Multiobjective optimization of structures with and without control

A multiobjective optimization algorithm is introduced, and the effect of different objective functions on structural design is investigated. The basic idea of this approach is to support the decisionmaker by directly selecting the best compromise solution from the Pareto optimal solutions. A payoff matrix is first constructed by optimizing each objective function subject to the given constraints; a substitute function is then formed. Under the original constraint conditions, maximizing the substitute function gives the best compromise solution. This research shows that multiobjective optimization should be carried out to obtain a rational structural design. Two structural optimal design examples—one frame structure and one frame structure with active control—illustrate the application of this approach. Numerical results show that the rational compromise solutions are achieved by multiobjective optimization procedure.