Optimization software packages

In 1996, Snyder and Dolan elaborated the linear solvent strength (LSS) approach allowing the evaluation of log few from a single gradient run and its precise determination from two gradient runs [48]. From a practical point of view, LSS is the most useful approach to describe theoretical aspects and LSS gradients are convenient for optimization studies. Several commercially available optimization software packages which are able to predict resolution or retention in RPLC are currently based on this approach. 

The optimization problem formed by expressions (3.12) and (3.16)—i.e., minimize objective function (3.12) subject to constraint (3.16)—can be solved explicitly with any number of optimization software packages as well. To demonstrate this, let us first express (3.16) in a way that gathers the decision variables on a single side of the expression, specifically,... 

An optimal control strategy and algorithm using commercial optimization software packages connected to reliable DAE/ODE solvers are successful for the determination of optimal trajectories with good convergence properties. This implies that under certain conditions, the more complicated optimal control algorithms, such as that based on the well-known Pontrya-gin s maximum principle, could be avoided. 

Using a commercial optimization software package, the fits to the data in Figures l.S-1.1 were obtained. With five fitting parameters, one can validly argue that a very satisfactory fit should have been possible however, as discussed previously, criteria are available to evaluate these rate parameters. The optimum parameters at four temperatures, given in Table 7.3, where k = Lki and K = KaceK /K2, provide very linear Arrhenius plots for... 

Mobile phase composition is optimized by obtaining and evaluating a number of trial chromatograms, often with the aid of computer optimization software packages. A t)q)ical series of chromatograms for a reversed-phase separation on a hydrocarbon bonded phase column is shown in Figure 5. 

Once the objective and the constraints have been set, a mathematical model of the process can be subjected to a search strategy to find the optimum. Simple calculus is adequate for some problems, or Lagrange multipliers can be used for constrained extrema. When a Rill plant simulation can be made, various alternatives can be put through the computer. Such an operation is called jlowsheeting. A chapter is devoted to this topic by Edgar and Himmelblau Optimization of Chemical Processes, McGraw-HiU, 1988) where they list a number of commercially available software packages for this purpose, one of the first of which was Flowtran. 

The algorithms of solving the task of creating an optimal schedule of measurement are discussed. In addition, they are realized in the software package OPTIMIZM. 

Increasing complexity of optical sensing circuits is not just doing more of the same. Progress has to be made in several fields. New software tools have to be developed which allow optimization of circuits with a large number of functions. There are commercial software packages available for single... 

One issue related to supporting a metabolic stability assay with HPLC/MS/MS is the need to set up an MS/MS method for each compound. While it may only take 10 min to infuse a compound solution and find the corresponding precursor and product ions (along with minimal optimization of the collision energy), the processes of MS/MS development would require 4 hr per day if one wanted to assay 25 compounds per day. MS vendors have responded to this need by providing software tools that can perform the MS/MS method development step in an automated fashion. Chovan et al.68 described the use of the Automaton software package supplied by PE Sciex (Toronto, Canada) as a tool for the automated MS/MS method development for a series of compounds. The Automaton software was able to select the correct precursor and product ions for the various compounds and optimize the collision energy used for the MS/MS assays of each compound. They found that the Automaton software provided similar sensitivity to methods that would have been developed by manual MS/MS procedures. Chovan et al. also reported that the MS/MS method development for 25 compounds could be performed in about an hour with the Automaton software and required minimal human intervention. 

Model parameters are usually determined from experimental data. In doing this, sensitivity analysis is valuable in identifying the best experimental conditions for the estimation of a particular model parameter. Sensitivity analysis is easy effected with MADONNA, and sensitivity analysis is also provided in other more advanced software packages, such as ACSL-OPTIMIZE. 

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