Expanding the Normal Boundary Intersection Method to Completely Capture Many Objective Pareto Sets

A typical approach to solving many-objective optimization problems is to identify non-dominated points in the objective space as an approximation of the Pareto front. However, discovering the Pareto front becomes increasingly difficult as the number of objectives exceeds three. The Normal Boundary Intersection (NBI) method is of particular interest due to its objective-space-based formulation, but it suffers from well-known limitations when applied to many-objective problems. This paper introduces an extension to the NBI method, termed NBI+, which addresses these limitations and more effectively captures Pareto fronts in high-dimensional objective spaces. The benefits of the NBI+ algorithm are demonstrated on two benchmark problems, highlighting its improvements over the original NBI method.