# An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering +
## 2 Related Work
### Cluster-Based Multiobjective Optimisation  
An early work on cluster-based solution selection in the Pareto set was proposed by [11], applied to generate a reduced Pareto set to solve the scaling and high-dimensional problems in many-objective optimization (MaOO). There is an increasing number of works that apply such an approach to improve the MOO solution selection. Here, the fitness values of solutions are clustered to find representatives (cluster centers). This means that solutions with similar fitness values are grouped together and a representative for each group is generated for guiding the solution selection or for the evolution of the solutions. [PERSON] et al. [16] applied fuzzy clustering in multiobjective particle swarm optimization to perform electrical power dispatching, particularly to minimize fuel cost and emission. Their technique outperformed traditional MOO techniques, including NSGA, NPGA and SPEA. In [17], a density-based clustering approach DBSCAN was applied in MOO to find diverse optimal and near-optimal Pareto fronts to solve water resource problems. During dominance check, only local comparisons with solutions sharing the same clusters were checked.The authors stated that the introduction of a dissimilar index in the clustering for deciding whether to select or remove solutions for further evolution gave users more control as decision support. [PERSON] et al. [18] used an agglomerative hierarchical cluster-based approach with [PERSON]'s linkage in MOEA to guide selection in a way that maintains diversity and reduces convergence time. Their technique was applied to solve the problem of poor solutions selection due to an irregular Pareto front. The authors shared that using K-means generated spherical clusters and required a prior number of clusters. [PERSON] et al. [12] proposed a flexible similarity metric for cluster-based MOEA to handle both convex- and concave-shaped Pareto fronts.  
[PERSON] et al. [14] applied density-based Fuzzy C-means in clustering in a dynamic nondominated sorting multiobjective genetic algorithm to determine Pareto fronts distribution, applied to improve traffic congestion. In their previous work [19], they applied a clustering method that was based on the VAR and PRE method. While these cluster-based approaches improve MOO algorithms, to the best of our knowledge, such approaches are not commonly applied to data clustering problems. So far, we found only [20], who applied cluster-based MOO for data clustering, proposing the hierarchical topology-based cluster representation, which is based on a tree-based graph for multiobjective clustering (HT-MOC), scalable to large datasets. The approach involves the use of a seeding algorithm followed by the use of the formulation of minimum spanning trees before MOC clustering processes, which include an ensemble operator to produce consensus clusterings before the final selection operator is employed. As such cluster-based MOO techniques have shown to improve optimized solutions, we opted to apply K-means, as it is simple to implement and works fast, compared to density-based clustering. We understand that the shape of the Pareto front may not be convex, but we proceeded with k equaling two. As there is little work on cluster-based MOO for clustering, we chose simple techniques to evaluate the effective of the approach. Our approach is different from [20], as we did not apply ensemble, nor is our cluster-representation tree-based. We used the generic centroid-based encoding.