Multi-objective optimisation of damper placement in dynamically similar adjacent buildings is considered with identical viscoelastic dampers used for vibration control. An exhaustive search is used to describe the solution space in terms of various quantities of interest such as maximum top floor displacement, maximumfloor acceleration, base shear and inter-storey drift. With the help of examples, it is pointed out that the Pareto fronts in these problems contain a very small number of solutions. The effectiveness of two commonly used multiobjectiveevolutionary algorithms, viz. NSGA-II and MOPSO, is evaluated for a specific example.