scholarly journals On an iterative method for solving linear programming problems on cluster computing systems

2020 ◽  
pp. 329-340
Author(s):  
И.М. Соколинская ◽  
Л.Б. Соколинский
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Cluster Computing ◽  
Parallel Implementation ◽  
Computing System ◽  
Feasible Region ◽  
Computing Systems ◽  
C Language ◽  
Linear Programming Problems ◽  
Predictor Corrector

Статья посвящена исследованию нового метода решения сверхбольших задач линейного программирования. Указанный метод получил название "апекс-метод". Апекс-метод работает по схеме предиктор-корректор. На фазе предиктор находится точка, лежащая на границе <em>n</em>-мерного многогранника, задающего допустимую область задачи линейного программирования. На фазе корректор организуется итерационный процесс, в результате которого строится последовательность точек, сходящаяся к точному решению задачи линейного программирования. В статье дается формальное описание апекс-метода и приводятся сведения о его параллельной реализации на языке C++ с использованием библиотеки MPI. Приводятся результаты масштабных вычислительных экспериментов на кластерной вычислительной системе по исследованию масштабируемости апекс-метода. The paper is devoted to a new method for solving large-scale linear programming (LP) problems. This method is called the apex-method. The apex-method uses the predictor–corrector framework. Thepredictor step calculates a point belonging to the feasible region of the LP problem. The corrector step calculates a sequence of points converging to the exact solution of the LP problem. The paper gives a formal description of the apex-method and provides information about its parallel implementation in C++ language using the MPI library. The results of large-scale computational experiments on a cluster computing system to study the scalability of the apex method are discussed.

scholarly journals On validation of solutions to linear programming problems on cluster computing systems

2021 ◽  
pp. 252-261
Author(s):  
Л.Б. Соколинский ◽  
И.М. Соколинская
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Large Scale ◽  
Cluster Computing ◽  
Parallel Implementation ◽  
Main Idea ◽  
Small Radius ◽  
Feasible Region ◽  
Computing Systems ◽  
Scalable Algorithm

В статье представлен параллельный алгоритм валидации решений задач линейного программирования. Идея метода состоит в том, чтобы генерировать регулярный набор точек на гиперсфере малого радиуса, центрированной в точке тестируемого решения. Целевая функция вычисляется для каждой точки валидационного множества, принадлежащей допустимой области. Если все полученные значения меньше или равны значению целевой функции в точке, проверяемой как решение, то эта точка считается корректным решением. Параллельная реализация алгоритма VaLiPro выполнена на языке C++ с использованием параллельного BSF-каркаса, инкапсулирующего в проблемно-независимой части своего кода все аспекты, связанные с распараллеливанием программы на базе библиотеки MPI. Приводятся результаты масштабных вычислительных экспериментов на кластерной вычислительной системе, подтверждающие эффективность предложенного подхода. The paper presents and evaluates a scalable algorithm for validating solutions to linear programming (LP) problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validation set) on a small-radius hypersphere centered at the solution point submitted to validation. The objective function is computed at each point of the validation that belongs to the feasible region. If all the values are less than or equal to the value of the objective function at the point that is to be validated, then this point is the correct solution. The parallel implementation of the VaLiPro algorithm is written in C++ through the parallel BSF-skeleton, which encapsulates all aspects related to the MPI-based parallelization of the program. We provide the results of large-scale computational experiments on a cluster computing system to study the scalability of the VaLiPro algorithm.

scholarly journals A scalable algorithm for solving non-stationary linear programming problems

2018 ◽  
pp. 540-550
Author(s):  
И.М. Соколинская ◽  
Л.Б. Соколинский
Keyword(s):  
Linear Programming ◽  
High Dimension ◽  
Upper Bound ◽  
Cluster Computing ◽  
Computation Model ◽  
Computing Systems ◽  
Scalable Algorithm ◽  
Linear Programming Problems ◽  
Algorithm Implementation ◽  
Algorithm Scalability

