Finding Numerical Solutions of Diophantine Equations using Ant Colony Optimization
This addresses a challenging mathematical problem for researchers in computational mathematics and optimization, but it is incremental as it applies an existing metaheuristic to a new domain.
The paper tackles the problem of finding numerical solutions for Diophantine equations, which lack general solution methods, by proposing an ant colony optimization-based approach and shows it is effective compared to other machine intelligence techniques.
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.