Running performance metrics for evolutionary multi-objective optimizations

It is now well established that more than one performance metrics are necessary for evaluating a multi-objective evolutionary algorithm (MOEA). Although there exist a number of performance metrics in the MOEA literature, most of them are applied to the final non-dominated set obtained by an MOEA to evaluate its performance. In this paper, we suggest a couple of running metrics-one for measuring the convergence to a reference set and other for measuring the diversity in population members at every generation of an MOEA run. Either using a known Pareto-optimal front or an agglomeration of generation-wise populations, the suggested metrics reveal important insights and interesting dynamics of the working of an MOEA or help provide a comparative evaluation of two or more MOEAs.