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1 2007

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Formalization of Location and Spacing Tasks Modern Methods of Design

Chura I., Kernytskyy A.

Machine Dynamics Problems

2007

Vol. 31, No. 3

15-24

Tasks of optimal location and spacing of geometric objects arising during material cutting, animation, design of PCBs, design of plans of both habitual and industrial areas, location of equipments and loads and design of economic processes belongs to the class of the abovementioned problems. Therefore, the problem of ES development for the location and spacing problems solution is vital. Interest to the location and spacing tasks solution is determined by the wide spectrum of practical applications from the one side and by the complication and no triviality of the development of mathematical models vital for their adequate description. Regardless the variety of such problems, all of them include the formulation: it is necessary to locate the geometric objects in the given region taking into account terms and limitations so that achieved value of an efficiency function are the nearest ones to the optimum. The tasks of location and spacing of flat objects depending on their application domain are classified in the paper. On the basis of the conducted analysis of practical problems mathematical formalization is presented. As a result of analysis of the known practical problems of location and spacing their similarity by input an output data is distinguished. All formalized problems are joined by main properties: a) there is questions about location of geometric objects of arbitrary form in the regions of arbitrary geometric form, b) each of problems is formalized, at least verbally, as the problem of mathematical programming. In other words, a problem appears as some terms that are limitations on the parameters of placing of objects at implementation of which it is necessary to achieve put objective. Under achievement of purpose the receipt of the best quality or optimum quantity is understood, that are expressed by correlations and relied on the parameters of placing of objects. It is known, that such correlations in the mathematical programming are named functions or functions of quality having a special purpose.