Sentence examples for for solving MaOPs from inspiring English sources

However, directional mutation operators for solving MaOPs are scarce.

In this subsection, we evaluate the effectiveness of non-dominated sorting in MOEAs for solving MaOPs.

First, non-dominated sorting is very helpful for KnEA to achieve a set of non-dominated solutions with better quality for solving MaOPs.

From the table, it can be seen clearly that A-ENS is more efficient than T-ENS in MOEAs for solving MaOPs.

There are also some non-dominated sorting methods specially tailored for solving MaOPs, such as corner sort [30], T-ENS [23], and A-ENS [31].

In the following, we empirically verify the efficiency of A-ENS and the influence on performance of MOEAs by embedding it into two MOEAs, KnEA and Two_Arch2, developed recently for solving MaOPs.

The above approaches improve the efficiency of solving MaOPs in various ways.

It is necessary to note that non-dominated sorting can still determine a few candidate solutions in the combined population unsuitable for surviving for next population in solving MaOPs, which is helpful for promoting population of KnEA to converge to the Pareto fronts.

We verify the effectiveness of non-dominated sorting by considering two popular MOEAs developed for solving MOPs and MaOPs, NSGA-II and KnEA.

The enhanced performance of KnEA and Two_Arch2 may show that the errors introduced by approximate non-dominated sorting are helpful for MOEAs to improve the performance in solving MaOPs.

Therefore, we can summarize that non-dominated sorting is also important for developing a promising MOEA to solve MaOPs, especially for some complex MaOPs, such as those with multiple local Pareto fronts.