Registration Number
0218U002193,
0115U002392
, R & D reports
Title
Mathematical models and algorithms solving continuous set covering problems based on the set partitioning theory
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Head
Kiseleva Elena Mikhaylovna, Доктор фізико-математичних наук
Registration Date
30-01-2018
Organization
Oles Honchar Dnipro National University
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The object of research is the theory of continuous problems of optimal sets covering (OSC) as nonclassical problems of infinite-dimensional mathematical programming with Boolean values of variables. The purpose of research work is to create mathematical models, to develop and substantiate the methods of solving continuous problems of optimal covering of sets of n-dimensional Euclidean space with the balls of the minimal radius on the basis of the theory of optimal sets partitioning (OSP); development and program realization of algorithms on the basis of the proposed methods; the application of the developed theoretical apparatus and the software to the solution of some practical optimization problems. The expansion of problems of one-time sets covering to a new class of continuous problems of OSC - problems of multiple coverage, which are problems of infinite-dimensional mathematical programming with Boolean variables, is proposed. New models of such problems for dynamical and stochastic cases, with and without constraints, with fixed and non-fixed centers are constructed and analyzed. The transition to the problems of the OSP theory is substantiated. The revealed properties of the obtained models and solutions of problems are executed in the form of corresponding theorems and lemmas. Methods and algorithms for solving all types of proposed problems have been constructed. The software that implements the proposed methods and algorithms are created. The newness of the research work is to create new approaches to solving the problem of multiple coverage, which is implemented in two algorithms: the first one is based on the discretization of the area and the use of algorithms for sorting the array of distances from a fixed point to the specified centers; the second one based on using non-differentiated optimization methods. The proposed algorithm for solving continuous problems of OSC, developed on the basis of OSP theory, in comparison with algorithms of foreign and domestic scientists, has the following advantages: its implementation does not depend on the geometric features of the covered space, the size of space and the choice of quasimetrics; at each step of its iterative process, the location of all the centers is simultaneously improved; its simplicity is assumed for program realization; it is easily generalized in the event of restrictions on the location of the centers. The results can be used in the economy, especially in solving the problems of placing logistics, distribution, service centers, emergency response services, cellular stations, ATMs in the regions, which will contribute to the conservation of energy resources and the improvement of the economic and social situation of the country.
Product Description
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Балейко Наталія Вікторівна
Бойко Лідія Трохимівна
Гарт Людмила Лаврентіївна
Громов Василь Олександрович
Довгай Павло Олександрович
Кузенков Олександр Олександрович
Навоєнко Валерія Ігорівна
НаконечнаТетяна Всеволодовівна
Притоманова Ольга Михайлівна
Турчина Валентина Андріївна
Фірсова Тетяна Олександрівна
Яцечко Наталія Євгенівна
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2020-04-02
