A Hierarchical Decomposition-Based Evolutionary Many-Objective Algorithm

The evolutionary multiobjective algorithms have been demonstrated the effectiveness in dealing with multiobjective optimization problems. However, when solving the problems with many objectives, i.e., the number of objectives is greater than three, it needs a large population size to maintain population diversity and provide a good approximation to the Pareto front. The dilemma between limited computational resources and the exponentially increasing population size is a big challenge. Thus, we suggest a hierarchical decomposition-based evolutionary algorithm for solving many-objective optimization problems in this paper. Specifically, it constructs a binary tree on a set of large-scale uniform weight vectors. We only compare a candidate solutions with the solutions on the path from root to a leaf node of the tree to assign it into an appropriate node. The proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of the proposed algorithm is \(\mathcal {O}(Mlog(\mathbb {N}))\) for dealing with a new candidate solution. Empirical results fully demonstrate the effectiveness and competitiveness of the proposed algorithm.