A Deterministic Model for Analyzing the Dynamics of Ant System Algorithm and Performance Amelioration through a New Pheromone Deposition Approach

Ant Colony Optimization (ACO) is a metaheuristic for solving difficult discrete optimization problems. This paper presents a deterministic model based on differential equation to analyze the dynamics of basic Ant System algorithm. Traditionally, the deposition of pheromone on different parts of the tour of a particular ant is always kept unvarying. Thus the pheromone concentration remains uniform throughout the entire path of an ant. This article introduces an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of basic Ant System algorithm. The idea here is to introduce an additional attracting force to guide the ants towards destination more easily by constructing an artificial potential field identified by increasing pheromone concentration towards the goal. Apart from carrying out analysis of Ant System dynamics with both traditional and the newly proposed deposition rules, the paper presents an exhaustive set of experiments performed to find out suitable parameter ranges for best performance of Ant System with the proposed deposition approach. Simulations reveal that the proposed deposition rule outperforms the traditional one by a large extent both in terms of solution quality and algorithm convergence. Thus, the contributions of the article can be presented as follows: i) it introduces differential equation and explores a novel method of analyzing the dynamics of ant system algorithms, ii) it initiates an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of algorithm in terms of solution quality and convergence time, iii) exhaustive experimentation performed facilitates the discovery of an algebraic relationship between the parameter set of the algorithm and feature of the problem environment.Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 200

Clustering using Vector Membership: An Extension of the Fuzzy C-Means Algorithm

Clustering is an important facet of explorative data mining and finds extensive use in several fields. In this paper, we propose an extension of the classical Fuzzy C-Means clustering algorithm. The proposed algorithm, abbreviated as VFC, adopts a multi-dimensional membership vector for each data point instead of the traditional, scalar membership value defined in the original algorithm. The membership vector for each point is obtained by considering each feature of that point separately and obtaining individual membership values for the same. We also propose an algorithm to efficiently allocate the initial cluster centers close to the actual centers, so as to facilitate rapid convergence. Further, we propose a scheme to achieve crisp clustering using the VFC algorithm. The proposed, novel clustering scheme has been tested on two standard data sets in order to analyze its performance. We also examine the efficacy of the proposed scheme by analyzing its performance on image segmentation examples and comparing it with the classical Fuzzy C-means clustering algorithm.Comment: 6 pages, 8 figures and 1 table (Conference Paper