Most design problems have multiple conflicting
objectives, and a compromise between
various objectives is required when choosing the optimal solution. For example, the cost and weight of
a product are normally in direct opposition to its strength,
quality, and reliability.
Results Analytics provides two algorithms for ranking data points:
- Weighted Sum
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Weighted sum is the best known and simplest algorithm for evaluating the goodness of multiple alternatives in terms of several objectives. The score value of each data point is simply a sum of all objective values, each multiplied by the final weight factor.
- Technique for Order of Preference by Similarity to Ideal
Solution (TOPSIS)
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TOPSIS is a multi-criteria ranking algorithm that employs
the concepts of the positive ideal point (the best objective values for
all criteria) and the negative ideal point (the worst objective values
for all criteria) in the objective domain. Alternatives are
ranked based on the shortest geometric distance from the positive
ideal point and the longest geometric distance from the negative
ideal point in terms of the objective values.
The TOPSIS algorithm will rank a balanced solution higher, even if the alternative is dominated; the weighted sum algorithm will rank a cutting edge or non-dominated solution higher. You should take this difference into account when choosing the ranking algorithm.