Steepest Descent Algorithm Research Articles

An adaptive guided variable neighborhood search based on honey-bee mating optimization algorithm for the course timetabling problem

A standard honey-bee mating optimization algorithm (HBMO) utilizes the steepest descent local search algorithm as a worker. The steepest descent algorithm has the advantage of being simple to understand, fast and is easy to implement. However, it can easily trapped in a local optimum and subsequently restrict the performance of HBMO. Furthermore, the type of neighborhood structures that are used within the local search algorithm might impact on the performance of algorithm. This work aimed to enhance the performance of HBMO by using an adaptive guided variable neighborhood search (AGVNS) as a worker. The AGVNS algorithm is a variant of variable neighborhood search algorithm that incorporates some problem-specific knowledge and utilizes an adaptive learning mechanism to find the most suitable neighborhood structure during the searching process. In order to evaluate the effectiveness of the proposed algorithm, the Socha course timetabling dataset has been chosen as the tested domain problem. The results demonstrated that the performance of the proposed algorithm is comparable to other approaches in the literature. Indeed, the proposed algorithm obtained the best results as compared to other approaches on some instances. These results indicate the effectiveness of combining HBMO and AGVNS for solving course timetabling problems, hence demonstrated that the AGVNS can enhance the performance of HBMO.

A new approach to design safe-supported HDD against random excitation by using optimization of rubbers spatial parameters

Hard disk drives (HDDs) of laptop personal computers (LPCs) are devices vulnerable in harsh mechanical environments. Hence, they need to be protected against damages due to vibration in order to have better read/write performance. In the present study, a LPC and its HDD are modeled as a system with two degrees of freedom and the nonlinear optimization method is employed to perform a passive control through minimizing the root mean square of HDD absolute acceleration due to a base random excitation. The presented random excitation is considered as a stationary, zero mean process with Gaussian distribution. In addition, eleven inequality constraints are defined based on geometrical limitations and allowable intervals of lumped modal parameters. The target of the optimization is to obtain optimum modal parameters of rubber mounts and rubber feet as design variables and subsequently propose new characteristics of rubber mounts and rubber feet to be manufactured for HDD protection against random excitation. In this paper, a nonlinear optimization problem is separately solved for three widely-used cases of HDD by using modified constrained steepest descent algorithm (PLBA) which was extended based on sequential quadratic programming. Finally, the genetic algorithm is used to verify results of the PLBA algorithm.

Inexact steepest descent algorithm for obtaining t-best approximation in a fuzzy normed space

The main aim of this paper is to find t-best approximation in a fuzzy normed space via the optimization formulation. It is formulated as a constrained minimization problem which is solved by using penalty method. Each penalty is solved by using inexact steepest descent algorithm.

A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.

A quantum bi-directional self-organizing neural network (QBDSONN) architecture for binary object extraction from a noisy perspective

This article proposes an efficient technique for binary object extraction in real time from noisy background using quantum bi-directional self-organizing neural network (QBDSONN) architecture. QBDSONN exploits the power of quantum computation. It is composed of three second order neighborhood topology based inter-connected layers of neurons (represented by qubits) arranged as input, intermediate and output layers. In the suggested network architecture, the inter-connection weights and activation values are represented by rotation gates. A self-supervised learning algorithm, suggested in this proposed architecture, relies on the steepest descent algorithm. The quantum neurons enjoy full-connectivity in each layer of the network architecture. The image pixels in terms of qubits are self-organized in between the intermediate or hidden and output layers of the QBDSONN architecture using counter-propagation of the quantum states to obviate time consuming quantum back propagation algorithm. In the final phase, quantum measurement is carried out at the output layer to eliminate superposition of the quantum states of the outputs. In order to establish the result, the proposed QBDSONN architecture is applied on an artificial synthetic and on a real life spanner image with different degrees of uniform and Gaussian noises. Experimental results show that QBDSONN outperforms both its classical counterpart and the supervised auto-associative Hopfield network as far as extraction time is concerned and it retains the shapes of the extracted images with great precision. Experiments are also carried out using a linear method named local statistics (Wiener filter) and a nonlinear technique named median filter with adaptive discrete wavelet transformations (DWT) for binary object extraction to show the dominance of the proposed QBDSONN with respect to the quality of extracted images. Finally, a statistical significance of the proposed QBDSONN is reported by applying 2 sample one sided Kolmogorov–Smirnov test with the existing methods.

