  The paper presents an exponential pheromone deposition rule to modify the
basic ant system algorithm which employs constant deposition rule. A stability
analysis using differential equation is carried out to find out the values of
parameters that make the ant system dynamics stable for both kinds of
deposition rule. A roadmap of connected cities is chosen as the problem
environment where the shortest route between two given cities is required to be
discovered. Simulations performed with both forms of deposition approach using
Elitist Ant System model reveal that the exponential deposition approach
outperforms the classical one by a large extent. Exhaustive experiments are
also carried out to find out the optimum setting of different controlling
parameters for exponential deposition approach and an empirical relationship
between the major controlling parameters of the algorithm and some features of
problem environment.
