Algorithm for the simplification of solution to discrete optimization problems

Chernov, Sergii; Titov, Serhii; Chernova, Lyudmila; Gogunskii, Viktor; Chernova, Liubava; Kolesnikova, Kateryna

doi:10.15587/1729-4061.2018.133405

Cited by 20 publications

(8 citation statements)

References 11 publications

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“…The applied value of the proposed approach is the use of the obtained result to enable the improvement of complex systems described by systems of linear equations with systems of linear constraints [19]. A large number of mathematical models in project management have a description of linear optimization problems.…”

Section: Discussion Of the Results Of The Study Of Dual Problemsmentioning

confidence: 99%

Development of a formal algorithm for the formulation of a dual linear optimization problem

Chernova

Titov

Chernov

et al. 2019

EEJET

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Запропоновано строгий формальний алгоритм побудови двоїстої задачі для різних випадків запису (загальна, основна, стандартна та канонічна) прямої задачі лінійного програмування. На початку наведено означення пари двоїстих задач для стандартної форми запису прямої задачі лінійного програмування. Такий підхід обґрунтовується з тих позицій, що за часом така пара була означена першою, оскільки мала змістовну інтерпретацію. Економічною інтерпретацією стандартної задачі є максимізація прибутку при виробництві та реалізації деяких видів продукції. Такий підхід змістовно вказує на існування прямої задачі (I) та строго відповідної до неї двоїстої (спряженої) (II). Супутня до прямої задачі є задача про мінімізацію витрат. Базовим поняттям теорії двоїстості в задачах лінійного програмування є той факт, що пара задач є взаємно спряженимиотримання двоїстої від двоїстої призводить до прямої задачі. Строгий підхід до отримання алгоритму складання двоїстої задачі ґрунтується на твердженні-двоїста задача від двоїстої є прямою (вихідною) задачею. Для різних пар двоїстих задач строго доводиться виконання такого твердження. Існуючі схеми переходу від прямої задачі до двоїстої носять змістовний характер. З огляду на цей факт, запропоновано та строго доведено алгоритм загального підходу до складання пар спряжених задач. Формалізація розробленої схеми дозволяє легко отримувати пари відомих двоїстих задач. Це дозволило запропонувати та довести істинність алгоритму побудови двоїстої задачі для довільної форми представлення прямої задачі Ключові слова: лінійне програмування, пряма задача, двоїста задача, двоїстість, цільова функція, система обмежень, пари спряжених задач

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Section: Discussion Of the Results Of The Study Of Dual Problemsmentioning

confidence: 99%

Development of a formal algorithm for the formulation of a dual linear optimization problem

Chernova

Titov

Chernov

et al. 2019

EEJET

Self Cite

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“…The organizational maturity of projects is investigated, in particular the success of realization of programs and portfolio of projects [13]. The process of algorithmization of simplifica tion the solutions for discrete problems of optimization of the projects is described [14]. The application of the method for synthesis of project management methodology with fuzzy in put data is investigated [15].…”

Section: Information Technologies Systems Analysis and Administrationmentioning

confidence: 99%

Models of technical systems management for the forest fire prevention

Zachko¹,

Chalyy²,

Kobylkin³

2020

Nauk. visn. nat. hirn. univ.

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Today, in Ukraine and in the world, despite the rapid development of science and technology, there is a problem of developing as well as improving and adapting information, organizational and technical systems capable of preventing forest fires. The object of the study is the process of identification and formation the parameters of safetyoriented management of technical systems of forest fire prevention.Purpose. To develop new approaches to the safetyoriented project management of technical systems of forest fire prevention, and their modeling, based on the principles of system analysis.Methodology. Using the general scientific principles and fundamental provisions of the project management methodology, including system analysis, modeling tools, proactive and reactive management mechanisms, we form a triad of creating the con cept of designing a portfolio of technical systems for environmental protection against forest fires. findings. A conceptual triad of modelscheme of formation of the portfolio of projects of technical systems for protection of environment from forest fires is presented. A cybernetic model of the "black box" for decision making management during the implementation of the project of the technical system of forest fire prevention is adapted; the impact of factors that may occur under the influence of turbulent internal and external environment on the project is described. A safetyoriented model of project management of the technical system of forest fire prevention is developed, which is characterized by the presence of subphases of the life cycle, which are critical places of the project, have their own time frame of operation and resource consumption.originality. The model of safetyoriented project management of the technical system of forest fire prevention is developed and subphases in the basic phases of the project life cycle are identified. The developed models are adapted for use in different countries because they are formed in accordance with international standards for project, programs and portfolio of projects management P2M, PmBok, PRINCE2, AGILE, KANBAN.Practical value. It is possible to use the obtained results in the practical activities of project, operational and management teams of authorities, emergency services and managers in the formation of national projects to prevent forest fires.

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“…The methods of discrete optimization problems solution that have been developed by now require development of algorithms which allow obtaining an approximate solution with guaranteed estimate of deviation from the optimum. Simplification algorithms in discrete optimization problems provide an efficient method of searching for an optimization problem solution [16,17,18]. Should a multidimensional process be projected onto the twodimensional surface, this will enable visualization of the acceptable set (array) of the problem parameters.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…We can make a lower-and an upper-bound estimate of the problem target function values and dynamically evaluate the possibility to diversify basis optimum variables with guaranteed accuracy. Solving contradictions between requirements to completeness of modelling views in active systems and methods of obtaining solutions of their mathematical models is possible due to reasonable reduction of the algorithms of complicated equation systems solution [17]. Lack of problem solution as regards searching for solutions in discrete optimization problems consists in the need for developing and implementing the procedure of simplifying the combinatorial solution of a discrete optimization problem.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The research has proposed and exactly grounded an approach to finding the optimum solution of a broad class of multidimensional knapsack problems. The principle of the method proposed consists in using the feature of convex polyhedral area I  provided by a system of linear algebraic inequalities or equations in the form of a direct sum of subspace and kernel [10,17]. Provided that the polyhedral kernel is two-dimensional, an optimization problem can be reduced to a twodimensional one.…”

Section: Optimization Problem Decomposition Combinatory Enumeration mentioning

confidence: 99%

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The Maple ® symbolic mathematics system in the method of projections for discrete optimization problems

Chernova¹

2019

Visn. Zaporiz. nac. univ., Ekon. nauki

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Algorithm for the simplification of solution to discrete optimization problems

Cited by 20 publications

References 11 publications

Development of a formal algorithm for the formulation of a dual linear optimization problem

Development of a formal algorithm for the formulation of a dual linear optimization problem

Models of technical systems management for the forest fire prevention

The Maple ® symbolic mathematics system in the method of projections for discrete optimization problems

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