LADRC-based attitude decoupling control for helicopter and parameters tuning

To meet the ADS-33E-PRF flight quality and effectively overcome the influence of external disturbance,an attitude control strategy based on a linear active disturbance rejection control( LADRC) is proposed for helicopter. Flight dynamics model of UH-60 A and the wind model were established. UH-60 A was trimmed for verifying accuracy of dynamic model and trim algorithm. Helicopter attitude decoupling control loop based on the single input / single output second-order LADRC controller was set up with stabilization feedback loop. The controller parameter tuning problem was transformed into constrained optimization problem in time and frequency domain according to quality requirement of ADS-33E-PRF. Combining H-infinity synthesis algorithm and steepest descent algorithm,the optimization of parameters was calculated. Quality assessment of attitude control was made and the control loop was applied to the attitude hold control simulation in atmospheric disturbance. The results of simulation and quality evaluation show that the attitude control system based on LADRC has good decoupling performance and capability of anti-disturbance.

A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition

In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel and easily implementable, we first presents it in a general linear algebra setting, then we highlight its applicability to a parabolic optimal control problem, where we consider the blocs of unknowns with respect to the time dependency of the control variable. The parallel tasks, in the last problem, turn “on” the control during a specific time-window and turn it “off” elsewhere. We show that our algorithm significantly improves the computational time compared with recognized methods. Convergence analysis of the new optimal control algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency and the rapid convergence of the method.

Mann-type hybrid steepest-descent method for three nonlinear problems

We introduce a Mann-type hybrid steepest-descent iterative algorithm for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of general system of variational inequalities, the set of solutions of finitely many variational inequalities, and the set of common fixed points of finitely many nonexpansive mappings and a strict pseudocontraction in a real Hilbert space. We derive the strong convergence of the iterative algorithm to a common element of these sets, which also solves some hierarchical variational inequality.

A New Assisted History Matching Approach for Complex Reservoirs

This article describes the integration of mathematical models (Simplex and steepest descent algorithm) with global modification (through deeply geological studies) to increase the efficiency of history matching. This method can take full advantage of the gradient-based method (fast rate of convergence) and guarantee of finding a global minimum for inverse problems. The above method is applied to the Lower Miocene reservoir at White Tiger field, a highly heterogeneous reservoir, which has been producing under a naturally edge-water mechanism. A model that covers the upper formation of White Tiger field with 27 production wells and 8 injection wells is conditioned to 23 years of production history. The new assisted history matching approach provides an excellent match between simulation results and production data.

Stable adaptive output feedback controller for a class of uncertain non‐linear systems

This study deals with design of an adaptive output feedback tracking controller for a class of non-linear systems with unknown fixed control direction. By using neural networks and deriving adaptive rules based on the steepest descent algorithm, the authors present a stable output feedback control scheme, which is applicable to a wide class of unknown complicated non-linear systems. Therefore an approach based on the dynamic back propagation algorithm is proposed to develop the adaption laws for systems with more general model structure. Using Lyapunov's direct method, uniformly ultimately boundedness of all signals of the closed-loop system is also ensured. Moreover, it is shown that the bounds on the tracking errors depend on the designing parameters. Hence, an arbitrarily small tracking error can be achieved by adjusting the parameters properly. Finally, simulation results performed on a non-affine uncertain non-linear system having internal dynamics are given to demonstrate the effectiveness of the proposed scheme and the theoretical discussions.

Automated Kernel Independent Component Analysis Based Two Variable Weighted Multi-view Clustering for Complete and Incomplete Dataset

In recent years, data are collected to a greater extent from several sources or represented by multiple views, in which different views express different point of views of the data. Even though each view might be individually exploited for discovering patterns by clustering, the clustering performance could be further perfect by exploring the valuable information among multiple views. On the other hand, several applications offer only a partial mapping among the two levels of variables such as the view weights and the variables weights views, developing a complication for current approaches, since incomplete view of the data are not supported by these approaches. In order to overcome this complication, proposed a Kernel-based Independent Component Analysis (KICA) based on steepest descent subspace two variables weighted clustering in this study and it is named as KICASDSTWC that can execute with an incomplete mapping. Independent Component Analysis (ICA) which exploit distinguish operations depending on canonical correlations in a reproducing kernel Hilbert space. Centroid values of the subspace clustering approaches are optimized depending on steepest descent algorithm and Artificial Fish Swarm Optimization (AFSO) algorithm for the purpose of weight calculation to recognize the compactness of the view and a variable weight. This framework permits the integration of complete and incomplete views of data. Experimental observations on three real-life data sets and the outcome have revealed that the proposed KICASDSTWC considerably outperforms all the competing approaches in terms of Precision, Recall, F Measure, Average Cluster Entropy (ACE) and Accuracy for both complete and incomplete view of the data with respect to the true clusters in the data.

