An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimaization (Q2770891)

The authors address the problem of multicriteria structural optimization. They propose a new multibounds formulation (MBF) for the weighting method. The key is to introduce additional (slack) variables serving as an upper bound for the respective addend in the objective function, which in turn is transformed into an inequality constraint. Although the MBF is equivalent to the original weighting method, the advantage is that one can deal now with a linear objective function. The authors show that they recover the one-bound formulation with their approach, and outline the relationship with the trade-off method. Using MBF, the multicriteria optimization problem can be tackled by convex programming methods. As an application, the authors use the CONLIN optimizer for numerical design of two different shell structures.