An improved $${\alpha }$$α-dominance strategy for many-objective optimization problems

The convergence ability of Pareto-based evolutionary algorithms sharply reduces for many objective optimization problems because the solutions are difficult to rank by the Pareto dominance. To increase the selection pressure toward the global optimal solutions and well-maintain the diversity of obtained solutions, in this paper, an improved $${\alpha }$$α-dominance strategy is proposed. The proposal assigns $${\alpha }$$α values based on an elliptic function used to rank the solutions to enhance the convergence pressure, and it can also well maintain the diversity of obtained solutions through assigning different values of $${\alpha }$$α for different solutions, i.e., the solutions whose objective vectors locate in the objective space are assigned a larger $${\alpha }$$α. Experimental results show that the improved $${\alpha }$$α-dominance strategy can guide the searching process to converge to the Pareto Front and maintain the diversity of obtained solutions for many-objective optimization problems.