Статья посвящена исследованию алгоритма NSLP для решения нестационарных задач линейного программирования сверхбольшой размерности, ориентированного на кластерные вычислительные системы. В основе анализа лежит модель параллельных вычислений BSF, основанная на моделях BSP и SPMD. Даются краткие описания алгоритма NSLP и модели BSF. Рассматривается реализация алгоритма NSLP в виде BSF-программы. На базе стоимостной метрики модели BSF выводится верхняя граница масштабируемости алгоритма NSLP и оценивается эффективность его параллелизации. Описывается реализация алгоритма NSLP на основе программного каркаса BSF на языке Си и приводятся результаты экспериментов, исследующих масштабируемость указанной реализации на модельной задаче линейного программирования. Делается сравнение результатов, полученных аналитическим и экспериментальным путем. This paper is devoted to the scalability study of an NSLP algorithm for solving non-stationary high-dimension linear programming problems on cluster computing systems. The analysis is based on the BSF model of parallel computations. The BSF model is a new parallel computation model designed on the basis of BSP and SPMD models. The brief descriptions of the NSLP algorithm and the BSF model are given. The NSLP algorithm implementation in the form of a BSF program is considered. On the basis of the BSF cost metric, the upper bound of the NSLP algorithm scalability is derived and its parallel efficiency is estimated. The NSLP algorithm implementation using BSF skeleton is described. The scalability estimates obtained analytically and experimentally are compared.

scholarly journals A Survey on Machine-Learning Based Security Design for Cyber-Physical Systems

2021 ◽  
Vol 11 (12) ◽  
pp. 5458
Author(s):  
Sangjun Kim ◽  
Kyung-Joon Park
Keyword(s):  
Machine Learning ◽  
Physical System ◽  
Large Scale ◽  
Computing System ◽  
Future Research ◽  
Physical Security ◽  
Computing Systems ◽  
Physical Systems ◽  
Security Research ◽  
Simultaneous Control

A cyber-physical system (CPS) is the integration of a physical system into the real world and control applications in a computing system, interacting through a communications network. Network technology connecting physical systems and computing systems enables the simultaneous control of many physical systems and provides intelligent applications for them. However, enhancing connectivity leads to extended attack vectors in which attackers can trespass on the network and launch cyber-physical attacks, remotely disrupting the CPS. Therefore, extensive studies into cyber-physical security are being conducted in various domains, such as physical, network, and computing systems. Moreover, large-scale and complex CPSs make it difficult to analyze and detect cyber-physical attacks, and thus, machine learning (ML) techniques have recently been adopted for cyber-physical security. In this survey, we provide an extensive review of the threats and ML-based security designs for CPSs. First, we present a CPS structure that classifies the functions of the CPS into three layers: the physical system, the network, and software applications. Then, we discuss the taxonomy of cyber-physical attacks on each layer, and in particular, we analyze attacks based on the dynamics of the physical system. We review existing studies on detecting cyber-physical attacks with various ML techniques from the perspectives of the physical system, the network, and the computing system. Furthermore, we discuss future research directions for ML-based cyber-physical security research in the context of real-time constraints, resiliency, and dataset generation to learn about the possible attacks.

scholarly journals A Comparative Study of Redundant Constraints Identification Methods in Linear Programming Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Paulraj S. ◽  
Sumathi P.
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Linear Functions ◽  
Redundant Constraints ◽  
Computer Scientists ◽  
Constraints Solving ◽  
Linear Programming Problems

The objective function and the constraints can be formulated as linear functions of independent variables in most of the real-world optimization problems. Linear Programming (LP) is the process of optimizing a linear function subject to a finite number of linear equality and inequality constraints. Solving linear programming problems efficiently has always been a fascinating pursuit for computer scientists and mathematicians. The computational complexity of any linear programming problem depends on the number of constraints and variables of the LP problem. Quite often large-scale LP problems may contain many constraints which are redundant or cause infeasibility on account of inefficient formulation or some errors in data input. The presence of redundant constraints does not alter the optimal solutions(s). Nevertheless, they may consume extra computational effort. Many researchers have proposed different approaches for identifying the redundant constraints in linear programming problems. This paper compares five of such methods and discusses the efficiency of each method by solving various size LP problems and netlib problems. The algorithms of each method are coded by using a computer programming language C. The computational results are presented and analyzed in this paper.

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