An evaluation of non-redundant objective sets based on the spatial similarity ratio

Multi-objective optimization is a challenging task in many disciplines. Although a number of algorithms have simplified this problem by degenerating redundant objectives into low-dimensional sets, there is currently no consensus method for evaluating their performance. In this paper, we propose an evaluation method that uses a spatial similarity ratio (SSR) to determine the quality of non-redundant objective sets (NRSs). We consider the reduction of all NRSs of three functions from 5D to 2D or 3D using our SSR-based method, and compare the results to those given by an inverted generational distance-based method. The results demonstrate that our method is more accurate, as it takes information from both the non-redundant and redundant objective sets into consideration. In addition, using the proposed SSR-based approach, no prior knowledge of the true Pareto set is required. Therefore, we can conclude that our SSR-based method is feasible for the assessment of non-redundant objective sets.