topsisOpt {multiDoE} | R Documentation |
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 |
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