Abstract: Because the topology of structure and the sizes of cross sections must be designedin the topology optimization, two kinds of variables, topology variables al and size variables ofcross sections Al are included in the mathematics model of topology optimization. The model isa mixed discrete programming or a pure discrete one including two kinds of variables. It is morecomplex and difficult to be solved than sizing optimization of structures, so it is a challengingproblem in the field of structural optimizatio...