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EN
Vertex Bisection Minimization problem (VBMP) consists of partitioning a vertex set V of graph G = (V, E) into two sets B and B′ where ∣B∣ = [\v|/2] such that vertex width (VW) is minimized where vertex width is defined as the number of vertices in B which are adjacent to at least one vertex in B′. It is an NP-complete problem in general. VBMP has applications in fault tolerance and is related to the complexity of sending messages to processors in interconnection networks via vertex disjoint paths. In this paper, we have proposed a new integer linear programming (ILP) and quadratically constrained quadratic programming (QCQP) formulation for VBMP. Both of them require number of variables and constraints lesser than existing ILPs and QCQP. We have also implemented ILP and obtained optimal results for various classes of graphs. The result of the experiments with the benchmark graphs shows that the proposed model outperforms the state of the art. Moreover, proposed model obtains optimal result for all the benchmark graphs.
EN
Bound-constrained Support Vector Machine(SVM) is one of the stateof- art model for binary classification. The decomposition method is currently one of the major methods for training SVMs, especially when the nonlinear kernel is used. In this paper, we proposed two new decomposition algorithms for training bound-constrained SVMs. Projected gradient algorithm and interior point method are combined together to solve the quadratic subproblem effciently. The main difference between the two algorithms is the way of choosing working set. The first one only uses first order derivative information of the model for simplicity. The second one incorporate part of second order information into the process of working set selection, besides the gradient. Both algorithms are proved to be global convergent in theory. New algorithms is compared with the famous package BSVM. Numerical experiments on several public data sets validate the effciency of the proposed methods.
EN
The problem of portfolio optimization with its twin objectives of maximizing expected portfolio return and minimizing portfolio risk renders itself difficult for direct solving using traditional methods when constraints reflective of investor preferences, risk management and market conditions are imposed on the underlying mathematical model. Marginal risk that represents the risk contributed by an asset to the total portfolio risk is an important criterion during portfolio selection and risk management. However, the inclusion of the constraint turns the problem model into a notorious non-convex quadratic constrained quadratic programming problem that seeks acceptable solutions using metaheuristic methods. In this work, two metaheuristic methods, viz., Evolution Strategy with Hall of Fame and Differential Evolution (rand/1/bin) with Hall of Fame have been evolved to solve the complex problem and compare the quality of the solutions obtained. The experimental studies have been undertaken on the Bombay Stock Exchange (BSE200) data set for the period March 1999-March 2009. The efficiency of the portfolios obtained by the two metaheuristic methods have been analyzed using Data Envelopment Analysis.
EN
This paper is concerned with a computationally efficient (suboptimal) non-linear Model Predictive Control (MPC) algorithm based on two types of neural models: Multilayer Perceptron (MLP) and Radial Basis Function (RBF) structures. The model takes into account not only controlled but also the uncontrolled input of the process, i.e. the measured disturbance. The algorithm is computationally efficient, because it results in a quadratic programming problem, which can be effectively solved on-line by means of a numerically reliable software subroutine. Moreover, the algorithm gives good closed-loop control performance, comparable to that obtained in the fully-fledged non-linear MPC technique, which hinges on non-linear, usually non-convex optimisation.
EN
This paper describes a computationally efficient (sub-optimal) nonlinear predictive control algorithm. The algorithm uses a modified dual-mode approach which guarantees closed-loop stability. In order to reduce the computational burden, instead of online nonlinear optimisation used in the classical dual-mode control scheme, a nonlinear model of the plant is linearised on-line and a quadratic programming problem is solved. Calculation of the terminal set and implementation steps of the algorithm are detailed, especially for input-output models, which are widely used in practice.
6
Content available remote A family of model predictive control algorithms with artificial neural networks
EN
This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used on-line to determine local linearisation and a nonlinear free trajectory. Single-point and multi-point linearisation methods are discussed. The MPC-NPL structure is far more reliable and less computationally demanding in comparison with the MPC-NO one because it solves a quadratic programming problem, which can be done efficiently within a foreseeable time frame. At the same time, closed-loop performance of both algorithm classes is similar. Finally, a hybrid MPC algorithm with Nonlinear Prediction, Linearisation and Nonlinear optimisation (MPC-NPL-NO) is discussed.
7
Content available remote Advanced predictive control of a distillation column with neural models
EN
This paper describes application of linear and nonlinear Model Predictive Control (MPC) algorithms to a cyclohexane-heptane distillation column. Two nonlinear MPC techniques are compared in terms of control accuracy and computational complexity: MPC with Nonlinear Optimization (MPC-NO) and MPC with Nonlinear Prediction and Linearization (MPC-NPL). In nonlinear MPC a feedforward neural model is used rather than significantly complicated and causing numerical problems fundamental model of the process.
