A Cone Decomposition Many-Objective Evolutionary Algorithm with Adaptive Direction Penalized Distance

The effectiveness of most of the existing decomposition-based multi-objective evolutionary algorithms (MOEAs) is yet to be heightened for many-objective optimization problems (MaOPs). In this paper, a cone decomposition evolutionary algorithm (CDEA) is proposed to extend decomposition-based MOEAs to MaOPs more effectively. In CDEA, a cone decomposition strategy is introduced to overcome potential troubles in decomposition-based MOEAs by decomposing a MaOP into several subproblems and associating each of them with a unique cone subregion. Then, a scalarization approach of adaptive direction penalized distance is designed to emphasize boundary subproblems and guarantee the full spread of the final obtained front. The proposed algorithm is compared with three decomposition-based MOEAs on unconstrained benchmark MaOPs with 5 to 10 objectives. Empirical results demonstrate the superior solution quality of CDEA.