  Many theoretical and experimental studies have used heuristic methods to
investigate the dynamic behaviour of the passive coupling of adjacent
structures. However, few papers have used optimization techniques with
guaranteed convergence in order to increase the efficiency of the passive
coupling of adjacent structures. In this paper, the combined problem of optimal
arrangement and mechanical properties of dampers placed between two adjacent
buildings is considered. A new bi-level optimization approach is presented. The
outer-loop of the approach optimizes damper configuration and is solved using
the ``inserting dampers'' method, which was recently shown to be a very
effective heuristic method. Under the assumption that the dampers have varying
damper coefficients, the inner-loop finds the optimal damper coefficients by
solving an $n$-dimensional optimization problem, where derivative information
of the objective function is not available. Three different non-gradient
methods are compared for solving the inner loop: a genetic algorithm (GA), the
mesh adaptive direct search (MADS) algorithm, and the robust approximate
gradient sampling (RAGS) algorithm. It is shown that by exploiting this new
bi-level problem formulation, modern derivative free optimization techniques
with guaranteed convergence (such as MADS and RAGS) can be used. The results
indicate a great increase in the efficiency of the retrofitting system, as well
as the existence of a threshold on the number of dampers inserted with respect
to the efficiency of the retrofitting system.
