Examples of Subject Areas of Multicriteria Problems

Examples of Subject Areas of Multicriteria Problems

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


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={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={IA, 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 xX.

Multicriteria synthesis of materials with desired properties are invited to perform on the modelx*=arg [I(x)],where


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