“Tensegrity” refers to a class of discrete structures with two force members (bars and cables) wherein bars only take tensile loads and cables only take compressive loads. The pre stressed members are interconnected so as to form a self equilibrium structure. Compared to a truss supporting the same external loading, a tensegrity structure has fewer members and could weigh less. Determining the stable topology (member connectivities), form (node coordinates) and size (cross sectional areas of members) of a tensegrity structure for weight minimization is a challenging task, as the governing equations are nonlinear and the conventional matrix analysis methods cannot be used. This article addresses the weight minimization of a class one tensegrity structure with a given number of bars and cables, anchored at certain nodes and supporting given load(s) at certain node(s). Member connectivities and their cross sectional areas and force densities are taken as design variables, whereas the members’ strength and buckling requirements and maximum nodal displacements constitute the constraints, along with the coordinates of the floating nodes to make the structure symmetric. Constraints are evaluated through the nonlinear shape design of the self equilibrium structure and the linear analysis of the loaded structure, assuming small displacements. Using a novel approach, optimization is simultaneously performed in multiple promising areas of the solution space, resulting in multiple, optimum solutions. The diversity of the solutions is demonstrated by applying the proposed approach to a number of structural design problem.