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Recursive Ant Colony Optimization for estimation of parameters of a function

This paper introduces a new optimization technique termed as Recursive Ant Colony Optimization (RACO), a modified form of ant colony method (ACO), for finding best probable solution to a combinatorial problem. ACO simulates the social behavior of ants, optimizing their path from the nest to food source. The movement of an ant is random and the shortest path is found on the basis of the pheromone laid on the path by other ants. RACO applies ACO recursively introducing an additional term `depth' which decides the extent of recursion. Each depth is a usual ACO with three steps per iteration, `pheromone tracking', `pheromone updating' and `city selection'. Results of each depth contribute towards constructing models for the following depth and the range of values for each parameter is reduced around the actual solution. The algorithm is tested on two simple functions and to further test its efficiency and stability in real world, it has been applied to a geophysical problem of self-potential anomaly due to a inclined sheet like body buried inside the earth. The results are found to be very good and they describe the effectiveness and practicability of this method.