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According to the author's graduate path taught over a long time in numerous physics departments, this 2006 publication takes a 'reductionist' view of statistical mechanics, whereas describing the most principles and strategies underlying its functions. It implicitly assumes that the physics of complicated platforms as saw is attached to basic actual legislation represented on the molecular point through Newtonian mechanics or quantum mechanics.
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According to Fig. 7b, variable X3 is input to model6, but the real model6 has X3 as output (see Fig. 7a). Such a modiﬁcation is not present in any other model. Hence, based on rule 6, model6 is chosen for guessing the input and output variables. The three different possible guesses for model6 are shown in Fig. 8. Each arrangement for model6 replaces the sixth row of model6 of the populated matrix shown in Fig. 7b. The results obtained for each case, by further populating based on the ﬂowchart in Fig.
5, are shown in Fig. 9. The guess for model6 shown in Fig. 8c generated two solutions after population. These are shown in Fig. 9c and Fig. 9d, respectively. In the ﬁgures, model4 is not displayed because its corresponding row in the incidence matrix was already fully populated by applying IMM (refer to Fig. 7b), and hence is not part of an SCC. Fig. 8 Alternative guesses for i/o variables of model6. MDO AT PREDESIGN STAGE 33 Fig. 9 Populated incidence matrix with the three guessed inputs and outputs for model6 (0s not shown in the ﬁgures for clarity).
Obtaining a well-distributed set of Pareto points is essential for the GFCL approach to be effective. Because the Pareto front cannot be obtained as a function of the design variables x, but only a ﬁnite set of Pareto points can be obtained, it is fundamental that the Pareto points are well distributed on the full extent of the Pareto front, hence allowing a complete representation of the Pareto front in all of its regions. It has been demonstrated that conventional MDO AT PREDESIGN STAGE 41 approaches, such as the weighted sum method , are not suitable for generating well-distributed Pareto points.