jats:p External prestressed carbon fibre reinforced polymer straps can be used to strengthen shear-deficient reinforced concrete structures. For an efficient shear retrofitting system, the optimum combinations of parameters such as the number of straps, strap locations, strap stiffness and initial strap prestress need to be identified. The modified compression field theory and the shear friction theory have previously been applied to carbon fibre reinforced polymer strap strengthened beams. As implemented, both of these methods are iterative. Particle swarm optimisation and genetic algorithm stochastic optimisation methods were used to reduce the computational cost associated with the shear strength evaluation and also to search the design space for carbon fibre reinforced polymer strap strengthened beams. An initial comparison across several test functions showed that the preferred optimisation algorithm depended on the characteristics of the design space. When applied to a reinforced concrete case study, the genetic algorithm was better for searching the shear friction theory shear strength design space that was characterised by several peaks. However, for the smoother modified compression field theory shear strength evaluation space, and for the design space for the carbon fibre reinforced polymer strengthened beams calculated using either the modified compression field theory or the shear friction theory, the particle swarm optimisation converged more quickly and accurately. The optimised solutions reflect the assumptions within the underlying evaluation methods. </jats:p>