Multimodal genetic programming by using tree structure similarity clustering

This paper proposes a multimodal genetic programming (GP) that incorporates a clustering of a population based on the tree structure similarity into GP and simultaneously acquires multiple local optimal solutions including a global optimal solution. The multimodal optimization problem aims to acquire not only a global optimal solution but also multiple local optimal solutions in a single optimization process. In general, although continuous real-valued optimizations are mainly targeted for multimodal optimization problems, problems with other solution structures, like a program in GP, have not been dealt with. This paper designs a multimodal program optimization problem that has a global and a local optimal solution and proposes a multimodal GP to acquires multiple local optimal programs including a global optimal one. Concretely, the proposed method separates the population into several clusters based on the similarity of tree structure, which is used as program expression in GP. Then, local optimum programs with different structure are acquired by optimizing each cluster separately. In order to investigate the effectiveness of the proposed method, we compare the proposed method with a simple GP without clustering on the designed multimodal GP benchmark. The experimental result reveals that the proposed method can acquire both the global and the local optimal programs at the same time.