A Convergence Indicator for Multi-Objective Optimisation Algorithms

Abstract

The algorithms of multi-objective optimisation had a relative growth in the last years.
Thereby, it's requires some way of comparing the results of these. In this sense, performance
measures play a key role. In general, it's considered some properties of these algorithms such as
capacity, convergence, diversity or convergence-diversity. There are some known measures such as  generational distance (GD), inverted generational distance (IGD), hypervolume (HV),
Spread($\Delta$), Averaged Hausdorff distance ($\Delta_p$), R2-indicator, among others. In this
paper, we focuses on proposing a new indicator to measure convergence based on the traditional
formula for Shannon entropy. The main features about this measure are: 1) It does not require tho know  the true Pareto set and 2) Medium computational cost when compared with Hypervolume.