Towards a more general many-objective evolutionary optimizer using multi-indicator density estimation

Recently, it was shown that Many-Objective Evolutionary Algorithms (MaOEAs) that employ a set of convex weight vectors are overspecialized in solving certain benchmark problems. This over-specialization is due to a high correlation between the Pareto fronts of the test problems and the simplex formed by the weight vectors. In furtherance of avoiding this issue, we propose a novel steady-state MaOEA that does not require weight vectors and adaptively chooses between two density estimators: one based on the IGD+ indicador that strengthens convergence to the Pareto front and another one, based on the s-energy indicator, which improves the diversity of the solutions. This approach, called sIGD+-MOEA, is compared with respect to NSGA-III, MOEA/D, IGD+-EMOA and MOMBI2 (which are MaOEAs that employ convex weight vectors) on the test suites WFG and WFG-1, using the hypervolume indicator. Experimental results show that sIGD+-MOEA is a promising alternative that can solve many-objective optimization problems whose Pareto fronts present different geometries.