By integrating stimuli-responsive materials, 4D Printing enables the Additive Manufacture (AM) of shape morphing structures that change their shape and function when actuated by an environmental stimulus. Among 4D Printed shape morphing structures, morphing strands demonstrate unique properties because they can achieve large and complex deformations even when the active materials used only release a small strain during actuation. However, designing a 4D printed strand such that it achieves a target deformation during actuation is highly challenging due to the complex interactions among stimulus, material response and material distribution. Computational design methods offer a way to address this problem. Existing methods, however, are computationally expensive, can often only handle small deformations or only allow for predicting a deformation given a material distribution. Further, the design of multi-state strands, i.e. strands that respond to several stimuli, is not addressed by existing methods. In this work, a computational design method for morphing strands is presented that can efficiently handle large and complex displacements and multiple states. To solve this problem, the strand is divided into small segments that have a constant cross-section. First, a set of possible cross-sections consisting of active and passive materials is generated and for each possible cross-section, the change of curvature and longitudinal strain during actuation is calculated. Then, a genetic algorithm is used to assign one of the possible cross-sections to each segment. Rather than optimizing the entire strand simultaneously, the strand is divided into smaller parts. Since finite element simulations are not required to evaluate the deformation of the overall structure and several small optimization problems are solved rather than a single large one, the computational cost remains low. The method is benchmarked and validated experimentally, where PLA is used as both the active and passive material and to render the PLA active, a pre-strain is introduced during the AM process. By enabling the efficient and predictable design of strands that undergo large and complex shape changes during actuation, this work makes the potential offered by 4D Printing technology more accessible to designers.