Algorithm to solve a problem of optimum separation of sets with additional couplings
Journal Title: Комп’ютерне моделювання: аналіз, управління, оптимізація - Year 2017, Vol 2, Issue 2
Abstract
Problems of manufacturing arrangement have been considered for more than a century. However, they are still topical. For instance, despite the fact that a number of models and techniques to solve discrete problems of arrangement have been proposed, studies concerning continual problems are not practically available. At the same time, production development involves solution of a variety of problems which are described with the help of such models. Problems of multistage production to minimize total cost of product delivery and raw material as well as to provide coverage of a certain service area are among them. In this context, original set is continuous by its nature, and available discrete models need a great number of simplifications being detrimental to the final result. The paper considers a problem of optimum separation of sets with additional connections and arrangement of centres of subsets, which is a mathematical model of two-stage continual location-allocation problem. Complexity of the studies is that a mathematical model involves both discrete part and continual one thus requiring combined solution techniques. The necessity to develop such algorithms is undisputable since such models describe a number of important practical problems including those concerning the arrangement of points for natural raw material accumulating and processing. Moreover, the considered problem develops the theory of optimum separation of sets, and so it is important in terms of theory as well. Specific attention has been paid to the approach for the problem solving. The approach is to transform the original problem into a problem of infinite-dimensional mathematical programming and then into a problem of finite-dimensional optimization with the help of Lagrange function. Algorithm to solve a problem of optimum separation of sets with additional connections has been represented. The algorithm may be important from the viewpoint of its application to solve applied problems as well as from the viewpoint of further development of the theory of optimum separation of sets.
Authors and Affiliations
С. А. Ус, О. Д. Станіна
Keywords
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