A New Convergence Measure based on Shannon Entropy for Multi-Objective Optimization Algorithms
Thiago F. Santos1; Sebastião Xavier1
1 Universidade Federal de Ouro Preto
Resumo
The algorithms of multi-objective optimization 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 (S-Metric), 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.
Palavras-chave: Multi-Objective Optimization Algorithms; Performance Measure; Shannon Entropy