# An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering +
###### Abstract  
Previously, cluster-based multi or many objective function techniques were proposed to reduce the Pareto set. Recently, researchers proposed such techniques to find better solutions in the objective space to solve engineering problems. In this work, we applied a cluster-based approach for solution selection in a multiobjective evolutionary algorithm based on decomposition with bare bones particle swarm optimization for data clustering and investigated its clustering performance. In our previous work, we found that MOEA/D with BBPSO performed the best on 10 datasets. Here, we extend this work applying a cluster-based approach tested on 13 UCI datasets. We compared with six multiobjective evolutionary clustering algorithms from the existing literature and ten from our previous work. The proposed technique was found to perform well on datasets highly overlapping clusters, such as CMC and Sonar. So far, we found only one work that used cluster-based MOEA for clustering data, the hierarchical topology multiobjective clustering algorithm. All other cluster-based MOEA found were used to solve other problems that are not data clustering problems. By clustering Pareto solutions and evaluating new candidates against the found cluster representatives, local search is introduced in the solution selection process within the objective space, which can be effective on datasets with highly overlapping clusters. This is an added layer of search control in the objective space. The results are found to be promising, prompting different areas of future research which are discussed, including the study of its effects with an increasing number of clusters as well as with other objective functions. multiobjective evolutionary algorithm; multiobjective; genetic algorithm; particle swarm optimization; evolutionary algorithm; data clustering; bare bones particle swarm optimization +
Footnote †: This paper is an extended version of our paper published in 2021 IEEE Congress on Evolutionary Computation (CEC). where \(m\), the fuzzy parameter, is 2. With a single objective function, different characteristics of hidden structures found in the dataset may not be well captured [1]. Combining multiple objectives into one may not fully reflect conflicting characteristics, such as cluster compactness and separation [2]. Thus, multiple objective functions that are optimized simultaneously in an evolving population of solutions were developed [3]. In this way, cluster characteristics can be more accurately defined, evolving to better solutions. Applications of multiobjective evolutionary algorithms (MOEA) in clustering have shown to be effective in identifying meaningful clusters [1; 3; 4]. In MOEA clustering or multiobjective clustering (MOC), many works focused on improving the algorithms through the treatment of chromosome encoding, use of objective functions [5], choice of MOEA, incorporation of other techniques, such as swarm intelligence, choice of evolutionary operations and selection of the final solution [6; 7]. While applications of MOEAs are covered in many works and surveys [1; 6], there is a research gap where few studies have applied newer MOEA strategies in data clustering problems, tested on datasets with different characteristics [8; 9; 10]. With this motivation, we previously investigated the application of a variety of MOEA algorithms to QPSO, BBPSO and fuzzy clustering algorithms tested on 10 UCI datasets [4]. Decomposition-based MOEA with bare bones particle swarm optimization (MOEA/D BBPSO) performed the best on most datasets. In this work, as continuation, we applied a cluster-based MOEA/D optimization technique to BBPSO clustering (CM-BBPSO) to introduce good Pareto solutions into the Pareto set to be considered for selection and investigated its performance for data clustering problems. To the best of our knowledge, there is very little work done in cluster-based MOEA for data clustering. Most cluster-based MOEA are for solving other engineering problems but not data clustering.