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1
Content available Optimization of support parameters for reusable mining excavations based on a neuro-heuristic prognostic model
Babets Dmytro, Sdvyzhkova Olena, Dyczko Artur, Gliwiński Łukasz
Mining Machines
|
2023
|
vol. 41, iss. 3
200--211
EN
This publication delves into geomechanical processes encountered during sequential longwall mining of coal seams, with a unique focus on reusing the conveyor track of the prior longwall as the ventilation pathway for the subsequent longwall. An in-depth geomechanical rationale is provided for the reuse of excavations within jointed rock formations.To ascertain the critical roles played by various support and protective elements at each distinct mining stage, a comprehensive analysis is performed using finite element techniques to delineate thethree-dimensional stress-strain characteristics of the rock mass.Employing an innovative methodology integrating multifactorial analysis, contemporary structural identification algorithms, and a neuro-heuristic approach for predictive mathematical modeling, an integral stability metric for reusable mining excavations isintroduced. Specifically, this metric quantifies the relative preservation of theexcavation's cross-sectional area following its connection to thesecond longwall.Furthermore, the study tackles the challenge of nonlinear optimization through the application of the generalized reduced gradient method (Frank-Wolfe), ultimately deriving the optimal combination of factors that maximizes the preservation of the cross-sectional area for these reusable excavations.
2
Content available Nonlinear optimization approach to determine optical dispersion in liquid crystals
Marciniak P., Moszczyński P.
Optica Applicata
|
2016
|
Vol. 46, nr 4
619--628
EN
We report the method of calculating optical dispersion of selected nematic liquid crystals using maxima positions of a transmittance filled Fabry–Pérot filter. Additionally, the profiles of a dispersive phase of reflection have been calculated. The transmittance of Fabry–Pérot filter was described as a form of a modified Airy formulae (with parameters dependence on wavelength and phase of reflection). To correctly use this function, additionally the phase of reflection is defined, taking into account the problem of a beam penetrating the mirror structure. The authors of this work assume that the point where the beam is reflected is not created strictly on the boundary of media, but it is moved into the mirror structure. The depth of the penetration changes the optical way of the wave and in consequence – the optical width of the Fabry–Pérot filter cavity. The parameter describing this phenomenon was named as a phase of reflection. This work presents how to calculate: the phase of reflection, one of refractive indices of birefringent medium inside Fabry–Pérot filter and the cavity width at the same time with the use of composed nonlinear optimization methods. The proposed method is an alternative for a reverse task solution which is hard to define properly here.
3
Content available Estimation of composite load model parameters as a constrained nonlinear problem
Regulski P.
Present Problems of Power System Control
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2015
|
Nr 6
33--42
EN
This paper presents the results of application of sequential quadratic programming to the estimation of the unknown composite load model parameters. Traditionally applied estimation methods, such as nonlinear least squares or genetic algorithms, suffer from a number of issues. Genetic algorithms exhibit premature convergence and require high computational resources and nonlinear least squares method is very sensitive to the initial guess and can diverge easily. This paper provides a comparison of all three methods based on computer-generated signals serving as field measurements. Accuracy and precision are assessed as well as computational requirements.
4
Algorytm mrówkowy w optymalizacji dyskretnych problemów nieliniowych
Krenich S.
Logistyka
|
2014
|
nr 6
6032-6040
PL
Artykuł prezentuje zastosowanie algorytmu mrówkowego w optymalizacji problemów o dyskretnym i nieliniowym charakterze. Algorytm mrówkowy zaliczany jest do grupy algorytmów rojowych, które są inspirowane zachowaniem stad lub rojów zwierząt, ptaków czy owadów podczas poszukiwania pożywienia czy przemieszczania się. Algorytmy te stosowane są głównie do rozwiązywania problemów opisanych za pomocą grafów i sieci. W niniejszej pracy przedstawiono modyfikację klasycznego algorytmu mrówkowego i jego przystosowanie do rozwiązywania zadań optymalizacji jednokryterialnej konstrukcji z ograniczeniami, które nie są modelowane jako grafy z wyraźnie zaznaczonymi węzłami i krawędziami przejść o określonym ściśle koszcie lub wartości drogi. Wprowadzono modyfikację w wyznaczaniu prawdopodobieństwa wyboru tzw. krawędzi przejścia oraz w obliczaniu wartości feromonu na tych krawędziach. Wartości te zależą nie tylko od liczby przejść sztucznych mrówek, ale także dodatkowo od dynamicznie ustalanej wartości pozostawianego przez mrówki feromonu. Eksperymenty przeprowadzono na dwóch przykładach dyskretnej optymalizacji sprzęgła wielopłytkowego oraz układu koncentrycznych sprężyn poddanych zmiennemu obciążeniu z wykorzystaniem zmodyfikowanego algorytmu mrówkowego oraz dodatkowo w celu porównania z wykorzystaniem algorytmu ewolucyjnego i losowego. Wyniki wskazują, iż algorytm mrówkowy może być efektywnym narzędziem w programowaniu dyskretnym.
