Optimal structure design using branch and bound

A branch and bound algorithm is used to determine optimal spring rates and damping coefficients in flexible structures although the formalism is easily adaptable to designing passive control systems. The goal is to minimize the H_∞ norm from disturbance forces to displacements and velocities of selected degrees of freedom. The success of the branch and bound algorithm largely depends upon the quality of upper and lower bounds for the objective function. A comparison of two design problems is made between a tight, but computationally expensive, lower bound, and a simple, computationally cheap, lower bound. Our conclusion is that the extra investment in time to compute the tight bound is well worth the effort and leads to a dramatic savings in overall computation time