Global optimization method calculations

This criterion resumes all the a priori knowledge that we are able to convey concerning the physical aspect of the flawed region. Unfortunately, neither the weak membrane model (U2 (f)) nor the Beta law Ui (f)) energies are convex functions. Consequently, we need to implement a global optimization technique to reach the solution. Simulated annealing (SA) cannot be used here because it leads to a prohibitive cost for calculations [9]. We have adopted a continuation method like the GNC [2]. 

The obvious alternative to the sequential optimization methods is the use of an interpretive optimization method. In such a method a limited number of experiments is performed and the results are used to estimate (predict) the retention behaviour of all individual solutes as a function of the parameters considered during the optimization (retention surfaces). Knowledge of the retention surfaces is then used to calculate the response surface, which in turn is searched for the global optimum (see the description of interpretive methods in section 5.5). For programmed temperature GC the framework of such an interpretive method has been described by Grant and Hollis [614] and by Bartu [615]. 

The steam reforming of methane to produce syngas includes nine basic reactions. The global equilibrium yield (GEY) and the potential maximal equilibrium yield (PMEY) can be calculated by a new method proposed by this paper. The optimal reaction assemblage (ORA) can be constructed by an optimization method. Where hydrogen is the desired product, the ORA is composed of reactions (1) and (2) in the nine-reaction system. The observed peak yield (OPY) of hydrogen equals 2.410 (mole fraction), its PMEY and GEY equal 3.341 (mole fraction). If carbon monoxide is the desired product, the ORA includes only reaction (1) in the nine-reaction system and the OPY, GEY and PMEY of carbon monoxide equal 0.344, 0.2767 and 0.9789 (mole fraction) respectively. Construction of the ORA is the key and fundamental way to improve the yield of a desired product. In this paper, the method of constructing the ORA is developed. 

Some problems may have multiple optima. Although a local optimum may be acceptable in some situations and industrial practice, only the global optimum is the correct solution in certain applications (for example, equilibrium calculations by free energy minimization). Hence, an optimization method should be selected carefully for solving the optimization problem based on its characteristics and need to find the global optimum. 

Particle Swarm Optimization (PSO) The optimization method based on the study of social behaviour in a self-organized population system (i.e., ant colonies, fish schools). Itisanon-gradient, heuristic method which requires calculation of the objective function only. This method is able to find a global solution to non-convex optimization problem and problems which have many local minima. 

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