Abstract: Although real spatial structures are often analyzed and constructed as a set of discrete elements, there are relatively few optimal design methods that can directly handle the geometric information of discrete structures. In this presentation, techniques that capture the geometric information of discrete structures are introduced for two different approaches, machine learning and variational principle, with the aim of designing rational discrete structures in view of structural and constructional performance. By introducing these techniques, it becomes possible to design structures that were previously difficult to design manually in real time.