A dual distance dominance based evolutionary algorithm with selection-replacement operator for many-objective optimization

Most existing dominance relations give higher priority to convergence than diversity and cannot offer reasonable selection pressure according to the evolution status. This easily makes the population converge to a sub-region of the Pareto front, and further leads to the imbalance between the convergence and diversity of population. To address the problem, we propose a dual distance dominance based evolutionary algorithm with selection-replacement operator for many-objective optimization (3DEA). In 3DEA, a dual distance dominance is proposed to strike a good balance between the convergence and diversity of population, where the dual distance is designed to measure the convergence of individuals and can adapt to different Pareto fronts. This dominance relation also combines the angle based niche to emphasize the diversity of individuals, in which the niche size is dynamically adjusted according to the number of objectives and evolution status. Meanwhile, a selection-replacement operator is developed to further maintain the population diversity and contribute to the convergence. In addition, a special points guided classification mutation mechanism is designed to generate excellent individuals in sparse regions and regions close to the Pareto front, and further improve the search efficiency of 3DEA. To verify the performance of 3DEA, we compare 3DEA with seven state-of -the-art methods on 30 test problems with the number of objectives varying from 5 to 20 and three practical applications. Experimental results demonstrate the proposed 3DEA has higher competitiveness on most test problems compared with seven state-of-the-art methods.