A Parameterless Penalty Rule-Based Fitness Estimation for Decomposition-Based Many-Objective Optimization Evolutionary Algorithm

Many-objective optimization problems (MaOPs) present a huge challenge to the traditional Pareto-based multi-objective algorithms because the increase of the objectives results in the low-efficiency of the Pareto dominance in distinguishing the relationships between the solutions during the environmental selection. To enhance the selection pressure, in this paper, through redefining each objective function by a non-linear transformation, we first propose a new dominance method called NLAD-dominance, in which a dynamic parameter adjusting scheme is designed to dynamically adjust parameter α according to different numbers of objectives and different evolutionary states. As a result, NLAD-dominance can provide proper selection pressure for different kinds of MaOPs in different stages of evolution. Then, based on NLAD-dominance, we design a new fitness estimation strategy which takes both convergence and diversity into account, and adaptively balances them by a parameterless penalty rule. Thus, it can well evaluate the quality of each solution. At last, we conduct the experiments and compare the proposed algorithm with five state-of-the-art algorithms on 80 test instances of 16 benchmark problems with up to 20 objectives. The experimental results indicate that the proposed algorithm is highly competitive in terms of both convergence enhancement and diversity maintenance.