Novel Extreme Point Estimation and Normalization for Many-objective Evolutionary Algorithms

This paper proposes an improvement on an extreme point estimation and normalization for Non-dominated Sorting Genetic Algorithms (NSGAs). NSGA performs normalization to population at every generation to solve scalable multi-objective optimization problems. The normalization is generally performed based on ideal and nadir points of the population. The nadir point is obtained by extreme points corresponding to objective axes. However, when the conventional normalization method proposed in NSGA-III, for example, is applied, the search direction does not face to the direction of Pareto optimal front sometimes. Although, in order to avoid such problems, alternative extreme point estimations have been proposed, when the number of objectives is large, the normalization direction becomes inappropriate as above. This paper proposes an extreme point estimation technique for proper normalization even in many-objective optimization. Furthermore, a novel normalization method that does not depned on maximization/minimization before/after the normalization is also proposed in this paper.