Optimal Layering Time Control for Stepped-Concurrent Radiative Curing Process

This paper makes the following main proposals: (1) a stepped-concurrent curing (SCC) approach for making thick parts using ultraviolet (UV) radiative curing and (2) an optimal interlayer hold time control scheme to maximize the benefit of the SCC approach. The SCC approach seeks to reduce cure level deviations across a thick part by introducing new layers before earlier ones cure completely. A model of the UV curing process that includes the coupled cure kinetics and heat transfer is used to motivate the SCC scheme as well as the inherent optimization problem in this process. Then, the SCC process is cast as a hybrid system in which the addition of each layer switches the underlying state space to one with a higher dimension. Minimization of the overall cure deviation is set as the objective of the process and the necessary conditions for the optimal interlayer hold time control sequence are explicitly derived and solved via a steepest descent algorithm. Applications of the proposed scheme to a composite laminate curing process show that the so computed optimal layering time control sequence indeed gives the best performance in terms of closely tracking a target cure level distribution, compared to equal-time SCC or one-shot curing of the whole thick part.

A study on the optimal double parameters for steepest descent with momentum.

This letter presents the stability analysis for two steepest descent algorithms with momentum for quadratic functions. The corresponding local optimal parameters in Torii and Hagan ( 2002 ) and Zhang ( 2013 ) are extended to the global optimal parameters, that is, both the optimal learning rates and the optimal momentum factors are obtained simultaneously which make for the fastest convergence.

Iterative methods for triple hierarchical variational inequalities with mixed equilibrium problems, variational inclusions, and variational inequalities constraints

In this paper, we introduce and analyze a multi-step hybrid steepest-descent extragradient algorithm and multi-step composite Mann-type viscosity iterative algorithm for finding a solution of triple hierarchical variational inequalities defined over the common set of solutions of mixed equilibrium problems, variational inclusions, variational inequalities, and fixed point problems. Under appropriate assumptions, we prove that the proposed algorithms converge strongly to a common element of the fixed point set of a strict pseudocontractive mapping, a solution set of finitely many generalized mixed equilibrium problems, a solution set of finitely many variational inclusions, and a solution set of a general system of variational inequalities. Such an element is a unique solution of a triple hierarchical variational inequality problem. In addition, we also consider as an application the proposed algorithm to solve a hierarchical variational inequality problem defined over the set of common solutions of finitely many generalized mixed equilibrium problems, finitely many variational inclusions, and a general system of variational inequalities. The results obtained in this paper improve and extend the corresponding results announced by many other authors.

3D from 2D for Nano images using images processing methods

The scanning electron microscope (SEM) remains a main tool for semiconductor and polymer physics but TEM and AFM are increasingly used for minimum size features which called nanomaterials. In addition some physical properties such as microhardness, grain boundaries and domain structure are observed from optical and polarizing microscope which gives poor information and consequentially the error probability of discussion will be high. Thus it is natural to squeeze out every possible bit of resolution in the SEM, optical and polarizing microscopes for the materials under test. In our paper we will tackling this problem using different image processing techniques to get more clarify and sufficient information. In the suggested paper we will obtain set of images for prepared samples under different conditions and with different physical properties. These images will be analyzed using the above mentioned technique which starting by converting the prepared samples images (gray scale or colored images) to data file (*.dat) in two dimensional using programming. The 2D data will convert to 3D data file using FORTRAN programming. All images will subject to the generate filter algorithm for 3D data file. After filtering the 3D data file we can establish histogram, contours and 3D surface to analysis the image. Another technique will be prepared using Visual FORTRAN for steepest descent algorithm (SDA) which gives the vector map for the obtained data. Finally the depth from one single still image will be created and determine using OpenGL library under Visual C++ language, as well as, perform texture mapping. The quality of filtering depends on the way the data is incorporated into the model. Data should be treated carefully. From our paper we can analysis any part from any image without reanalysis the image, all size of the image as in this paper we take three samples with different size (256 * 256), (400 * 400), (510 * 510), this method decrees the cost of hardware and sample.

