A compromise programming method using multibounds formulation and dual approach for multicriteria structural optimization

To enhance the reliability and e ciency of the multicriteria optimization procedure, a compromise programming method using multibounds formulation (MBF) is proposed in this paper. This method can be used either to obtain the Pareto optimum set or to nd the ‘best’ Pareto optimum solution in the sense of having the minimum distance to the utopia point. By introducing a set of arti cial design variables, it is shown that a simpli ed and easy-to-use formulation can be established for practical applications. Particularly, this formulation is well adapted to the e cient dual solution approach due to the convexity of objective function. Theoretically, based on the Kuhn–Tucker optimality conditions, demonstrations show that the new formulation is equivalent to its original form and thus retains the basic properties of the latter. Numerical examples will be solved to show the capacity of this method