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, in all ant system algorithms developed so far, the deposition of pheromone on different parts of the tour of a particular ant is always kept unvarying. This implies that 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 with this empirically obtained parameter set 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.