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By Mark Sh. Levin (auth.)

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5. Poset Ordinal Ordinal Poset Poset 26 COMBINATORIAL ENGINEERING OF DECOMPOSABLE SYSTEMS Obviously, the problem involves the following main components: (i) initial different ordinal scales; (ii) additional information on correspondence between elements of the scale; (iii) models and procedures to build a resultant scale. The same monotonicity of initial scales is assumed . It is reasonable to consider three basic series stages of the coordination process: (1) analysis of initial scales {Ll k Ii = 1, ...

Minimax problems, linear integer problems, bilinear and quadratic problems) can be rewritten as a linear BPP [522]. , network design/management, facility location) have discrete nature, and are similar to combinatorial synthesis. ): (1) extreme point algorithms (linear BPPs, linear-quadratic BPPs); (2) branch and bound algorithms (convex BP, integer linear BPP, integer quadratic BPP); (3) complimentary pivot algorithms (linear BPPs, linear-quadratic BPPs); (4) descent methods (convex BP, nonlinear BPPs); (5) penalty function methods; and (6) artificial intelligent based approaches.

T . g(x, y) ~ =0 O. Step 3. , weight, cost); h(x, y) = 0 represents the performance or analysis equations; and g(x, y) ~ 0 represents the design specifications and logical constraints. For many engineering applications in synthesis, the dominant structure is that the MINLP is most often linear in 0/1- variables with nonlinearities being present in the continuous variables. ): (a) the branch and bound method for MILP; (b) specialized combinatorial optimization techniques; (c) the reduced gradient method ; and (d) interior point methods .

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