  Inverted Generational Distance (IGD) has been widely considered as a reliable
performance indicator to concurrently quantify the convergence and diversity of
multi- and many-objective evolutionary algorithms. In this paper, an IGD
indicator-based evolutionary algorithm for solving many-objective optimization
problems (MaOPs) has been proposed. Specifically, the IGD indicator is employed
in each generation to select the solutions with favorable convergence and
diversity. In addition, a computationally efficient dominance comparison method
is designed to assign the rank values of solutions along with three newly
proposed proximity distance assignments. Based on these two designs, the
solutions are selected from a global view by linear assignment mechanism to
concern the convergence and diversity simultaneously. In order to facilitate
the accuracy of the sampled reference points for the calculation of IGD
indicator, we also propose an efficient decomposition-based nadir point
estimation method for constructing the Utopian Pareto front which is regarded
as the best approximate Pareto front for real-world MaOPs at the early stage of
the evolution. To evaluate the performance, a series of experiments is
performed on the proposed algorithm against a group of selected
state-of-the-art many-objective optimization algorithms over optimization
problems with $8$-, $15$-, and $20$-objective. Experimental results measured by
the chosen performance metrics indicate that the proposed algorithm is very
competitive in addressing MaOPs.
