scholarly journals Transformation Method for Solving System of Boolean Algebraic Equations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3299
Author(s):  
Dostonjon Barotov ◽  
Aleksey Osipov ◽  
Sergey Korchagin ◽  
Ekaterina Pleshakova ◽  
Dilshod Muzafarov ◽  
...  
Keyword(s):  
Harmonic Polynomial ◽  
Optimization Methods ◽  
Optimization Method ◽  
Transformation Method ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Algebraic Equations ◽  
Logical Operations ◽  
Dimensional Cube ◽  
The Right

: In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube Kn with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.

scholarly journals Advanced Interior Optimization Methods with Electronics Applications

2021 ◽  
pp. 97-110
Author(s):  
Francisco Casesnoves
Keyword(s):  
Nonlinear Systems ◽  
Numerical Optimization ◽  
Global Minimum ◽  
Optimization Methods ◽  
Optimization Method ◽  
Systems Of Nonlinear Equations ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Further Development

<p>In a previous contribution, the mathematical-computational base of Interior Optimization Method was demonstrated. Electronics applications were performed with numerical optimization data and graphical proofs. In this evoluted-improved paper a series of electronics applications of Interior Optimization in superconductors BCS algorithms/theory are shown. In addition, mathematical developments of Interior Optimization Methods related to systems of Nonlinear Equations are proven. The nonlinear multiobjective optimization problem constitutes a difficult task to find/determine a global minimum, approximated-global minimum, or a convenient local minimum whith/without constraints. Nonlinear systems of equations principles set the base in the previous article for further development of Interior Optimization and Interior-Graphical Optimization [Casesnoves, 2016-7]. From Graphical Optimization 3D optimization stages [Casesnoves, 2016-7], the demonstration that solution of nonlinear systems of equations is not unique in general emerges. Software-engineering and computational simulations are shown with electronics superconductors [several elements, Type 1 superconductors] and electronics physics applications. Extensions to similar applications for materials-tribology models and Biomedical Tribology are explained.</p>

CAN GLOBAL OPTIMIZATION TECHNIQUE COMPENSATE FOR MARKER SKIN MOVEMENT IN RAT KINEMATICS?

2014 ◽  
Vol 14 (05) ◽  
pp. 1450065 ◽  
Author(s):  
FILIPA JOÃO ◽  
ANTÓNIO VELOSO ◽  
SANDRA AMADO ◽  
PAULO ARMADA-DA-SILVA ◽  
ANA C. MAURÍCIO
Keyword(s):  
Global Optimization ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Optimization Methods ◽  
Optimization Method ◽  
Anatomical Landmarks ◽  
Global Optimization Method ◽  
Skin Deformation ◽  
Angular Displacements ◽  
The Right

The motion of the skeletal estimated from skin attached marker-based motion capture(MOCAP) systems is known to be affected by significant bias caused by anatomical landmarks mislocation but especially by soft tissue artifacts (such as skin deformation and sliding, inertial effects and muscle contraction). As a consequence, the error associated with this bias can propagate to joint kinematics and kinetics data, particularly in small rodents. The purpose of this study was to perform a segmental kinematic analysis of the rat hindlimb during locomotion, using both global optimization as well as segmental optimization methods. Eight rats were evaluated for natural overground walking and motion of the right hindlimb was captured with an optoeletronic system while the animals walked in the track. Three-dimensional (3D) biomechanical analyses were carried out and hip, knee and ankle joint angular displacements and velocities were calculated. Comparison between both methods demonstrated that the magnitude of the kinematic error due to skin movement increases in the segmental optimization when compared with the global optimization method. The kinematic results assessed with the global optimization method matches more closely to the joint angles and ranges of motion calculated from bone-derived kinematics, being the knee and hip joints with more significant differences.

scholarly journals Target Localization Based on Bistatic T/R Pair Selection in GNSS-Based Multistatic Radar System

2021 ◽  
Vol 13 (4) ◽  
pp. 707
Author(s):  
Yu’e Shao ◽  
Hui Ma ◽  
Shenghua Zhou ◽  
Xue Wang ◽  
Michail Antoniou ◽  
...  
Keyword(s):  
Optimization Methods ◽  
Optimization Method ◽  
Satellite System ◽  
Radar System ◽  
Target Localization ◽  
Computational Load ◽  
Matrix Fusion ◽  
Global Navigation Satellite ◽  
Multistatic Radar ◽  
Combined Algorithm

To cope with the increasingly complex electromagnetic environment, multistatic radar systems, especially the passive multistatic radar, are becoming a trend of future radar development due to their advantages in anti-electronic jam, anti-destruction properties, and no electromagnetic pollution. However, one problem with this multi-source network is that it brings a huge amount of information and leads to considerable computational load. Aiming at the problem, this paper introduces the idea of selecting external illuminators in the multistatic passive radar system. Its essence is to optimize the configuration of multistatic T/R pairs. Based on this, this paper respectively proposes two multi-source optimization algorithms from the perspective of resolution unit and resolution capability, the Covariance Matrix Fusion Method and Convex Hull Optimization Method, and then uses a Global Navigation Satellite System (GNSS) as an external illuminator to verify the algorithms. The experimental results show that the two optimization methods significantly improve the accuracy of multistatic positioning, and obtain a more reasonable use of system resources. To evaluate the algorithm performance under large number of transmitting/receiving stations, further simulation was conducted, in which a combination of the two algorithms were applied and the combined algorithm has shown its effectiveness in minimize the computational load and retain the target localization precision at the same time.

