Multi-parameter optimization

Liquid chromatography/ultraviolet detection Monoamine oxidase Mechanism-based inhibition Metabolic intermediate complex Molybdenum-containing oxidase Multi parameter optimization... 

In principle, all methods can be adapted to include multi-parameter optimization, but graphical methods are then no longer possible. 

On the other hand, the practical characteristics of the Simplex method show that its application is usually staightforward (even for multi-parameter optimizations) and requires little knowledge or computational effort. This explains the popularity of the Simplex methods for the optimization of chromatographic selectivity, despite its obvious fundamental shortcomings. 

Campbell et al. [70] developed a BASIC program, LESTEQ, for calculation of the exact equivalence point volume in spectrophotometric titrations by use of ancillary indicators. The program is based on the non-llnear least-squares fit of the titration data to a model equation by means of a modification of the Gauss-Newton multi-parameter optimization method, and calculates the indicator and stability constants. The form of the model equation used by LESTEQ depends on the stoichiometry of the titration reaction and on the nature of the indicator reaction. The equation... 

Since some of the requirements described above are contradictory in effect (e.g. minimization of reactant transport in the electrolyte while maintaining sufficient transport in the electrode), it is not possible to maximize a single parameter or property without affecting others. Proper fuel cell design always involves compromises while doing simultaneous multi parameter optimizations. 

The catalyst layer must also maintain open porosity in order to homogeneously supply reactants to the reaction sites. Therefore, additives in the catalyst layer can be used to maintain open gas transport pores by creating hydrophobic zones as well as additives preventing the radical attack to the ionomer phase. Stability of the ionomer and the other additives in the electrolyte layer are important for the overall endurance of the MEA. The ratio of catalyst mass to ionomer and additive mass requires a careful multi parameter optimization and is depending on the overall amount of platinum present in the catalyst layer and the ratio of noble metal to support material in the catalyst powder [54, 55]. 

Segall, M.D. (2012) Multi-parameter optimization identifying high quality compounds with a balance of properties. Current Pharmaceutical Design, 18, 1292-1310. 

Because the current estimates of the interaction parameters are used when solving the above equations, convergence problems are often encountered when these estimates are far from their optimal values. It is therefore desirable to have, especially for multi-parameter equations of state, an efficient and robust estimation procedure. Such a procedure is presented next. 

Clearly what is needed in SFC for samples with diverse, wide-ranging compounds is a systematic approach to optimization, applicable when two or more variables are changed simultaneously. The remainder of this chapter is therefore devoted to the description of some systematic, multi-parameter approaches, with a natural emphasis on those strategies for which experimental results are available. 

Multi-dimensional optimization Impractical above 2 parameters... 

Istadi and Amin, N. A. S. (2005). A hybrid numerical approach for multi-responses optimization of process parameters and catalyst compositions in CO2 OCM process over CaO-MnO/Ce02 catalyst, Chem. Eng. J., 106, pp. 213-227. 

We can say that interactive methods have not been used to optimize SMB processes and, usually, only one or two objective functions have been considered. The advantages of interactive multi-objective optimization in SMB processes has been demonstrated in Hakanen et al. (2008, 2007) for the separation of fructose and glucose (the values of the parameters in the SMB model used come from Hashimoto et al. (1983) Kawajiri and Biegler (2006b)). In Hakanen et al. (2008, 2007), the problem formulation consists of four objective functions maximize throughput (T, m/h ), minimize consumption of solvent in the desorbent stream (D, m/h ), maximize product... 

Solver needs reasonably close initial estimates of the parameter values, otherwise it can easily produce non-optimal results. If at all possible, subject a subset of the data to a linear least squares analysis to get an idea of at least some of the parameter values. And wherever possible, use a graph to see how close your initial estimate is, and follow the progress of the iterations visually, even though that slows down Solver. Where this is not feasible, as in multi- parameter fits, at least inspect the orders of magnitude of the values in the two columns Solver compares yexp and yca c. 

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