W-440_e Kaisa Miettinen kansi 080108.indd

Nadir objective vector is constructed with the worst Pareto-optimal objective values in a multi-objective optimization problem and is an important entity to compute because of its importance in estimating the range of objective values in the Pareto-optimal front and also in using many interactive multi-objective optimization techniques. It is needed, for example, for normalizing purposes. The task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and is reported to be a difficult task using other approaches. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search towards the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, the proposed procedures are found to be capable of finding a near nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task of nadir objective vector estimation.