Adaptive parametric scalarizations in multicriteria optimization (Q2875213)

The author derives an adaptive parameter scheme for the augmented weighted Tchebycheff method. He constructs all parameters of the method in an adaptive way such that every nondominated point of a discrete multicriteria optimization problem can be generated and the augmentation parameter can be chosen as large as possible up to a feasible upper bound. Besides, the author considers a generalized problem formulation that contains an augmentation parameter for each objective. For bicriteria problems she proposes an adaptive parameter scheme that takes all parameters, i.e. also the weights, into account. Augmented variants of the \(\epsilon\)-constraint method are discussed. It is shown that the augmentation parameter of an augmented \(\epsilon\)-constraint scalarization can be determined in the same way as it is proposed for the augmented weighted Tchebycheff method. This book presents the general framework of an adaptive parametric algorithm that is based on a systematic decomposition of the search region, i.e., the region potentially containing further nondominated points. Finally, the theoretical results are validated computationally.