Backtrack method with applications to DSO

The backtrack discrete mathematical programming method is described giving a detailed flow chart. If a continuous mathematical method is used and discrete series of values are given for variables, the discrete optima can be determined by a complementary discretization which is also explained. Optimum design problems of stiffened and cellular plates, tubular trusses, welded box beams and welded steel silos are treated. In these applications the discrete variables appear in various forms. In the cost function the material and fabrication (welding) costs are formulated. It is shown that the optimum number of ribs in stiffened or cellular plates depends on the fabrication cost factor. In the optimization of trusses it is verified that the use of the Euler buckling formula gives unsafe solutions and the optimum geometry depends on the profile shape of compression members. In the multiobjective optimization of welded box beams the deflection is formulated as the third objective function in addition to the cost and weight functions. The systematic incorporation of the cost analysis in the optimization procedure is shown in the case of a welded steel silo. The detailed strength and cost calculation is carried out for the main structural parts of a silo for several discrete values of the height/diameter ratio to find the optimum one.