  The paper attempts to find numerical solutions of Diophantine equations, a
challenging problem as there are no general methods to find solutions of such
equations. It uses the metaphor of foraging habits of real ants. The ant colony
optimization based procedure starts with randomly assigned locations to a fixed
number of artificial ants. Depending upon the quality of these positions, ants
deposit pheromone at the nodes. A successor node is selected from the
topological neighborhood of each of the nodes based on this stochastic
pheromone deposit. If an ant bumps into an already encountered node, the
pheromone is updated correspondingly. A suitably defined pheromone evaporation
strategy guarantees that premature convergence does not take place. The
experimental results, which compares with those of other machine intelligence
techniques, validate the effectiveness of the proposed method.
