The aim of the paper is to investigate the optimum design of truss structures by considering different stress and displacement constraints. For that reason, the flower pollination algorithm based methodology was applied for sizing optimization of space truss structures. Flower pollination algorithm is a metaheuristic algorithm inspired by the pollination process of flowering plants. By the imitation of cross-pollination and self-pollination processes, the randomly generation of sizes of truss members are done in two ways and these two types of optimization are controlled with a switch probability. In the study, a 72 bar space truss structure was optimized by using five different cases of the constraint limits. According to the results, a linear relationship between the optimum structure weight and constraint limits was observed.