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Wyświetlanie 1-15 z 147
Tytuł:
Topological sensitivity analysis for a coupled nonlinear problem with an obstacle
Autorzy:
Abdelbari, M.
Nachi, K.
Sokolowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/205653.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
topological derivative
shape optimization
SteklovPoincaroperator
Signorini problem
variational inequality
Helmholtz equation
coupled partial differential equations
conical differential
asymptotic expansions
singular perturbations of geometrical Romains
truncated domain
Opis:
The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-differential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.
Źródło:
Control and Cybernetics; 2017, 46, 1; 5-25
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape sensitivity of optimal control for the Stokes problem
Autorzy:
Abdelbari, Merwan
Nachi, Khadra
Sokolowski, Jan
Szulc, Katarzyna
Powiązania:
https://bibliotekanauki.pl/articles/2049935.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Stokes equations
optimal control problem
coupled partial differential equations
shape optimization
shape gradient
Opis:
In this article, we study the shape sensitivity of optimal control for the steady Stokes problem. The main goal is to obtain a robust representation for the derivatives of optimal solution with respect to smooth deformation of the flow domain. We introduce in this paper a rigorous proof of existence of the material derivative in the sense of Piola, as well as the shape derivative for the solution of the optimality system. We apply these results to derive the formulae for the shape gradient of the cost functional; under some regularity conditions the shape gradient is given according to the structure theorem by a function supported on the moving boundary, then the numerical methods for shape optimization can be applied in order to solve the associated optimization problems.
Źródło:
Control and Cybernetics; 2020, 49, 1; 11-40
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of a Solidification Problem
Autorzy:
Aboulaich, R.
Haggouch, I.
Souissi, A.
Powiązania:
https://bibliotekanauki.pl/articles/908072.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
optymalizacja
metoda elementów skończonych
Stefan problem
free boundary
shape optimization
Euler method
finite element method
Opis:
A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocci, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al.., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2-rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 4; 921-955
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adjustable Robust Counterpart Optimization Model for Maximum Flow Problems with Box Uncertainty
Autorzy:
Agustini, Rahmah Arie
Chaerani, Diah
Hertini, Elis
Powiązania:
https://bibliotekanauki.pl/articles/1031851.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Adjustable Robust Counterpart
Linear Programming
Maximum flow problem
Robust Optimization
Opis:
The maximum flow problem is an optimization problem that aims to find the maximum flow value on a network. This problem can be solved by using Linear Programming. The obstacle that is often faced in determining the maximum flow is the magnitude of the capacity of each side of the network can often be changed due to certain factors. Therefore, we need one of the optimization fields that can calculate the uncertainty factor. The field of optimization carried out to overcome these uncertainties is Robust Optimization. This paper discusses the Optimization model for the maximum flow problem by calculating the uncertainties on parameters and adjustable variables using the Adjustable Robust Counterpart (ARC) Optimization model. In this ARC Optimization model it is assumed that there are indeterminate parameters in the form of side capacity in a network and an uncertain decision variable that is the amount of flow from the destination point (sink) to the source point (source). Calculation results from numerical simulations show that the ARC Optimization model provides the maximum number of flows in a network with a set of box uncertainty. Numerical simulations were obtained with Maple software.
Źródło:
World Scientific News; 2020, 141; 91-102
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A logistic optimization for the vehicle routing problem through a case study in the food industry
Autorzy:
Akpinar, Muhammet Enes
Powiązania:
https://bibliotekanauki.pl/articles/1835487.pdf
Data publikacji:
2021
Wydawca:
Wyższa Szkoła Logistyki
Tematy:
vehicle routing problem
time windows
optimization
metaheuristic algorithm
genetic algorithm
trasa pojazdu
okna czasowe
optymalizacja
algorytm metaheurystyczny
algorytm genetyczny
Opis:
In this study, the food delivery problem faced by a food company is discussed. There are seven different regions where the company serves food and a certain number of customers in each region. The time of requesting food for each customer varies according to the shift situation. This type of problem is referred to as a vehicle routing problem with time windows in the literature and the main aim of the study is to minimize the total travel distance of the vehicles. The second aim is to determine which vehicle will follow which route in the region by using the least amount of vehicle according to the desired mealtime. Methods: In this study, genetic algorithm methodology is used for the solution of the problem. Metaheuristic algorithms are used for problems that contain multiple combinations and cannot be solved in a reasonable time. Thus in this study, a solution to this problem in a reasonable time is obtained by using the genetic algorithm method. The advantage of this method is to find the most appropriate solution by trying possible solutions with a certain number of populations. Results: Different population sizes are considered in the study. 1000 iterations are made for each population. According to the genetic algorithm results, the best result is obtained in the lowest population size. The total distance has been shortened by about 14% with this method. Besides, the number of vehicles in each region and which vehicle will serve to whom has also been determined. This study, which is a real-life application, has provided serious profitability to the food company even from this region alone. Besides, there have been improvements at different rates in each of the seven regions. Customers' ability to receive service at any time has maximized customer satisfaction and increased the ability to work in the long term. Conclusions: The method and results used in the study were positive for the food company. However, the metaheuristic algorithm used in this study does not guarantee an optimal result. Therefore, mathematical models or simulation models can be considered in terms of future studies. Besides, in addition to the time windows problem, the pickup problem can also be taken into account and different solution proposals can be developed.
