Penalty-based Boundary Intersection Scalarization

Source: R/scalarization_pbi.R

Perform PBI Scalarization for the MOEADr package.

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

Arguments

Y

matrix of objective function values

W

matrix of weights.

minP

numeric vector containing estimated ideal point

aggfun

list containing parameters for the aggregation function. Must contain the non-negative numeric constant aggfun$theta.

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 PBI method.

References

Q. Zhang and H. Li, "MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition", IEEE Trans. Evol. Comp. 11(6): 712-731, 2007.

H. Li, Q. Zhang, "Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II", IEEE. Trans. Evol. Comp. 12(2):284-302, 2009.

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)
aggfun <- aggfun    <- list(name = "pbi", theta = 5)
Z      <- scalarization_pbi(Y, W, minP, aggfun)