Cartesian ant programming with transition rule considering internode distance

In recent years, Cartesian Ant Programming (CAP) has been proposed as a swarm-based automatic programming method, which combines graph representations in Cartesian Genetic Programming with search mechanism of Ant Colony Optimization. In CAP, once an ant jumps a number of nodes, the skipped nodes are not utilized and wasted in search. To make the use frequency of nodes uniform, we propose CAP with transition rule considering internode distance. We focus on the distance at the beginning of search to utilize a large number of nodes for exploration of search. As the search proceeds, the search comes to depend on the pheromone information for exploitation of search. In addition, to prevent the excessive use of the unnecessary nodes, we modify the method of dynamic symbol assignments to nodes so that not only functional symbols but also terminal symbols can be assigned to the respective nodes. We examined the effectiveness of our proposed method by applying it to symbolic regression problems. From the experimental results, we confirmed the improvement of performance and the relief of bias in use frequency of nodes by our proposed method.