EN
The paper presents an approach to design optimization for discrete and nonlinear problems using ant colony based algorithm. This algorithm belongs to the group of swarm algorithms inspired by behavior of birds, animals and bugs during their life or movement. Generally it is used for solving tasks which are modeled as grid or network problems. In the work a modification of the classical ant colony algorithm and its adaptation for problems that are not modeled as a network task with marked nodes and edges is described. New dependencies for dynamic calculating of pheromone on the edges and for probability of their choosing are introduced. Experiments were carried out for two examples of discrete optimization. The first one deals with the coupling system and the second one solves the set of concentric springs. Additionally, in order to compare generated optimal solutions, an evolutionary algorithm and a random search method are used. The obtained results indicate that the ant colony based algorithm can be an effective tool for discrete programming.
5
Content available remote SVD as a preconditioner in nonlinear optimization
Pazdanowski M.
Computer Assisted Methods in Engineering and Science
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2014
|
Vol. 21, no. 2
141--150
EN
Finding a solution of nonlinear constrained optimization problem may be very computer resources consuming, regardless of solution method adopted. A conceptually simple preconditioning procedure, based on singular value decomposition (SVD), is proposed in the current paper in order to speed up the convergence of a gradient based algorithm to solve constrained minimization problem having quadratic objective function. The efficiency of the proposed procedure is tested on a constrained minimization problem with quadratic objective function and quadratic constraints. Accuracy of the results obtained using proposed preconditioning method is checked and verified against the results determined without the preconditioning procedure. Results obtained so far seem to indicate a significant speedup of the calculations at the expense of, negligible from the engineering point of view, loss of accuracy.
6
Metoda optymalizacji rozmieszczenia generacji nieregulowanej w systemie elektroenergetycznym wykorzystująca zmodyfikowany algorytm tabu search
Słabosz S., Sobierajski M.
Rynek Energii
|
2013
|
Nr 3
45--49
PL
W pracy przedstawiono metodę optymalizacji węzłowej generacji nieregulowanej w systemie elektroener-getycznym z wykorzystaniem zmodyfikowanego algorytmu Tabu Search. Funkcją celu jest maksymalna sumaryczna generacja nieregulowana przy spełnieniu następujących ograniczeń: dopuszczalne obciążenie linii i transformatorów, dopuszczalne saldo wymiany zagranicznej, regulacyjne minimum techniczne mocy w elektrowniach konwencjonalnych. Modyfikacja algorytmu polega na wykluczania rozwiązań, w których następuje przekroczenie już na etapie pośrednim. Wprowadzono funkcję promującą rozwiązania oddalone od przekroczeń. Rozważania zilustrowano przykładem obliczeniowym, wyniki porównano z optymalizacją liniową.
EN
In the paper the optimization method of unregulated generation in a electric power system using the modified Tabu Search algorithm was presented. The goal function is the maximal total unregulated generation with the following constraints: permissible lines and transformers loading, permissible international exchange balance, technical constraints of the power of regulated power stations. The algorithm modification relies on elimination of solutions in which in the middle stages the overrun occurs. A function promoting solutions far from overruns was introduced. The considerations were illustrated by a computational example and the results were compared with linear optimization.
7
Content available remote Metoda rzutowania gradientu w optymalizacji parametrów konstrukcyjnych napięciowego transformatora pomiarowego
Piaskowy A., Roj J.
Przegląd Elektrotechniczny
|
2013
|
R. 89, nr 1a
91--93
PL
W pracy sformułowano problem optymalizacji parametrów konstrukcyjnych precyzyjnych transformatorów pomiarowych. Zaproponowano metodę optymalizacji bazującą na rzutowaniu gradientu na podprzestrzeń styczną do ograniczeń aktywnych oraz przedstawiono algorytm.
EN
The design optimization problem of precise measuring transformers is formulated in the paper. Gradient projection on active tangent subspace method is proposed for the task solutions and algorithm is shown.
