CHALLENGE - A multi-objective sizing optimization of a steel girder bridge under permanent, variable and seismic loads is a crucial task in preliminary structural design phases. In fact both the initial cost and the life–cycle cost of a civil structure (like a building or a bridge) are strictly related to the dimensions of its structural elements in that they determine the structure weight and resistance. The structure considered in this study is a bridge consisting of four identical and equally–spaced steel girders with ﬂanges welded to the web. The beams are supposed to bear a concrete slab, an asphalt layer and two sidewalks.
SOLUTION - A reference optimization is performed by using the modeFRONTIER MOGA-II algorithm in order to find a series of compromise solutions between small seismic horizontal displacements and small weight values, i.e. compromise solutions between small initial and maintenance costs. Thus, a subsequent optimization in a speciﬁc region of the objective space with the TP-MOGA-II algorithm is run to try to fill the gap in the horizontal shift values. As it appears from Fig. b, several candidate optimal solutions are found in the target objective space region. These solutions are characterized by medium/large horizontal and vertical shift values (a larger exploration for larger seismic shifts values is attained if compared with the reference optimization) and small/medium weight values (corresponding to a small initial cost of the structure).
BENEFITS - Based on tests performed on mathematical problems and a structural engineering application, the TP approach appears to be simple and effective in exploring target regions of the objective space by initially narrowing the search to the region speciﬁed by the user.