topsisOpt: Technique for Order of Preference by Similarity to Ideal...

In multiDoE: Multi-Criteria Design of Experiments for Optimal Design

Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

Description

This function implements Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). This approach is based on the principle that the best solutions must be near to a positive ideal solution (I+) and far from a negative ideal solution (I-) in the criteria space. The weighted distance measure used to detect these similarities allows the user to possibly assign different importance to the criteria considered. The distance measure used is:

L_p(a,b) = \left[ \sum_{j=1}^{m}(w_j)^p(|a-b|)^p\right] ^(1/p)

The metric on the basis of which solution ranking occurs is:

S(x) = \frac{L_p(x,I-)}{(L_p(x,I+) + L_p(x,I-)}

Usage

topsisOpt(out, w = NULL, p = 2)

Arguments

out	A list as the megaAR list returned by runTPLS.
w	A vector of weights. It must sum to 1. The default wights are uniform.
p	A coefficient. It determines the type of distance used. The default value is 2.

Value

The function returns a list containing the following items:

• ranking: A dataframe containing the ranking values of S(x) and the ordered indexes according to the TOPSIS approach (from the best to the worst).

• bestScore: The scores of the best solution.

• bestSol: The best solution.

References

M. Méndez, M. Frutos, F. Miguel and R. Aguasca-Colomo. TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem. Mathematics, 2020. https://www.mdpi.com/2227-7390/8/11/2072

multiDoE documentation built on April 4, 2025, 2:32 a.m.