scholarly journals GENETIC ALGORITHMS FOR MULTIDIMENSIONAL SCALING / GENETINIŲ ALGORITMŲ TAIKYMAS DAUGIAMATĖMS SKALĖMS

2015 ◽  
Vol 7 (3) ◽  
pp. 275-279 ◽  
Author(s):  
Agnė Dzidolikaitė
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Multidimensional Scaling ◽  
Optimization Problem ◽  
Dimensional Space ◽  
Local Solution ◽  
Multidimensional Data ◽  
Global Optimization Problem ◽  
Lower Dimensional Space ◽  
Lower Dimensional

The paper analyzes global optimization problem. In order to solve this problem multidimensional scaling algorithm is combined with genetic algorithm. Using multidimensional scaling we search for multidimensional data projections in a lower-dimensional space and try to keep dissimilarities of the set that we analyze. Using genetic algorithms we can get more than one local solution, but the whole population of optimal points. Different optimal points give different images. Looking at several multidimensional data images an expert can notice some qualities of given multidimensional data. In the paper genetic algorithm is applied for multidimensional scaling and glass data is visualized, and certain qualities are noticed. Analizuojamas globaliojo optimizavimo uždavinys. Jis apibrėžiamas kaip netiesinės tolydžiųjų kintamųjų tikslo funkcijos optimizavimas leistinojoje srityje. Optimizuojant taikomi įvairūs algoritmai. Paprastai taikant tikslius algoritmus randamas tikslus sprendinys, tačiau tai gali trukti labai ilgai. Dažnai norima gauti gerą sprendinį per priimtiną laiko tarpą. Tokiu atveju galimi kiti – euristiniai, algoritmai, kitaip dar vadinami euristikomis. Viena iš euristikų yra genetiniai algoritmai, kopijuojantys gyvojoje gamtoje vykstančią evoliuciją. Sudarant algoritmus naudojami evoliuciniai operatoriai: paveldimumas, mutacija, selekcija ir rekombinacija. Taikant genetinius algoritmus galima rasti pakankamai gerus sprendinius tų uždavinių, kuriems nėra tikslių algoritmų. Genetiniai algoritmai taip pat taikytini vizualizuojant duomenis daugiamačių skalių metodu. Taikant daugiamates skales ieškoma daugiamačių duomenų projekcijų mažesnio skaičiaus matmenų erdvėje siekiant išsaugoti analizuojamos aibės panašumus arba skirtingumus. Taikant genetinius algoritmus gaunamas ne vienas lokalusis sprendinys, o visa optimumų populiacija. Skirtingi optimumai atitinka skirtingus vaizdus. Matydamas kelis daugiamačių duomenų variantus, ekspertas gali įžvelgti daugiau daugiamačių duomenų savybių. Straipsnyje genetinis algoritmas pritaikytas daugiamatėms skalėms. Parodoma, kad daugiamačių skalių algoritmą galima kombinuoti su genetiniu algoritmu ir panaudoti daugiamačiams duomenims vizualizuoti.

scholarly journals TESTING THE RELATIONAL PERSPECTIVE MAP FOR VISUALIZATION OF MULTIDIMENSIONAL DATA

2006 ◽  
Vol 12 (4) ◽  
pp. 289-294 ◽  
Author(s):  
Rasa Karbauskaitė ◽  
Virginijus Marcinkevičius ◽  
Gintautas Dzemyda
Keyword(s):  
Dimensional Space ◽  
Multidimensional Data ◽  
Two Dimensional ◽  
Relational Perspective ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Better Than ◽  
Closed Plane

This paper deals with a method, called the relational perspective map that visualizes multidimensional data onto two‐dimensional closed plane. It tries to preserve the distances between the multidimensional data in the lower‐dimensional space. But the most important feature of the relational perspective map is the ability to visualize data in a non‐overlapping manner so that it reveals small distances better than other known visualization methods. In this paper, the features of this method are explored experimentally and some disadvantages are noticed. We have proposed a modification of this method, which enables us to avoid them.

Methods for Binary Multidimensional Scaling

2002 ◽  
Vol 14 (5) ◽  
pp. 1195-1232 ◽  
Author(s):  
Douglas L. T. Rohde
Keyword(s):  
Neural Networks ◽  
Multidimensional Scaling ◽  
Dimensional Space ◽  
Discrete Space ◽  
High Dimensional ◽  
Continuous Space ◽  
Low Dimensional ◽  
Set Of Points ◽  
Lower Dimensional Space ◽  
Lower Dimensional

Multidimensional scaling (MDS) is the process of transforming a set of points in a high-dimensional space to a lower-dimensional one while preserving the relative distances between pairs of points. Although effective methods have been developed for solving a variety of MDS problems, they mainly depend on the vectors in the lower-dimensional space having real-valued components. For some applications, the training of neural networks in particular, it is preferable or necessary to obtain vectors in a discrete, binary space. Unfortunately, MDS into a low-dimensional discrete space appears to be a significantly harder problem than MDS into a continuous space. This article introduces and analyzes several methods for performing approximately optimized binary MDS.

