Many structural components are routinely manufactured in only a limited range of discrete sizes;for example, reinforcing bars and steel sections are readily available in certain standardized sizes.Other non-standard sizes could be manufactured to special order but would be very expensive.In designing a practical structure, engineers are therefore inclined to select components among those sizes which are commonly available, and to avoid non-standard sizes.Such a process of searching has been commonly known as discrete structural optimization.Compared with continuous problem, the discrete problem presents a great increase in difficulty.In general, the discrete design space is disjoint and non-convex, thus the powerful continuous optimization methods cannot be directly used to solve the discrete and mixed-discrete problems.