An augmented weighted Tchebycheff method with adaptively chosen parameters for discrete bicriteria optimization problems

For discrete bicriteria optimization problems we derive a method for a problem dependent determination of all parameters of the augmented weighted Tchebycheff norm such that all nondominated points can be found and ρ is as large as possible. In a computational study based on randomly generated instances of a bicriteria knapsack problem, the resulting adaptive augmented weighted Tchebycheff method is compared with the lexicographic weighted Tchebycheff method and with the augmented weighted Tchebycheff method with preset parameter values as well as with augmented ε-constraint scalarizations.