Adaptive normal vector guided evolutionary multi- and many-objective optimization

Abstract Most existing multi-objective evolutionary algorithms relying on fixed reference vectors originating from an ideal or a nadir point may fail to perform well on multi- and many-objective optimization problems with various convexity or shapes of Pareto fronts. A possible reason could be the inaccurate measurement of the diversity of solutions or the failure of the fixed reference vectors in guiding the rapidly changing population. To meet this challenge, this work develops an adaptive normal reference vector-based decomposition strategy for guiding the search process, which is able to handle various convexity and shapes of Pareto fronts. Specifically, the normal vector passing through the center of each cluster in a constructed hyperplane is adopted as the reference vector for guiding the search process. Then, a selection strategy is put forward based on the positions of solutions in the current population and the normal vectors for the environmental selection. Based on the adaptive normal vectors, the proposed algorithm can not only rapidly adapt to the changing population but also alleviate the influence of the convexity of Pareto fronts on the measurement of diversity. Experimental results show that the proposed algorithm performs consistently well on various types of multi-/many-objective problems having regular or irregular Pareto fronts. In addition, the proposed algorithm is shown to perform well in the optimization of the polyester fiber esterification process.