Approximating the Pareto curve to help solve biobjective design problems

Abstract.When faced with multiple objectives, designers have to find ways to combine these objectives to find the solution that satisfies acceptable trade-off levels. In this paper, we present a methodology based on approximating the Pareto set of biobjective problems and presenting these trade-off graphs to the designer to facilitate decisions on trade-off. Once a solution is selected from the approximated set, the designer can select to either set a target on one or both objectives and use one of two methods to find the sought after solution. The paper details the methodology and applies it to three structural problems of increasing complexity, showing that the procedure provides also useful feedback even in the case of nonconvex Pareto sets.

[1]  Glynn J. Sundararaj,et al.  Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers , 2000 .

[2]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[3]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[4]  Margaret M. Wiecek,et al.  Augmented Lagrangian and Tchebycheff Approaches in Multiple Objective Programming , 1999, J. Glob. Optim..

[5]  Georges M. Fadel,et al.  Detecting local convexity on the pareto surface , 2002 .

[6]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[7]  W. Stadler.  Multicriteria Optimization in Engineering and in the Sciences , 1988 .

[8]  C. Hwang,et al.  Fuzzy Multiple Objective Decision Making: Methods And Applications , 1996 .

[9]  Wei Chen,et al.  A robust concept exploration method for configuring complex systems , 1995 .

[10]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Georges M. Fadel,et al.  Approximating Pareto curves using the hyper-ellipse , 1998 .

[12]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[13]  Elliot R. Lieberman,et al.  Multi-objective programming in the USSR , 1991 .

[14]  Achille Messac,et al.  Physical programming - Effective optimization for computational design , 1996 .

[15]  P. Papalambros,et al.  A NOTE ON WEIGHTED CRITERIA METHODS FOR COMPROMISE SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION , 1996 .

[16]  J. Koski.  Defectiveness of weighting method in multicriterion optimization of structures , 1985 .