Structure optimization of reservation by precise quadratic regularization

A. I. Kosolap, A. A. Dovgopola


The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straight- dual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.


backup system; optimization; multiextremal problems; the exact method of quadratic regularization


Erschova N.M. and Kosolap A.I. Matematicheskie metody issledovaniya operatsiy [Mathematical methods of re- search of operations]. Dnepropetrovsk: PGASA, 2015, 256 p. (in Russian).

Kapur K.C. and Lamberson L.R. Nadezhnost' i proektirovanie sistem [Reliability and design of systems]. Moskow: Mir, 1980, 604 p. (in Russian).

Kosolap A.I. Metody global'noy optimizatsii [Methods of global optimization]. Dnepropetrovsk: Nauka i obrazovanie, 2013, 316 p. (in Russian).

Kosolap A.I. Global'naya optimizatsiya. Metod tochnoy kvadratichnoy regulyarizatsii [Global optimisation. A method of exact quadratic regularization]. Dnepropetrovsk: PGASA, 2015, 164 p. (in Russian).

Lvovich Ya.E., Kashirin I.L. and Tuzikov A.A. Geneticheskiy algoritm resheniya mnogokriterial'noy zadachi povysheniya nadezhnosti re-zervirovaniya [Genetic algorithm of the solution multicriteria problems of increase of reliability of reservation]. Informatsionnye tekhnologii [Information technologies]. 2012, no. 6, pp. 56-60. (in Rus- sian).

Belyaev Yu.K., Bogatyrev V.A. and Bolotin V.V. Nadezhnost' tekhnicheskikh siste [Reliability of Technical Sys- tems]. Moskow: Radio i svyaz’, 1985, 608 p. (in Russian).

Norkin V.I. and Onishchenko B.O. Optimizatsiya nadezhnosti slozhnoy sistemy stokhasticheskim metodom vetvey i granits [Optimization of reliability of a complex system by stochastic method of branches and borders]. Kibernetika i sistemny analiz [Cybernetics and system analysis]. 2008, no. 3, pp. 129-141. (in Russian).

Ushakov I.A. Veroyatnostnye modeli nadezhnosti informatsionno-vychislitel'nykh sistem [Probabilistic models of reliability of information systems]. Moskow: Radio i svyaz’, 1991, 132 p.

Ushakov I.A. Kurs teorii nadezhnosti system [Course of the theory of reliability of systems]. Moskow: Drofa, 2008, 239 p. (in Russian).

Shklyar V.N. Nadezhnost' sistemy upravleniya [The reliability of the control system]. Tomsk: Izdatelstvo Tomskogo politekhnicheskogo universiteta, 2011, 126 p. (in Russian).

Birolini A. Reliability engineering: theory and practice. London; New York: Springer, 2014, 630 p.

Elmakias D. New computational methods in power system reliability. Berlin, Heidelberg: Springer-Verlag, 2008, 419 p.

Nocedal J. and Wright S.J. Numerical optimization. London, New York: Springer, 2006, 685 p.

GOST Style Citations

Ершова Н. М. Математические методы исследования операций / Н. М. Ершова, А. И. Косолап. – Днепропет- ровск : ПГАСА, 2015. – 256 с.


Капур К. Надежность и проектирование систем / К. Капур, Л. Л. Ламберсон ; пер. с англ. Е. Г. Коваленко ; под ред. И. А. Ушакова. – Москва : Мир, 1980. – 604 с.


Косолап А. И. Методы глобальной оптимизации / А. И. Косолап. – Днепропетровск : Наука и образование, 2013. – 316 с.


Косолап А. И. Глобальная оптимизация. Метод точной квадратичной регуляризации / А. И. Косолап. – Дне- пропетровск : ПГАСА, 2015. – 164 с.


Львович Я. Е. Генетический алгоритм решения многокритериальной задачи повышения надежности резер- вирования / Я. Е. Львович, И. Л. Каширина, А. А. Тузиков // Информационные технологии. – 2012. – № 6. – С. 56-60.


Надежность технических систем : справочник / Ю. К. Беляев, В. А. Богатырев, В. В. Болотин [и др.] ; под ред. И. А. Ушакова. – Москва : Радио и связь, 1985. – 608 с.


Норкин В. И. Оптимизация надежности сложной системы стохастическим методом ветвей и границ / В. И. Норкин, Б. О. Онищенко // Кибернетика и системный анализ. – 2008. − № 3. – С. 129-141.


Ушаков И. А. Вероятностные модели надежности информационно-вычислительных систем / И. А. Ушаков. – Москва : Радио и связь, 1991. – 132 с.


Ушаков И. А. Курс теории надежности систем / И. А. Ушаков. – Москва : Дрофа, 2008. – 239 с.


Шкляр В. Н. Надежность системы управления : учеб. пособие / В. Н. Шкляр. – Томск : Изд-во Томского по- литехн. ун-та, 2011. – 126 с.


Birolini A. Reliability engineering: theory and practice / A. Birolini. – London ; New York : Springer, 2014. – 630 p.


New computational methods in power system reliability / еd. D. Elmakias. – Berlin ; Heidelberg : Springer-Verlag, 2008. – 419 p.


Nocedal J. Numerical optimization / J. Nocedal, S. J. Wright. – London ; New York : Springer, 2006. – 685 p.

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