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

scholarly journals Interface-targeted seismic velocity estimation using machine learning

2019 ◽  
Vol 218 (1) ◽  
pp. 45-56 ◽  
Author(s):  
C Nur Schuba ◽  
Jonathan P Schuba ◽  
Gary G Gray ◽  
Richard G Davy
Keyword(s):  
Neural Network ◽  
Regression Model ◽  
Dimensional Space ◽  
Seismic Profile ◽  
Velocity Estimation ◽  
Seismic Survey ◽  
Wide Angle ◽  
Seismic Velocities ◽  
Lower Dimensional Space ◽  
Lower Dimensional

SUMMARY We present a new approach to estimate 3-D seismic velocities along a target interface. This approach uses an artificial neural network trained with user-supplied geological and geophysical input features derived from both a 3-D seismic reflection volume and a 2-D wide-angle seismic profile that were acquired from the Galicia margin, offshore Spain. The S-reflector detachment fault was selected as the interface of interest. The neural network in the form of a multilayer perceptron was employed with an autoencoder and a regression layer. The autoencoder was trained using a set of input features from the 3-D reflection volume. This set of features included the reflection amplitude and instantaneous frequency at the interface of interest, time-thicknesses of overlying major layers and ratios of major layer time-thicknesses to the total time-depth of the interface. The regression model was trained to estimate the seismic velocities of the crystalline basement and mantle from these features. The ‘true’ velocities were obtained from an independent full-waveform inversion along a 2-D wide-angle seismic profile, contained within the 3-D data set. The autoencoder compressed the vector of inputs into a lower dimensional space, then the regression layer was trained in the lower dimensional space to estimate velocities above and below the targeted interface. This model was trained on 50 networks with different initializations. A total of 37 networks reached minimum achievable error of 2 per cent. The low standard deviation (<300  m s−1) between different networks and low errors on velocity estimations demonstrate that the input features were sufficient to capture variations in the velocity above and below the targeted S-reflector. This regression model was then applied to the 3-D reflection volume where velocities were predicted over an area of ∼400 km2. This approach provides an alternative way to obtain velocities across a 3-D seismic survey from a deep non-reflective lithology (e.g. upper mantle) , where conventional reflection velocity estimations can be unreliable.

Optimization of Radial Cams with Translating Roller Follower through Genetic Algorithms

2015 ◽  
Vol 783 ◽  
pp. 83-94
Author(s):  
Alberto Borboni
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Contact Pressure ◽  
Optimization Problem ◽  
Optimization Method ◽  
Optimization Process ◽  
Radius Of Curvature ◽  
Design Problems ◽  
Computational Optimization ◽  
Different Types

In this work, the optimization problem is studied for a planar cam which rotates around its axis and moves a centered translating roller follower. The proposed optimization method is a genetic algorithm. The paper deals with different design problems: the minimization of the pressure angle, the maximization of the radius of curvature and the minimization of the contact pressure. Different types of motion laws are tested to found the most suitable for the computational optimization process.

Optimization of Multi-Modal Discrete Functions Using Genetic Algorithms

1993 ◽  
Vol 207 (1) ◽  
pp. 53-59 ◽  
Author(s):  
D T Pham ◽  
Y Yang
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimization Problem ◽  
Approximate Solutions ◽  
Solution Set ◽  
Preliminary Design ◽  
Potential Solution ◽  
Reproduction Cycle ◽  
Fitness Sharing ◽  
Discrete Functions

Four techniques are described which can help a genetic algorithm to locate multiple approximate solutions to a multi-modal optimization problem. These techniques are: fitness sharing, ‘eliminating’ identical solutions, ‘removing’ acceptable solutions from the reproduction cycle and applying heuristics to improve sub-standard solutions. Essentially, all of these techniques operate by encouraging genetic variety in the potential solution set. The preliminary design of a gearbox is presented as an example to illustrate the effectiveness of the proposed techniques.

scholarly journals Truss’ topology and shape optimization by genetic algorithms

2021 ◽  
Vol 47 ◽  
Author(s):  
Dmitrij Šešok ◽  
Paulius Ragauskas
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Search Algorithm ◽  
Truss Topology ◽  
Modified Genetic Algorithm ◽  
Topology And Shape Optimization ◽  
System Characteristics

In the paper the global optimization problem of truss systems is studied.  The genetic algorithms are employed for the optimization. As the objective function the structure mass is treated; the constraints include equilibrium, local stability and other requirements.  All the truss system characteristics needed for genetic algorithm are obtained via finite element solution. Topology optimization of truss system is performed using original modified genetic algorithm, while the shape optimization – using ordinary genetic algorithm. Numerical solutions are presented. The obtained solutions are compared with global extremes obtained using full search algorithm.  All the numerical examples are solved using original software.

Research on Multi-Objective Transmission Planning in Electricity Markets

2012 ◽  
Vol 516-517 ◽  
pp. 1429-1432
Author(s):  
Yang Liu ◽  
Xu Liu ◽  
Feng Xian Cui ◽  
Liang Gao
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Genetic Algorithms ◽  
Electricity Markets ◽  
Optimization Problem ◽  
Nsga Ii ◽  
Transmission Planning ◽  
Multi Objective ◽  
Complex Optimization ◽  
The Mathematical Model

Abstract. Transmission planning is a complex optimization problem with multiple deciding variables and restrictions. The mathematical model is non-linear, discrete, multi-objective and dynamic. It becomes complicated as the system grows. So the algorithm adopted affects the results of planning directly. In this paper, a fast non-dominated sorting genetic algorithm (NSGA-II) is employed. The results indicate that NSGA-II has some advantages compared to the traditional genetic algorithms. In transmission planning, NSGA-II is feasible, flexible and effective.

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