved.

关键词： nonlinear programming