Repeated $\epsilon$-Sampling for Many-Objective Optimization

Many-objective optimizers based on Pareto domi-nance and its extensions rely on the effectiveness of the diversity preservation mechanism embedded in survival selection to achieve good performance. This work proposes Repeated
$\varepsilon$
-Sampling, a survival selection method designed for elitist multi-objective algorithms to select a sample of well-distributed solutions in objective space from the non-dominated solutions set. The proposed method iteratively applies
$\varepsilon$
-Sampling, a procedure that uses
$\varepsilon$
-dominance to determine near solutions, increasing at each iteration the expansion rate used to compute
$\varepsilon$
-dominance, gradually eliminating near solutions in objective space, starting with the closest ones. Compared to an adaptive
$\varepsilon$
-Sampling method, we show that the proposed method improves the unifor-mity of the sample, leading to substantially better performance in many-objective epistatic problems in terms of convergence and diversity. We also show that a Pareto dominance-based many-objective optimizer with the proposed method finds Pareto sets with significantly better hypervolume than MOEA/D, a well-known decomposition-based algorithm.