Clustering is an important unsupervised classification technique where a set of patterns, usually vectors in multidimensional space, are grouped into clusters based on some similarity or dissimilarity criteria. In crisp clustering, each pattern is assigned to exactly one cluster, whereas in fuzzy clustering, each pattern is given a membership degree to each class. Fuzzy clustering is inherently more suitable for handling imprecise and noisy data with overlapping clusters. Clustering techniques aim to find a suitable grouping of the input dataset so that some criteria are optimized. Hence the problem of clustering can be posed as an optimization problem.

The objectives to be optimized may represent different characteristics of the clusters, such as compactness, separation, and connectivity. A straightforward way to pose clustering as an optimization problem is to optimize some cluster validity index that reflects the goodness of the clustering solutions. All possible partitionings of the dataset and the corresponding values of the validity index define the complete search space. Traditional partitional clustering techniques, such as K-means and fuzzy C-means, employ greedy search techniques over the search space to optimize the compactness of the clusters. Although these algorithms are computationally efficient, they often get stuck at some local optima depending on the choice of the initial cluster centers.Moreover, they optimize a single cluster validity index (compactness in this case), and therefore do not cover different characteristics of the datasets. To overcome the problem of local optima, some global optimization tools such as Genetic Algorithms (GAs) have been widely used to reach the global optimum value of the chosen validity measure. GAs are randomized search and optimization techniques guided by the principles of evolution and natural genetics, and have a large amount of implicit parallelism. GAs perform multimodal search in complex landscapes and provide near-optimal solutions for the objective or fitness function of an optimization problem. ConventionalGA-based clustering techniques use some validity measure as the fitness value. However, no single validity measure works equally well for different kinds of datasets. Thus it is natural to simultaneously optimize multiple such measures for capturing different characteristics of the data.