# Multi-Objective Optimization for High-Dimensional Maximal Frequent Itemset Mining
## 5 Discussion and Conclusions
A classical algorithm attempts to search for all possible solutions, and the time complexity of the algorithm is unacceptable because of the explosion of space. However, the evolutionary algorithm overcomes this characteristic and it always sets the algorithm parameter in the acceptable range, which makes it feasible to solve the combinatorial explosion problem. The evolutionary and other swarm intelligence algorithms can feasibly work with high-dimensional and mass transactions datasets. They have different advantages and disadvantages. The proposed algorithm takes the maximal frequent itemset as the optimization objective, which is slightly different from existing algorithms. Hence, it is not comparable with existing algorithms. According to two tests of transaction sets with different characteristics, the proposed algorithm is feasible, and its time complexity is acceptable with respect to practicability. The accurate optimal solution cannot be verified in most cases because the solution space of high-dimensional data is explosive. The proposed method is verified by small-scaled data, and it can almost find all maximal frequent itemsets. However, whether all maximal frequent itemsets of high-dimensional transaction sets of large-scaled data have been gained remains unknown. From the maximal frequent itemsets mining of supermarket data, we realize that users often need to know what the most supported 2-itemsets are, what the most supported 3-itemsets are, etc. However, our problem description is to give a support threshold and then find the maximal frequent itemsets whose support is greater than the threshold. This makes it possible for an item to combine the 2-itemsets with the maximum support into a 3-itemsets with small support. This is inconsistent with the user's requirements. The future direction of frequent itemsets mining should be to change the definition of the problem and try to meet the characteristics of each practical problem, rather than looking for common problems. Future research should abandon the use of support thresholds and develop an algorithm to find a list of frequent itemsets with the highest support during a given period. **Author Contributions:** Conceptualization, Y.Z. and W.Y. ; methodology, Y.Z., W.Y., X.M. and H.O. ; software, Y.Z. ; validation, D.Y., W.Y. and Y.Z. ; formal analysis, D.Y. ; investigation, W.Y. ; resources, W.Y. ; data curation, Y.Z. ; writing--original draft preparation, Y.Z. ; writing--review and editing, Y.Z. ; visualization, Y.Z. ; supervision, W.Y. ; project administration, Y.Z. ; funding acquisition, W.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by the Zhejiang Basic Public Welfare Research Plan Projects (Item No. LGG19F030009, LGG19F020005) funded by the Science Technology Department of Zhejiang Province, China. Not applicable. **Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: [[http://fimi.uantwerpen.be/data](http://fimi.uantwerpen.be/data)]([http://fimi.uantwerpen.be/data](http://fimi.uantwerpen.be/data)) (accessed on 28 February 2020). This work was supported by the Zhejiang Basic Public Welfare Research Plan Projects (Item No. LGG19F030009, LGG19F020005) funded by the Science Technology Department of Zhejiang Province, China. We would like to extend our gratitude to the website [[http://fimi.uantwerpen.be/data](http://fimi.uantwerpen.be/data)]([http://fimi.uantwerpen.be/data](http://fimi.uantwerpen.be/data)) (accessed on 28 February 2020) for providing the open test transaction set to a wide range of researchers. This work was also supported by my friend, who is a supermarket owner and provided the real sales data for the research in this work. The authors declare no conflict of interest.