Mchrom Scout provides several tools designed to help the chromatographer to obtain a more efficient method development for RPLC separations. These tools are under the ‘Utilities’ tab and are divided into three main groups of tools:

  • Gradient utilities
  • Pareto Optimality
  • Resolution maps

These tools are available via the Utilities menu when you require them. They are organized for easy use as a function of the project type selected as well as during the current stage of specific optimization process.

This tutorial will show you one of these three utilities tools used to handle Pareto fronts. These are applicable for both, Type I and II projects:

 

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Pareto optimality tools

Mchrom Scout includes two specific tools helping the efficient handling of optimal Pareto fronts of solutions.

The enhanced objectivity of Pareto strategy derived from the fact that solutions are selected once the optimization process has finished. It does not use weighting coefficients or linear combinations of the objectives before doing the optimization. This has been explained in the Starting Guides for types I and II projects.

Frequently there is the need of inspecting several solutions to select the most convenient to be implemented in the laboratory. Quite logically this inspection process is the more problematic the greater the number of solutions captured in the Pareto front, especially when the Pareto front is not continuous. Something which is very frequent in chromatography optimization.

Mchrom Scout provides two helping tools that make use of cluster algorithms as grouping strategies for solutions. One of them is derived from the known parallel coordinates plots and the other one provides a graphical representation similar to heat maps.

Clustered Parallel Coordinates Plots (CPCP)

A CPCP is essentially a parallel coordinates graph produced by combining the information provided by the dendrograms calculated in the decision and/or the objectives spaces to provide a plot where the non-dominated solutions are organized according to groupings defined in the dendrograms.

Parallel coordinates graphs are a common way to visualize high-dimensional spaces and analyze multivariate data using polylines with vertices on the parallel variable axes.

This graphical tool has been extensively studied and developed by Alfred Inselberg (Parallel Coordinates, Visual Multidimensional Geometry and its Applications, Springer 2009). The application to Pareto fronts was developed by Cela et al.  (New cluster mapping tools for the graphical assessment of non-dominated solutions in multi-objective optimization, Chemom. Intell. Lab. Sys, 114 (2012) 72-86).

After the Pareto optimization process, when the Pareto front is readily available, this tool can be invoked from the utilities menu. Groupings can be formed in the operational decision variables space

 

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and also from the objectives space as shown below:

 

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Groups are formed interactively in the corresponding dendrograms and the parallel coordinates plot updated to show the structure of the particular Pareto front considered. In multi-objective optimization problems, similarity of solutions in both spaced do not need to be the same so both views are necessary as well as a simple plot helping to evaluate the correlation between both spaces as regards the solutions similarity.

 

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Several clustering algorithms and data pretreatments are available as options of these helping tools.

 

Cluster Maps (CMs)

A CM is a graphical tool which allows combining the dendrograms produced in the cluster analysis of the pareto front solutions with an interpolation procedure of the objective’s values to provide a visual map of groupings and values.

CMs can consider both the decision and the response spaces simultaneously or can be simplified to study both spaces separately when convenient. The theory and practical applications to several numerical and laboratory examples can be found in New cluster mapping tools for the graphical assessment of non-dominated solutions in multi-objective optimization, Chemom. Intell. Lab. Sys, 114 (2012) 72-86.

Results for this tool are presented in the following container, which is divided into five sections:

1) The dendrogram for the decision variables space (top left)

2) The dendrogram for the objectives space (bottom right)

3) The cluster map (bottom left)

4) The color scale for the objective or combination of objectives used to colorize the cluster map (center right just above the objectives space dendrogram), and

5) The information panel giving details of user selections and algorithms applied.

 

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Now, some solutions can be taken from each grouping to be inspected thus making easy and shortening significantly the inspection process.

Further inspections in the vicinity of the chosen solution can help to refine the search. Crosshairs in graphs allow connecting both dendrograms and the cluster map plotsimplify the navigation by the tool.

If you are specifically interested in the groups of solutions belonging to the decision variables space or the objectives space the tool can be configured to this alternative mode. For this, just select from the “cluster-mapping options” drop down menu at the top right of the dialog form. In that case only the appropriated graphs are plotted, but the selection process is entirely similar to that described previously.

Again a number of clustering algorithms and data pre-treatment are available, shared with the CPCC tool.

 

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Last modified: April 6, 2017 by Enrique Sánchez