Examples of Subject Areas of Multicriteria Problems

Examples of Subject Areas of Multicriteria Problems

DOI: 10.4018/978-1-5225-2509-7.ch012

Abstract

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.
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Synthesis Of Materials With Desired Properties

Desired material properties are given by s-dimensional vector of quantitative characteristics y={y978-1-5225-2509-7.ch012.m01}978-1-5225-2509-7.ch012.m02 (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=978-1-5225-2509-7.ch012.m03. The components of the vector criterion are defined inM={I978-1-5225-2509-7.ch012.m04978-1-5225-2509-7.ch012.m05A978-1-5225-2509-7.ch012.m06, k978-1-5225-2509-7.ch012.m07[1,s]},where A978-1-5225-2509-7.ch012.m08 – restrictions given for physical reasons.

Criteria I978-1-5225-2509-7.ch012.m09 are functions of n-dimensional vector of control parameters x={x978-1-5225-2509-7.ch012.m10}978-1-5225-2509-7.ch012.m11 (dosage ingredients, catalysts, additives, temperature and other parameters of the technology). The components of the vector x are defined in a given area x978-1-5225-2509-7.ch012.m12X.

Multicriteria synthesis of materials with desired properties are invited to perform on the modelx*=arg 978-1-5225-2509-7.ch012.m13978-1-5225-2509-7.ch012.m14[I(x)],where

978-1-5225-2509-7.ch012.m15=978-1-5225-2509-7.ch012.m16[A978-1-5225-2509-7.ch012.m17-I978-1-5225-2509-7.ch012.m18(x)]978-1-5225-2509-7.ch012.m19,

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