scholarly journals Application of dynamic programming methods for solving a problem on recruiting with considering specific content of military technical education

2021 ◽  
Vol 10 (2) ◽  
pp. 309-314
Author(s):  
Tatiana Evgenjevna Tarasova ◽  
Anatoly Vladimirovich Tarasov ◽  
Tatiana Sergeevna Smirnova
Keyword(s):  
Dynamic Programming ◽  
Computer Science ◽  
Military Service ◽  
Optimization Problems ◽  
Practical Knowledge ◽  
Optimization Theory ◽  
Task Assignment ◽  
Specific Content ◽  
Training Approach ◽  
High Level

This paper discusses the use of dynamic programming technologies in teaching cadets of military universities to solve optimization problems in the course of computer science. One of the key topics in such courses as higher mathematics and computer science in all civil and military technical universities is the optimization theory, familiarization with which is based on learning methods for solving a transport task, assignment problem, traveling salesman problem and others. An effective solution to this type of tasks is possible through automated computing tools, tabular processors, and programming systems. The specifics of training cadets at military universities dictates the need to formulate tasks with a focus on military-technical research. Optimization issues are considered as applied to possible real situations in the military service of future officers. The staffing task is solved through high-level programming. Some results of the comparative analysis of educational material assimilation in the control and experimental groups are given. A deeper understanding of the theoretical material by the cadets and confident practical knowledge of programming technologies and solving problems in general with the specified training approach are noted, and its confirmed by the results of the tests conducted by the authors of the paper.

HIGH LEVEL PARALLEL SKELETONS FOR DYNAMIC PROGRAMMING

2008 ◽  
Vol 18 (01) ◽  
pp. 133-147
Author(s):  
IGNACIO PELÁEZ ◽  
FRANCISCO ALMEIDA ◽  
DANIEL GONZÁLEZ
Keyword(s):  
Dynamic Programming ◽  
Problem Solving ◽  
Optimization Problems ◽  
Design Strategy ◽  
Parallel Architectures ◽  
Test Problems ◽  
Parallel Skeletons ◽  
Wide Range ◽  
Algorithmic Techniques ◽  
High Level

Dynamic Programming is an important problem-solving technique used for solving a wide variety of optimization problems. Dynamic Programming programs are commonly designed as individual applications and software tools are usually tailored to specific classes of recurrences and methodologies. That contrasts with some other algorithmic techniques where a single generic program may solve all the instances. We have developed a general skeleton tool providing support for a wide range of dynamic programming methodologies on different parallel architectures. Genericity, flexibility and efficiency are basic issues of the design strategy. Parallelism is supplied to the user in a transparent manner through a common sequential interface. A set of test problems representative of different classes of Dynamic Programming formulations has been used to validate our skeleton on an IBM-SP.

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

scholarly journals High-Level Parallel Ant Colony Optimization with Algorithmic Skeletons

2021 ◽  
Author(s):  
Breno A. de Melo Menezes ◽  
Nina Herrmann ◽  
Herbert Kuchen ◽  
Fernando Buarque de Lima Neto
Keyword(s):  
Ant Colony Optimization ◽  
High Performance ◽  
Optimization Problems ◽  
Programming Model ◽  
Parallel Implementation ◽  
Ant Colony ◽  
Algorithmic Skeletons ◽  
Low Level ◽  
Programming Patterns ◽  
High Level

AbstractParallel implementations of swarm intelligence algorithms such as the ant colony optimization (ACO) have been widely used to shorten the execution time when solving complex optimization problems. When aiming for a GPU environment, developing efficient parallel versions of such algorithms using CUDA can be a difficult and error-prone task even for experienced programmers. To overcome this issue, the parallel programming model of Algorithmic Skeletons simplifies parallel programs by abstracting from low-level features. This is realized by defining common programming patterns (e.g. map, fold and zip) that later on will be converted to efficient parallel code. In this paper, we show how algorithmic skeletons formulated in the domain specific language Musket can cope with the development of a parallel implementation of ACO and how that compares to a low-level implementation. Our experimental results show that Musket suits the development of ACO. Besides making it easier for the programmer to deal with the parallelization aspects, Musket generates high performance code with similar execution times when compared to low-level implementations.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

