Abstract
Multicriterion structural optimization problems pertaining to minimization of the maximum (or maximization of the minimum) of a set of weighted criteria are considered. In order to alleviate the inherent difficulty of non-differentiability of min-max problems, we adopt a so-called “bound formulation” and show that this approach even provides us with a very simple means of performing a switch from a prescribed-resource to a cost-minimization formulation of a given type of problem. The bound approach was found very useful in admitting the treatment of min-max problems by usual variational analysis; we demonstrate in this paper that the technique is also extremely well-suited to mathematical programming. Illustrative examples are presented at the end of the paper.
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References
Bendsøe, M.P.; Olhoff, N. ; Taylor, J.E. 1983: A variational formulation for multicriteria structural optimization,J. Struct. Mech. 11, 523–544
Fleury, C. 1987: Computer aided optimal design of elastic structures. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structural and mechanical systems, pp. 831–900. Berlin, Heidelberg, New York: Springer
Fleury, C.; Braibant, V. 1986: Structural optimization: a new dual method using mixed variables.Int. J. Num. Meth. Engrg. 23, 409–428
Olhoff, N. 1977: Maximizing higher order eigenfrequencies of beams with constraints on the design geometry.J. Struct. Mech. 5, 107–134
Olhoff, N.; Parbery, R. 1984: Designing vibrating beams and rotating shafts for maximum difference between adjacent natural frequencies.Int. J. Solids Struct. 20, 63–75
Olhoff, N.; Rasmussen, S.H. 1977: On single and bimodal optimum buckling loads of clamped columns.Int. J. Solids Struct. 13, 605–614
Osyczka, A.; Koski, J. 1982: Selected works related to multicriterion optimization methods for engineering design. In: Eschenauer, H. and Olhoff, N. (eds.)Optimization methods in structural design, Proc. Euromech Colloquium 164, Siegen, FRG, pp. 176–181. Mannheim, FRG: Wissenschaftsverlag
Stadler, W. 1983: Applications of multicriterion optimization in engineering and the sciences (A survey). In: Zeleny, M. (ed.)MCDM - past decade and future trends, pp. 51–84. Greenwich, Conn.: JAI Press
Stadler, W. 1984: Application of multicriterion optimization in mechanics,Appl. Mech. Rev. 37, 277–286
Taylor, J.E. 1987: Distributed parameter optimal structural design: some basic problem formulations and their application. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structural and mechanical systems, pp. 3–86. Berlin, Heidelberg, New York: Springer
Taylor, J.E.; Bendsøe, M.P. 1984: An interpretation of minmax structural design problems including a method for relaxing constraints.Int. J. Solids Struct. 20, 301–314
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Olhoff, N. Multicriterion structural optimization via bound formulation and mathematical programming. Structural Optimization 1, 11–17 (1989). https://doi.org/10.1007/BF01743805
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DOI: https://doi.org/10.1007/BF01743805