scholarly journals A MODEL AND METHOD FOR SOLVING A DYNAMIC TRANSPORT PROBLEM

2004 ◽  
Vol 5 (2) ◽  
pp. 67-76
Author(s):  
Gediminas Davulis
Keyword(s):  
Optimization Methods ◽  
Fixed Time ◽  
Linear Constraints ◽  
Network Development ◽  
Network State ◽  
Convex Problem ◽  
Convex Objective Function ◽  
Universal Solution ◽  
Solution Methods ◽  
Cargo Transportation

The problem of optimal development of transport network is considered. We have to define a plan of network development, i.e. a network state at fixed time moments possible the scope of allocated resources such that the total expenses for reconstruction of the network and construction of its new elements as well as for passenger and cargo transportation be the lowest. Thus the problem considered can be described by the optimization model with a non‐linear non‐convex objective function and linear constraints of special structures. Since that is a non‐convex problem with a lot of extreme therefore one can expect to find only an approximate solution, close to a global one, at best. There is no effective and universal solution methods for this problem even in the sense of a local solution. This paper discusses a method for solving the problem using the synthesis of static section, that allows us to decompose dynamic problem into the set of static problems of a smaller volume, and contour optimization methods. The experimental calculation confirm that the proposed method is suitable for solving problem represented in the paper.

scholarly journals Оптимизация алюминиевой крышки люкового закрытия сухогрузного судна

2020 ◽  
Author(s):  
G.B. Kryzhevich ◽  
A.R. Filatov
Keyword(s):  
Shape Optimization ◽  
Parametric Optimization ◽  
Optimization Methods ◽  
Topological Optimization ◽  
Design And Technology ◽  
Bulk Carrier ◽  
Material Consumption ◽  
Considerable Decrease ◽  
Bulk Carriers ◽  
Cargo Transportation

Объектом исследования является крышка люкового закрытия сухогрузного судна, служащая для обеспечения непроницаемости грузовых помещений и перевозки на ней грузов и обеспечивающая безопасность сухогрузных судов и осуществляемой на них морской перевозки грузов. Большая материалоемкость крышек снижает экономическую эффективность судна, ведет к необходимости использования мощных и массогабаритных средств подъема крышек (для съемных люковых закрытий), либо поворота и передвижения крышек (для шарнирно-откидных закрытий). Целью статьи является существенное снижение материалоемкости крышек люкового закрытия за счет рационального выбора их материала и конструктивного оформления при одновременном обеспечении требуемого уровня их надежности. Параметрическая оптимизация традиционной стальной крышки люкового закрытия сухогрузного судна проекта RSD59 может привести к снижению ее массы не более чем на 15-17. Поэтому для достижения цели работы решается задача оптимизации конструкции алюминиевой крышки на основе комплексного подхода, состоящего в последовательном использовании топологических и параметрических оптимизационных методов и выполнении на последней стадии работы снижения уровня концентрации напряжений путем оптимизации формы узлов крышки. При этом на стадии выбора конструктивно-силовой схемы крышки применяются приёмы топологической оптимизации, на стадии выбора толщин и параметров силовых элементов способы параметрической оптимизации, а на стадии конструктивно-технологического оформления узлов методы оптимизации формы. Выполненные расчетные исследования привели к следующим основным результатам: к выявлению прогрессивных конструктивно-силовых схем и конструктивно-технологических решений, обеспечивающих значительное снижению массы крышек люковых закрытий при умеренных затратах на их изготовление к высоким оценкам эффективности использования современных алюминиевых сплавов для изготовления люковых закрытий, способствующим существенному снижению их материалоемкости (примерно двукратному и более по сравнению с использованием стали), улучшению условий их функционирования и проведения погрузочно-разгрузочных работ на сухогрузных судах к выводу об эффективности использования разработанных конструкторских решений для крышек люковых закрытий при создании перспективных сухогрузных судов.A bulk carrier hatch cover, which provides cargo compartments impermeability and cargo transportation on the cover, as well as safety of bulk carriers and sea cargo transportation in them, is studied. Cover high material consumption decreases vessel profitability, causes the necessity to use either powerful and mass-dimensional cover lifting devices (for removable hatch covers) or covers rotation and movement (for hinged covers). The purpose of this paper consists in considerable decrease of hatch cover material consumption through rational selection of covers material and design at provision of the required covers reliability level. Parametric optimization of a conventional steel cover of RSD59 project bulk carrier could result in cover mass decrease by more than 15 to 17. Therefore, to achieve the work purpose, a problem of aluminum cover structural optimization was solved based on a comprehensive approach that consisted in successive use of topologic and parametric optimization methods and decrease of the stress concentration level at the last step via cover assemblies shape optimization. At that topological optimization methods were applied at the stage of selecting cover structural arrangement parametric optimization methods were applied at the stage of selecting load-carrying elements thickness and parameters, and shape optimization methods were used at the stage of structural and technology design of assemblies. The performed calculation studies resulted in the following: revealing the advanced structural arrangements and design and technology solutions that provide considerable hatch covers mass decrease at reasonable costs for their manufacture high assessment of using advanced aluminum alloys for manufacturing hatch covers that promote considerable decrease of their material consumption (approximately up to twofold or greater in comparison with steel), improving conditions of cover functioning and handling operation in bulk carriers conclusion on effectiveness of using developed design solutions for hatch covers when creating prospective bulk carriers.

