In recent years, there has been many examples of applying evolutionary multi-criterion optimization (EMO) to practical problems in many fields. On the other hand, a new problem of how to analyze non-dominated solutions (NDSs) with many design variables and many objectives arises. For this problem, we has provided our original analysis support system using association rules, which is correlation-based information hierarchical structuring method (CIHSM). CIHSM could extract features of NDSs through objective analysis using association rules and visually present result of analyses as a hierarchical tree. However, there remains two problems in our CIHSM; the parameter setting related to association rules and the feature extraction required by user's interest. In this paper, we have proposed a modified CIHSM having two mechanism for dissolving these two problems. We called it ``on-demand CIHSM''. The first mechanism is the feature selection according to user's interest region in objective space. The important point of this mechanism is that user can select his interests region visually. And the second mechanism is to tune the value of minimum support parameter automatically. The setting of this parameter has a strong influence for the number of extracted rules. But this mechanism could provide use's requirement number of rules without tuning the value of this parameter. To investigate the effectiveness of on-demand CIHSM, we applied it to the conceptual design problem of hybrid rocket engine(HRE) problem, which is a real problem provided by JAXA. Through this experiments, it was verified that our on-demand CIHSM is very useful to extract features of NDS according to user's interest.