Adjusted Weighted Tchebycheff Scalarization

Perform Adjusted Weighted Tchebycheff Scalarization for the MOEADr package.

scalarization_awt(Y, W, minP, eps = 1e-16, ...)

Arguments

Y

matrix of objective function values

W

matrix of weights.

minP

numeric vector containing estimated ideal point

eps

tolerance value for avoiding divisions by zero.

...

other parameters (included for compatibility with generic call)

Value

Vector of scalarized performance values.

Details

This routine calculates the scalarized performance values for the MOEA/D using the Adjusted Weighted Tchebycheff method.

References

Y. Qi, X. Ma, F. Liu, L. Jiao, J. Sun, and J. Wu, “MOEA/D with adaptive weight adjustment,” Evolutionary Computation, vol. 22, no. 2, pp. 231–264, 2013.

R. Wang, T. Zhang, and B. Guo, “An enhanced MOEA/D using uniform directions and a pre-organization procedure,” in IEEE Congress on Evolutionary Computation, Cancun, Mexico, 2013, pp. 2390–2397.

F. Campelo, L.S. Batista, C. Aranha (2020): The MOEADr Package: A Component-Based Framework for Multiobjective Evolutionary Algorithms Based on Decomposition. Journal of Statistical Software doi:10.18637/jss.v092.i06

Examples

W    <- generate_weights(decomp = list(name = "sld", H = 19), m = 2)
Y    <- matrix(runif(40), ncol = 2)
minP <- apply(Y, 2, min)
Z    <- scalarization_awt(Y, W, minP)