R-HV: A metric for computing hyper-volume for reference point based EMOs

Abstract

For evaluating performance of a multi-objective optimization for finding the entire efficient front, a number of metrics, such as hypervolume, inverse generational distance, etc. exists. However, for evaluating an EMO algorithm for finding a subset of the efficient frontier, the existing metrics are inadequate. There does not exist many performance metrics for evaluating a partial preferred efficient set. In this paper, we suggest a metric which can be used for such purposes for both attainable and unattainable reference points. Results on a number of two-objective problems reveal its working principle and its importance in assessing different algorithms. The results are promising and encouraging for its further use.