Dimensionality reduction based on geometric projection for many- objective optimization

There can be a large number of objectives in a certain optimization problem, but not all objectives are necessarily in conflict with each other, while some objectives are redundant. The true dimensionality of the Pareto front is less than the original number of objectives. Such redundant objectives can be removed from the set of objectives without loss of the structure of the Pareto front to improve computation and convergence. An approach based on geometric projection is proposed for dimensionality reduction. In this approach, the Pareto front can be mapped to a 2-dimensional coordinate plane which consists of the two arbitrary objectives in the original set of objectives, and the borderline can be identified. The conflict degree between the two objectives can be calculated by calculating the area of the projection and analyzing the monotonicity of the borderline curve. Simulation results show the effectiveness of the approach.