Nodar Jibladze

The basis of the safe operation of ecologically dangerous objects is formed at the design stage. Therefore, the primary goal of this stage is, whenever possible, full execution of technical and safety requirements that provide reliable safety systems and their effective maintenance. Among ecologically dangerous objects, nuclear power stations (NPSs) are especially important, since their normal operation is a basic problem. Multicriteria design problems and maintenance strategies of NPS protection systems are investigated in this paper. Using the example of an NPS, three optimization models for effective design and operation of ecologically dangerous objects are developed. In particular the model for effective maintenance of the NPS protection system is constructed. The model of constructing the NPS reliable protection system with minimal expenditures with primitive constraints and generalized ones is designed as well. We reduce these problems to multiobjective optimization (MO) problems. We have developed our method, the appropriate algorithm and the corresponding software for solving MO problems based on the gravitation centers method. Our software yields solutions for MO problems of effective design and maintenance service of a NPS, minimizing the risk of abnormal functioning and providing design of a reliable system of protection at minimal expense.

Multicriteria (multiobjective) optimization is widely used for solving a variety of problems in all spheres of everyday life. This could be explained by the fact that such models make it possible to take into account goals which may be different in nature and very often quite contradictory Researchers have developed and continued to improve methods, algorithms and procedures for solving such problems. In this paper we investigate various multicriteria optimization methods and propose an approach for classification of these methods, so that a decision maker can choose from a great variety of procedures the one that best suits his/her goals. Further, we show how our gravitation centers method, developed earlier for solving single objective programs, can be implemented through the multicriteria or multiobjective case. 

The problem of the construction of an object functioning in the regime of optimum performance at the design stage is reduced to the solution of the problem of multicriterion optimization, where the quality criteria are chosen to be its most essential characteristics (parameters). At the same time in all methods of multicriterion optimization the vector quality criterion is considered basically in the linear Euclidean space. Actually, in most cases, the criterion space is non-Euclidean – it is curved. Therefore, such setting cannot give results adequately reflecting the processes running in real systems.

In order for the design system to really satisfy the optimality requirements the authors of the given paper offer an absolutely new approach to the solution of the problems of multicriterion optimization based on the definition of the quality criteria space and on finding an invariant corresponding to the distance between any two points of that space.

The idea of the study of the metric properties of the quality criteria space and their use in solving problems of multicriterion optimization was offered in the work [1]. But that idea, due to its complexity, has not been completely realized until now. When solving such problems the quality criteria space was automatically identified with the Euclidean space with corresponding metrics. In the general case this could not give results adequately reflecting the processes occurring in real systems.

In the present paper metric properties of space criteria are studied for the first time, using as the main instrument the mathematical apparatus of tensor analysis, Riemannian geometry, differential equations in partial derivatives etc. Boundary problems relative to the components of the metric tensor of the n-dimensional space of the phenomenon states enabling to determine its metric properties are posed. The knowledge of the metric tensor furthers the objective appraisal of the phenomenon state and the definition of the optimal state.