As advantages of foldable or deployable structures have been established, origami artists and engineers have started to study the engineering applications of origami structures. Methods of computational origami design that serve different types of origami have already been developed. However, most of the existing design methods focus on automatically deriving the crease pattern to realize a given folded finished shape, without actually designing the finished shape itself. To include final shape design into the computational origami design and optimization process, this paper presents a genetic algorithm that aims to develop origami structures featuring optimal geometric, functional, and foldability properties. In accordance with origami, the genetic algorithm is adapted both in the aspects the individual encoding method and the evolutionary operators. To compliment the Genetic algorithms (GA), a new origami crease pattern representation scheme is created. The crease pattern is analogous to the ice-cracks on a frozen lake surface, where each crack is equivalent to a crease and each forking point to a vertex. Thus to form the creases and vertices in an “ice-cracking”-like origami crease pattern, we pick one vertex as the starting location, and let the rest of the creases and vertices grow in the same manner that cracks extend and fork form in ice. In this research, the GA encodes the geometric information of forming the creases and vertices according to the development sequence through the ice-cracking process. Meanwhile, we adapt the evolutionary operators and introduce auxiliary mechanisms for the GA, so as to balance the preservation of both elitism and diversity and accelerate the emergence of optimal design outcomes through the evolutionary design process.