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

Abstract

SUMMARYTo 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 ÿnd the 'best' Pareto optimum solution in the sense of having the minimum distance to the utopia point. By introducing a set of artiÿcial design variables, it is shown that a simpliÿed 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.

Selection of the Gridded Temperature Dataset for Assessment of Thermal Bioclimatic Environment Changes in Amu Darya River Basin

“…It is less computationally intensive and avoids decision makers' choices (Gan et al, 1996). The major strength of CP is to find the real Pareto optimum curve when the optimal points are heterogeneously distributed, a task that the conventional weighting methods are failed to do (Zhang, 2003). Statistical measures fail when the gridded data over-and underestimate in-situ data simultaneously.…”

“…It is used to analyze multi-objective problems based on the concept of choosing a solution from a set of solutions considering the nearest to the optimum points (Zeleny, 1973). Its strength over the conventional weighting approach is that it measures the minimum distance Pareto optimal point, especially when the distribution of the points is nonlinear (Zhang, 2003). CP was originally introduced by Zeleny (1973) and later used by many researchers related to their fields of studies, including analyzing hydrological and environmental issues (Brahim and Duckstein, 2011).…”

Optimum Structural Design Using Bio-Inspired Search Methods: A Survey and Applications

“…Zhang [132] presents an improved method of compromise programming, supplemented with a multifrontier formulation. It is successfully applied to optimize various structural problems, both truss bar structures and plates modeled with finite elements.…”

Robustness-based design optimization under data uncertainty

“…Other methods include goal programming (Zou and Mahadevan, 2006), compromise decision support problem Mistree, 1993, 1995;Chen et al, 1996), compromise programming (CP) (Zalney, 1973;Zhang, 2003;Chen et al, 1999) and physical programming (Messac, 1996;Messac et al, 2001;Messac and Ismail-Yahaya, 2002;Chen et al, 2000). Each of these methods has its own advantages and limitations.…”