A new diversity performance indicator for many-objective optimisation problems

Current performance indicators for assessing the diversity of many-objective optimisation approximations are often underperforming as the number of objectives increases, particularly for complex optimisation problems. In this article, a new pure unary diversity indicator is proposed, Inverse Ratio of Net Avertence angle (IRNA), which is formulated by minimising the sum of the included angles between approximation set and a set of reference vectors. It is achieved by effectively rotating the reference vectors system in all dimensions simultaneously with an optimised spatial angle. Any potential systematic bias in included angles is removed, and the highest possible diversity score of a solution set is obtained. Numerical results from evaluating performance on synthetic solutions on a unit simplex plane and benchmark functions of MaF show that the proposed performance indicator IRNA is more sensitive to capturing diversity changes as the number of objectives increases compared to other popular indicators.