About stability of mixed integer optimization problems under perturbations of input data of vector criterion

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of mixed integer optimization vector problems. In the optimization problems, including problems with vector criterion, small perturbations in initial data can result in solutions strongly different from the true ones. The problem of stability of the indicated tasks is studied from the point of view of direct coupled with her question in relation to stability of solutions belonging to some subsets of feasible set.

Stability kernel of vector optimization problems under perturbations of criterion functions

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of optimiza-tion multicriterial problems. In the optimization problems, including problems with vector criterion, small per-turbations in initial data can result in solutions strongly different from the true ones. The results of the con-ducted researches allow us to extend the known class of vector optimization problems, stable with respect to in-put data perturbations in vector criterion. We are talking about stability in the sense of Hausdorff lower semicontinuity for point-set mapping that characterizes the dependence of the set of optimal solutions on the input data of the vector optimization problem. The conditions of stability against input data perturbations in vector criterion for the problem of finding Pareto optimal solutions with continuous partial criterion func-tions and feasible set of arbitrary structure are obtained by studying the sets of points that are stable belonging and stable not belonging to the Pareto set.

Method for Assessing the Ecological Risk to the Population in Areas Outside the Planning Zones of Emergency Protection Measures Around the NPP

The article offers a method for assessing the environmental risk in the territories adjacent to the planning zone of emergency protection measures around the NPP. The method is based on simulation modeling of territory pollution, which is formed at the late stage of a radiation accident and zoning of territories by risk, taking into account the characteristics of the population’s life in a potentially dangerous territory. A vector criterion of environmental risk is proposed that allows zoning these territories according to the degree of danger to the population.

Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

A Method of Selecting the Number of Coordinates of a Vector Criterion in a Polyoptimal Decision-Making Process

An important problem when formulating multicriteria optimization tasks is the selection of such a number of partial criteria that their meaning, number, and order correspond to the modeled decision situation. The paper proposes a method of selecting the number of criteria in polyoptimal decision-making process. The conditions of completeness, coherence, and nonredundancy that must be met by the vector criterion adopted for the assessment of the decision situation were discussed. Using these conditions, the principles of selecting the number of partial criteria in the vector criterion were specified, specifying the theorem on extending or reducing the scalar criterion. Using the formulated method, a vector quality criterion was selected for the task of controlling the movement of a sailing object. The method proposed in the work can be useful for modeling any decision-making situation in such issues as designing complex systems, controlling complex objects in conditions of uncertainty, and making decisions in other systems.

SEARCH ALGORITHM THE BASIC CRITERION IN THE DESIGN OF COMPLEX TECHNICAL SYSTEMS

In this article the model of the analysis of a multicriteria problem allowing to reduce significantly the problems arising at design of complex technical systems in cases when it is required to reduce significantly dimension of a vector criterion in case of its redundancy, or to show that such reduction is impossible is considered.