scholarly journals Exploration of Semantic Geo-Object Recognition Based on the Scale Parameter Optimization Method for Remote Sensing Images

2021 ◽  
Vol 10 (6) ◽  
pp. 420
Author(s):  
Jun Wang ◽  
Lili Jiang ◽  
Qingwen Qi ◽  
Yongji Wang
Keyword(s):  
Parameter Optimization ◽  
Scale Parameter ◽  
Human Perception ◽  
Optimization Methods ◽  
Optimization Method ◽  
Initiation Point ◽  
Scale Parameters ◽  
Object Based ◽  
Geographic Object ◽  
Multiresolution Segmentation

Image segmentation is of significance because it can provide objects that are the minimum analysis units for geographic object-based image analysis (GEOBIA). Most segmentation methods usually set parameters to identify geo-objects, and different parameter settings lead to different segmentation results; thus, parameter optimization is critical to obtain satisfactory segmentation results. Currently, many parameter optimization methods have been developed and successfully applied to the identification of single geo-objects. However, few studies have focused on the recognition of the union of different types of geo-objects (semantic geo-objects), such as a park. The recognition of semantic geo-objects is likely more crucial than that of single geo-objects because the former type of recognition is more correlated with the human perception. This paper proposes an approach to recognize semantic geo-objects. The key concept is that a single geo-object is the smallest component unit of a semantic geo-object, and semantic geo-objects are recognized by iteratively merging single geo-objects. Thus, the optimal scale of the semantic geo-objects is determined by iteratively recognizing the optimal scales of single geo-objects and using them as the initiation point of the reset scale parameter optimization interval. In this paper, we adopt the multiresolution segmentation (MRS) method to segment Gaofen-1 images and tested three scale parameter optimization methods to validate the proposed approach. The results show that the proposed approach can determine the scale parameters, which can produce semantic geo-objects.

Comparison between Optimization Method and Experience-Based Method in Soil Conservation

2013 ◽  
Vol 726-731 ◽  
pp. 3811-3817
Author(s):  
Yuan Feng ◽  
Ji Xian Wang
Keyword(s):  
Slope Stability ◽  
Soil Conservation ◽  
Computer Aided Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Interaction Function ◽  
The Standard Model ◽  
Computer Aided ◽  
Slice Method ◽  
Aided Design

The analysis of the slope stability is important in soil conservation. To analyze the slope stability, optimization methods were coded and compared with the traditional experience-based methods. Furthermore, the results were visualized in the program, so that the user can easily check the results and can designate an area, in which the program seeks the center and radius of the most hazardous slide arc. Moreover, the graphic interaction function was implemented in the program. In addition, the Standard Model One, recommended by ACAD (The Association for Computer Aided Design), was calculated by the program, of which the results (safety factor Ks=0.95~0.96) were smaller than the official recommend value (Ks=1). It is because that the traditional slice method, which neglects the normal stress and shear stress between the slices, was applied for calculation of Ks.

Nonsmooth Optimization Method for Image Restoration

1995 ◽  
Author(s):  
Kazufumi Ito ◽  
Karl Kunisch
Keyword(s):  
Image Restoration ◽  
Nonsmooth Optimization ◽  
Numerical Optimization ◽  
Augmented Lagrangian ◽  
Energy Criterion ◽  
Optimization Methods ◽  
Optimization Method ◽  
Augmented Lagrangian Methods ◽  
Active Set ◽  
First Order

Abstract In this paper we discuss applications of the numerical optimization methods for nonsmooth optimization, developed in [IK1] for the variational formulation of image restoration problems involving bounded variation type energy criterion. The Uzawa’s algorithm, first order augmented Lagrangian methods and Newton-like update using the active set strategy are described.

Design Optimization Method for MR-Brake Actuators

2011 ◽  
Author(s):  
Ozan G. Erol ◽  
Hakan Gurocak ◽  
Berk Gonenc
Keyword(s):  
Optimal Solution ◽  
Volume Ratio ◽  
Optimization Methods ◽  
Search Space ◽  
Optimization Method ◽  
Friction Torque ◽  
Element Analysis ◽  
Taguchi Design Of Experiments ◽  
Variable Friction ◽  
Electronically Controllable

