Optimization set up

Type II (blind) projects in Mchrom Scout are intended to optimize the separation of  mixtures of unknown identity or number of components. Project configuration is quite similar to that shown for type I projects. However, if the nature of sample components is unknown, the selection of an adequate chromatographic column and/or the mobile phase is slightly more complicated and some of them have to be tested.

Accordingly, the project definition will additionally include a number of columns and mobile phases to test to the usual variables (modifier range and gradient times, temperature, pH, etc.).

 

mchrom-scout-type-ii-configuration

 

Chromatographic columns and mobile phases are taken from the same databases as per type I projects. Project configuration will be updated as soon as new components are added. The total number of experiments to be carried out is permanently indicated to advise you about the experimental effort required as a function of the different choices.

Of course, objective functions for type II (blind) projects need to be different to those used in type I projects. This is because the peaks cannot be tracked in the chromatograms. Elemental criteria based on direct measurements of the chromatograms are used in this case. You can choose from a variety of that criteria such as the apparent number of peaks in the chromatograms (large and minor peaks), the number of well resolved pairs or the number of symmetrical peaks and, of course, the total run time.

 

mchrom-scout-type-ii-configuration02

 

The program develops an appropriate design and provides the experimental plan using a similar template as per type I projects. Also in this case it is highly recommended to use test points in the design.

 

mchrom-scout-type-ii-experimental-plan

 

As in type I projects, the program is now stopped and resumed once the results for the experiments in the table are available.  You can paste these results (some additional options are available to paste the data directly provided by the instrument data system) and develop the regression model to evaluate the results.

 

mchrom-scout-type-ii-model-results

 

Viewing results for type II projects

In Mchrom Scout Type II (blind) projects, results of the optimization can adopt three different approaches:

  1. Contour plots (including an exploring of the design space, as an independent option, once the contour plots have been calculated)
  2. Desirability function plots
  3. Pareto optimality

All results are presented (both in graphical and tabular form) as soon as the models have been calculated or when a stored project is opened.

 

1- Contour plots

Contour plots are graphical representations of the response surfaces corresponding to each objective function in the search space defined for the problem.

 

mchrom-scout-type-ii-contour-plots

 

These results are also provided as a table summary. This table allows you to evaluate the possibility of an optimal experimental performance.

 

 

mchrom-scout-type-ii-experimental-plan02

 

It is clear that for projects configured as multi-objective, the optimum corresponding to a particular objective function does not necessarily match the optimum of others. Thus, a convenient optimum range must be obtained by the intersection of all considered response surfaces, provided that this intersection is not empty. Otherwise, optimum values corresponding to each objective function should be traded off in order to provide a populated practical working region. A special tool is accessed by clicking the “design space” button to help this process.

 

mchrom-scout-type-ii-model-results-03

 

2- Desirability function plots

Desirability functions allow transforming the multi-objective problem into a uni-objective optimization by defining partial desirability functions corresponding to each defined objective.

Desirability functions may be uni- or bi-lateral and are defined to maximize or minimize the objective functions. For example the following image corresponds to the default desirability function for the large peaks criterion. As shown, two limiting values are defined for the criterion. Chromatograms with values of large peaks under the lower limit are assigned a zero value. Similarly, for chromatograms showing a number of large peaks above the upper limit, a value of one is assigned.

Finally, for chromatograms showing intermediate responses, the value defined by the transition line between limits is assigned. This transition function can adopt several shapes from a straight line to quadratic and sigmoidal curves.

 

mchrom-scout-type-ii-graphs

 

Finally, all partial desirability functions are combined into a global desirability which is used as the optimization function for the problem. Thus, the final view offered to the user is a conventional response function corresponding to that global desirability.

 

mchrom-scout-type-ii-model-results-04

 

Notice that response functions corresponding to desirability functions are continuous while response functions corresponding to each optimization criteria show discrete regions because the criteria represent integer values (e.g. the number of peaks in the chromatogram).

Depending on the number of decision variables considered, the plot of desirability response can be viewed as in the above image or by the representation of the region for a defined desirability limit as shown in the next image.

 

mchrom-scout-type-ii-model-results-05

 

Of course, desirability results are also included in the tables for type II project’s results.

3- Pareto optimality

Finally, for Pareto optimality, no trade-offs between criteria should be developed. Each criterion defined an independent dimension in the objectives space so the results are compared to select, possibility using secondary utility criteria those solutions better adapted to our goals. To avoid an excessive number of solutions in the optimal Pareto front, some constraints are defined with the help of the program which proposes default values as a function of the results produced for the response surfaces.

 

mchrom-scout-type-ii-constraints

mchrom-scout-type-ii-constraints02

 

Pareto front results are presented as graphs, similar to those used for type I projects although in that case, tabular results, also provided, are generally more convenient.

mchrom-scout-type-ii-model-results-06

Additionally, full practical details about the solutions forming the pareto front are given in the tables page as shown below:

 

mchrom-scout-type-ii-model-results-07

 

A clear advantage of Pareto optimality is the gain of objectivity in the process of decision taking because all decisions are taken after the optimization process has ended by inspecting and comparing the Pareto optimal solutions. Any other option to deal with multi-objective problems means adopting some trade-offs before the optimization is done so, that decisions can bias  the final results in an unpredictable way. On the other side, Pareto optimality may appear confusing to some chromatographers because no unique optimum solution but a set of optimal solutions is produced, and these solutions need to be revised.

 

mchrom-scout-type-ii-utilities-menu02

 

To help the solution’s review process, Mchrom Scout provides two specific graphical tools, based on parallel coordinates plots and cluster maps (Chemom. Intell. Lab. Sys, 114 (2012) 72). These tools allow organization of the solutions to select the most appropriate even in cases of rather large number of solutions as in the case shown below. It corresponds to one of these tools (cluster maps).

 

mchrom-scout-type-ii-graphs-02

 

Further details about these tools are provided in the starting guide for utilities and several of the tutorials associated to Mchrom Scout.

 

 

 

 

 


Last modified: April 6, 2017 by Enrique Sánchez