Multicriteria Optimization Procedures in Application on Structural Mechanics Systems

Summary

This paper reports on investigations carried out in the field of vector optimization and its practical application on a structural mechanics system. The main reason is that in addition to the minimization of costs for developing and manufacturing machines and plants, some other objectives such as shape accuracy, reliability and others are playing an important role as well. These problems can be formulated as “Optimization Problems with Multiple Objectives” (Vector-Optimization, PARETO-Optimization). Most of the objectives are non-linear and besides that competing. Thus, they do not lead to one or several solutions for the optimum but rather to a “functional-efficient” solution set, i.e. the decision maker is able to select out of this set the most efficient compromise solution. Moreover, the vector optimization problem is transformed into a scalar substitute problem by means of a preference function. This so-called optimization strategy is an important part of the modelling. For carrying out the transformation, several preference functions, e.g. objective weighting, distance functions, constraint oriented transformation (Trade-off Method), and Min-Max-Formulation have been analysed and tested. The investigations showed that the efficiency of the single preference function is problem-dependent and furthermore dependent on the adapting on special optimization algorithms (Methods of Mathematical Programming). Within the scope of this contribution the application of multicriteria optimization techniques in structural mechanics systems is shown, e.g. the shape optimization of a special shell structure (conveyer belt drum).