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:
$$S(x) = \frac{L_p(x,I-)}{(L_p(x,I+) + L_p(x,I-)}$$
topsisOpt(out, w = NULL, p = 2)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.
A list as the megaAR list returned by runTPLS.
A vector of weights. It must sum to 1. The default wights are uniform.
A coefficient. It determines the type of distance used. The default value is 2.
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