SUMMARYIt is well known that the weighting method may fail in generating the Pareto optimal set of a multicriterion problem in non-convex cases. In this paper, two simple truss examples, one static and one dynamic problem, are presented to show that this situation easily occurs in optimum structural design also.
SUMMARYMethods for generating Pareto optimal solutions to a multicriterion optimization problem are considered. The norm methods based on the scalarization of the original multicriterion problem by using the [,-norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested. In addition, an alternative approach which, instead of scalarization, reduces the dimension of the multicriterion problem is proposed. This is called thc partial weighting method and it can be interpreted as a generalization of the traditional scalarization technique whcrc thc wcightcd sum of the criteria is used as the objective function. The first of these two approaches (norm method) is very flexible from a designer's point of view and it can be applied also in non-convex cases to the detcrmination ofthe Pareto optimal set whereas the latter (partial weighting method) is especially suitable for problems where the number of criteria is large. Throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design.
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