# Multi-Objective Optimization for High-Dimensional Maximal Frequent Itemset Mining
## 5 Discussion and Conclusions  
The proposed algorithm scans the transaction sets before iterations and then generates the reduced transaction sets. All the follow-up operations are based on the reduced transaction sets and have two advantages. First, it significantly decreases the searching space. Second, it accelerates the assessment on follow-up individual quality. These are qualitative \begin{table}
\begin{tabular}{c c c} \hline \hline
**Itemset** & **Support** & **List of Items** \\ \hline \multirow{8}{*}{Top 10 1-itemsets} & 0.008465 & Caramel treats in bulk \\ \cline{2-3}  & 0.007171 & Fresh grade breast \\ \cline{2-3}  & 0.007171 & Homemade candy \\ \cline{2-3}  & 0.006901 & Garlic peanuts \\ \cline{2-3}  & 0.006739 & Wine cake \\ \cline{2-3}  & 0.006631 & Caterpillar vegetable \\ \cline{2-3}  & 0.006631 & Daliyuan small bread \\ \cline{2-3}  & 0.006631 & Ham butt \\ \cline{2-3}  & 0.006524 & Northeast crystal rice in bulk \\ \cline{2-3}  & 0.006362 & Crown pear \\ \hline \multirow{8}{*}{Top 5 2-itemsets} & 0.005230 & Chinese cabbage, chopped ribs \\ \cline{2-3}  & 0.004744 & Garlic, mature ginger \\ \cline{2-3}  & 0.004691 & Chinese cabbage, garlic \\ \cline{2-3}  & 0.004691 & Chinese cabbage, meteor cabbage \\ \cline{2-3}  & 0.004637 & Chinese cabbage, broccoli \\ \hline \multirow{3}{*}{Top 3 3-itemsets} & 0.003612 & Chinese cabbage, needle mushroom, domestic banana \\ \cline{2-3}  & 0.002480 & Chinese cabbage, domestic banana, winter bamboo shoots \\ \cline{1-1} \cline{2-3}  & 0.002103 & Chinese cabbage, domestic banana, chili pepper \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Top frequent itemsets. advantages, and the amplitudes of advantages vary for different transaction sets. For a transaction set with uniform support distribution and relatively high maximum supports, the generated transaction sets were slightly reduced in horizontal and longitudinal directions. The support of the transaction sets was generally small, and sparse transaction sets were associated. The reduced transaction sets horizontally and longitudinally show sharp reduction amplitudes, which significantly influence the time and space of the algorithm. At present, most algorithms focus on searching for frequent itemsets. Thus, they gain several solutions. Frequent itemsets that are newly generated in each evolution have to avoid being repeatedly recorded with the gained solution. If the maximal frequent itemset is used as the searching object, then all subsets of the maximal frequent itemset are frequent itemsets, and they all evolve towards the increasing number of items in the itemset. As such, all frequent itemsets cannot only be easily obtained but excessive storage solutions can be avoided, and the duplicate checking time can be decreased, thereby enabling the acceleration of the operation velocity of the algorithm. Association rule mining is divided into Boolean and numerical rules. This study processed the Boolean transaction sets. The gained frequent itemsets and the association rules, which were calculated in the next step, were also of Boolean type. The data of Boolean transaction sets only express existence and do not consider quantity. The numerical transaction sets can also be converted into Boolean type through discretization, which have certain universality with the Boolean frequent itemset mining. However, numerical transaction sets can explore multi-layer and more complicated association rules. Hence, the proposed and existing algorithms have advantages and disadvantages. Theoretically, classical and traditional algorithms can process high-dimensional Boolean transaction set data, but they are unfeasible with respect to time. A classical algorithm cannot work with data with high dimensions or mass transactions. It is even unfeasible to work data with slightly high dimensions or a slightly higher number of transactions. The combinatorial optimization problem cannot be solved by classical algorithms because of the solution space explosion problem.