An alpha-Dominance Expandation Based Algorithm for Many-Objective Optimization

Abstract

The convergence ability of Pareto-based evolutionary algorithms sharply reduces for many-objective optimization problems because the Pareto dominance is inefficient to rank the solutions and result in too many solutions becoming the non-dominated solutions. To overcome this shortcoming, it is necessary to increase the selection pressure toward the global optimal solutions and well-maintain the diversity of obtained non-dominated solutions. In this paper, an improved α-dominance based on expanding the dominated area of α-dominance is proposed. By redefining each objective function and the optimization problem through non-linear transformations, the dominated area of each solution is further expanded compared to that expanded by α-dominance, which can further enhance the selection pressure. Besides, the new dominance can well maintain the diversity of obtained solutions since the dominated area flexibly changes with different solutions. Moreover, this new dominance can be integrated into any multi-objective evolutionary algorithm to improve the performance of this algorithm. To demonstrate the effectiveness of the new dominance, we conduct the experiments on algorithm NNIA combined by the new dominance (briefly NNIA-NLAD). The experimental results show that the improved α-dominance can help NNIA to find better Pareto Front and maintain the diversity of obtained solutions for many-objective optimization problems.