Pareto Filtering

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Definition: Pareto Filtering

The Pareto principle (also known as the 80-20 rule) states that, for any event, 80% of the effects are the result of 20% of the causes. This is a handy feature when a dimension, like customer, has a huge number of categories and we want to identify the 20% of our clients who brings in 80% of the sales. Pareto Filtering is based on this principle wherein the categories (<20% of a row/column in this case) are automatically grouped into ‘others’ category.


In some practical cases, a more useful distribution of Pareto points is one that has a judiciously variable density of points. The density should be higher where there is significant tradeoff and lower where the tradeoff is insignificant. Such a distribution is called a smart set of Pareto points. A method is incorporated which allows designers to comment on what they consider to be significant or insignificant tradeoff between two specific designs. The method then results in a reduced set of designs all of which exhibit significant tradeoff. The resulting smaller set eliminates the designer’s need to compare large number of designs. In this method the smart Pareto set is obtained through filtering an initially large number of Pareto solutions. This is called Pareto Filtering.


There are various types of filtering techniques followed according to requirements. Two important classes of Pareto Filters are: a) involves filtering to eliminate all non-Pareto and locally Pareto solutions from a given set of design points. The result is a set of globally Pareto optimal solutions b) involves filtering a global set to remove Pareto solutions that are deemed undesirable or less useful.

 

Thus Pareto Filter is a function which extracts non dominated solution from a set.

Calling Sequence example:

[F_out, X_out, Ind_out] = pareto_filter (F_in, X_in)


Description of Arguments:

• F_in - the set of multi-objective function values from which we want to extract the non-dominated solutions.

• X_in - the associated values in the parameters space.

• F_out - the set of non-dominated multi-objective function values.

• X_out - the associated values in the parameters space.

• Ind_out - the set of indexes of the non-dominated individuals selected from the set X_in.

 

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