Crossover controlling the number of crossed genes (CCG) significantly improves the search performance of NSGA-II in many-objective optimization problems (MaOPs). Since the conventional NSGA-II deteriorates convergence of solutions toward the optimal Pareto front in MaOPs, to improve the search performance it is desirable to combine CCG crossover with a parent selection method based on fine-grained ranking of solutions. However, the search performance is not improved when CCG crossover is employed in IBEA_ε+, which also realizes fine-grained ranking of solutions. That is, in some cases, the search performance is not improved by CCG crossover depending on the parent selection method combined. To further improve the search performance of MOEAs in MaOPs, in this paper we propose a MOEA which employs CCG crossover with a particular parent selection based on fine-grained ranking of solutions. First, to clarify the feature of parent selection improving its search performance by employing CCG, we analyze difference of solutions search between NSGA-II and IBEA_ε+. As a result, we show that diversity preservation mechanism is absolutely imperative in parent selection to search Pareto optimal solutions of MaOPs broadly distributed in objective/variable space by using CCG crossover. That is, to further improve the search performance, it is necessity to make fine-grained rank of solutions while keeping diversity of solutions in parent selection. To satisfy this requirements in the parent selection, in this work we combine CCG crossover with self-controlling dominance area of solutions (S-CDAS) as the particular parent selection method. Through performance verification using many-objective knapsack problems with 4~10 objectives, we show that the search performance of S-CDAS combined with CCG crossover significantly improves by keeping the number of crossed genes very small. Also, we show that the effectiveness of CCG operator becomes significant as we increase the number of objectives and search performance of S-CDAS with CCG is higher than NSGA-II and IBEA_ε+ with CCG.