8
Content available remote Projektowanie topografii systemów VLSI. Cz. 3. Metody analityczne
PL
Niniejsza praca jest trzecią częścią przeglądu metod rozmieszczania modułów, stosowanych podczas projektowania topografii układów VLSI. W pracy szczegółowo został opisany algorytm zamiany parami oraz metody analityczne. Przedstawiono liczne modyfikacje algorytmu zamiany parami, łącznie z algorytmami wykorzystującymi metody relaksacyjne. Modyfikacje algorytmu zamiany parami oraz metody relaksacyjne są stosowane w programach rozmieszczania opartych na metodach analitycznych. Następnie, opisano podstawy zastosowania programowania kwadratowego i liniowego w rozmieszczaniu modułów. Ze względu na dużą liczbę rozwiązań stosowanych w metodach analitycznych, poszczególne rozwiązania szczegółowo przedstawiono na przykładzie wybranych programów rozmieszczania. W tym celu scharakteryzowano następujące programy rozmieszczania: GORDIAN / DOMINO, KraftWerk, FastPlace, mPL, PROUD, ATLAS, FAR, mFAR, BloBB, APlace. Przedstawiono również sposób zastosowania metody relaksacyjnej w układach o topografii swobodnej oraz możliwość optymalizacji topografii układu ze względu na aspekt termiczny.
EN
The design process of the VLSI circuits requires the use of computer aided design tools. This paper is the third part of the survey of the cell placement techniques for digital VLSI circuits. In this part of the survey, the pairwise interchange algorithm and some analytical methods are presented. The force-directed placement algorithm and some modifications of the pairwise interchange algorithm, which are used in analytical algorithms are described. Then, the nonlinear programming, quadratic programming and linear programming techniques are presented. An application of these techniques to the cell placement problem is described. Nowadays the tools used for the cell placement, which utilize the presented algorithms are characterized: GORDIAN, DOMINO, KraftWerk, FastPlace, mPL, PROUD, ATLAS, FAR, mFAR, BloBB, APlace. A force-directed placer for a building block design style is described. The principles of the multilevel optimization for the cell placement problem are presented. Applications of the flow network and branch and bound algorithm to the cell placement are characterized. Some conclusions concerning described techniques and tools are presented.
EN
Elastic-plastic beam structures, subjected by distributed loads, optimization problems are considered in this paper. Mixed method is suggested to form static and geometrical equations by setting the finite element interpolation functions of internal forces and displacements. That allows forming optimization problems with restricted middle cross-sections of beams. General expressions of static and geometrical equations are presented for a beam subjected by a distributed load. The optimization mathematical models of elastic-plastic beam structures with linear hardening are formulated as quadratic programming problems. Results of numerical example are presented and briefly discussed.
PL
W rozprawach optymalizacji prętowych elastyczno-plastycznych konstrukcji rozpatruje się najczęściej systemy obciążane siłami skupionymi. Praca jest poświęcona udoskonaleniu algorytmów optymalizacji prętowych konstrukcji obciążonych siłami ciągłymi. Równania statyczne oraz geometryczne elementu skończonego i całej j konstrukcji proponuje się tworzyć metodą kombinowaną, zadając funkcje interpolacyjne przemieszczeń oraz sit. To sprzyja sformułowaniu zadania optymalizacji, w którym można ograniczyć ugięcia środkowego przekroju w elementach zginanych. Przedstawiono ogólne formy równań statycznych oraz geometrycznych dla pręta obciążanego ciągłym obciążeniem. Zadania optymalizacji prętowych elastyczno-plastycznych konstrukcji wyprodukowanych z liniowo wzmacniającego się materiału są przedstawione jak zadania kwadratowego programowania. Przedstawione są rezultaty analizy obliczeniowej.
EN
In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.
11
Content available remote Label placement for dynamic objects
EN
Placing object labels in dynamic scenes requires the label positions themselves to be dynamic. Algorithms for dynamic label placement are presented that tend to avoid overlaps and consider aesthetic preferences. The procedures are derived from a quadratic program. As a special feature, hysteresis is incorporated to restrict the optical flow induced by label changes.
EN
Model Predictive Control (MPC) represents a major paradigm shift in the field of automatic control. This radically affects synthesis techniques (illustrated by control of an unstable system) and underlying concepts (illustrated by control of a multivariable system), as well as lifting the Control engineer's focus from prescriptions to specifications ("what" not "how", illustrated by emulation of a conventional autopilot). Part of the objective of this paper is to emphasise the significance of this paradigm shift. Another part is to consider the fact that this shift was missed for many years by the academic community, and what this tells us about teaching and research in the field.
EN
The mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. Im a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is transformed into an easy to solve linear programming program. In this paper we poesent a recursive procedure which allows to identify optimal portfolio of the MAD model depending on investor's downside risk aversion.
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