Effective Clustering with Firefly Algorithms : A Variant with Centroid Movements

Abstract

Clustering is a fundamental problem in data analysis, often used to partition datasets into meaningful groups. However, the effectiveness of clustering methods largely depends on the nature of the dataset and the specific objectives of the task. Traditional clustering methods, such as K-Means, have limitations in handling datasets with varying distributions, cluster shapes, and densities. Moreover, these methods often require pre-specifying the number of clusters (K), which may not align with real-world data complexities. This thesis addresses these limitations by proposing a modified Firefly Algorithm (FA) for automatic clustering with centroid movements. The proposed algorithm integrates meta-heuristic principles to overcome the challenges associated with traditional clustering methods. Unlike canonical approaches that rely solely on proximity, our method introduces a multi-objective fitness function that considers compactness, separation, and a novel total Traveling Salesman Problem (TSP) penalty to ensure both efficient clustering and optimal navigation within clusters. The algorithm employs a self-tuning mechanism to adaptively determine the optimal number of clusters (K) and uses a unique centroid movement strategy to refine cluster boundaries dynamically. These innovations allow the algorithm to achieve robust clustering outcomes without reliance on initial cluster center selection or manual specification of K. The practical application of the proposed algorithm is also explored in the thesis in the context of a robotic sensor network for the persistent monitoring of large areas. The dataset used for experiments consists of two-dimensional spatial data, reflecting the challenges of clustering in real-world scenarios. Computational experiments compare the performance of the modified Firefly Algorithm with the K-Means algorithm, revealing that the proposed approach not only mitigates initialization dependency but also produces clusters that facilitate shorter navigation paths within clusters. For instance, the total path distance for clusters formed using the proposed method was reduced significantly compared to K-Means, emphasizing its suitability for navigation-centric applications. The findings demonstrate the effectiveness of the Firefly Algorithm in addressing clustering problems characterized by complex data distributions and multi-objective goals. Future work will explore extending the algorithm’s capabilities to higher-dimensional data and developing self-tuning mechanisms for algorithmic parameters, further enhancing its adaptability and applicability in diverse clustering scenarios.