# Identifying Hyper-Heuristic Trends through a Text Mining Approach on the Current Literature
## 4 Results
### Clustering  
As mentioned before, we decided on the number of clusters using the elbow method and the total within-cluster sum of squares of each configuration, which recommended to have nine clusters (\(k=9\)). Based on our experience and the nature of the hyper-heuristics, we eliminated two groups, one related to engineering and software and the other to combinatorial optimization. We removed the first cluster because of its lack of relevance to hyper-heuristics and the second cluster because it did not show favorable results in generating similar characteristics within itself. Table 2 illustrates the seven remaining clusters along with their corresponding sizes (number of publications in the cluster), the word counts, and the most critical compound words.  
By analyzing the clusters generated, we have identified some exciting patterns in their contents. For example, most clusters involve genetic algorithms as their solution approach. We highlight some particular findings for each achieved cluster as follows.  
\begin{table}
\begin{tabular}{c c l l} \hline \hline
**Cluster** & **Size** & **Words** & **Compund-Words** \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{84} & shop (99) & shop, scheduling (83) \\  & & genetic (98) & - \\  & & job (67) & - \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{369} & hyper (92) & packing, problem (19) \\  & & evolutionary (73) & bin, packing, problem (16) \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{56} & vehicle (59) & combinatorial, optimization (20) \\  & & genetic (57) & capacitated (28) & capacitated, arc, routing (19) \\  & & capacitated (25) & routing, policies (13) \\  & & network (25) & - \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{140} & evolutionary (84) & particle, swarm (35) \\  & & genetic (58) & swarm, optimization (30) \\  & & hyper (55) & - \\  & & multiobjective (52) & - \\ \hline \multirow{3}{*}{5} & \multirow{3}{*}{45} & genetic (30) & resource-constrained, project (15) \\  & & resource (24) & resource-constrained, project, scheduling (15) \\  & & project (20) & - \\ \hline \multirow{3}{*}{6} & \multirow{3}{*}{57} & scheduling (37) & combinatorial, optimization (15) \\  & & hyper (29) & university, course (13) \\ \cline{1-1}  & & examination (24) & simulated, annealing (11) \\ \cline{1-1}  & & graph (19) & exam, timetabling (10) \\ \cline{1-1}  & & - & course, timetabling (8) \\ \cline{1-1}  & & - & school, timetabling (7) \\ \hline \multirow{3}{*}{7} & \multirow{3}{*}{21} & satisfaction (25) & variable, ordering (14) \\ \cline{1-1}  & & hyper (11) & - \\ \cline{1-1}  & & genetic (10) & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Clusters related to hyper-heuristics in the literature. The count of each word or compound word is illustrated between parentheses.  
* Cluster 1 (with 84 documents) deals with scheduling problems with a strong focus on job-shop scheduling. This cluster is characterized by extensive usage of genetic algorithms throughout the solution process.
* Cluster 2 (with 369 reports) is the largest and contains methods mainly using evolutionary algorithms, particularly genetic algorithms.
* Cluster 3 (with 56 records) primarily relates to vehicle routing and capacitated routing problems. It also includes other works on combinatorial optimization. Genetic algorithms also play an important role in this cluster.
* Cluster 4 (with 140 articles) mainly corresponds to optimization problems, including multi-objective ones. Although genetics is one of its main words, the term evolutionary is more relevant in general.
* Cluster 5 (with 45 reports) mostly includes scheduling problems, as was the case for Cluster 1, but it excludes the works on genetic algorithms.
* Cluster 6 (with 57 documents) addresses timetabling and scheduling problems, presenting its applications in different areas of education.
* Finally, Cluster 7 (with 21 articles) deals with constraint satisfaction problems.