8
Content available remote The p-Factor Method for Nonlinear Optimization
Szczepanik E.., Prusińska A., Tret’yakov A.
Schedae Informaticae
|
2012
|
Vol. 21
141--157
EN
We present the main concept and results of the p-regularity theory (also known as p-factor analysis of nonlinear mappings) applied to nonlinear optimization problems. The approach is based on the construction of p-factor operator. The main result of this theory gives a detailed description of the structure of the zero set of irregular nonlinear mappings. Applications include a new numerical method for solving nonlinear optimization problems and p- order necessary and sufficient optimality conditions. We substantiate the rate of convergence of p-factor method.
9
Ocena możliwości przyłączeniowych węzłów systemu elektroenergetycz-nego. Część III - nieliniowa optymalizacja generacji wiatrowej
Kacejko P., Pijarski P., Sobierajski M., Robak S.
Rynek Energii
|
2012
|
Nr 3
44--51
PL
W części III cyklu artykułów o możliwościach przyłączeniowych SEE przedstawiono nieliniową optymaliza-cję wartości mocy farm wiatrowych przyłączonych do sieci przesyłowej. Funkcją celu jest maksymalna sumaryczna moc generowana w farmach wiatrowych, przy uwzględnieniu dopuszczalnych obciążeń linii i transformatorów, dopuszczalnego salda wymiany zagranicznej oraz regulacyjnego minimum technicznego mocy generowanej w elektrowniach konwencjo-nalnych. W celu spełnienia przez rozwiązanie optymalne kryterium N-1 (wyłączenia pojedynczych elementów), zostały one włączone do zbioru ograniczeń. W wyniku zastosowania heurystycznego algorytmu symulowanego wyżarzania otrzymano wektor mocy, których wartości spełniają zarówno ograniczenia dla stanu normalnego jak i stanów N-1 oraz zapewniają maksymalne wykorzystanie możliwości farm. Rozważania zilustrowano przykładem optymalizacji generacji wiatrowej w sieci testowej C7M.
EN
In the third part of the paper, the nonlinear optimization of wind generation in power system is presented. Wind generation affects power flows and transmission lines and transformers may be overloaded after interconnecting wind farms into the grid. Wind generation results in decreasing conventional generation but the technical minimum of a thermal unit in power stations must not be violated. The assessment of wind generation optimal level has been formulated as the minimization of a goal function subjected to nonlinear equality (generation and demand balance) and inequality constraints (permissible branch flows and the technical minimum of thermal unit generation). Contingency cases were also include to the set of equality constrains. Heuristic algorithm of simulated annealing was applied together with effective Power World computational engine. The example computations of C7M test system were successfully performed.
10
Content available Algorytmy stadne w problemach optymalizacji
Filipowicz B., Kwiecień J.
Pomiary Automatyka Robotyka
|
2011
|
R. 15, nr 12
152-157
PL
W artykule przedstawiono zastosowanie algorytmu optymalizacji rojem cząstek, algorytmu pszczelego i algorytmu świetlika do wyznaczenia optymalnego rozwiązania wybranych testowych funkcji ciągłych. Przedstawiono i porównano wyniki badań dla funkcji Rosenbrocka, Rastrigina i de Jonga.
EN
This paper presents particle swarm optimization, bee algorithm and firefly algorithm, used for optimal solution of selected continuous well-known functions. Results of these algorithms are compared to each other on Rosenbrock, Rastrigin and de Jong functions.
11
Content available remote Optimization-based approach to path planning for closed chain robot systems
Szynkiewicz W., Błaszczyk J.
International Journal of Applied Mathematics and Computer Science
|
2011
|
Vol. 21, no 4
659-670
EN
An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a "quasi-dynamic" NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used, which implements a nonlinear primal-dual interior-point method, one of the leading techniques for large-scale nonlinear optimization.
12
Content available remote Modeling Proteolysis from Mass Spectrometry Proteomic Data
Gambin A., Kluge B.
Fundamenta Informaticae
|
2010
|
Vol. 103, nr 1-4
89-104
EN
In this paper we propose a mathematical model of the proteolysis process. Protein digestion is modelled with the use of chemical master equation (CME), i.e. the system of stochastic differential equations corresponding to the network of enzymatic reactions. We present an efficient approach to model parameters’ estimation (i.e. enzyme activities) from time series of mass spectrometry data. These results extend previous results in three directions: by relaxing the stationarity of the proteolysis process assumption, by allowing cuts at arbitrary sites in the peptide sequence and by incorporating knowledge from biological databases.
