Abstract: This paper addresses dynamic data clustering as an optimization problem and propose techniques for finding optimal (number of) clusters in a multi-dimensional data or feature space. In order to accomplish this objective we first propose two novel techniques, which successfully address several major problems in the field of Particle Swarm Optimization (PSO) and promise a significant breakthrough over complex, multi-modal optimization problems at high dimensions. The first one, so-called Multi-Dimensional (MD) PSO, re-forms the native structure of swarm particles in such a way that they can make inter-dimensional passes with a dedicated dimensional PSO process. Therefore, in a multidimensional search space where the optimum dimension is unknown, swarm particles can seek both positional and dimensional optima. This eventually removes the necessity of setting a fixed dimension a priori, which is a common drawback for the family of swarm optimizers. Nevertheless, MD PSO is still susceptible to premature convergences due to lack of divergence. To address this problem we propose Fractional Global Best Formation (FGBF) technique, which basically collects all promising dimensional components and fractionally creates an artificial global-best particle (aGB) that has the potential to be a better “guide ” than the PSO’s native gbest particle. We investigated both individual and mutual applications of the proposed techniques and demonstrated that the best clustering performance can be achieved by their mutual operation. In order to test and evaluate their clustering performance in terms of accuracy, robustness and scalability, a synthetic data-set, which contains ground-truth clusters and offers a broad range of complexity levels is used. An extensive set of experiments demonstrate that the proposed dynamic clustering technique based on MD PSO with FGBF can extract the optimal (number of) clusters by converging to the global optimum of the validity index function at the true dimension.

Many real-world optimization problems are dynamic in nature. The interest in the Evolutionary Algorithms (EAs) community in applying EA variants to dynamic optimization problems has increased greatly. Differential Evolution (DE) belongs to the group of evolutionary algorithms which operate in continuous search spaces. DE has been successfully applied to many stationary problem domains. Recently there has been some research into applying DE to dynamic optimization problems too. Many real-world problems consist of decision variables which require the optimization algorithm to work with binary parameters. This makes it impossible to apply DE in its basic form. For this purpose, binary differential evolution (BDE) approaches have been introduced. The main focus of this paper is to perform a series of experiments to test the behavior of a simple BDE under different change conditions. A simple bit-matching problem is chosen as the test environment. The results of this preliminary study show that further study is needed to make BDEs suitable to work in dynamic environments.

Particle swarm optimization (PSO) has been initially proposed as an optimization technique for static environments; however, many real problems are dynamic, meaning that the environment and the characteristics of the global optimum can change over time. Thanks to its stochastic and population based nature, PSO can avoid being trapped in local optima and find the global optimum. However, this is never guaranteed and as the complexity of the problem rises, it becomes more probable that the PSO algorithm gets trapped into a local optimum due to premature convergence. In dynamic environments the optimization task is even more difficult, since after an environment change the earlier global optimum might become just a local optimum, and if the swarm is converged to that optimum, it is likely that new real optimum will not be found. For the same reason, local optima cannot be just discarded, because they can be later transformed into global optima. In this paper, we propose novel techniques, which successfully address these problems and exhibit a significant performance over multi-modal and non-stationary environments. In order to address the premature convergence problem and improve the rate of PSO’s convergence to global optimum, Fractional Global Best Formation (FGBF) technique is developed. FGBF basically collects all the best dimensional components and fractionally creates

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