Many-objective evolutionary algorithm based on relative non-dominance matrix.

Various evolutionary algorithms have been proposed for tackling many-objective optimization problems over the past three decades. However, these algorithms still suffer from the loss of selection pressures due to the existence of dominance resistance. To tackle this issue, this paper proposes a relative non-dominance matrix, based on which a fitness formula is defined. Empirical analyses show that solutions with smaller fitness values are likely to dominate more other solutions in the future evolutionary process, and play a vital role in enhancing the convergence toward to the true Pareto fronts. Additionally, to further ensure the diversity, k -means clustering strategy is combined with the relative non-dominance matrix for a new design of the environmental selection, where parameter k in the clustering strategy is adjusted adaptively. The proposed algorithm is extensively tested with four state-of-art algorithms on WFG, MaF and DTLZ test suites. Empirical comparisons demonstrate the competitiveness of the proposed algorithm regarding to the convergence, diversity and spread. [ABSTRACT FROM AUTHOR]