scholarly journals JUMPING FROG METHOD FOR OPTIMAL CLASSIFICATIONS

2021 ◽  
Author(s):  
Kozin I. V. ◽  
Selyutin E. K. ◽  
Polyuga S. I.
Keyword(s):  
Optimization Problem ◽  
Tolerance Relation ◽  
Suboptimal Solutions ◽  
Finite Set ◽  
Set Of Permutations ◽  
Optimal Classification

In the article the problem of finding optimal classifications on a finite set is investigated. It is shown that the problem of finding an optimal classification is generated by a tolerance relation on a finite set. It is also reduced to an optimization problem on a set of permutations. It is proposed a modification of the mixed jumping frogs to find suboptimal solutions of the problem of classification.

GENERALIZATION OF BAYESIAN RULE OF MANY SIMPLE HYPOTHESES TESTING

2003 ◽  
Vol 02 (01) ◽  
pp. 41-70 ◽  
Author(s):  
K. J. KACHIASHVILI
Keyword(s):  
Unconstrained Optimization ◽  
Bayesian Approach ◽  
Optimization Problem ◽  
Classical Case ◽  
Hypotheses Testing ◽  
Unconstrained Optimization Problem ◽  
Finite Set ◽  
Statistical Hypotheses ◽  
Space Point ◽  
Statistical Hypotheses Testing

There are different methods of statistical hypotheses testing.1–4 Among them, is Bayesian approach. A generalization of Bayesian rule of many hypotheses testing is given below. It consists of decision rule dimensionality with respect to the number of tested hypotheses, which allows to make decisions more differentiated than in the classical case and to state, instead of unconstrained optimization problem, constrained one that enables to make guaranteed decisions concerning errors of true decisions rejection, which is the key point when solving a number of practical problems. These generalizations are given both for a set of simple hypotheses, each containing one space point, and hypotheses containing a finite set of separated space points.

scholarly journals Generating Functions for Permutations which Contain a Given Descent Set

10.37236/299 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Jeffrey Remmel ◽  
Manda Riehl
Keyword(s):  
Symmetric Group ◽  
Generating Functions ◽  
Symmetric Function ◽  
Schur Functions ◽  
Permutation Statistics ◽  
Finite Set ◽  
Set Of Permutations ◽  
Descent Set ◽  
Positive Integers

A large number of generating functions for permutation statistics can be obtained by applying homomorphisms to simple symmetric function identities. In particular, a large number of generating functions involving the number of descents of a permutation $\sigma$, $des(\sigma)$, arise in this way. For any given finite set $S$ of positive integers, we develop a method to produce similar generating functions for the set of permutations of the symmetric group $S_n$ whose descent set contains $S$. Our method will be to apply certain homomorphisms to symmetric function identities involving ribbon Schur functions.

New proposals for modelling and solving the problem of covering solids using spheres of different radii

2020 ◽  
Vol 54 (3) ◽  
pp. 873-882
Author(s):  
Pedro Henrique González Silva ◽  
Ana Flávia U. S. Macambira ◽  
Renan Vicente Pinto ◽  
Luidi Simonetti ◽  
Nelson Maculan ◽  
...  
Keyword(s):  
Data Mining ◽  
Convex Optimization ◽  
Objective Function ◽  
Hybrid Method ◽  
Optimization Problem ◽  
Compact Set ◽  
Computational Results ◽  
Quadratic Constraints ◽  
Convex Optimization Problem ◽  
Finite Set

Given a solid T, represented by a compact set in ℝ3, the aim of this work is to find a covering of T by a finite set of spheres of different radii. Some level of intersection between the spheres is necessary to cover the solid. Moreover, the volume occupied by the spheres on the outside of T is limited. This problem has an application in the planning of a radio-surgery treatment known by Gamma Knife and can be formulated as a non-convex optimization problem with quadratic constraints and linear objective function. In this work, two new linear mathematical formulations with binary variables and a hybrid method are proposed. The hybrid method combines heuristic, data mining and an exact method. Computational results show that the proposed methods outperform the ones presented in the literature.

Solving the Processor Configuration Problems with a Mutation-Based Genetic Algorithm

1997 ◽  
Vol 06 (04) ◽  
pp. 567-585 ◽  
Author(s):  
T. L. Lau ◽  
E. P. K. Tsang
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problem ◽  
Real Life ◽  
Communication Channels ◽  
Data Representation ◽  
Maximum Distance ◽  
Constraint Optimization ◽  
Finite Set ◽  
Efficient Data ◽  
Configuration Problem

The Processor Configuration Problem (PCP) is a real life Constraint Optimization Problem. The task is to link up a finite set of processors into a network, whilst minimizing the maximum distance between these processors. Since each processor has a limited number of communication channels, a carefully planned layout will help reduce the overhead for message switching. In this paper, we present a Genetic Algorithm (GA) approach to the PCP. Our technique uses a mutation-based GA, a function that produces schemata by analyzing previous solutions, and an efficient data representation. Our approach has been shown to out-perform other published techniques in this problem.

scholarly journals A Computational Approach to Log-Concave Density Estimation

2015 ◽  
Vol 23 (3) ◽  
pp. 151-166
Author(s):  
Fabian Rathke ◽  
Christoph Schnörr
Keyword(s):  
Maximum Likelihood ◽  
Density Estimation ◽  
Optimization Problem ◽  
Higher Dimensions ◽  
Computational Approach ◽  
Estimation Accuracy ◽  
Trade Off ◽  
Computational Costs ◽  
Shape Restrictions ◽  
Finite Set

Abstract Non-parametric density estimation with shape restrictions has witnessed a great deal of attention recently. We consider the maximum-likelihood problem of estimating a log-concave density from a given finite set of empirical data and present a computational approach to the resulting optimization problem. Our approach targets the ability to trade-off computational costs against estimation accuracy in order to alleviate the curse of dimensionality of density estimation in higher dimensions.