13
Podstawowe problemy optymalizacji z ograniczeniami
Ruchaj M.
Zeszyty Naukowe. Elektryka / Politechnika Opolska
|
2007
|
Vol. 322, z. 59
35-36
EN
This paper reviews fundamental problems of constrained optimization and generally describes methods for linear and nonlinear constrained optimization. A job scheduling example of nonlinear integer constrained optimization is shown to illustrate the considerations.
14
Content available remote A Method for Constructing ε-value Functions for The Bolza Problem of Optimal Control
Pustelnik J.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 2
177-186
EN
The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function.
15
Content available Some variants of projection methods for large nonlinear optimization problems
Białoń P.
Journal of Telecommunications and Information Technology
|
2003
|
nr 3
43-49
EN
Two ideas of modifying projection methods for the case of smooth nonlinear optimization are presented. Projection methods were originally successfully used in solving large- scale linear feasibility problems. The proposed instantiations of projection methods fall into two groups. One of them is a decomposition approach in which projections onto sets are realized as optimization problems which themselves involve much portions of original problem constraints. There are two subproblems: one build with linear constraints of the original problem and the second one build with original nonlinear constraints. These approaches use special accelerating cuts so that the separation of nonlinear and linear constraints can be effective and some problem sparsity preserved. The second group bases on penalty-shifting/multiplier methods and draws from the observation that unconstrained subproblems obtained there may solve very slowly due to their nonsmooth character. Thus it is proposed to solve them with modified projection methods which inherit from conjugate gradient methods a multi-dimensional subspace in one epoche.
16
Semi-automatic quantitative histogram analysis of the CT and MRI images
Chlebiej M., Kuczyński K., Stegierski R., Mikołajczak P.
Journal of Medical Informatics & Technologies
|
2001
|
Vol. 2, Part. 2
MT57--MT65
EN
This paper presents results on voxel histogram analysis for quantification of brain image sequence. We model the histogram as a sum of parameterized gaussian functions, where each function represents the distribution of samples for a single material in the volume. We find parameters for the collection of gaussian functions with the help of Levenberg-Marquardt method that make the model agrees with the histogram.
17
Content available remote Analysis of an Isope-Type Dual Algorithm for Optimizing Control and Nonlinear Optimization
Tadej W., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
|
2001
|
Vol. 11, no 2
429-457
EN
First results concerning important theoretical properties of the dual ISOPE (Integrated System Optimization and Parameter Estimation) algorithm are presented. The algorithm applies to on-line set-point optimization in control structures with uncertainty in process models and disturbance estimates, as well as to difficult nonlinear constrained optimization problems. Properties of the conditioned (dualized) set of problem constraints are investigated, showing its structure and feasibility properties important for applications. Convergence conditions for a simplified version of the algorithm are derived, indicating a practically important threshold value of the right-hand side of the conditioning constraint. Results of simulations are given confirming the theoretical results and illustrating properties of the algorithms.
18
Content available remote An Algorithm for Construction of varepsilon-Value Functions for the Bolza Control Problem
Jacewicz E.
International Journal of Applied Mathematics and Computer Science
|
2001
|
Vol. 11, no 2
391-428
EN
The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an varepsilon-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an varepsilon-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.
19
Content available remote Manufacturing tolerances of truss members' lengths in minimum weight design
Bauer J., Latalski J.
Computer Assisted Mechanics and Engineering Sciences
|
2000
|
Vol. 7, No. 4
461-469
EN
In most cases a safety of optimal construction may be limited by the violation of stress, buckling or displacement constraints. An unexpected exceed of these constraints may be caused by manufacturing tolerances of structural elements (differences between assumed and obtained dimensions). This requires an incorporation of tolerance problem in optimum design. One may deal with two different tolerances - the first case is when it's related to the members' cross-section variations, whereas the second notion represents the variation of elements' lengths. Considering operation conditions and manufacturing techniques the second case of tolerance seems to be more important. This approach states the problem of minimum weight design of a structure with initial distortions. A standard solution algorithm with the Kuhn-Tucker theorem was used with the adjoint variable method. Necessary optimality conditions have the form of equations and inequalities. The equality constraints were put forward for the average values of design variables l, while tolerances t_j were introduced into inequality equations i.e. the limit values of stresses and displacements were diminished by the positive products of appropriate sensitivities and tolerances. The method was next illustrated by an example of a ten bar bench-mark problem - a typical one for testing algorithms in structural optimization. The idea presented in this paper may be used not only for truss structures but it can be easily extended to other kinds of structures like frames, composites etc.
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