scholarly journals MODELING IN STUDYING COMPUTER GRAPHICS IN THE FUNDAMENTALIZATION OF COMPUTER SCIENCE

2019 ◽  
Vol 16 (32) ◽  
pp. 755-767
Author(s):  
L. B. RAKHIMZHANOVA ◽  
S. N. ISSABAYEVA ◽  
M. A. ZHUMARTOV ◽  
K. T. NAZARBEKOVA ◽  
K. E. TURGANBAY
Keyword(s):  
Computer Graphics ◽  
Computer Science ◽  
Practical Knowledge ◽  
Probabilistic Method ◽  
Evaluation Criteria ◽  
Information Modeling ◽  
Information Models ◽  
Development Levels ◽  
Diagnostic Complex ◽  
Main Components

The aim of the study was to develop an effective method of teaching computer graphics using information models. The authors conducted a pedagogical experiment, which consisted of two stages: ascertaining and teaching. The experiment involved 30 students and teachers in computer science. At the ascertaining stage, the state of students' practical knowledge and skills in computer graphics was analyzed. The authors had the following tasks at the first stage: to develop and describe the components, evaluation criteria and development levels of the motivation for studying computer graphics; design a diagnostic complex aimed at studying the development of the main components of the motivation for studying computer graphics; to identify the features of the development of the main components and levels of motivation for studying computer graphics in traditional learning environments. The teaching stage allowed to check the effectiveness of the task system developed by the authors, as well as the author’s methodology of using information modeling in computer graphics. In order to test the accuracy of experimental learning, the authors used the method of comparing the level of mastering the educational material of students in the control and experimental classes and the probabilistic method. For this purpose, control tests were conducted, the results of which were subjected to qualitative analysis. The results of the pedagogical experiment indicated the effectiveness of the proposed method of using computer information modeling in teaching computer graphics. Also, the authors developed a set of teaching and applied research tasks.

scholarly journals On implicit variables in optimization theory

2021 ◽  
Vol Volume 2 (Original research articles) ◽  
Author(s):  
Matúš Benko ◽  
Patrick Mehlitz
Keyword(s):  
Optimization Problems ◽  
Constraint Qualifications ◽  
Optimization Theory ◽  
Mathematical Optimization ◽  
General Setting ◽  
Necessary Optimality Conditions ◽  
Detailed Comparison ◽  
Mordukhovich Stationarity ◽  
Stationarity Conditions ◽  
The One

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming, evaluated multiobjective optimization, or nonlinear optimization problems with slack variables. In order to deal with implicit variables, they are often interpreted as explicit ones. Here, we first point out that this is a light-headed approach which induces artificial locally optimal solutions. Afterwards, we derive various Mordukhovich-stationarity-type necessary optimality conditions which correspond to treating the implicit variables as explicit ones on the one hand, or using them only implicitly to model the constraints on the other. A detailed comparison of the obtained stationarity conditions as well as the associated underlying constraint qualifications will be provided. Overall, we proceed in a fairly general setting relying on modern tools of variational analysis. Finally, we apply our findings to different well-known problem classes of mathematical optimization in order to visualize the obtained theory. Comment: 34 pages

A Dynamic-Programming-Styled Algorithm for a Class of Multi-Agent Optimal Task Assignment

2001 ◽  
Author(s):  
Guang Yang ◽  
Vikram Kapila ◽  
Ravi Vaidyanathan
Keyword(s):  
Dynamic Programming ◽  
Task Assignment ◽  
Research Activity ◽  
Spacecraft Formation ◽  
Assignment Algorithm ◽  
Decentralized Decision Making ◽  
Current Research Activity ◽  
Multi Agent ◽  
Global Optimal ◽  
Multiple Spacecraft

Abstract In this paper, we use a dynamic programming formulation to address a class of multi-agent task assignment problems that arise in the study of fuel optimal control of multiple agents. The fuel optimal multi-agent control is highly relevant to multiple spacecraft formation reconfiguration, an area of intense current research activity. Based on the recurrence relation derived from the celebrated principle of optimality, we develop an algorithm with a distributed computational architecture for the global optimal task assignment. In addition, we propose a communication protocol to facilitate decentralized decision making among agents. Illustrative studies are included to demonstrate the efficacy of the proposed multi-agent optimal task assignment algorithm.

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