A New Method for Generating and Indexing Reference Points in Many Objective Optimisation
Kai Eivind Wu, George Panoutsos · 2020
A new method for the creation of reference points is proposed, for use in reference point-based Many objective Optimisation Problems. Unlike the current common practice of generating reference points on a unit simplex plane by Dan and Dennis method, which leads to uneven distribution of reference points on actual Pareto Front (PF) that the generated reference points are projected onto, the reference points are more evenly generated on an m dimensional B-norm surface which is created adaptively by tracking the true PF. The method is thus named as B-norm based PF tracking method (Bn-PFt). To ease the work of algorithmic development, an indexing system of reference points is also proposed. Systematic numerical studies performed on B-norm surfaces of various B values show that reference points created by the proposed Bn-PFt method are more evenly distributed on the surfaces than those of the projected onto the same surfaces generated using Dan and Dennis method. Simulation results using NSGA III on benchmark problems MaF3 and MaF5 with 3, 5, and 7 objective functions, show that the candidate solution sets obtained, via adopting reference points with the proposed method, have better diversity.