Abstract

The problem of optimizing a control system for an object created to fulfill several purposes is considered. Such a system has limited resources, determined during the administration process, based on the real capabilities of the developer. When optimizing the system, it is necessary to take these restrictions into account without violating them. This explains the presence of so-called “red lines”, approaching which is undesirable or completely unacceptable. The optimization problem contains optimization arguments that deliver the extremum to the objective function. The objective function is based on the concept of a nonlinear trade-off scheme, for which the “away from restrictions” principle is satisfied. The optimization problem is solved formally, without the direct participation of the Decision Maker (DM). We consider an object O, the state of which is determined by a set of values x₁,x₂,...,x_n, from the admissible region X that make up the vector . An object pursues several goals, the degree of achievement of each of them is expressed by the corresponding criterion y_k(x),k ∈[1,...s]. The criteria form a vector . Area M is determined by restrictions obtained during the administration process. This is the analytical expression of “red lines”. The optimization problem is to determine the arguments x₁,x₂,...,x_n by extremizing the objective function Y[y(x)]. Essentially, this function is a scalar convolution of the criteria vector y(x) , reflecting the utility function of the Decision Maker (DM) when solving a specific optimization problem. Scalar convolution is the act of composing criteria. A criterion y_k(x) is a measure of the quality of functioning of object O in relation to the achievement of the k-th goal. If “more” means “better,” then to improve quality this criterion must be maximized. Otherwise, the criterion is minimized. For definiteness, we consider the optimization problem with minimized quality criteria.

Keywords:Administration; Restrictions; Red lines; Multi-criteria; Scalar convolution; Tension of the situation; Non-linear compromise scheme.