In Chapter 12, the examples of subject areas of multicriteria problems are described. Some areas are considered: synthesis of materials with desired properties; pharmacology and medicine; agrotechnics; orientation of spacecraft; multicriteria optimization of communications networks structure; solving ill-posed mathematical problems; expert model optimization of perspective space facilities.
TopSynthesis Of Materials With Desired Properties
Desired material properties are given by s-dimensional vector of quantitative characteristics y={y
}
(hardness, transparency, tensile strength, abrasion resistance, electrical resistance, ductility, heat resistance, etc.). A material with ideal properties is characterized by the vector y*. The actual material is characterized by a vector difference y-y*. Vector criterion characterizing the degree of approximation of the real to the ideal material can be represented by a symmetrical-even function of the difference vector, for example, I=
. The components of the vector criterion are defined inM={I
A
, k
[1,s]},where A
– restrictions given for physical reasons.
Criteria I
are functions of n-dimensional vector of control parameters x={x
}
(dosage ingredients, catalysts, additives, temperature and other parameters of the technology). The components of the vector x are defined in a given area x
X.
Multicriteria synthesis of materials with desired properties are invited to perform on the modelx*=arg 
[I(x)],where
=
[A
-I
(x)]
,