A novel optimisation method is developed for optimum strengthening design of 2D multi-story steel moment resisting frames using buckling restrained brace (BRB) dampers and externally welded steel plates in compliance with ASCE 41-06. The proposed method is based on the concept of Uniform Distribution of Deformation (UDD), in which structural materials are redistributed from strong to weak parts of a structure until the material capacity is fully exploited. For the first time, an adaptive power function is introduced to improve the computational efficiency and convergence speed of the UDD optimisation method. The results of the proposed optimisation method are compared with metaheuristic optimisation methods using Genetic Algorithm (GA) and Particle Swarm Optimisation (PSO) for a three story and a nine story frame. The demand to capacity ratios of deformation-controlled and force-controlled structural members based on ASCE 41-06 are considered as design constraints in the optimisation process. The results demonstrate the efficiency of the proposed optimisation method in finding the optimum design solution with significantly less computational costs (up to 300 times less number of analyses) compared to both GA and PSO methods. It is shown that, in general, a more suitable distribution of dampers is accompanied by a more uniform distribution of demand to capacity ratios, which confirms the concept of UDD optimisation method.