  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.
