Equality-constrained selection

The specific explanation structure for the flowshop problem is given in Fig. 10. In the example we have assumed that the sufficient condition is satisfied by having all the end-times of x less than or equal to those of y. Thus the proof begins by selecting the appropriate variable set, and proceeds to prove that each variable is more loosely constrained in x than in y. The intersituational variables in the flowshop problem are the start-times of the next state. 

Fig. 7. (A) The crosses show a run where library size is constrained, but no constraints are placed on library configuration. The solid squares show the effect of also constraining configuration so that between 15 and 20 reactants are used from each pool. The solid line shows the ideal solution in terms of efficiency, that is, equal numbers of reactants are selected from each reactant pool. (B) No loss of diversity is seen in the configuration-constrained library relative to the less efficient unconstrained solutions.

The most constrained and less potent among the known a,-AR antagonists confirmed its low potency and showed little subtype selectivity. Although corynanthine is rq>orted to be a selective a,-adrenoceptor antagonist, afSnities for a,- and o -ARs were nearly equal... 

The number of independent variables in a constrained optimization problem can be found by a procedure analogous to the degrees of freedom analysis in Chapter 2. For simplicity, suppose that there are no constraints. If there are Ny process variables (which includes process inputs and outputs) and the process model consists of Ne independent equations, then the number of independent variables is Np = Ny - Ne-This means Np set points can be specified independently to maximize (or minimize) the objective function. The corresponding values of the remaining (Ny - Np) variables can be calculated from the process model. However, the presence of inequality constraints that can become active changes the situation, because the Np set points cannot be selected arbitrarily. They must satisfy all of the equality and inequality constraints. 

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