A Many-Objective Evolutionary Algorithm Based on Non-Linear Dominance

With the increase in the number of objectives, the number of non-dominated solutions will also increase sharply. The sorting method based on the traditional Pareto dominance is not sufficiently distinguishable from the solutions and cannot provide enough selection pressure when the population size is small. In this article, a new non-linear dominance (NLD) method is proposed. The main motivation of this method is from the perspective of storage solutions. The number of solutions is small and the difference between each component is as large as possible, so the part of the first quadrant, the second, and the fourth quadrant near the first quadrant becomes the dominant interval, except for the distance too far also defined as the dominant interval, for which construct a parabolic shape of the non-dominant interval. Based on this relationship, the authors propose a non-linear dominated many-objective evolutionary algorithm (NLDEA), which can solve the irregular Pareto front. Experiments show that NLDEA is competitive with the most advanced methods for various scalable benchmark problems.