Źródło:
LogForum; 2021, 17, 3; 387-397
1734-459X
Pojawia się w:
LogForum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimization of empty truck runs. Formulation of problem
Autorzy:
Ambroziak, Tomasz
Pawłowski, Daniel
Powiązania:
https://bibliotekanauki.pl/articles/409210.pdf
Data publikacji:
2019
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
transportation problem
empty truck runs
graphs
optimization
routes and schedules
Opis:
The article formulates the issue of minimizing empty runs. Then, the interpretation of the issue of empty runs on numerical examples is presented. The formulation of the issue of minimizing empty runs requires the formulation of two optimization problems. The first one concerns distribution of commodities with minimal cost. The optimization problem formulated in this way is a well-known transport problem with the objective function being the costs of transport. The second one concerns commodity transport with distance minimization. After solving these two issues, the circulation problem of transport means is solved. Thanks to which we obtain the minimum number of empty runs expressed in distance units.
Źródło:
Research in Logistics & Production; 2019, 9, 2; 77-87
2083-4942
2083-4950
Pojawia się w:
Research in Logistics & Production
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape differentiability of the Neumann problem of the Laplace equation in the half-space
Autorzy:
Amrouche, C.
Necasova, S.
Sokołowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/970287.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
shape optimization
Neumann problem
unbounded domain
material derivative
Opis:
We deal with the existence of the material derivative of the Laplace equation with the Neumann boundary condition in the half space. We consider two different perturbations of domains to get the existence of weak Gateaux material derivative and the existence of Fréchet material derivatives.
Źródło:
Control and Cybernetics; 2008, 37, 4; 747-769
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order convexity and a modified objective function method in mathematical programming
Autorzy:
Antczak, T.
Powiązania:
https://bibliotekanauki.pl/articles/969778.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
programowanie matematyczne
mathematical programming
second order modified objective function optimization problem
second order convex function
second order optimality conditions
Opis:
An approach to nonlinear constrained mathematical programming problems which makes use of a second order derivative is presented. By using a second order modified objective function method, a modified optimization problem associated with a primal mathematical programming problem is constructed. This auxiliary optimization problem involves a second order approximation of an objective function constituting the primal mathematical programming problem. The equivalence between the original mathematical programming problem and its associated modified optimization problem is established under second order convexity assumption. Several practical O.R. applications show that our method is efficient. Further, an iterative algorithm based on this approach for solving the considered nonlinear mathematical programming problem is given for the case when the functions constituting the problem are second order convex. The convergence theorems for the presented algorithm are established.
Źródło:
Control and Cybernetics; 2007, 36, 1; 161-182
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse backward problem for degenerate two-dimensional parabolic equation
Autorzy:
Atifi, Khalid
Essoufi, El-Hassan
Khouiti, Bouchra
Powiązania:
https://bibliotekanauki.pl/articles/255085.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
data assimilation
adjoint method
regularization
heat equation
inverse problem
degenerate equations
optimization
Opis:
This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation [formula], where Ω is an open, bounded subset of R2, a [formula] with a ≥0 everywhere, and [formula], with initial and boundary conditions [formula] from final observations. This inverse problem is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. To show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of the Tikhonov functional. Also we present some numerical experiments to show the performance and stability of the proposed approach.
Źródło:
Opuscula Mathematica; 2020, 40, 4; 427-449
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The "Thirty-seven Percent Rule" and the secretary problem with relative ranks
Autorzy:
Bajnok, Béla
Semov, Svetoslav
Powiązania:
https://bibliotekanauki.pl/articles/729810.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
secretary problem
relative ranks
stopping rule
optimization
Opis:
We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ~ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest rank; however, with the optimally chosen l, here we can get the expected rank of the item selected to be less than any positive power of n (as n approaches infinity). We also introduce a common generalization where our goal is to minimize the expected rank of the item selected, but this rank must be within the lowest d.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2014, 34, 1-2; 5-21
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A hybrid algorithm for solving inverse problems in elasticity
Autorzy:
Barabasz, B.
