An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization

This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation-based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  C. Fleury.  First and second order convex approximation strategies in structural optimization , 1989 .

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

[3]  Daniel P. Giesy,et al.  Pareto-optimal multi-objective design of airplane control systems , 1980 .

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

[5]  I. St. Doltsinis.  Multicriteria optimization in engineering and in the sciences mathematical concepts and methods in science and engineering, volume 37: W. Stadler, ed., (Plenum, New York and London, 1988), ISBN 0 306426 560 , 1989 .

[6]  Dimitris A. Saravanos,et al.  Multiobjective shape and material optimization of composite structures including damping , 1992 .

[7]  JiGuan G. Lin.  Multiple-objective problems: Pareto-optimal solutions by method of proper equality constraints , 1976 .

[8]  R. Grandhi,et al.  Compound scaling algorithm for multiobjective functions , 1995 .

[9]  M. Domaszewski,et al.  Developments of sizing sensitivity analysis with the ABAQUS code , 1999 .

[10]  M. Bendsøe,et al.  A Variational Formulation for Multicriteria Structural Optimization , 1983 .

[11]  J. Pietrzak.  A systematic search for Pareto optimum solutions , 1999 .

[12]  S. Taylor,et al.  Multicriterion optimization in engineering: Andrzej Osyczka. John Wiley & Sons, New York, 1984 , 1985 .

[13]  J. Dennis,et al.  NORMAL-BOUNDARY INTERSECTION: AN ALTERNATE METHOD FOR GENERATING PARETO OPTIMAL POINTS IN MULTICRITERIA OPTIMIZATION PROBLEMS , 1996 .

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

[15]  N. Olhoff.  Multicriterion structural optimization via bound formulation and mathematical programming , 1989 .

[16]  Juhani Koski,et al.  Multicriteria Design Optimization , 1990 .