This paper focuses on discrete sizing optimization of frame structures using commercial profile catalogs. The optimization problem is formulated as a mixed-integer linear programming (MILP) problem 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. Both the displacement and stress constraints are formulated such that for each member limit values can be imposed at predefined locations along the member. A valuable feature of the formulation, lacking in most contemporary approaches, is that global optimality of the solution is guaranteed by solving the MILP using branch-and-bound techniques. The method is applied to three design problems: a portal frame, a two-story frame with three load cases and a multiple-bay multiple-story frame. Performance profiles are determined to compare the MILP reformulation method with a genetic algorithm. Global optimization discrete optimization sizing optimization frame structures mixed-integer linear programming c s ′ ij ,s ′ ij artificial upper/lower bounds for s ij c a assuming that profile j is selected. b assuming that non-nodal loads are replaced with equivalent nodal loads. c these matrices and vectors refer to displacements or stresses at a limited number of prescribed output locations along member i.

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This paper presents a new method to find the global solution of combined truss-frame sizing optimization problems taking into account all relevant Eurocode constraints. The approach is based on a reformulation of the optimization problem as a Mixed-Integer Linear Programming problem (MILP) which is solved by means of a branch-and-bound method. A portal frame that consists of both beam and truss elements is adopted as a test case. The optimal sections of the portal frame have to be selected from a square hollow sections catalog. The design of the portal frame has to meet the requirements prescribed by the Eurocodes. These requirements are adopted as constraints by reformulating them as or approximating them by a linear equation. Not only the Eurocode constraints related to member strength and stability but also all Eurocode constraints related to the joints of the structure are taken into account during the optimization. As a consequence, a post-processing step to account for other constraints is avoided, therefore optimality is retained and additional engineering time is reduced. The optimization results are presented and the influence of the different Eurocode constraints on the optimal design is discussed.

Abstract. This paper proposes a method to solve discrete size optimization problems of frame