Gajda-Zagórska, E.
Migórski, S.
Paszyński, M.
Schaefer, R.
Smołka, M.
Powiązania:
https://bibliotekanauki.pl/articles/331427.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
inverse problem
hierarchic genetic strategy
hybrid optimization
automatic hp adaptive finite element method
zagadnienie odwrotne
strategia genetyczna
optymalizacja hybrydowa
metoda elementów skończonych
Opis:
The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 865-886
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamics of Stochastic vs. Greedy Heuristics in Traveling Salesman Problem
Autorzy:
Białogłowski, M.
Staniaszek, M.
Laskowski, W.
Grudniak, M.
Powiązania:
https://bibliotekanauki.pl/articles/91276.pdf
Data publikacji:
2018
Wydawca:
Warszawska Wyższa Szkoła Informatyki
Tematy:
traveling salesman problem
Nearest Neighbor
Monte Carlo
Simulated Annealing
Genetic Algorithm
particle swarm optimization (PSO)
Opis:
We studied the relative performance of stochastic heuristics in order to establish the relations between the fundamental elements of their mechanisms. The insights on their dynamics, abstracted from the implementation details, may contribute to the development of an efficient framework for design of new probabilistic methods. For that, we applied four general optimization heuristics with varying number of hyperparameters to traveling salesman problem. A problem-specific greedy approach (Nearest Neighbor) served as a reference for the results of: Monte Carlo, Simulated Annealing, Genetic Algorithm, and Particle Swarm Optimization. The more robust heuristics – with higher configuration potential, i.e. with more hyperparameters – outperformed the smart ones, being surpassed only by the method specifically designed for the task.
Źródło:
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki; 2018, 12, 19; 7-24
1896-396X
2082-8349
Pojawia się w:
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Variational approach to some optimization control problems
Autorzy:
Bianchini, R.
Powiązania:
https://bibliotekanauki.pl/articles/1359657.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
tangent vectors
variational cone
local controllability
Mayer's optimization problem
Opis:
This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.
Źródło:
Banach Center Publications; 1995, 32, 1; 83-94
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bicriteria Optimization in the Newsvendor Problem with Exponentially Distributed Demand
Autorzy:
Bieniek, Milena
Powiązania:
https://bibliotekanauki.pl/articles/578568.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Ekonomiczny w Katowicach
Tematy:
Bicriteria optimization
Newsvendor problem
Stochastic process
Optymalizacja dwukryterialna
Proces stochastyczny
Zagadnienie gazeciarza
Opis:
In this paper exponential distribution is implemented as a demand distribution in newsvendor model with two different and conflicting goals. The first goal is the standard objective of maximization of the expected profit. The second one is to maximize the probability of exceeding the expected profit, called survival probability. Using exponential distribution as the demand distribution allows us to obtain the exact solutions. Also for this distribution we can study the monotonicity of survival probability with respect to various model parameters analytically. Additional results are obtained when various sets of the parameters are considered. Finally, the bicriteria index which combines these conflicting objectives is optimized which gives the compromise solution. Moreover, in order to illustrate theoretical results, we present numerical examples and graphs of auxiliary functions.
Źródło:
Multiple Criteria Decision Making; 2016, 11; 20-35
2084-1531
Pojawia się w:
Multiple Criteria Decision Making
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bicriteria Optimization in the Risk-Adjusted Newsvendor Problem
Autorzy:
Bieniek, Milena
Powiązania:
https://bibliotekanauki.pl/articles/578584.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Ekonomiczny w Katowicach
Tematy:
Bicriteria optimization
Newsvendor problem
Risk
Optymalizacja dwukryterialna
Ryzyko
Zagadnienie gazeciarza
Opis:
In this paper, we study the newsvendor problem with various degrees of risk tolerance. We consider bicriteria optimization where the first objective is the classical maximization of the expected profit and the second one is the satisficing-level objective. The results depend on the risk coefficient and are different for a risk-neutral, a risk-averse, and a risk-seeking retailer. We find the compromise solution of the bicriteria newsvendor problem numerically, since the two objectives are mutually conflicting. The formulas obtained are illustrated with exponentially distributed demand.
Źródło:
Multiple Criteria Decision Making; 2017, 12; 9-21
2084-1531
Pojawia się w:
Multiple Criteria Decision Making
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 147

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