Pareto Compliance of Multiobjective Optimization Indicators

The aim of this project is to establish appropriate conditions ensuring the Pareto compliance of the performance indicators associated to the Generational Distances GD_p and GD_{p,q}, and the Inverted Generational Distances GD_p and GD_{p,q}, by means of mathematical criteria involving the behavior of candidate solutions, and summarize at the end the consequences for the compliance of the Averaged Hausdorff Distances Delta_p and Delta_{p,q}. These results will help to elucidate the convenience of these indicators for applications to MOPs and to show possible directions for further and possibly more convenient generalizations.