Multicriterion structural optimization via bound formulation and mathematical programming

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.