MR-brakes work by varying viscosity of a magnetorheological (MR) fluid inside the brake. This electronically controllable viscosity leads to variable friction torque generated by the actuator. A properly designed MR-brake can have a high torque-to-volume ratio which is quite desirable for an actuator. However, designing an MR-brake is a complex process as there are many parameters involved in the design which can affect the size and torque output significantly. The contribution of this study is a new design approach that combines the Taguchi design of experiments method with parameterized finite element analysis for optimization. Unlike the typical multivariate optimization methods, this approach can identify the dominant parameters of the design and allows the designer to only explore their interactions during the optimization process. This unique feature reduces the size of the search space and the time it takes to find an optimal solution. It normally takes about a week to design an MR-brake manually. Our interactive method allows the designer to finish the design in about two minutes. In this paper, we first present the details of the MR-brake design problem. This is followed by the details of our new approach. Next, we show how to design an MR-brake using this method. Prototype of a new brake was fabricated. Results of experiments with the prototype brake are very encouraging and are in close agreement with the theoretical performance predictions.

scholarly journals Evolutionary optimization in classification of early-MCI patients from healthy controls using graph measures of resting-state fMRI

2021 ◽  
Author(s):  
Jafar Zamani ◽  
Ali Sadr ◽  
Amir-Homayoun Javadi
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Functional Connectivity ◽  
Evolutionary Algorithms ◽  
Resting State ◽  
Optimization Methods ◽  
Resting State Fmri ◽  
Optimization Method ◽  
Effective Parameters

AbstractsIdentifying individuals with early mild cognitive impairment (EMCI) can be an effective strategy for early diagnosis and delay the progression of Alzheimer’s disease (AD). Many approaches have been devised to discriminate those with EMCI from healthy control (HC) individuals. Selection of the most effective parameters has been one of the challenging aspects of these approaches. In this study we suggest an optimization method based on five evolutionary algorithms that can be used in optimization of neuroimaging data with a large number of parameters. Resting-state functional magnetic resonance imaging (rs-fMRI) measures, which measure functional connectivity, have been shown to be useful in prediction of cognitive decline. Analysis of functional connectivity data using graph measures is a common practice that results in a great number of parameters. Using graph measures we calculated 1155 parameters from the functional connectivity data of HC (n=36) and EMCI (n=34) extracted from the publicly available database of the Alzheimer’s disease neuroimaging initiative database (ADNI). These parameters were fed into the evolutionary algorithms to select a subset of parameters for classification of the data into two categories of EMCI and HC using a two-layer artificial neural network. All algorithms achieved classification accuracy of 94.55%, which is extremely high considering single-modality input and low number of data participants. These results highlight potential application of rs-fMRI and efficiency of such optimization methods in classification of images into HC and EMCI. This is of particular importance considering that MRI images of EMCI individuals cannot be easily identified by experts.

scholarly journals CONSTRUCTAL DESIGN AND SIMULATED ANNEALING EMPLOYED FOR GEOMETRIC OPTIMIZATION OF A Y-SHAPED CAVITY INTRUDED INTO CONDUCTIVE WALL

2015 ◽  
Vol 14 (1) ◽  
pp. 79
Author(s):  
G. V. Gonzales ◽  
E. D. Dos Santos ◽  
L. R. Emmendorfer ◽  
L. A. Isoldi ◽  
E. S. D. Estrada ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Solid Wall ◽  
Internal Heat ◽  
Optimization Methods ◽  
Optimization Method ◽  
Internal Heat Generation ◽  
Geometric Optimization ◽  
Constructal Design ◽  
Optimal Shapes

he problem study here is concerned with the geometrical evaluation of an isothermal Y-shaped cavity intruded into conducting solid wall with internal heat generation. The cavity acts as a sink of the heat generated into the solid. The main purpose here is to minimize the maximal excess of temperature (θmax) in the solid. Constructal Design, which is based on the objective and constraints principle, is employed to evaluate the geometries of Y-shaped cavity. Meanwhile, Simulated Annealing (SA) algorithm is employed as optimization method to seek for the best shapes. To validate the SA methodology, the results obtained with SA are compared with those achieved with Genetic Algorithm (GA) and Exaustive Search (ES) in recent studies of literature. The comparison between the optimization methods (SA, GA and ES) showed that Simulated Annealing is highly effective in the search for the optimal shapes of the studied case.

Smart Optimization of Machine Systems Using Hierarchical Genotype Representations

1999 ◽  
Author(s):  
Masataka Yoshimura ◽  
Kazuhiro Izui
Keyword(s):  
Structural Design ◽  
Hierarchical Structures ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Problems ◽  
Design Variables ◽  
The Hierarchical Structure ◽  
Machine Systems ◽  
System Designs ◽  
Crossover And Mutation

Abstract Design problems for machine products are generally hierarchically expressed. With conventional product optimization methods, it is difficult to concurrently optimize all design variables of portions within the hierarchical structure. This paper proposes a design optimization method using genetic algorithms containing hierarchical genotype representations, so that the hierarchical structures of machine system designs are exactly expressed through genotype coding, and optimization can be concurrently conducted for all of the hierarchical structures. Crossover and mutation operations for manipulating the hierarchical genotype representations are also developed. The proposed method is applied to a machine-tool structural design to demonstrate its effectiveness.

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