Global discrete structural size optimization using a mixed-variable approach

Structural design optimization can reduce both the consumption of natural resources by the construction industry and the engineering effort and therefore cost by automation of some of the most repetitive tasks in the design process. However, practicing structural engineers appear to be reluctant to adopt optimization as a daily design tool. One of the reasons is that real-world design problems are often governed by a number of practical constraints described by the building codes. In addition, the optimization problem contains discrete design variables since the member profiles have to be chosen from a catalog of commercially available alternatives. Several optimization methods have been proposed to solve a practical structural optimization problem. However, none of these methods guarantee global optimality. A new method to find the global solution of combined truss-frame size optimization problems is presented. The adopted approach is to reformulate the optimization problem as a Mixed-Integer Linear Program (MILP) by including the equations of structural analysis as constraints. The internal forces of the members are taken as continuous state variables. Binary variables are used for choosing the member profiles from a catalog. Global optimality of the solution is guaranteed by solving the MILP using branchand-bound techniques. A portal frame that consists of both beam and truss elements is adopted as a test case. The design of the portal frame should meet the requirements prescribed by the Eurocodes, which are design rules developed by the European Committee for Standardization. These requirements are adopted as constraints by reformulating them as or approximating them by a linear equation.status: publishe