On Maximum Discounted Effort Reward Search Problem

2016 ◽  
Vol 33 (03) ◽  
pp. 1650019 ◽  
Author(s):  
Mohamed Abd Allah El-Hadidy
Keyword(s):  
Optimization Problem ◽  
Random Variable ◽  
Fixed Number ◽  
Search Model ◽  
Search Problem ◽  
Time Intervals ◽  
Search Effort ◽  
Stochastic Optimization Problem ◽  
Finite Set ◽  
Fuzzy Parameter

In this paper, we formulate a new search model for detecting two related targets that randomly located in a finite set of different cells or randomly moved through those cells. We assume that the search effort at each fixed number of time intervals is a random variable with a normal distribution. Rather than minimizing the expected effort of detecting two related targets, the proposed mathematical model allows us to include the search effort as a function with fuzzy parameter (discounted parameter). Another feature of this paper is considering a fuzzy extension of a stochastic optimization problem, which is interesting. We present an algorithm that gives the optimal distribution of an effort which makes the discounted effort reward of finding the targets is maximum. Two numerical examples are illustrated to show the effectiveness of this model by setting some parameters to represent some situations, such as detecting the enemy ships, fighters and the landmines in the war.

scholarly journals Simulated annealing method for equilibrium placement problem

2021 ◽  
pp. 152-158
Author(s):  
Igor Kozin ◽  
Natalia Maksyshko ◽  
Yaroslav Tereshko
Keyword(s):  
Simulated Annealing ◽  
Optimization Problem ◽  
Simulated Annealing Algorithm ◽  
Optimal Solution ◽  
Placement Problem ◽  
Fragmentary Structure ◽  
Simulating Annealing ◽  
Set Of Permutations ◽  
Annealing Algorithm ◽  
The Traveling Salesman Problem

The paper proposes a modification of the simulated annealing algorithm as applied to problems that have a fragmented structure. An algorithm for simulating annealing for the traveling salesman problem is considered and its applicability to the optimization problem on a set of permutations is shown. It is proved that the problem of equilibrium placement of point objects on a plane has a fragmentary structure and, therefore, reduces to an optimization problem on a set of permutations. The results of numerical experiments for various types of algorithms for finding the optimal solution in the equilibrium placement problem are presented.

Constructing and Deconstructing Concepts

2016 ◽  
Vol 63 (5) ◽  
pp. 249-262 ◽  
Author(s):  
Charles A. Doan ◽  
Ronaldo Vigo
Keyword(s):  
Information Theory ◽  
Model Performance ◽  
Unsupervised Classification ◽  
Family Resemblance ◽  
Category Membership ◽  
Formal Models ◽  
Human Beings ◽  
One Dimensional ◽  
Relational Patterns ◽  
Optimal Classification

Abstract. Several empirical investigations have explored whether observers prefer to sort sets of multidimensional stimuli into groups by employing one-dimensional or family-resemblance strategies. Although one-dimensional sorting strategies have been the prevalent finding for these unsupervised classification paradigms, several researchers have provided evidence that the choice of strategy may depend on the particular demands of the task. To account for this disparity, we propose that observers extract relational patterns from stimulus sets that facilitate the development of optimal classification strategies for relegating category membership. We conducted a novel constrained categorization experiment to empirically test this hypothesis by instructing participants to either add or remove objects from presented categorical stimuli. We employed generalized representational information theory (GRIT; Vigo, 2011b , 2013a , 2014 ) and its associated formal models to predict and explain how human beings chose to modify these categorical stimuli. Additionally, we compared model performance to predictions made by a leading prototypicality measure in the literature.

Exergy and sensibility analysis of each individual effect in a kraft multiple effect evaporator

TAPPI Journal ◽  
2019 ◽  
Vol 18 (10) ◽  
pp. 607-618
Author(s):  
JÉSSICA MOREIRA ◽  
BRUNO LACERDA DE OLIVEIRA CAMPOS ◽  
ESLY FERREIRA DA COSTA JUNIOR ◽  
ANDRÉA OLIVEIRA SOUZA DA COSTA
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Kraft Pulping ◽  
Steam Temperature ◽  
Input Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Multiple Effect ◽  
Sensibility Analysis ◽  
Exergetic Analysis

The multiple effect evaporator (MEE) is an energy intensive step in the kraft pulping process. The exergetic analysis can be useful for locating irreversibilities in the process and pointing out which equipment is less efficient, and it could also be the object of optimization studies. In the present work, each evaporator of a real kraft system has been individually described using mass balance and thermodynamics principles (the first and the second laws). Real data from a kraft MEE were collected from a Brazilian plant and were used for the estimation of heat transfer coefficients in a nonlinear optimization problem, as well as for the validation of the model. An exergetic analysis was made for each effect individually, which resulted in effects 1A and 1B being the least efficient, and therefore having the greatest potential for improvement. A sensibility analysis was also performed, showing that steam temperature and liquor input flow rate are sensible parameters.

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