Minlp Optimization of a Cantilever Roof Structure

This paper presents the simultaneous cost, standard sizes and rounded dimension optimization of a cantilever roof structure. Since the standard and rounded dimensions are proposed to be handled explicitly in the discrete type of the optimization, the mixed-integer non-linear programming (MINLP) is applied. The structure is built from the standard hot rolled steel I sections for columns, beams and struts, and from the reinforced concrete bases. The MINLP optimization model of the cantilever roof structure is developed. The model comprises the objective function of the structure’s self-manufacturing costs and the design, resistance and dimensioning (in)equality constraints. The latter are defined in accordance with the Eurocode 2, 3 and 7 specifications. The modified outer-approximation/equality- relaxation (OA/ER) algorithm is used. The MINLP optimization of a cantilever roof structure for a small football stadium near the city of Maribor in Slovenia is presented at the end of the paper. The obtained optimal result includes the minimal production costs of the structure, the optimal standard sections of steel elements and the optimal rounded dimensions of the concrete bases.