scholarly journals Creating Better Collision-Free Trajectory for Robot Motion Planning by Linearly Constrained Quadratic Programming

2021 ◽  
Vol 15 ◽  
Author(s):  
Yizhou Liu ◽  
Fusheng Zha ◽  
Mantian Li ◽  
Wei Guo ◽  
Yunxin Jia ◽  
...  
Keyword(s):  
Quadratic Programming ◽  
Motion Planning ◽  
Trajectory Optimization ◽  
Optimization Technique ◽  
Optimization Methods ◽  
Linear Constraints ◽  
Task Constraints ◽  
Probabilistic Sampling ◽  
Smooth Path ◽  
Linearly Constrained

Many algorithms in probabilistic sampling-based motion planning have been proposed to create a path for a robot in an environment with obstacles. Due to the randomness of sampling, they can efficiently compute the collision-free paths made of segments lying in the configuration space with probabilistic completeness. However, this property also makes the trajectories have some unnecessary redundant or jerky motions, which need to be optimized. For most robotics applications, the trajectories should be short, smooth and keep away from obstacles. This paper proposes a new trajectory optimization technique which transforms a polygon collision-free path into a smooth path, and can deal with trajectories which contain various task constraints. The technique removes redundant motions by quadratic programming in the parameter space of trajectory, and converts collision avoidance conditions to linear constraints to ensure absolute safety of trajectories. Furthermore, the technique uses a projection operator to realize the optimization of trajectories which are subject to some hard kinematic constraints, like keeping a glass of water upright or coordinating operation with dual robots. The experimental results proved the feasibility and effectiveness of the proposed method, when it is compared with other trajectory optimization methods.

scholarly journals An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations

2020 ◽  
Vol 5 (1) ◽  
pp. 337-348 ◽  
Author(s):  
Nihal İnce ◽  
Aladdin Shamilov
Keyword(s):  
Probability Density Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Density Function ◽  
Model Fitting ◽  
Random Variable ◽  
Optimization Methods ◽  
Fixed Time ◽  
New Method

AbstractIn this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.

scholarly journals Using concave optimization methods for inexact quadratic programming problems with an application to waste management

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sumati Mahajan ◽  
S. K. Gupta ◽  
Izhar Ahmad ◽  
S. Al-Homidan
Keyword(s):  
Waste Management ◽  
Quadratic Programming ◽  
Optimization Methods ◽  
Linear Constraints ◽  
Strategic Decision ◽  
Public Welfare ◽  
Management Problem ◽  
Quadratic Programming Problems ◽  
Inexact Quadratic Programming ◽  
Real World Problems

AbstractQuadratic programming is potentially capable of strategic decision making in real world problems. However, practical problems rarely conform to crisp parameters, and hence the prospects of these problems with inexact parameters are inevitably higher. The existing studies regarding public welfare schemes/ organizations reveal that their objectives end up as minimization of cost functions and are governed by linear or concave quadratic programming problems. The present study proposes a method that can be applied to concave type quadratic objective function subject to linear constraints with inexact parameters. A comparison is also drawn with existing methods to establish its simplicity and efficiency. Further, a numerical example is illustrated, and finally, a waste management problem is formulated and solved using the proposed method.

Scalable Optimization Methods for Incorporating Spatiotemporal Fractionation into Intensity-Modulated Radiotherapy Planning

2021 ◽  
Author(s):  
Ali Adibi ◽  
Ehsan Salari
Keyword(s):  
Quadratic Programming ◽  
Large Scale ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Radiotherapy Planning ◽  
Quadratic Program ◽  
Clinical Cancer ◽  
Therapeutic Gain ◽  
Solution Methods ◽  
Quadratically Constrained

It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadratically constrained quadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadratic programming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%–12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We test the performance of the proposed methods on deidentified clinical cancer cases. The proposed methods in this study can, in principle, be applied to solve other QCQP formulations, which commonly arise in several application domains, including graph theory, power systems, and signal processing.

