A Convergence indicator for Multi-Objective Optimisation Algorithms
This is an incremental contribution for researchers in multi-objective optimization, providing a new tool for algorithm comparison.
The paper tackles the problem of comparing multi-objective optimization algorithms by proposing a new convergence indicator based on Shannon entropy, which does not require knowledge of the true Pareto set and has medium computational cost compared to hypervolume.
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($Δ$), Averaged Hausdorff distance ($Δ_p$), 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.