This two part paper focuses on the optimum placement of a limited number of dampers, i.e. fewer than the number of blades, on a bladed disk to induce the smallest possible amplitude of blade response with or without involuntary, random mistuning. Intentional mistuning is also considered as an option to reduce the amplitude of blade response and the pattern of two blade types (referred to as A and B blades) is then part of the optimization effort in addition to the location of the dampers on the disk. This first part focuses on the formulation and validation of dedicated algorithms for the selection of the damper locations and, when appropriate, of the intentional mistuning pattern. Given the limited number of dampers, there is a concern that the failure of one or several of them could lead to a sharp rise in blade response and this issue is addressed by including the possibility of damper failure in the optimization process to yield a fail-safe optimized solution. The high efficiency and accuracy of the optimization algorithms is assessed in comparison with computationally very demanding exhaustive search results.