Optimization Methods in Modeling the Mechanical Properties of Heavy Steel Plates / Metody Optymalizacyjne W Modelowaniu Własności Mechanicznych Blach Grubych

2012 ◽  
Vol 57 (4) ◽  
pp. 971-979
Author(s):  
A.Z. Grzybowski
Keyword(s):  
Mechanical Properties ◽  
Steel Production ◽  
Optimization Methods ◽  
Linear Constraints ◽  
Steel Plates ◽  
Chance Constrained Programming ◽  
Optimization Approach ◽  
Industrial Manufacturing ◽  
Optimization Task ◽  
Constrained Programming

The paper is devoted to an optimization approach to a problem of statistical modeling of mechanical properties of heavy steel plates during a real industrial manufacturing process. The approach enables the manufacturer to attain a specific set of the final product properties by optimizing the alloying composition within the grade specifications. Because this composition has to stay in the agreement with earlier indicated specifications, it leads to the large system of linear constraints, and the problem itself can be expressed in the form of linear programming (LP) task. It turns out however, that certain of the constraints contain the coefficients which have to be estimated on the base of the data gathered in the production process and as such they are uncertain. Consequently, the initial optimization task should be modeled as so-called Chance Constrained Programming problem (CCP), which is a special class within the stochastic programming problems. The paper presents mathematical models of the optimization problem that result from both approaches and indicates differences which are important for the decision makers in the production practice. Some examples illustrating the differences in solutions resulting from LP and CCP models are presented as well. Although the statistical analysis presented in this paper is based on the data gathered in the ISD Czestochowa Steelworks, the proposed approach can be adopted in any other process of steel production.

Grillage Optimization with Multiple Objectives

2006 ◽  
Vol 306-308 ◽  
pp. 517-522
Author(s):  
Ki Sung Kim ◽  
Kyung Su Kim ◽  
Ki Sup Hong
Keyword(s):  
Structural Optimization ◽  
Structural Design ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Pareto Optimal Solution ◽  
Multiple Objectives ◽  
Pareto Optimal ◽  
Design Environment ◽  
Design Problems ◽  
Solution Methods

The structural design problems are acknowledged to be commonly multicriteria in nature. The various multicriteria optimization methods are reviewed and the most efficient and easy-to-use Pareto optimal solution methods are applied to structural optimization of grillages under lateral uniform load. The result of the study shows that Pareto optimal solution methods can easily be applied to structural optimization with multiple objectives, and the designer can have a choice from those Pareto optimal solutions to meet an appropriate design environment.

Efficient gradient computation for optimization of hyperparameters

2021 ◽  
Author(s):  
Jingyan Xu ◽  
Frédéric Noo
Keyword(s):  
Automatic Differentiation ◽  
Learning Strategy ◽  
Computation Time ◽  
Proximal Mapping ◽  
Convex Problems ◽  
Numerical Studies ◽  
Convex Problem ◽  
Convex Objective Function ◽  
Gradient Computation ◽  
Initial Results

Abstract We are interested in learning the hyperparameters in a convex objective function in a supervised setting. The complex relationship between the input data to the convex problem and the desirable hyperparameters can be modeled by a neural network; the hyperparameters and the data then drive the convex minimization problem, whose solution is then compared to training labels. In our previous work [1], we evaluated a prototype of this learning strategy in an optimization-based sinogram smoothing plus FBP reconstruction framework. A question arising in this setting is how to efficiently compute (backpropagate) the gradient from the solution of the optimization problem, to the hyperparameters to enable end-to-end training. In this work, we first develop general formulas for gradient backpropagation for a subset of convex problems, namely the proximal mapping. To illustrate the value of the general formulas and to demonstrate how to use them, we consider the specific instance of 1-D quadratic smoothing (denoising) whose solution admits a dynamic programming (DP) algorithm. The general formulas lead to another DP algorithm for exact computation of the gradient of the hyperparameters. Our numerical studies demonstrate a 55%- 65% computation time savings by providing a custom gradient instead of relying on automatic differentiation in deep learning libraries. While our discussion focuses on 1-D quadratic smoothing, our initial results (not presented) support the statement that the general formulas and the computational strategy apply equally well to TV or Huber smoothing problems on simple graphs whose solutions can be computed exactly via DP.

Optimization Algorithms and ODE’s in MDO

2013 ◽  
Author(s):  
C. Bakker ◽  
G. T. Parks ◽  
J. P. Jarrett
Keyword(s):  
Differential Geometry ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multidisciplinary Design Optimization ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Multidisciplinary Design ◽  
Theoretical Understanding ◽  
Solution Methods ◽  
Systems Of Odes

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework’s tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context.

On the Derivation of Continuous Piecewise Linear Approximating Functions

2020 ◽  
Vol 32 (3) ◽  
pp. 531-546 ◽  
Author(s):  
Lingxun Kong ◽  
Christos T Maravelias
Keyword(s):  
Piecewise Linear ◽  
Linear Constraints ◽  
Programming Models ◽  
Mixed Integer ◽  
Pointwise Error ◽  
Convex Objective Function ◽  
Minimum Number ◽  
Data Points ◽  
Break Points ◽  
Number Of Segments

We propose mixed-integer programming models for fitting univariate discrete data points with continuous piecewise linear (PWL) functions. The number of approximating function segments and the locations of break points are optimized simultaneously. The proposed models include linear constraints and convex objective function and, thus, are computationally more efficient than previously proposed mixed-integer nonlinear programming models. We also show how the proposed models can be extended to approximate univariate functions with PWL functions with the minimum number of segments subject to bounds on the pointwise error.

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