By Lahbib Chibani

This e-book offers the built-in technique of research and optimum layout of constructions. This strategy, that is easier than the so-called nested procedure, has the trouble of producing a wide optimization challenge. to beat this challenge a technique of decomposition via multilevel is built. this method, that's additionally compatible for implementation on parallel processing pcs, has the good thing about decreasing the dimensions of the optimization challenge generated. The geometric programming for either equality and inequality constraints is utilized in the optimization.

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Exists C! :5 c, :5 c:/ H. ) :5 0 such that, Find c M, DM HM - Dft cft min ZM :5 DM :5 DJ; :5 CM :5 cJ; "M(CM,D M ) -0 'M( CM,DM) :5 0 - First level Fig. 4 Two-Level Solution by Goal Coordination 55 Step 1: Choose initial values of A; Step 2: Solve the first-level subproblems described by Eqs. 44) ; it increases; Step 4: Repeat steps 2 and 3 until maximum H(A) is achieved. PI ' is solution of the primal problem. Lasdon (1970) discusses and presents some algorithms suitable for the solution of the dual problem.

And Kirsch (1975). The approxim ate techniques in optim ization often seek the solution of the original optimization in a reduced subspace that is a subset of the entire feasible domain. Basis reductions are examples of these techniques, here the subspaces are often spanned by base vectors formed of partial solutions of 41 the original problem, Wang et al (1984)' Rajaraman and Schmit (1981), Weiji (1984), and Picket et al (1973). The dimensionality of large structural optimization problems can also be reduced through the variable linking technique.

4 The Goal Coordination Method A coupled system cannot merely be separated into two parts and solved separately if overall optimality is to be achieved. The goal coordination method provides the means for decomposing the system. All links between its subsystems are cut, and the variables C , which are called the interaction variables, are allowed to differ on the two ends of each cut as shown in Fig. 3. 0 ..... - 8ub8YBtem 1 n+1 C_,_+1 Fig. 3 System Partition by Goal Coordination Let G. be the vector of these variables associated with the n'· subsystem.

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