Structural learning of neural networks by differential evolution with degeneration using mappings

Structural learning, in which the structure of estimation systems are optimized, has been actively studied in researches on supervised learning of neural networks and fuzzy rules. The GA^d (genetic algorithm with degeneration) is one of the structural learning methods, which is modeled on genetic damage and degeneration. In GA^d, a gene is defined by a pair of a normal value and a damaged rate that shows how much the gene is damaged. Simple one-point crossover and Gaussian mutation are adopted to deal with the pair. It was very difficult to incorporate newly proposed genetic operations such as blend crossover in GA or operations in differential evolution (DE). In this study, we propose a new idea to incorporate such operations by unifying the values according to a mapping, applying operations and separating the values according to the inverse mapping. This idea is applied to differential evolution, which is known to be an efficient and robust algorithm and DE^d (differential evolution with degeneration) is proposed. To show the advantage of DE^d, it is applied to the structural learning of a simple test function and neural networks. It is shown that DE^d is more robust to high degeneration pressure and can find better estimation models faster, which have less number of parameters and less estimation errors, than GA^d.