Norm methods and partial weighting in multicriterion optimization of structures

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Abstract
Methods 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 l‐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 the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted 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 determination of the 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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