3D from 2D for Nano images using images processing methods

The scanning electron microscope (SEM) remains a main tool for semiconductor and polymer physics but TEM and AFM are increasingly used for minimum size features which called nanomaterials. In addition some physical properties such as microhardness, grain boundaries and domain structure are observed from optical and polarizing microscope which gives poor information and consequentially the error probability of discussion will be high.Thus it is natural to squeeze out every possible bit of resolution in the SEM, optical and polarizing microscopes for the materials under test. In our paper we will tackling this problem using different image processing techniques to get more clarify and sufficient information.In the suggested paper we will obtain set of images for prepared samples under different conditions and with different physical properties. These images will be analyzed using the above mentioned technique which starting by converting the prepared samples images (gray scale or colored images) to data file (*.dat) in two dimensional using programming. The 2D data will convert to 3D data file using FORTRAN programming. All images will subject to the generate filter algorithm for 3D data file. After filtering the 3D data file we can establish histogram, contours and 3D surface to analysis the image. Another technique will be prepared using Visual FORTRAN for steepest descent algorithm (SDA) which gives the vector map for the obtained data. Finally the depth from one single still image will be created and determine using OpenGL library under Visual C++ language, as well as, perform texture mapping. The quality of filtering depends on the way the data is incorporated into the model. Data should be treated carefully. From our paper we can analysis any part from any image without reanalysis the image, all size of the image as in this paper we take three samples with different size (256 * 256), (400 * 400), (510 * 510), this method decrees the cost of hardware and sample.

Optimization on the space of rigid and flexible motions: an alternative manifold optimization approach.

In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.

Optimal Forebody Shape for Minimum Drag in Supersonic Flow

In this work, a simple and efficient numerical approach to determine the shape of the minimum-drag axisymmetric forebody in inviscid supersonic flow with an attached shock constraint has been described. Taylor–Maccoll equation in conjunction with the tangent cone method is employed to estimate the pressure drag coefficient which is also chosen as the cost function. The forebody geometry is parameterized using a Non-Uniform Rational B-Splines (NURBS) curve whose control points are the design variables for optimisation using the steepest descent algorithm. Numerical studies demonstrate that the optimal forebody geometry for a given length and base radius has as much as 15 % lesser drag, depending on the Mach number than a cone of the same fineness ratio and that the convergence to the optimal solution exhibits a relatively weak Mach-number dependence.

Linear Relaying Design for Spectrum Sharing Non-regenerative MIMO Cognitive Multiple-Relay Systems

In this paper, we study optimal precoding matrix for spectrum sharing multiple-input multiple-output (MIMO) cognitive multiple-relay systems. Our aim is to maximize the system capacity subject to the total relay transmit power constraint and the interference power constraint at the primary user. For general case, all the nodes have multiple antennas. The precoder design problem is a non-convex problem. Currently there is no global optimal solution for it. We propose a suboptimal algorithm in which we first transform the original precoder design problem to a unitary matrix constrained problem. And then, we develop a modified Riemannian steepest descent algorithm (MRSDA) to solve it. For the special case that the secondary user has a single antenna and other nodes have multi-antennas, we propose an optimal solution based on rank-one decomposition theorem to transform the original problem into a semidefinite programming. Simulation results demonstrate the effectiveness of the proposed precoding matrix design algorithms.

Comparison of Split-Step Fourier Schemes for Simulating Fiber Optic Communication Systems

This paper mainly focuses on efficient schemes for simulating propagation in optical fibers. Various schemes based on split-step Fourier techniques to solve the nonlinear Schrodinger equation (NLSE), which describes the propagation in optical fibers, are compared. In general, the schemes in which the loss operator is combined with nonlinearity operator are found to be more computationally efficient than the schemes in which the loss is combined with dispersion. When the global error is large, the schemes with variable step size outperform the ones with uniform step size. The schemes based on local error and/or minimum area mismatch (MAM) further improve the computational efficiency. In this scheme, by minimizing the area mismatch between the exponential profile and its stepwise approximation, an optimal step size distribution is found. The optimization problem is solved by the steepest descent algorithm. The number of steps to get the desired accuracy is determined by the local error method. The proposed scheme is found to have higher computational efficiency than the other schemes studied in this paper. For QPSK systems, when the global error is 10 -8 , the number of fast Fourier transforms (FFTs) needed for the conventional scheme (loss combined with dispersion and uniform step size) is 5.8 times that of the proposed scheme. When the global error is 10 -6 , the number of FFTs needed for the conventional scheme is 3.7 times that of the proposed scheme.