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Page 10 of 15 Cui et al. Complex Eng Syst 2023;3:3 I http://dx.doi.org/10.20517/ces.2022.57

Figure 4. The flowchart of NSGA-II.

Firstly, multi-objective optimization method and multi-objective collaborative optimization method are com-
pared. The distribution of the Pareto solutions obtained by only the NSGA-II is similar to the result by the
NSGA-II with CO. 278 Pareto solutions are obtained by the NSGA-II with CO, and form a near-complete
Pareto front. However, the number of Pareto solutions (104) obtained by the multi-objective optimization
(NSGA-II) is too few to form a near-complete Pareto front. Furthermore, due to the insufficient number of
solutions, poor non-dominant solutions cannot be eliminated, resulting in a low quality of the optimization
solution set. Thus, it could be concluded that the multi-objective collaborative optimization has better solution
set diversity and higher solution quality than the multi-objective optimization.

Secondly, the results obtained by CO combing with different multi-objective algorithms are compared. The
MOPSO gets 53 Pareto solutions, while the NCGA and the NSGA-II have 269 and 278 Pareto solutions, respec-
tively. Due to the neighborhood cultivation mechanism of the NCGA algorithm, excellent parent generations
could be preserved in the next generation, which guarantees more Pareto solutions obtained, and the Pareto
solutions distribution is more concentrated. In terms of NSGA-II algorithm, the elitist strategy is introduced;