Towards a More General Many-objective Evolutionary Optimizer

Recently, it has been shown that the current Many-Objective Evolutionary Algorithms (MaOEAs) are overspecialized in solving certain benchmark problems. This overspecialization is due to a high correlation between the Pareto fronts of the test problems with the convex weight vectors commonly used by MaOEAs. The main consequence of such overspecialization is the inability of these MaOEAs to solve the minus versions of well-known benchmarks (e.g., the DTLZ\(^{-1}\) test suite). In furtherance of avoiding this issue, we propose a novel steady-state MaOEA that does not require weight vectors and uses a density estimator based on the IGD\(^+\) indicator. Moreover, a fast method to calculate the IGD\(^+\) contributions is integrated in order to reduce the computational cost of the proposed approach, which is called IGD\(^+\)-MaOEA. Our proposed approach is compared with NSGA-III, MOEA/D, IGD\(^+\)-EMOA (the previous ones employ convex weight vectors) and SMS-EMOA on the test suites DTLZ and DTLZ\(^{-1}\), using the hypervolume indicator. Our experimental results show that IGD\(^+\)-MaOEA is a more general optimizer than MaOEAs that need a set of convex weight vectors and it is competitive and less computational expensive than SMS-EMOA.