# Multi-Objective Optimization for High-Dimensional Maximal Frequent Itemset Mining
## 1 Introduction  
The big data association rule analysis was mainly finished in two steps. First, all frequent itemsets whose frequency of occurrence exceeded the threshold were recognized from the database. Second, all association rules that meet the minimum confidence threshold are produced by frequent itemsets. The mining of frequent itemsets is the key difficulty in association rules analysis because the overall performance in the mining of association rules is mainly determined by the performance in the first step. The mining of frequent itemsets aims to find itemsets whose frequency of occurrence exceeds the preset frequency threshold of the given mass transaction sets. The given transaction sets correspond to the object of big data. The occurrence frequency of an itemset is called the support degree, and the given frequency threshold is called the minimum support threshold. The mining of the frequent itemset can present variables that often occur together in transaction sets, which provide support for possible decisions. The mining of frequent itemsets is also the basis of various important data mining tasks, such as correlation analysis, causal relationship, sequence itemset, local periodicity, and plot fragments. For example, in their story of beer and diapers, Walmart found that beer and diapers were often bought together through big data analysis, which indicates that beer buyers often need to buy diapers, or diaper buyers often also buy beer. Thus,-frequent itemsets, such as shopping basket data analysis [1], webpage prefetching [2], cross-shopping [3], personalized websites [4], and network intrusion detection [5], have been extensively applied. The mining algorithms of frequent itemset can generally be divided into two types, namely accurate and heuristic algorithms. The most classical accurate algorithms include Apriori [6], FP-Growth [7], and many derived algorithms [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. The theory of accurate algorithms seems to be perfect. However, they are inapplicable to big data and high-dimensional transaction sets. The fundamental causes include the serious consumption of time and storage capacity due to the exponential explosive growth of solution space and the consequent abundant candidate itemsets and complicated data structure. Therefore, many researchers began to consider applicable heuristic algorithms. For example, the evolutionary computation and swarm intelligence algorithm were applied to solve problems [21; 22; 23; 24; 25; 26]. If frequent itemsets are explored by the evolutionary algorithm, then an itemset can be used as an individual of the solution space. Many individuals form a population that is optimized in the iteration. Compared with accurate algorithms, the evolutionary algorithm might not be the best, but it can avoid the explosive solution space, thereby making the time and storage space acceptable in the face of big data and high-dimensional data. Many studies have applied many particle swarm optimization (PSO) and genetic algorithms in heuristic algorithms to solve the mining frequent itemset. [PERSON] et al. [21] designed a binary PSO to mine frequent itemsets. This algorithm could cut the relieved pressure over storage and CPU time dynamically in the process of population initialization and evolution. It has also been applied to four different transaction sets. Among these four transaction sets, the number of transactions in one set was 500, and the number of transactions in the three other sets were 1000. [PERSON] et al. [22] applied the genetic algorithm to explore the frequent itemset in the data stream; it is novel that the conceptual drift was determined by frequent itemsets. The number of dimensions and transactions was not very high because the objects use some data within a slipping window frame of data flow. [PERSON] et al.