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to Optimize Neural Network Stru tures Kunikazu Kobayashiy and Masanao Ohbayashi Department of Computer S ien e & Systems Engineering, Fa ulty of Engineering, Yamagu hi University ye-mail: k sse.yamagu hi-u.a .jp Abstra t A new en oding method for optimizing neural network stru tures is proposed. It is based on an indire t en oding method with variable length gene ode. The sear h ability for nding an optimal solution is higher than the dire t en oding methods be ause redundant information in gene ode is redu ed and the sear h spa e is also redu ed. The proposed method easily operates adding and deleting hidden units. The performan e of the proposed method is evaluated through omputer simulations. Introdu tion In designing neural networks (NNs), it is ru ial to optimize network stru tures to derive both optimal approximation ability and generation ability Geneti algorithm (GA) [1, 2℄ has been su essfully applied to variety kinds of optimization problems, su h as traveling salesman problem and s heduling problem. In neural omputing, there are also a lot of work on designing NNs using GA. One of the most important points is how to en ode a network stru ture and parameters of NN (phenotype) in gene ode (genotype), i.e. oding s heme. Dasgupta et al. proposed a design algorithm using stru tured GA based on a dire t en oding method [3℄, where the network stru ture and the parameters are dire tory en oded in gene strings and the optimal solutions of both are sear hed by GA. On the other hand, Kitano proposed NGL (Neurogeneti Learning) [4℄. NGL is based on an indire t en oding method and has interesting properties. In the present paper, a new en oding method for optimizing neural network stru tures is proposed. It is based on the indire t en oding method with variable length gene ode. The sear h ability for nding an optimal solution is higher than than the dire t en oding methods be ause redundant information in gene ode is redu ed and the sear h spa e is also redu ed. It is also possible to easily add or delete hidden units. The performan e of the proposed method is evaluated through omputer simulations. En oding Method A oding s heme is shown in Fig.1. This an be appliable to three-layered NNs.